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Characterising the Snap-back

Response of Single Piles in Stiff Clays

By Ryan J. M. Millin

A thesis submitted in partial fulfilment of the requirements for the degree of Master of

Engineering

Supervised by Dr Liam Wotherspoon

Prof Michael Pender

Department of Civil and Environmental Engineering

The University of Auckland

December 2012

i

ABSTRACT

A problem evident in current engineering practice is the separated manner in which geotechnical

and structural engineers go about the design of commercial buildings and infrastructure.

Wotherspoon (2009) has shown an integrated approach is required. This study investigates non-

linear pile-soil interaction through field testing and numerical modelling, considering Soil-

Foundation-Structure Interaction (SFSI).

Full-scale snap-back testing has been carried out to simulate pile response to earthquake forces.

Two 273 mm diameter steel tube single free-headed piles were tested at an existing stiff clay site

in Albany, Auckland. The test pile was pulled towards a reaction pile using a hydraulic jack, and

then released from a target pull-back force and the response measured. Non-linear geometrical

effects were reported from testing. Non-linear damping and stiffness were also determined. The

pull-back phase of snap-back tests measures the static pile lateral response. Free-vibration

hammer tests were used to evaluate any changes in the natural period of the pile-soil system due

to geometric non-linearity developed during testing. The effect of varying the level of mass added

to the pile head was carried out during testing, with the comparative dynamic response between

each investigated.

Analysis of snap-back tests in the time domain found there to be significant impact effects

developed following the pile release from the pull-back peak into gapped soil. Inelastic and elastic

portions of the response were able to be separated in the time domain, and damping calculated for

each. Inconsistent damping was computed for lower mass tests, thus under similar conditions it is

recommended that piles are tested with a maximum frequency of 10 Hz. A significant reduction in

both stiffness and frequency occurred due to a documented increase in pile-soil gap depth.

The modal, pushover, and dynamic pile responses is modelled in Ruaumoko 3D using discrete

springs to represent the pile-soil interaction. Favourable comparisons have been obtained with the

full-scale response. Significant contact damping during testing has been accounted for using

contact members to provide additional damping, although this has resulted in divergence with test

data during the elastic cycles of the response.

ii

iii

ACKNOWLEDGEMENTS

I would firstly like to thank my supervisors Dr Liam Wotherspoon and Prof Michael Pender for

all of their help during this study. Liam, your interests in this area and the funding you provided

me were imperative in the happening of this research project, for which I am extremely grateful.

The initial direction you gave this research and your knowledge with regards to the numerical

phase of the study was also invaluable.

Mick, the enthusiasm and attention you gave this research project was really appreciated. Your

help during testing and the thoughts you shared with me whilst I was analysing test data were

critical. I should also mention you with regards to getting us all on board with this ground-

breaking research.

I would like to thank Dr Sherif Beskhyroun, for his help with regards to test data acquisition and

data analysis.

Thanks to Jeff Melster, Mark Liew and Lucas Hogan for the help you provided me on-site during

field testing, it is much appreciated.

I would also like to acknowledge Steve Warrington, Dan Ripley, Noel Perinpanayagam, Mark

Byrami and Mark Twiname, for the manufacture and supply of equipment used during field

testing.

Finally, to Natalie: thanks for your continued support during some of the more difficult times of

my research project.

iv

Table of contents

v

TABLE OF CONTENTS

ABSTRACT ............................................................................................................................................ I

ACKNOWLEDGEMENTS ..................................................................................................................III

TABLE OF CONTENTS ....................................................................................................................... V

LIST OF FIGURES .............................................................................................................................. IX

LIST OF TABLES ........................................................................................................................... XVII

NOTATION ...................................................................................................................................... XIX

CHAPTER 1 INTRODUCTION ...............................................................................................1

1.1 Overview .......................................................................................................................... 1

1.2 Objectives and scope of study .......................................................................................... 2

1.3 Thesis outline ................................................................................................................... 3

CHAPTER 2 LITERATURE REVIEW ....................................................................................5

2.1 Overview .......................................................................................................................... 5

2.2 Analytical studies of pile-soil interaction ......................................................................... 6

2.2.1 Winkler Spring model .............................................................................................. 6

2.2.2 Elastic Continuum Model (ECM) ............................................................................ 9

2.2.3 Comparison between Winkler Spring model and ECM ......................................... 11

2.2.4 Strain Wedge (SW) model ...................................................................................... 11

2.2.5 Finite Element Method (FEM) ............................................................................... 12

2.3 Experimental studies of pile-soil interaction .................................................................. 16

2.3.1 Servo-hydraulic shaker and eccentric rotating mass shaker ................................... 16

2.3.2 Snap-back testing on piles ...................................................................................... 17

2.3.3 Statnamic testing .................................................................................................... 17

2.3.4 Full-scale dynamic testing of piles in cohesive soils .............................................. 18

2.3.5 Full-scale dynamic testing of piles in cohesionless soils........................................ 23

2.4 Code approaches and Soil-Structure Interaction (SSI) ................................................... 27

2.5 Summary from previous research ................................................................................... 30

Table of contents

vi

CHAPTER 3 TEST SET-UP AND METHODOLOGY ......................................................... 33

3.1 Overview ........................................................................................................................ 33

3.2 Pile details and layout .................................................................................................... 34

3.3 Pile head preparation ...................................................................................................... 35

3.3.1 Pile 3 head details .................................................................................................. 35

3.3.2 Pile 4 head details .................................................................................................. 35

3.4 Geotechnical site conditions .......................................................................................... 37

3.4.1 Site location and description .................................................................................. 37

3.4.2 Laboratory and undrained shear strength tests ....................................................... 39

3.4.3 Wave activated stiffness (WAK) tests (M.Sa’don, 2012) ...................................... 42

3.4.4 Seismic cone penetrometer tests (SCPTs) (M.Sa’don, 2012) ................................ 44

3.4.5 Spectral analysis of surface waves (SASW) tests .................................................. 44

3.4.6 Summary of stiffness tests under small strain ........................................................ 47

3.4.7 Representative soil profile from site investigation data ......................................... 48

3.5 Instrumentation and data collection ............................................................................... 48

3.5.1 Pile 3 instrumentation ............................................................................................ 49

3.5.2 Pile 4 instrumentation ............................................................................................ 50

3.5.3 Gap monitoring around test pile ............................................................................. 52

3.6 Data preparation ............................................................................................................. 54

3.6.1 Data acquisition system ......................................................................................... 54

3.6.2 Pile 3 test data preparation ..................................................................................... 55

3.6.3 Pile 4 test data preparation ..................................................................................... 56

3.7 Test procedure and equipment ....................................................................................... 56

3.7.1 Free vibration hammer test details ......................................................................... 57

3.7.2 Snap-back test details ............................................................................................. 57

3.8 Test program .................................................................................................................. 59

3.8.1 Pile 3 test program ................................................................................................. 59

3.8.2 Pile 4 test program ................................................................................................. 60

Table of contents

vii

CHAPTER 4 STATIC PILE RESPONSE FROM FULL-SCALE FIELD TESTS ................61

4.1 Overview ........................................................................................................................ 61

4.2 Pull-back force-displacement response .......................................................................... 63

4.2.1 Pile 3 pull-back tests ............................................................................................... 63

4.2.2 Pile 4 pull-back tests ............................................................................................... 69

4.3 Pile-soil gap measurements and observations ................................................................ 70

4.3.1 Pile 3 gapping behaviour ........................................................................................ 71

4.3.2 Pile 4 gapping behaviour ........................................................................................ 73

4.4 Summary ........................................................................................................................ 76

CHAPTER 5 DYNAMIC PILE RESPONSE FROM FULL-SCALE FIELD TESTS ...........79

5.1 Overview ........................................................................................................................ 79

5.2 Response in the frequency domain ................................................................................. 81

5.2.1 Peak frequencies from the Fast Fourier Transform (FFT) ..................................... 81

5.2.2 Frequency between cycles in the time domain ....................................................... 92

5.3 Response in the time domain .......................................................................................... 96

5.3.1 Logarithmic decrement method (Thompson, 1988) ............................................... 96

5.3.2 SDOF displacement solution (Chopra, 2006) ....................................................... 102

5.3.3 Sensitivity analysis on noise filtering ................................................................... 119

5.3.4 Sensitivity analysis on SDOF displacement prediction ........................................ 121

5.3.5 Reference beam accelerations relative to test pile ................................................ 122

5.3.6 Ground motion decay ........................................................................................... 124

5.4 Hysteretic pile response ................................................................................................ 130

5.4.1 Strain gauge calibration ........................................................................................ 130

5.4.2 Pile 3 hysteretic response ..................................................................................... 132

5.4.3 Pile 4 hysteretic response ..................................................................................... 138

5.5 Summary ...................................................................................................................... 141

CHAPTER 6 NUMERICAL MODELLING OF LATERAL PILE RESPONSE .................145

6.1 Overview ...................................................................................................................... 145

6.2 Modal response ............................................................................................................. 147

Table of contents

viii

6.2.1 Model development in Ruaumoko 3D ................................................................. 147

6.2.2 Model comparison with Pile 3 hammer tests (natural period) ............................. 149

6.2.3 Model comparison with Pile 4 hammer tests (natural period) ............................. 151

6.3 Pushover response ........................................................................................................ 153

6.3.1 Model development in Ruaumoko 3D ................................................................. 153

6.3.2 Model comparison with Pile 3 pull-back tests ..................................................... 156

6.3.3 Model comparison with Pile 4 pull-back tests ..................................................... 162

6.4 Dynamic response ........................................................................................................ 168

6.4.1 Rayleigh damping ................................................................................................ 168

6.4.2 Soil damping ........................................................................................................ 170

6.4.3 Snap-back impact effects ..................................................................................... 175

6.4.4 Model comparison with dynamic tests carried out on Pile 3 ............................... 176

6.4.5 Model comparison with dynamic tests carried out on Pile 4 ............................... 188

6.5 Sensitivity analysis on key parameters of numerical models ....................................... 194

6.5.1 Pushover model (including modal analysis) sensitivity analysis ......................... 194

6.5.2 Dynamic sensitivity analysis ................................................................................ 197

6.6 Summary ...................................................................................................................... 206

CHAPTER 7 CONCLUSIONS ............................................................................................. 209

7.1 Recommendations for future research ......................................................................... 216

REFERENCES ................................................................................................................................... 219

APPENDIX A PILE 3 DYNAMIC DATA FILE INPUT INTO RUAUMOKO .................... A-1

APPENDIX B EXAMPLE DATA ANALYSIS FILE ON MATLAB ................................... B-1

List of figures

ix

LIST OF FIGURES

Figure 2-1: Rigid pile stresses developed under lateral loading (Kulhawy and Chen, 1995) .......... 7

Figure 2-2: Characteristic p-y curves for soft clays with free water (Matlock, 1970) ...................... 8

Figure 2-3: Dynamic Winkler model for piles (Pecker and Pender, 2000) ...................................... 9

Figure 2-4: Radiation damping of a horizontally vibrating pile (a) Berger et al. (1977); (b) Novak

et al. (1978); and (c) Gazetas and Dobry (1984) ............................................................................ 10

Figure 2-5: Strain Wedge model configuration and distribution of pile-soil reaction along

deflected pile (Ashour and Norris, 2000) ....................................................................................... 12

Figure 2-6: (a) Infinite and finite element mesh for a single isolated pile laterally loaded in

extended soil medium; (b) Deformed mesh; and (c) Cumulative displacement vectors (Chen and

Poulos, 1993) .................................................................................................................................. 13

Figure 2-7: Accumulated soil strains at a pile head deflection of 38 mm for (a) Von Moses model;

(b) Drucker-Prager model (Brown and Shie, 1990) ....................................................................... 14

Figure 2-8: Finite element mesh used to model different soil profiles (Yang and Jeremic, 2002) 15

Figure 2-9: Elevation sketch of Statnamic pile group lateral load test set-up (Rollins et al., 2000)

........................................................................................................................................................ 18

Figure 2-10: Pile-mass system (Blaney and O’Neill, 1986) (1 ft = 0.305 m) ................................ 19

Figure 2-11: Set-up for forced lateral vibration test (Boominathan and Ayothiraman, 2006) ....... 20

Figure 2-12: Forced vibration and quick release dynamic test set up of pile in saturated peat

(Crouse et al., 1993) (dimensions in m) ......................................................................................... 21

Figure 2-13: Snap-back test arrangement (Pender at al., 2011) ..................................................... 22

Figure 2-14: Field data for pile testing (Jennings et al., 1985) ....................................................... 24

Figure 2-15: Details of two piles for testing (Jennings et al., 1985) .............................................. 24

Figure 2-16: Elevated view of pile from group showing location of strain gauges (Brown et al.,

1988) (1 ft = 0.305 m; 1 in = 25.4 mm) .......................................................................................... 26

Figure 2-17: Superposition method for the Soil-Structure Interaction problem (Pecker and Pender,

2000) ............................................................................................................................................... 29

Figure 3-1: Pile details and instrumentation for (a) Pile 3; (b) Pile 4............................................. 34

Figure 3-2: Pile head set-up for Pile 3 ............................................................................................ 35

Figure 3-3: Drawings of steel tray manufactured for Pile 4 testing ............................................... 36

Figure 3-4: Different pile head arrangements for Pile 4; (a) no added lead masses (324 kg); (b) 15

lead masses (609 kg); (c) 50 lead masses (1275 kg) ...................................................................... 37

Figure 3-5: Aerial image of site location from Google Earth ......................................................... 38

Figure 3-6: Regional map of Auckland showing site location from Google Earth ........................ 38

Figure 3-7: Location of soil sampling at Albany site (M.Sa’don, 2012) ........................................ 40

List of figures

x

Figure 3-8: Auckland residual clay based on the plasticity index and liquid limit (M.Sa’don,

2012) .............................................................................................................................................. 40

Figure 3-9: Plan of site showing shear vane test and water content sample locations ................... 42

Figure 3-10: Experimental set-up for WAK and SASW testing (M.Sa’don, 2012) ...................... 42

Figure 3-11: Layout of test arrangement at Albany site (M.Sa’don.2012) .................................... 43

Figure 3-12: Schematic of SASW test set-up ................................................................................ 45

Figure 3-13: Phase difference between two geophone recordings at a range of frequencies for one

SASW test ...................................................................................................................................... 46

Figure 3-14: Representative soil profile from site investigation data ............................................ 48

Figure 3-15: External instrumentation attached to the test pile (Pile 3)......................................... 49

Figure 3-16: Plan of Albany site showing reference beam layout and instrumentation for Pile 3

testing ............................................................................................................................................. 50

Figure 3-17: External instrumentation attached to the test pile (Pile 4)......................................... 51

Figure 3-18: Plan of Albany site showing reference beam and instrumentation layout for Pile 4

testing ............................................................................................................................................. 51

Figure 3-19: Images of the four geophones used for Pile 4 testing ............................................... 52

Figure 3-20: Image of gapping around Pile 4 following a 120 kN snap-back at Albany .............. 53

Figure 3-21: Schematic view of the gap measurement process ..................................................... 53

Figure 3-22: Data acquisition set up at the Albany site (during Pile 3 testing) ............................. 54

Figure 3-23: Schematic of data acquisition process on site ........................................................... 55

Figure 3-24: Operator performing a free vibration test using the instrumented sledgehammer .... 57

Figure 3-25: Schematic illustrating snap-back set-up and equipment required ............................. 58

Figure 3-26: Snap-back testing set up on Pile 3 at the Albany site ................................................ 58

Figure 3-27: Quick-release mechanism following activation, showing it does not interfere with the

response of the pile ........................................................................................................................ 59

Figure 4-1: Force displacement curves for low pull-back forces on Pile 3 at Albany ................... 64

Figure 4-2: Force displacement curves for high force level pull-back tests on Pile 3 at Albany... 65

Figure 4-3: Effective ground level and gap depth illustration ....................................................... 66

Figure 4-4: Normalised force displacement relationship for 7.5, 60 and 120 kN pull-back tests .. 67

Figure 4-5: Accumulative residual displacement of Pile 3 versus pull-back test magnitude ......... 68

Figure 4-6: Displacement and gapping of soil behind pile during pull-back, due to horizontal earth

pressures ......................................................................................................................................... 68

Figure 4-7: Pull-back force displacement plots for 10 kN snap-back tests Pile 4 ......................... 69

Figure 4-8: Pull-back force displacement plots for 120 kN snap-back tests Pile 4 ....................... 70

Figure 4-9: Image looking east showing existing gapping on Pile 3 at Albany before testing on

29/03/2012 ..................................................................................................................................... 71

List of figures

xi

Figure 4-10: Gap developed behind the Pile 3 during the second 90 kN pull-back test at Albany 71

Figure 4-11: Residual gap, that could not be accurately measured due to excessive soil

deformation, behind the tension side of Pile 3 following the second 120 kN snap-back ............... 72

Figure 4-12: Gap growth development around Pile 3, (a) before testing; (b) following second 120

kN snap-back .................................................................................................................................. 73

Figure 4-13: No notable gap developed around Pile 4 following 10 kN snap-back series, (a) in

front/north side of pile; (b) behind/south side of pile ..................................................................... 74

Figure 4-14: Gap developed around Pile 4 during the 324 kg, 120 kN snap-back test one, (a)

behind pile (south side) at the end of the pull-back test; (b) in front of pile (north side) after snap-

back test .......................................................................................................................................... 74

Figure 5-1: Response in time and frequency domain from hammer test following first 30 kN snap-

back on Pile 3 ................................................................................................................................. 82

Figure 5-2: Response in time and frequency domain from hammer test following first 120 kN

snap-back on Pile 4 with 609 kg pile head ..................................................................................... 82

Figure 5-3: Natural elastic frequencies determined from FFT hammer response of Pile 3 ............ 83

Figure 5-4: Natural elastic frequencies determined from FFT hammer response of Pile 4 ............ 85

Figure 5-5: Snap-back response of Pile 3 from first 90 kN pull-back force and corresponding FFT

indicating cut-off frequency ........................................................................................................... 87

Figure 5-6: 324 kg pile head 120 kN snap-back 1 response in time and frequency domain .......... 88

Figure 5-7: 609 kg pile head 120 kN snap-back 1 response in time and frequency domain .......... 88

Figure 5-8: 1275 kg pile head 120 kN snap-back 1 response in time and frequency domain ........ 89

Figure 5-9: 15 lead mass (609 kg) pile head (a) before 120 kN snap-back 1; (b) after 120 kN snap-

back 1 ............................................................................................................................................. 90

Figure 5-10: Peak frequencies determined from FFT snap-back response of Pile 3 ...................... 91

Figure 5-11: Peak frequencies determined from FFT snap-back response of Pile 4 ...................... 92

Figure 5-12: Load-deformation plot illustrating stiffness change at different levels of soil

deformation .................................................................................................................................... 94

Figure 5-13: Graphical illustration of peaks used in the logarithmic decrement calculation for

damping .......................................................................................................................................... 97

Figure 5-14: Elastic damping of Pile 3 from dynamic testing at Albany ....................................... 99

Figure 5-15: Inelastic damping of Pile 3 from high force snap-back tests carried out at Albany 100

Figure 5-16: Pile 4 10 kN snap-back damping data with elastic filtered 120 kN snap-back

damping data ................................................................................................................................ 101

Figure 5-17: Pile 4 inelastic filtered 120 kN snap-back damping data ......................................... 102

Figure 5-18: Damping envelopes for hammer test following 120 kN snap 2 with 609 kg pile head

...................................................................................................................................................... 105

List of figures

xii

Figure 5-19: Unfiltered hammer test (3 blows) on open time domain following second 120 kN

snap-back with 609 kg added to Pile 4 ........................................................................................ 105

Figure 5-20: Damping envelopes and displacement prediction for 10 kN snap-back with 324 kg

pile head ....................................................................................................................................... 106

Figure 5-21: Damping envelopes and displacement prediction for 120 kN snap-back with 609 kg

pile head ....................................................................................................................................... 108

Figure 5-22: Effect of filtering technique to extract elastic/inelastic responses on 1275 kg 120 kN

snap-back 1 .................................................................................................................................. 110

Figure 5-23: Damping ratios computed from hammer tests on Pile 4; using the logarithmic

decrement method and exponential system damping envelopes .................................................. 112

Figure 5-24: Cycle damping ratio versus cycle number for hammer tests on 324 kg pile head .. 113

Figure 5-25: Cycle damping ratio versus cycle number for hammer tests on 609 kg pile head .. 113

Figure 5-26: Cycle damping ratio versus cycle number for hammer tests on 1275 kg pile head 114

Figure 5-27: Damping ratios computed from 10 kN snap-back tests on Pile 4; using the

logarithmic decrement method and exponential system damping envelopes .............................. 115

Figure 5-28: Cycle damping ratio versus cycle number for low force 10 kN snap-back tests on

Pile 4 ............................................................................................................................................ 115

Figure 5-29: Elastic damping ratios computed in the time domain from 120 kN snap-back tests on

Pile 4 ............................................................................................................................................ 116

Figure 5-30: Inelastic damping ratios computed from 120 kN snap-back tests on Pile 4 in the time

domain ......................................................................................................................................... 117

Figure 5-31: Exponential system damping for all snap-back tests, illustrating snap-back order . 118

Figure 5-32: Cycle damping ratio versus cycle number for high force 120 kN snap-back tests on

Pile 4 ............................................................................................................................................ 119

Figure 5-33: Noise filtering effects on the response of the first 120 kN snap-back with a 324 kg

pile head ....................................................................................................................................... 120

Figure 5-34: Sensitivity analysis on key parameters of damping ratio and damped natural

frequency for the SDOF displacement prediction model and corresponding damping envelopes

..................................................................................................................................................... 121

Figure 5-35: Accelerometer readings from 120 kN 1275 kg snap-back 1 ................................... 123

Figure 5-36: Accelerometer readings from 10 kN 1275 kg snap-back ........................................ 123

Figure 5-37: Geophone set-up for Pile 4 testing .......................................................................... 124

Figure 5-38: Geophone response signals during 10 kN snap-back .............................................. 125

Figure 5-39: Geophone response signals during 120 kN snap-back (1) ...................................... 125

Figure 5-40: Geophone response signals during 120 kN snap-back (2) ...................................... 126

List of figures

xiii

Figure 5-41: Geophone first peak signal versus distance from test pile for 10 kN snap-back tests

...................................................................................................................................................... 127

Figure 5-42: Geophone first peak signal versus distance from test pile for 120 kN snap-back tests

series one ...................................................................................................................................... 127

Figure 5-43: Geophone first peak signal versus distance from test pile for 120 kN snap-back tests

series two ...................................................................................................................................... 128

Figure 5-44: Normalised geophone first peak signals versus distance from test pile for all snap-

back tests ...................................................................................................................................... 129

Figure 5-45: Calibration factor variation between strain gauge and load cell pull-back force for

Pile 3 ............................................................................................................................................. 131

Figure 5-46: Pile 3 comparison between force displacement response using load cell, and the

force calculated using the average calibration factor ................................................................... 132

Figure 5-47: Pull and snap-back response for both of the 120 kN and the second 90 kN tests on

Pile 3 ............................................................................................................................................. 133

Figure 5-48: Hysteresis loops for various snap-back tests on Pile 3 at Albany ........................... 135

Figure 5-49: Eccentric mass shaker hysteresis loops at high and low force levels on Pile 4 at

Albany (M.Sa’don, 2012) ............................................................................................................. 135

Figure 5-50: Two 120 kN snap-back hysteresis loops with operational stiffness defined for each

...................................................................................................................................................... 136

Figure 5-51: Force on test pile during pull and snap-back versus displacement on Piles 2 and 4 not

participating in testing .................................................................................................................. 137

Figure 5-52: Snap-back hysteresis responses for low force level tests Pile 4 .............................. 138

Figure 5-53: Hysteresis loops with constant operational stiffness defined for each low force level

test ................................................................................................................................................ 139

Figure 5-54: Snap-back hysteresis responses for high force level tests Pile 4 ............................. 140

Figure 5-55: Hysteresis loops with operational stiffness defined for first series high force level

snap-back tests .............................................................................................................................. 140

Figure 6-1: (a) Field testing set-up; (b) Numerical Winkler Spring model representation .......... 146

Figure 6-2: Bi-linear slackness hysteresis used to represent residual soil gap (after Carr, 2004) 148

Figure 6-3: Model representation for modal analysis ................................................................... 149

Figure 6-4: P-y curves at representative depths developed from CPT data for the Albany Pile 3

model in stiff clay ......................................................................................................................... 155

Figure 6-5: Non-linear hysteresis rule used for soil springs in pushover model .......................... 155

Figure 6-6: Ruaumoko pushover modelling for 7.5, 15 and 30 kN series one pull-back tests Pile 3

...................................................................................................................................................... 157

List of figures

xiv

Figure 6-7: Ruaumoko pushover modelling for 60, 90 and 120 kN series one pull-back tests Pile 3

..................................................................................................................................................... 157

Figure 6-8: Ruaumoko pushover modelling for 60, 90 and 120 kN series two pull-back tests Pile 3

..................................................................................................................................................... 159

Figure 6-9: Ruaumoko pushover modelling for 7.5, 15 and 30 kN series two pull-back tests Pile 3

..................................................................................................................................................... 159

Figure 6-10: Graphical illustration of spring element behaviour in Ruaumoko .......................... 160

Figure 6-11: Ruaumoko pushover modelling for the first 10 kN pull-back test on Pile 4 ........... 163

Figure 6-12: Ruaumoko pushover modelling for the last three 10kN pull-back tests on Pile 4 .. 164

Figure 6-13: Ruaumoko pushover modelling for the first series of 120 kN pull-back tests on Pile 4

..................................................................................................................................................... 165

Figure 6-14: Ruaumoko pushover modelling for the second series of pull-back tests on Pile 4;

note manual offset introduced between each ............................................................................... 166

Figure 6-15: Fraction of critical damping relationship with natural frequency for Rayleigh

(proportional) damping (after Carr, 2004) ................................................................................... 169

Figure 6-16: Two soil element configurations to incorporate soil damping, (a) parallel radiation

damping model; (b) series radiation damping model (after Wotherspoon, 2009) ....................... 170

Figure 6-17: Pulse excitation results for parallel and series radiation damping models .............. 174

Figure 6-18: (a) Contact member arrangement within existing (b) series spring arrangement ... 176

Figure 6-19: Ruaumoko series spring model comparison with hammer test corresponding to 7.5

kN snap-back test two .................................................................................................................. 178

Figure 6-20: Ruaumoko series spring model comparison with hammer test corresponding to 120

kN snap-back test two .................................................................................................................. 179

Figure 6-21: Ruaumoko series spring model comparison to 7.5 kN snap-back two when released

from fourth peak .......................................................................................................................... 180

Figure 6-22: Ruaumoko series spring model comparison to 7.5 kN snap-back two when released

from third peak ............................................................................................................................. 181

Figure 6-23: Ruaumoko series spring model comparison to 7.5 kN snap-back two when released

from second peak ......................................................................................................................... 181

Figure 6-24: Ruaumoko contact model comparison with 7.5 kN snap-back test two.................. 183

Figure 6-25: Ruaumoko series spring model comparison to 120 kN snap-back two when released

from fourth peak .......................................................................................................................... 184

Figure 6-26: Ruaumoko contact model comparison to 120 kN snap-back two when released from

third peak ..................................................................................................................................... 185

Figure 6-27: Ruaumoko contact model comparison to 120 kN snap-back two when released from

second peak .................................................................................................................................. 185

List of figures

xv

Figure 6-28: Ruaumoko contact model comparison to 120 kN snap-back two when released from

pull-back peak .............................................................................................................................. 186

Figure 6-29: Ruaumoko series spring model comparison with hammer test before 324 kg 10 kN

snap-back test ............................................................................................................................... 189

Figure 6-30: Ruaumoko series spring model comparison with hammer test before 609 kg 10 kN

snap-back test ............................................................................................................................... 189

Figure 6-31: Ruaumoko series spring model comparison with hammer test before 1275 kg 10 kN

snap-back test ............................................................................................................................... 190

Figure 6-32: Ruaumoko series spring model comparison with 609 kg 10 kN snap-back test ..... 191

Figure 6-33: Ruaumoko series spring model comparison with 1275 kg 10 kN snap-back test ... 192

Figure 6-34: Ruaumoko contact model comparison with 324 kg 120 kN snap-back test one ..... 193

Figure 6-35: Sensitivity analysis on second 90 kN Ruaumoko pushover model part one ........... 195

Figure 6-36: Sensitivity analysis on second 90 kN Ruaumoko pushover model part two ........... 196

Figure 6-37: Sensitivity analysis on hammer series spring Ruaumoko model corresponding to

second 7.5 kN snap-back test part one ......................................................................................... 199

Figure 6-38: Sensitivity analysis on hammer series spring Ruaumoko model corresponding to

second 7.5 kN snap-back test part two ......................................................................................... 199

Figure 6-39: Sensitivity analysis on second 7.5 kN snap-back series spring Pile 3 model .......... 201

Figure 6-40: Sensitivity analysis on 609 kg 10 kN snap-back series spring Pile 4 model ........... 202

Figure 6-41: Sensitivity analysis on 1275 kg 10 kN snap-back series spring Pile 4 model ......... 203

Figure 6-42: Sensitivity analysis on second 7.5 kN snap-back contact member Pile 3 model part

one ................................................................................................................................................ 205

Figure 6-43: Sensitivity analysis on second 7.5 kN snap-back contact member Pile 3 model part

two ................................................................................................................................................ 205

List of figures

xvi

List of tables

xvii

LIST OF TABLES

Table 2-1: Average soil damping factors and average reduction factors for shear wave velocity

and shear modulus within 20 m depth. (after Eurocode 8 – Part 5, 2003) ..................................... 28

Table 3-1: Soil properties determined during current testing program, in comparison with results

from previous research ................................................................................................................... 41

Table 3-2: Auckland residual clay properties under small strain from WAK test analysis (after

M.Sa’don, 2012) ............................................................................................................................. 43

Table 3-3: Auckland residual clay properties under small strain from SCPT test analysis (after

M.Sa’don, 2012) ............................................................................................................................. 44

Table 3-4: Shear wave velocity computation from signal wave components of SASW tests ........ 46

Table 3-5: Summary of SASW tests at Albany on 29/03/2012, in comparison with previous

testing ............................................................................................................................................. 47

Table 3-6: Summary of Auckland residual clay properties under small strain from the present

study and previous in-situ testing ................................................................................................... 47

Table 4-1: Summary of gap measurements on the compression (north) side of Pile 3 at Albany . 73

Table 4-2: Gap measurements taken during Pile 4 testing on 06/09/2012 ..................................... 75

Table 5-1: Natural frequency from hammer tests carried out in four directions following testing on

Pile 3 ............................................................................................................................................... 84

Table 5-2: Time between successive peaks of half cycles and extrapolated whole cycle

frequencies for three dynamic tests on Pile 3 ................................................................................. 93

Table 5-3: Comparison of frequency between individual response cycles and FFT frequency for

Pile 4 ............................................................................................................................................... 95

Table 5-4: Damping and frequency data between peaks for the first series 120 kN snap-backs on

Pile 4 that were used to help assess the inelastic-elastic response division.................................. 109

Table 5-5: Operational stiffness in units of kN/mm and non-dimensionalised by the static (pull-

back) initial stiffness .................................................................................................................... 141

Table 6-1: Comparison of measured gap depths and natural periods from field testing on Pile 3 at

Albany site on 29/03/2012 with modal analyses on Ruaumoko .................................................. 150

Table 6-2: Comparison of measured gap depths and natural periods from field testing on Pile 4 at

Albany site on 06/09/2012 with modal analyses on Ruaumoko .................................................. 152

Table 6-3: Gap predictions by Ruaumoko in comparison with measured gap depths from field

testing of Pile 3 at Albany site on 29/03/2012, and gaps implemented in Ruaumoko ................. 161

Table 6-4: Gap predictions by Ruaumoko in comparison with gap measurements from field

testing of Pile 4 at Albany site on 06/09/2012, and gaps implemented in Ruaumoko ................. 167

Table 6-5: Summary of contact damping coefficient ratios for Pile 3 contact models ................ 187

List of tables

xviii

Table 6-6: Key parameters varied in the sensitivity analysis on the Pile 3 pushover model ....... 195

Table 6-7: Key parameters varied in the sensitivity analysis on the Pile 3 pushover model gap

depth predictions .......................................................................................................................... 197

Table 6-8: Key parameters varied in the sensitivity analysis on the Pile 3 hammer series spring

model ........................................................................................................................................... 198

Table 6-9: Key parameters varied in the sensitivity analysis on the Pile 3 snap-back series spring

model ........................................................................................................................................... 200

Table 6-10: Key parameters varied in the sensitivity analysis on the Pile 3 snap-back contact

member model ............................................................................................................................. 204

Notation

xix

NOTATION

Roman characters:

a0 dimensionless angular frequency

c damping coefficient

c damping matrix

cH radiation damping coefficient

d displacement

D pile diameter

Ep Young’s modulus of pile

Es Young’s modulus of soil

f frequency

F force

Fpre soil preforce

Fy soil yield force

g acceleration of gravity

Gs shear modulus of soil

Gs, max average shear modulus of soil at small strain

Im imaginary component of a complex number

Ip second moment of area of pile

k coefficient of subgrade reaction

K stiffness

K stiffness matrix

Kinn inner spring stiffness

Kout outer spring stiffness

Ktot total spring stiffness

Kv vertical soil stiffness

K0 coefficient of earth pressure at zero lateral strain

L pile length

Lt tributary pile length

m mass

m mass matrix

My pile yield moment

n mode of vibration number

nC ratio of contact damping coefficient to radiation damping coefficient on side of

pile where soil is loaded in compression during pull-back test

Notation

xx

nT ratio of contact damping coefficient to radiation damping coefficient on side of

pile where soil is loaded in tension during pull-back test

p lateral soil resistance per unit length of pile

pult ultimate lateral pressure of p-y relationship

Pxy cross power spectrum

qc CPT cone resistance

r bi-linear factor

Re Real component of a complex number

rinn inner spring bi-linear factor

rs inner to outer spring ratio

s pile spacing

S soil factor from Eurocode 8 (Eurocode 8 – Part 5, 2003)

su undrained shear strength

su-CPT undrained shear strength from CPT tests

su-VaneShear undrained shear strength from shear vane tests

Sx geophone signal one

Sy geophone signal two

Sy* complex conjugate of geophone signal two

t time

tw wall thickness of steel tube piles

u(t) displacement at time t for the under-damped displacement solution of an

equivalent-viscously damped Single-Degree-of-Freedom (SDOF) system

(0) initial velocity for the under-damped displacement solution of an equivalent-

viscously damped Single-Degree-of-Freedom (SDOF) system

VLa Lysmer’s wave velocity

VR Rayleigh wave velocity

Vs shear wave velocity

Vs, max average shear wave velocity at small strain

wN natural water content percentage

x receiver spacing

x1 peak one displacement

x2 peak two displacement

y p-y soil displacement

y50 p-y soil displacement at 50% of pult

z depth

Notation

xxi

Greek characters:

α Rayleigh damping mass coefficient

αPGA Peak ground acceleration coefficient

β Rayleigh damping stiffness coefficient

γs soil unit weight

ε50 Strain at 50% of pult

λR Rayleigh wavelength

νs soil Poisson’s ratio

ζ damping ratio

ζn damping ratio in mode n

ρs soil density

φ phase difference

φ’ soil internal angle of friction

ω circular frequency

ωn circular frequency in mode n

ωN un-damped natural circular frequency

ωD damped natural circular frequency

Sign convention during numerical modelling presentation (Chapter Six):

Compressive loads and deformations are positive for this thesis.

Tensile loads and deformations are positive in Ruaumoko 3D.

Notation used to define pile sides:

The side of the pile loading soil in compression during the pull-back test is referred to as the

‘compression side’ of the pile.

The side of the pile loading soil in tension during the pull-back test is referred to as the ‘tension

side’ of the pile.

Notation

xxii

Introduction

1

Chapter 1

Introduction

1.1 OVERVIEW

Foundation failures following earthquakes (Mexico City (1985), Kobe (1995), Adapazari

(Turkey) (1999), Chile (2010) and Christchurch (2011)) have highlighted a residual weakness in

the seismic design of commercial buildings and infrastructure. Often these foundation failures are

associated with little damage to the superstructure. Thus an integrated approach, involving more

communication between geotechnical and structural engineers, is required (Wotherspoon, 2009).

A robust foundation has also been shown to have a significant effect on the response of the

supported superstructure. Linear elastic Soil-Structure Interaction (SSI) has been developed in

some design codes to acknowledge this, however, kinematic response is still often ignored and

fixed base structural analyses carried out. Elastic behaviour of the pile-soil system is only evident

at small soil strains, beyond this non-linear soil deformation and non-linear geometrical effects

(for piles this is exhibited through gaps forming between the pile shaft and surrounding soil)

become apparent. Non-linear soil deformation occurs because of soil near the pile shaft yielding,

and results in an increase in damping and stiffness degradation of the pile-soil system. Recent

Introduction

2

work at the University of Auckland (Pender, 2007; Pender et al., 2009; Wotherspoon, 2009;

M.Sa’don, 2010; Orense et al., 2010; Pender et al., 2011; M.Sa’don, 2012; Pender et al., 2012a)

looks to incorporate non-linear soil deformation and non-linear geometrical effects in order to

consider Soil-Foundation-Structure-Interaction (SFSI).

The dynamic response of a pile subject to lateral loading is a complex phenomenon, resulting in

interactions between the pile and surrounding soil. This type of loading represents real life

scenarios of earthquake, wind, wave and machine vibration forces on a foundation. Earthquake

forces on the pile come from two forms of loading: kinematic and inertial interaction. Kinematic

interaction is unique to earthquakes and comes from vertical shear waves travelling up through

the near-field soil and interacting with the pile shaft; where a difference in stiffness between the

pile and surrounding soil causes a different pile response to the free-field motion of the soil.

Inertial interaction is applied forces to the pile head due to the acceleration and seismic mass of

the supported structure. Extensive research has been carried out in this area, in particular, small

scale model testing and the development of analytical and numerical models to simulate pile-soil

interaction on the response of a laterally loaded pile. Analytical models differ on how they treat

the soil surrounding the pile shaft. Previous dynamic full-scale testing has been carried out to get

an understanding of the response of single piles under different levels of excitation and non-linear

soil behaviour, observe gapping effects between the pile shaft and surrounding soil and determine

the level of damping and stiffness for the pile-soil system. Most full-scale testing has used forced

vibrations to get a dynamic response from the pile. However, recently snap-back testing

(simulating inertial interaction whilst neglecting kinematic interaction) has been shown to be a

more economical alternative, whilst still providing similar results to forced vibration tests

(M.Sa’don, 2010; Pender et al., 2011; M.Sa’don, 2012; Pender et al., 2012a). From the available

data it is still unclear what level of damping and stiffness should be used when considering non-

linear soil behaviour can cause a change in damping, and a degradation in stiffness. Full-scale

testing is preferred as scale model dynamic tests have associated issues (including the

requirements of dimensional similarity, the difficulties in modelling the stress-strain behaviour of

the soil around the pile and the boundary effects of the soil container).

1.2 OBJECTIVES AND SCOPE OF STUDY

Full scale snap-back testing of single piles was carried out in order to evaluate the level of non-

linear stiffness and damping associated with a given pile-soil system. Testing was carried out on

two different single piles at an Auckland residual clay site where previous testing had already

been carried out (M.Sa’don, 2010; Pender et al., 2011; M.Sa’don, 2012; Pender et al., 2012a). A

large variance in these critical parameters was experienced in previous studies due to soil and

Introduction

3

geometric non-linearity. The current study will focus on performing snap-back testing to measure

the lateral pile response at this site to get a better understanding of what stiffness and damping to

use, as well as trying to capture these effects with more rigorous numerical modelling using

Ruaumoko 3D (Carr, 2004). The pile head mass was also varied during testing to measure the

response at different natural frequencies, with the aim of achieving a lower natural frequency for

the pile-soil system. The testing and modelling of this study aims to provide data analysis and

numerical modelling approaches that can be replicated under different test conditions to those

considered in the present study, and thus enable an integrated pile foundation-structure model to

be developed.

The objectives for the current study are:

Determine new in-situ soil properties at the Auckland sand site by performing the

geophysical test; spectral analysis surface wave (SASW) method. From the test data, the

shear wave velocity, Vs and shear modulus, Gs of the soil under small strain can be

determined.

Perform series of full-scale snap-back tests on single piles at a stiff Auckland residual

clay site in Albany, at a range of release forces.

Perform free vibration hammer tests after each snap-back to obtain the elastic response

and monitor the change in natural frequency due to gap growth to complement gap

measurements on site.

Vary the level of mass attached to the pile head to accomplish lower pile natural

frequencies, and compare the dynamic response.

Gain a better understanding of the level of damping and stiffness for the piles at the

Auckland residual clay site.

Prepare numerical models on Ruaumoko 3D (Carr, 2004) utilising site investigation and

gap measurement data obtained during snap-back testing to predict the modal, static and

dynamic lateral responses of the piles and compare with field testing.

1.3 THESIS OUTLINE

This thesis is structured into seven chapters; each chapter describing a distinct step in the

research. The current study looks to gain insight into the dynamic lateral response of single piles

by determining an appropriate level of non-linear stiffness and damping, whilst also incorporating

different pile natural frequency responses, and trying to capture this in a numerical model. The

chapters are outlined on the following page.

Introduction

4

Chapter 2: Literature review – presents a summary of past research in topics related to the

dynamic lateral response of a single pile. This chapter is divided into analytical studies and

experimental studies. Analytical studies presented describe four methods for predicting the lateral

response of piles: Winkler Spring model, Elastic Continuum Model (ECM), Strain Wedge (SW)

model and Finite Element Method (FEM). Current code approaches and elastic Soil-Structure

Interaction (SSI) is also described in this chapter.

Chapter 3: Test set up and methodology – describes pile details and layout, geotechnical site

conditions, instrumentation, and data acquisition and analysis methods. Free vibration and snap-

back testing methodology is outlined, including the testing program at Albany.

Chapter 4: Static piles response from full-scale field tests – presents and discusses results

obtained from static pull-back tests on Piles 3 and 4. Pile head displacement versus applied force

is used to assess the non-linear pile head stiffness. Measurements of the gaps formed between the

pile and surrounding soil are also reported.

Chapter 5: Dynamic piles response from full-scale field tests – presents and discusses results

obtained from free-vibration hammer tests and snap-back tests at different force levels. An in-

depth analysis into the dynamic response of the different levels of pile head mass attached to Pile

4 is also carried out. Hammer tests are used to determine the fundamental frequency at different

stages of testing, and non-linear pile-soil damping and stiffness are determined from snap-back

tests.

Chapter 6: Numerical modelling of lateral pile response – the structural analysis program

Ruaumoko 3D (Carr, 2004) is used to model the response of single Piles 3 and 4, adopting a

Winkler spring model (Vesic, 1961; Matlock, 1970; Reese and Welch, 1975; Matlock et al., 1978;

Gazetas and Dobry, 1984; Wotherspoon, 2009). The modal, pushover and dynamic responses are

all modelled.

Chapter 7: Conclusions – the main conclusions from the thesis and research is summarised and

recommendations for future research in this area is provided.

Literature review

5

Chapter 2

Literature review

2.1 OVERVIEW

Studies on single piles under lateral loading have had significant attention to date, in particular

piles under dynamic loading. Lateral dynamic loading represents real life scenarios of earthquake,

wind, wave and machine vibration forces on foundations. Dynamic loading incorporates

important damping effects, for example, not captured by static loading. Earthquake loading is

unique due to two forms of loading on the pile: Kinematic and inertial interaction. Kinematic

interaction involves stressing of the pile as earthquake waves travel up through the soil profile,

and interact with the pile shaft. Inertial interaction occurs as the structure responds to the

earthquake and applies inertial forces to the pile head, also developed during wave, wind and

machine vibration loading. Previous research has been carried out to understand, and try to

represent the complex phenomena of pile-soil interaction during lateral dynamic loading. The

surrounding soil profile has an influence on both the stiffness of the foundation and the level of

damping. Most analytical methods have been developed to incorporate the non-linear response of

Literature review

6

the soil and pile. Large and small scale testing has been carried out to verify analytical methods.

However, there still uncertainty and debate as to how to account for pile response in design.

Some design codes and standards have been refined in recent years to allow for Soil-Structure-

Interaction (SSI) (Eurocode 8 – Part 5, 2003). This often involves superposition and hence only

applies to elastic response. Recent work at the University of Auckland (Pender, 2007; Pender et

al., 2009; Wotherspoon, 2009; M.Sa’don, 2010; Orense et al., 2010; Pender et al., 2011;

M.Sa’don, 2012; Pender et al., 2012a) has investigated non-linear soil deformation (soil yielding)

and geometrical effects (gaps forming between the soil and pile shaft); in order to consider Soil-

Foundation-Structure-Interaction (SFSI). Further large scale testing is required to determine what

level of stiffness and damping is associated with single piles, and a different modelling approach

is needed so this can be captured in integrated non-linear foundation-structure models.

2.2 ANALYTICAL STUDIES OF PILE-SOIL

INTERACTION

Briefly described in this section are four leading methods which have been developed to model

the response of piles under lateral loading. These are the Winkler Spring model, the Elastic

Continuum Model (ECM), the Strain Wedge (SW) model and Finite Element Method (FEM).

Each is able to account for the non-linear response of the soil. Modelling the non-linear response

of the soil-foundation interaction is critical for a well-represented analysis. A schematic of the

three dimensional stresses developed at the pile-soil interface is shown in Figure 2-1.

2.2.1 Winkler Spring model

The Winkler Spring model has been developed to invoke a series of independent non-linear

springs and parallel dashpots to represent the soil pressures acting on the pile and radiation

(elastic) damping. The initial Winkler model was elastic; this was extended using the p-y

approach to account for non-linear soil. This is also referred to as the Beam on Non-linear

Winkler Foundation (BNWF), or p-y method. The stiffness, or spring constant, is defined by a p-y

curve (Matlock, 1970), which describes the non-linear force-displacement relationship of the

spring. The p-y relationships for a given soil can be determined by back-figuring data from lateral

lead tests, and difficulties arise in finding a similar soil profile. Since independent springs are

used, soil continuity is also neglected. It is uncertain how the p-y curves are affected by pile head

fixity and the relative stiffness of the pile and soil (Budhu and Davies, 1988). Also, pile-soil

contact is assumed to occur over two dimensions, ignoring the three dimensional and radial

Literature review

7

components. Characteristic p-y curves, in non-dimensional form, developed by Matlock (1970)

for soft clays with free water are shown in Figure 2-2.

The gapping phenomenon was represented in the Winkler Spring model by modelling the

foundation system as two series of detachable Winkler springs on either side of the pile (Matlock

et al., 1978). The soil adjacent to the pile was modelled with zero tensile strength, hence when the

force in the spring reached zero, it detached from the pile. Here it had no influence on the

foundation system, as would be the case when gapping occurs during lateral loading. Once the

force in the spring was no longer tensile, it re-attached back to the pile.

The limitation of the models discussed above is that they primarily model pushover (static)

response and do not consider dynamic behaviour. Damping effects have been included in Winkler

models by attaching dashpots to the pile, with a similar layout to spring elements. This model

type neglects the kinematic response, considering only inertial interaction. Kinematic response

was considered by adopting the Beam on Dynamic Winkler Foundation (BDWF). The ends of the

spring and dashpot elements are connected to a representation of the free field soil, as opposed to

being fixed, see Figure 2-3. The motion of the free field soil serves as the input excitation for the

pile-soil system used in the previous models (Matlock and Foo, 1978; Makris and Gazetas, 1992;

Pecker and Pender, 2000; Wotherspoon, 2009).

Figure 2-1: Rigid pile stresses developed under lateral loading (Kulhawy and Chen, 1995)

Literature review

8

Figure 2-2: Characteristic p-y curves for soft clays with free water (Matlock, 1970)

Literature review

9

Figure 2-3: Dynamic Winkler model for piles (Pecker and Pender, 2000)

2.2.2 Elastic Continuum Model (ECM)

Poulos (1971a, 1971b) used the Elastic Continuum Model (ECM) to investigate the response of

an elastically loaded pile in an elastic soil. Several limitations were encountered in this study. A

homogeneous isotropic semi-infinite soil is unrealistic as the soil modulus in reality is likely to

vary with depth. The soil is also assumed to behave elastically, this approximation is only valid at

very small strains; at large deflections soil behaviour is highly non-linear, thus a linear

approximation is not valid. To overcome this limitation, Poulos considered local yielding of the

soil to account for the non-linearity of the soil. Randolph (1981) simplified expressions developed

by Poulos, which included pile length, by introducing the concept of active length for long,

flexible piles. This is the upper length of the pile where significant deformation occurs.

Expressions were valid provided the length of the pile was greater than the active length. When

kinematic interaction is considered, vertical shear waves travelling through the soil interact with

and deform the pile resulting in significant deformation along its entire length (Fan et al., 1991;

Makris and Gazetas, 1992; Kavvadas and Gazetas, 1993). This suggests a finite model is required

as opposed to the infinite active length concept. Also, the ECM accounts for soil continuity,

addressing the major limitation associated with the Winkler Spring model.

Equations were later developed for the ECM for constant Young’s modulus with depth (Davies

and Budhu, 1986), linear increase in Young’s modulus (Budhu and Davies, 1988) and parabolic

Literature review

10

variation of Young’s modulus (Gazetas, 1991). The displacements and rotations of the pile head

are calculated assuming elastic behaviour of the pile and soil, based on the applied horizontal load

and moment at the pile head, and flexibility coefficients.

Davies and Budhu (1986) extended the elastic equations to account for the non-linear behaviour

of the soil and pile. This introduced yield influence factors to the elastic displacements and

rotations. Pender et al. (2012b) developed these equations for cyclic lateral loading of a

homogeneous soil profile, and confirmed results with field testing of driven piles in Auckland

residual clay and Finite Element software OpenSeesPL (Lu et al., 2010). Wolf (1985) developed

an equivalent single degree of freedom (SDOF) model for the dynamic response.

The non-linear lateral load pile head displacement equations developed by Davies and Budhu

(1986) and Budhu and Davies (1988) were based on static loading of piles. They justify this

method to consider dynamic response because pile head stiffness was found not to be

significantly affected by the applied frequency.

In order to model a pile under seismic loading, the stiffness and damping of the pile-soil system

needs to be characterised. Methods have been developed to determine the damping characteristics,

which are functions of loading frequency (Gazetas and Dobry, 1974; Novak et al., 1978).

Damping consists of two components: Material, or hysteretic, damping and radiation damping.

Material damping (non-linear) dissipates energy due to the hysteretic damping in the soil.

Radiation damping (linear) is the ‘radiation’ of energy by P (compression) and S (shear) waves

spreading geometrically away from the pile-soil interface. Radiation damping of a pile has been

considered by several researchers using ECM’s (Berger et al., 1977; Novak et al., 1978; Gazetas

and Dobry, 1984), as an alternative to using FEM’s. A summary of these is illustrated in Figure 2-

4.

Figure 2-4: Radiation damping of a horizontally vibrating pile (a) Berger et al. (1977); (b) Novak et al. (1978);

and (c) Gazetas and Dobry (1984)

(a) (b) (c)

Literature review

11

2.2.3 Comparison between Winkler Spring model and ECM

To overcome the issue of soil continuity in the Winkler analysis, Vesic (1961) developed an

expression for the modulus of subgrade reaction (k), using material properties from the ECM.

√

(2-1)

where Es is Young’s modulus of the soil; νs is Poisson’s ratio; D is pile diameter; Ep is Young’s

modulus of the pile; Ip is the second moment of area of pile and k has units kN/m2.

2.2.4 Strain Wedge (SW) model

The Strain Wedge (SW) model was developed to characterise the effects of pile bending stiffness,

pile cross-sectional shape, pile head fixity and pile head embedment not accounted for in the

original p-y curves (Ashour and Norris, 2000). The SW model parameters are related to a 3D

passive wedge of soil developing in front of the pile, see Figure 2-5. The purpose of the SW

model is to relate stress-strain strength behaviour of the layered soil in the wedge to 1D Beam on

Elastic Foundation (BEF) parameters. The model can provide a link between complex 3D pile-

soil interaction with the simpler 1D BEF characterisation. This is done by relating the non-linear

variation in Young’s modulus of the soil to the non-linear variation in the modulus of subgrade

reaction associated with the BEF characterisation.

Literature review

12

Figure 2-5: Strain Wedge model configuration and distribution of pile-soil reaction along deflected pile (Ashour

and Norris, 2000)

2.2.5 Finite Element Method (FEM)

The Finite Element Method is a numerical analysis which has the ability to deal with complicated

configurations of structures and soil layers. The FEM has been developed for both two and three

dimensional models. The computational cost of carrying out complicated three dimensional

analyses is the main drawback of this numerical model; however, increasing computer capabilities

make this a more viable method. The location of the finite outer boundary is often crucial for

obtaining an accurate solution and requires experience and intuition (Chen and Poulos, 1993). It

can often require a greater number of elements to properly simulate the far-field behaviour. Chen

and Poulos combined the finite element approach developed by Yegian and Wright (1973), with

the infinite element approach (Damjanie and Owen, 1984) to model the far-field behaviour,

Literature review

13

(i) Isolated pile in extended

soil medium

(ii) Infinite and Finite

element mesh

(iii) Deformed mesh (iv) Cumulative

displacement vectors

(a) (b) (c)

illustrated in Figure 2-6 (a) for a single isolated pile. Figure 2-6 (b) shows the deformed mesh at

failure; note the gap developing at the back of the pile. Figure 2-6 (c) shows the cumulative

displacement of the soil, with soil moving backwards as the pile moves forwards. Reasonable

agreement was found between existing analytical solutions and the numerical method.

Figure 2-6: (a) Infinite and finite element mesh for a single isolated pile laterally loaded in extended soil medium;

(b) Deformed mesh; and (c) Cumulative displacement vectors (Chen and Poulos, 1993)

Brown and Shie (1990) analyse a pile subject to lateral loading using three dimensional finite

element constitutive non-linear soil models including a simple elastic-plastic model with a Von

Mises yield surface and associated flow and an extended Drucker-Prager model with non-

associated flow. Frictional interface elements were used to account for slippage at the pile/soil

interface and to allow gapping in the space behind the pile. The model is used as a basis for

parametric studies on the effects of pile spacing, pile head fixity and soil stiffness. This study

intended to provide data to evaluate more simple two dimensional approximations of the problem.

Also, bending moment data along the pile was reduced to obtain p-y curves in a similar manner to

that used to produce p-y curves in physical experiments. There were difficulties in modelling and

producing p-y curves for comparison for sand as a small amount of cohesion was required to

prevent soil elements falling immediately near the gap formation which would result in associated

convergence problems. Accumulated soil strains at a pile head deflection of 38 mm for each soil

model are displayed in Figure 2-7; where the pile elements have been removed to reveal soil

elements more clearly. Note extensive deformation away from the pile is mainly confined to the

top layers of soil.

Literature review

14

Figure 2-7: Accumulated soil strains at a pile head deflection of 38 mm for (a) Von Moses model; (b) Drucker-

Prager model (Brown and Shie, 1990)

Wu and Finn (1997a) use a quasi-three dimensional finite element method for the elastic response

of pile foundations. The method uses a simplified three dimensional wave equation for describing

the dynamic response of the soil. The response of the pile is computed directly without using any

pile-soil-pile interaction factors. This solution greatly reduces the computational cost for the

(a)

(b)

Literature review

15

direct analysis of pile groups. The method is presented as an elastic response so it could be

validated against existing more exact elastic solutions and low amplitude field vibration tests. The

soil is modelled as an eight node brick element and the pile is modelled as a two node beam

element. Nodal displacement for the soil is only allowed in the direction of shaking; both

translational displacement and rotational degrees of freedom are used to model the pile. Pile head

impedances and kinematic interaction is considered in the theoretical verification of the single

pile model. It was found to show good agreement with both existing elastic solutions and field

tests under damped linear elastic conditions; the method is extended to non-linear dynamic

response in an accompanying paper (Wu and Finn, 1997b).

Yang and Jeremic (2002) use OpenSees (1998-2002) finite element framework to explore the

behaviour of a single pile in different elastic-plastic soils. Pile behaviour in uniform sand, clay

soils, clay layer in sand deposit and sand layer in clay deposit were analysed and compared to

investigate layering effects. As with Brown and Shie (1990), finite element results were used to

generate p-y curves and then compared with those obtained from methods commonly used in

practice. The finite element mesh for each soil case is shown in Figure 2-8, where only half the

model is meshed due to symmetry. Twenty node, high accuracy, quadratic brick elements were

used to model the soil, pile and interface for each case. The square pile consisted of four elements

per cross-section, with the properties of aluminium. The fine mesh at the upper part of the model

was used to compute reliable shear forces and p-y curves as well as the investigation of layering

effects. Good agreement was found between p-y curves generated from centrifuge tests, OpenSees

(1998-2002) and LPILE (Reese et al., 2000), a programme readily used in practice.

Figure 2-8: Finite element mesh used to model different soil profiles (Yang and Jeremic, 2002)

Literature review

16

2.3 EXPERIMENTAL STUDIES OF PILE-SOIL

INTERACTION

This section outlines some of the different testing methods for full scale dynamic testing of piles,

as well as testing in cohesive (clays) and cohesionless (sands) soils.

2.3.1 Servo-hydraulic shaker and eccentric rotating mass shaker

Servo-hydraulic shakers and eccentric rotating mass shakers are methods of excitation that have

been used in the past for testing the dynamic response of single piles and pile groups. Many

excitation inputs are applied using either shaker. Different types of shakers have a considerable

amount of infrastructure that is required for operation; including power supplies, control hardware

and cooling systems. In general, they are not very portable and are relatively expensive (Farrar et

al., 1999).

Eccentric rotating mass shakers employ large rotating eccentric masses to produce a steady state

horizontal sinusoidal force. Waveform is typically harmonic, random or swept-sine signals.

Increasing the speed that the masses rotate alters the excitation frequency, and adjusting the

eccentricity of the masses will change the amplitude of the forcing. Adequate shaft speed control

is necessary in order obtain satisfactory results. The sinusoidal inputs usually offer a high signal

to noise ratio, thus reducing the possibility of contaminating the results. In practice mass shakers

have rarely been used to apply loads in the vertical direction (Farrar et al., 1999; Hseih et al.,

2006).

Servo-hydraulic shakers can provide high force levels, but have difficulties producing excitations

at high frequencies (greater than 100 Hz) (Farrar et al., 1999). This type of shaker generates

forces through the reciprocating motion induced by the high pressure flow of a liquid. The system

usually contains a servo-controlled hydraulic actuator that drives an attached moving dead mass;

the weight of this mass can be varied to obtain varying force magnitudes. The shaker can provide

relatively high vibration strokes and allow accurate excitation at different frequencies. They also

have the advantage of applying complex waveforms to the structure (Salawu and Williams, 1994).

More studies have been found to use eccentric rotating mass shakers to determine the dynamic

lateral pile response (Jennings et al., 1985; Blaney and O’Neill, 1986; Ting, 1987; Crouse et al.,

1993; Boominathan and Ayothiraman, 2006) than the servo-hydraulic shaker (Brown et al.,

1988).

Literature review

17

2.3.2 Snap-back testing on piles

M.Sa’don (2010, 2012) and Pender et al. (2011, 2012a) have carried out snap-back testing on

single piles in residual Auckland and shown that it is a viable means of evaluating the non-linear

soil response under dynamic loading. An advantage of the snap-back tests is the pull-back part of

the test gives data on the static non-linear load deformation properties of the pile. This

information would be of use in a pushover analysis, often carried out by the designer of piles

subject to earthquake loading. M.Sa’don (2010, 2012) found, in general, that the snap-back tests

were sufficient to induce vibration of the pile to replicate earthquake response history at a

relatively low cost. A limitation of snap-back testing is it is confined to testing on single piles as it

would be difficult to test a pile group simultaneously.

The equipment required for snap-back testing is relatively simple. Instrumentation and data

logging equipment are the same as needed for testing with an eccentric mass shaker. To apply the

snap-back force a hydraulic jack, load cell and quick release mechanism is needed. The reaction

to the pull-back force is obtained from a reaction pile or crane (Pender et al., 2011; Pender et al.,

2012a).

Several authors have performed snap-back tests, also referred to as quick-release or “pluck” tests,

on bridge decks, abutments and piers to determine modal characteristics and the dynamic

response of bridge structures, and the response of the pier-pile system (Douglas, 1976; Douglas

and Reid, 1982; Douglas and Richardson, 1984; Douglas et al., 1990; Gilani at al., 1995;

Wendichansky, 1996; Burdette et al., 2001; Chen et al., 2002). Crouse et al. (1993) and

Boominathan and Ayothiraman (2006) both performed quick-release tests on single piles, as well

as forced vibration tests, with Crouse et al. (1993) concluding that the less expensive quick-

release tests are favourable as they produced similar results to the forced vibration tests.

2.3.3 Statnamic testing

Statnamic testing is the most common rapid load pile test. During testing, fuel burns rapidly in a

combustion chamber mounted on the pile. The controlled venting of the gas and subsequent

pressure accelerates a reaction mass, resulting in loading of the pile for approximately 100

milliseconds. Derivation of the equivalent static pile behaviour from the Statnamic test requires

accurate determination of the variation of load, velocity and acceleration with time (Brown and

Hyde, 2006). Statnamic testing is generally easier and quicker to mobilise than classical static

tests, and less complex to analyse than dynamic load tests (Brown et al., 2006). Here Statnamic

testing applies vertical loads to the pile to assess the load-settlement static response.

Literature review

18

Statnamic testing was carried out by Rollins et al. (2000) and Rollins et al. (2003) to determine

the lateral dynamic response of a pile group. Here the resulting load pulse duration was 300

milliseconds. The dynamic resistance was found to be much greater than the (30 to 80%) static

resistance in all cases. An elevation sketch of the lateral dynamic Statnamic tests carried out by

Rollins et al. (2000) is shown in Figure 2-9.

Figure 2-9: Elevation sketch of Statnamic pile group lateral load test set-up (Rollins et al., 2000)

2.3.4 Full-scale dynamic testing of piles in cohesive soils

Blaney and O’Neill (1986) carried out dynamic lateral load tests on a cantilevered mass supported

by a single 273 mm diameter steel pipe pile, with a wall thickness of 9.27 mm, embedded in stiff

overconsolidated clay. An eccentric mass shaker was used to apply low frequencies to the mass;

in order to evaluate mathematical models that predict relatively low frequency dynamic pile

response. Frequency sweep shear forcing functions were applied at the top of the mass, which

simulated a simple structure. The pile cap system was used so that the resonant frequency would

be in the range of typical large buildings and off shore structures. The test set up is illustrated in

Figure 2-10. The resonant frequency was found to decrease from the initial sweep test, 2.3 Hz, to

the final one, 2.1 Hz. The frequency shift across testing reflects a decrease in the equivalent

SDOF stiffness, due to a 13 mm gap formed between the pile and the soil. The frequency

response near resonance for the 890 N applied load were relatively sharper and narrower than the

2.67 kN applied load, reflecting less hysteretic damping in the lower amplitude tests. Soil

attenuation data suggest inelastic behaviour in the soil was confined to an inverted cone centred

on the pile with a radius of 1.2 m at the surface, to a depth 1.5 m. It was recommended that for

practical design, the top 6 diameters (or 1.5 m in this case) should be concentrated on and the soil

outside of this could be characterised dynamically by field shear-wave velocity tests. The

equivalent SDOF damping ratio obtained directly from the measured sweep response was 10-

11%.

Literature review

19

Figure 2-10: Pile-mass system (Blaney and O’Neill, 1986) (1 ft = 0.305 m)

Boominathan and Ayothiraman (2006) carried out full-scale dynamic tests on 33 single piles of

varying types; driven precast concrete, driven cast in-situ concrete and bored cast in-situ concrete,

at different sites in India. The sites were predominately soft to stiff clays, with some sand and silt

present. The pile cap had dimensions of 750 x 750 x 750 mm, with a minimum ground clearance

of 150 mm, and was cast monolithically with the pile head for mounting the oscillator assembly

for dynamic testing. The test set up is shown in Figure 2-11. The free vibration response was also

determined using a snap-back type configuration. A lower natural frequency at high magnitudes

of force was found for the forced vibration tests, compared with the free vibration tests. This is

attributed to stiffness degradation at high magnitudes of dynamic force. It was found that the

lateral capacity and dynamic lateral pile-soil system stiffness depend mainly on the characteristics

of the top layers of soil, related to the concept of active length. The natural frequency of the pile-

soil system was also found to be greatly affected by the installation procedure, as well as the size

of the pile and the stiffness of the top soil layers.

Literature review

20

Figure 2-11: Set-up for forced lateral vibration test (Boominathan and Ayothiraman, 2006)

Crouse et al. (1993) conducted dynamic quick release and forced-harmonic vibration tests on a

steel pipe pile embedded in soft saturated peat. The test site is located within the Mercer Slough,

Washington on generally level ground with the water table at ground surface. The ground profile

consisted of 14.9m of thick highly compressible peat deposited over medium dense sand. The

steel pile pipe had an outside diameter of 200 mm and a thickness of 6.4 mm, and was driven

through the peat and into the medium dense sand. The set up for the eccentric mass shaker

vibration and quick release tests is shown in Figure 2-12. Quick release vibration tests were

performed at the beginning and end of the series of forced-harmonic vibration tests. Relatively

low soil modulus and low hysteretic damping over the upper portion of the pile where deflection

was large was attributed to a water-filled gap between the peat and the pile. Similar translational

stiffness and damping was found between forced-harmonic and quick release vibration tests,

suggesting the less expensive quick-release tests can yield sufficient results provided high quality

data acquisition equipment is used. The stiffness and damping values for the forced-vibration tests

were found to be independent of the applied frequencies between 1.8 and 3.0 Hz.

Literature review

21

Figure 2-12: Forced vibration and quick release dynamic test set up of pile in saturated peat (Crouse et al., 1993)

(dimensions in m)

M.Sa’don (2010, 2012) and Pender et al. (2011, 2012a) carried out dynamic testing on single piles

in stiff Auckland residual clay at the same site; using an eccentric mass shaker, an instrumented

sledgehammer and snap-back testing. Monotonic and cyclic static tests were also carried out by

M.Sa’don (2012). Pile foundations used for testing consisted of four driven closed end steel tubes

273 mm outside diameter and 9.3 mm wall thickness. The test set up for the snap back testing is

shown in Figure 2-13. A decrease in natural frequency and damping was found between

subsequent tests with the eccentric mass shaker because of a gap forming between the pile and

adjacent soil. This gap was measured and increased following subsequent tests. It is apparent that

at small loads the small strain shear modulus controls cyclic stiffness of the pile, however, at

larger cyclic force amplitudes the operational stiffness of the soil, which is an averaged stiffness

Literature review

22

based on the hysteresis loop, is much less than the small strain value. The damping ratios

determined for the high level forced vibration was greater than that of the low level forced

vibration. Load displacement curves correlating to the pull-back phase of snap-back testing

indicated a degrading soil stiffness for consequent tests as each snap-back test results in

progressive yielding of the surrounding soil. This degrading soil stiffness also resulted in a

reduction in computed natural frequencies from free vibration tests. Snap-back loads used in

testing were in the range of 10 kN to 100 kN, with larger loads causing residual displacement of

the pile. The logarithmic decrement method was used to evaluate damping values between 1%

and 30% increasing logarithmically with the displacement of the first cycle used to evaluate the

damping. From monotonic lateral load tests the pile was found not to return to its original

position; this has been attributed to the detached soil behind the pile moving into the space

created due to gapping, as the pile is displaced during testing.

Figure 2-13: Snap-back test arrangement (Pender at al., 2011)

Literature review

23

A case study of an elastic pile in medium-stiff clay originally developed by Pender and Pranjoto

(1996), was investigated by Allotey and Naggar (2008) and modelled the effects of soil cave-in

cohesive and non-cohesive soils; this had the effect of reducing the maximum pile bending

moment, moving the position of maximum bending moment closer to the surface and increasing

the hysteretic damping of the system. These effects were more pronounced when caving occurred

near the ground surface. It should be recognised that soil cave-in is not expected in stiff clays,

however some movement is possible before the soil and pile detach as stresses become tensile in

the soil, as confirmed during testing by M.Sa’don (2012).

2.3.5 Full-scale dynamic testing of piles in cohesionless soils

Jennings at al. (1985) conducted dynamic tests on 450 mm diameter piles, containing a wall

thickness of 10 mm, driven into saturated silty sands. The soil profile and pile details are

illustrated in Figures 2-14 and 2-15. Both piles were embedded 6.75 m below ground level, with

the piles extending 1.35 m above ground level. The piles were tested in the flood plain of the

Hunt River, 1km upstream from where the Hunt River discharges into Wellington Harbour, New

Zealand. A dry density of ρs = 1.65 g/cm3 and an internal angle of friction of φ’ = 35

o were

reported for the sand. Dynamic and cyclic tests were applied to the piles. Cyclic tests were applied

using a jack mounted between the piles, 1.35 m above ground level (at the top of the piles) and

dynamic loads were applied with a shaking machine on top of one of the piles. Initial testing

comprised of dynamic shaking of the west pile followed by slow cyclic loading at a rate of around

one cycle per hour. It was found, as with Blaney and O’Neill (1986), that there is a distinct natural

frequency when the pile was loaded dynamically at low levels of excitation. Based on ground

surface observations during loading, high pore water pressures were developed adjacent to the

pile, resulting in liquefaction and significant softening of the soil near the surface. This paper

focused on evaluating the coefficient of subgrade reaction from testing, based on dynamic and

slow cyclic tests, and how applicable it is to assume independence of soil strain.

Literature review

24

Figure 2-14: Field data for pile testing (Jennings et al., 1985)

Figure 2-15: Details of two piles for testing (Jennings et al., 1985)

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25

Ting (1987) presented the results for a full-scale cyclic dynamic single pile test series in sand, and

reduced these to yield dynamic p-y curves. Two 12.2 m long steel pipes were driven 9.75 m into a

medium dense, saturated, silty fine sand site, located in Seal Beach, California. The internal angle

of friction for the sand was reported to be φ’ = 31o. One pile with a diameter of 610 mm and 13

mm wall thickness was instrumented on site, with the other used as a reference pile. A loading

frame was welded to one of the piles and two eccentric mass shaking machines were used to

provide harmonic lateral excitation. The amplitude of forcing was varied up to 22 kN at higher

frequencies by changing the amount eccentric mass in the shaking machines. Inherent material

non-linearity, coupled with increasing pore water pressures and hence decreasing effective

stresses, resulted in an increasing non-linear p-y backbone curve. At higher load levels a

permanent gap formed between the pile and soil, reducing resistance. After many cycles, the soil

liquefied resulting in considerable strain softening of the p-y backbone curve and a large pile-soil

gap. Damping capacity of the soil system typically increased with increasing deformation level.

No significant variation of damping or stiffness was evident with increasing excitation frequency.

Brown et al. (1988) conducted two-way cyclic lateral loading tests on a large-scale group of steel

pipe piles and an isolated single pile. The piles had an outside diameter of 273 mm and a wall

thickness of 9.27 mm. The piles were originally driven in stiff clay, however this was excavated

and saturated (maintained during testing using perforated pipes) medium dense sand was placed

and compacted, to a depth of 2.9 m, around the piles. After compaction, the sand had an internal

angle of friction φ’ = 38.5o

and a dry density ρs = 1.58 g/cm3. Because the sand extended to a

depth greater than 10 pile diameters the behaviour of the pile was expected to be governed by the

sand. An elevated view of a typical pile is shown in Figure 2-16. The soil within the top five to

ten pile diameters was found to clearly dominate the response of the pile. The densification during

lateral loading appeared to be related to the compacted sand falling in the voids developed behind

the pile when the pile is pushed forward. Two way cyclic loading, compared with one way cyclic

loading, tended to produce a greater densification of sand and a relatively smaller loss in soil

resistance. Finally, cyclic loading in two directions was found to have a small effect on pile

response relative to similar tests conducted in clays.

Literature review

26

Figure 2-16: Elevated view of pile from group showing location of strain gauges (Brown et al., 1988) (1 ft = 0.305

m; 1 in = 25.4 mm)

Basack and Bhattacharya (2009) subjected a small-scale 2 x 2 pile group to cyclic loads in both

cohesionless and cohesive soils. For cohesionless soil tests, a progressive stiffening of the

surrounding soil lead to an improvement of the pile capacity. The repetitive strains induced on the

soil surrounding the pile cause the soil particles to realign and redistribute in a more compacted

manner. A basin-like depression in the ground surface has been observed as a result of this

compaction .This was not evident during cyclic loading in cohesive soils. Gaps and heaves at

ground surface were visible during cohesive soil tests. The fact that this soil densification may be

dependent on the relative density of the soil has been supported by full-scale testing carried out by

Gle and Woods (1984); who found that the damping ratio increased two fold during low-

amplitude steady state vibration tests, using an eccentric mass shaker. This occurred when the

Literature review

27

piles had a relatively loose granular soil around the pile head; when this was replaced with a

densely compacted granular backfill, this increase did not occur.

2.4 CODE APPROACHES AND SOIL-STRUCTURE

INTERACTION (SSI)

Earthquakes forces applied to the foundations come from two sources:

Inertial interaction – developed as the superstructure applies forces to the top of the

foundation

Kinematic interaction – a relative stiffness of the soil and foundation cause a modified

soil response as earthquake waves travel up the soil near the foundation; in turn the

foundation experiences bending, shear and axial forces

The generic term encompassing both phenomena is Soil-Structure Interaction (SSI); however,

this only considers elastic foundation response. Elastic behaviour only occurs at small strains,

and when inelastic foundation response is apparent, Soil-Foundation-Structure Interaction

(SFSI) is a better representation as it encompasses non-linear effects. Also, design engineers

often refer to inertial loading as SSI, ignoring the kinematic component. This stems from the

fact that (Pecker and Pender, 2000; Castelli and Maugeri, 2009):

No specific method or procedures are available to predict deformations or bending

moments for kinematic loading

Seismic building codes, apart from very few exceptions like Eurocode 8 (Eurocode 8

– Part 5, 2003), do not even mention it

Kinematic interaction effects are far more difficult to evaluate rigorously than inertial

interaction effects

The SSI problem can be split up into three tasks; site response analysis, kinematic interaction,

inertial interaction. This can be analysed together by a complicated and time consuming direct

interaction analysis or by using a multi-step process. The multi-step process splits the SSI

problem up and can be solved, for linear systems, using superposition; illustrated in Figure 2-17.

The nature of the incoming waves is dictated by seismological conditions; however geometry,

stiffness and damping characteristics of the soil deposit modify this motion. Castelli and Maugeri

(2009) discuss available methods for evaluating the kinematic interaction, including the pseudo-

static push over analysis using the p-y method. The inertial interaction can be further divided into

two steps (Pecker and Pender, 2000), illustrated on the following page.

Literature review

28

Computation of dynamic impendances (stiffness and damping) at the foundation level

Analysis of the dynamic response of the superstructure supported on the dynamic

impendances and subjected to the kinematic motion, also called effective foundation input

motion

Eurocode 8 states that SSI should be considered in:

Structures where P-δ (2nd

order) effects play a significant role;

Structures with massive or deep-seated foundations;

Slender tall structures;

Structures supported on very soft soils, with an average shear wave velocity is less than

100 m/s.

In addition, bending moments developed during kinematic interaction should only be computed

when all of the following conditions occur simultaneously:

The subsoil is of class C (soft soil) and contains consecutive layers of sharply differing

stiffness;

The zone is of moderate or high seismicity, αPGA > 0.1 (αPGA x g is the expected Peak

Ground Acceleration (PGA)), and the supported structure is of importance category I or

II.

A section from Eurocode 8 provides a transition from the linear elastic approach discussed above

to non-linear methods (discussed previously in 2.2). Table 2-1 acknowledges with increasing

ground accelerations and hence increasing soil strains next to the foundation, an increase in

material damping and decrease in stiffness will occur. These modified factors would then be

inputted into an elastic SSI calculation (elastic systems would have no frequency dependence on

stiffness and damping).

Table 2-1: Average soil damping factors and average reduction factors for shear wave velocity and shear

modulus within 20 m depth. (after Eurocode 8 – Part 5, 2003)

Ground acceleration

ratio, αPGA.S

Damping ratio, ζ Shear wave velocity

ratio, Vs/Vs, max

Shear modulus ratio,

Gs/Gs, max

0.10 0.03 0.90 (±0.07) 0.80 (±0.20)

0.20 0.06 0.70 (±0.15) 0.50 (±0.20)

0.30 0.10 0.60 (±0.15) 0.36 (±0.20)

Note: Vs, max = average Vs value at small strain (<10-5

), not exceeding 300 m/s; Gs, max = average shear

modulus at small strain; S = Soil factor

Literature review

29

Figure 2-17: Superposition method for the Soil-Structure Interaction problem (Pecker and Pender, 2000)

Literature review

30

2.5 SUMMARY FROM PREVIOUS RESEARCH

From the literature review described in this chapter, the following main points summarise

findings for a single pile subject to lateral loading:

A decrease in natural frequencies for subsequent forced vibration and snap-back tests

indicates that the pile-soil system is non-linear. This non-linearity arises from stiffness

degradation and increased hysteretic damping, and due to observed gaps forming in piles

embedded in clay between the soil and pile shaft.

A lower natural frequency at high magnitudes of force was found for the forced vibration

tests, compared with the free vibration tests. This is attributed to stiffness degradation at

high magnitudes of dynamic force.

It is apparent that at small loads the shear strain modulus controls cyclic stiffness of a

pile, however, at larger cyclic force amplitudes the operational stiffness of the soil is

much less than the small strain value.

Greater damping values were found with forced vibration tests and snap-back testing

compared with free vibration tests. This is likely caused by the additional hysteretic

damping from the non-linear soil behaviour.

The response of sand appears to be quite sensitive to load history because cyclic loading

was found to produce densification of sand, and in turn this provided improved soil

resistance.

The soil near the top of the pile (within the active length) governs the response of the

pile-soil system.

Pile and soil type, as well as installation procedure greatly influence the dynamic stiffness

of the pile-soil system.

Snap-back tests produced comparable results to the high level forcing amplitude of the

eccentric mass shaker. Thus, due to its time and cost benefits snap-back testing is

preferred.

Finite element methods are a powerful numerical analysis tool for that have the ability to

solve complex laterally loaded pile-soil systems. However, a large number of

geotechnical parameters are required and these are very time consuming analyses.

Simplified analytical methods such as the Winkler Spring Model, the Elastic Continuum

Model and the Strain Wedge model have been shown to produce similar results to the

complex numerical analyses. Fewer geotechnical parameters are required for these

analyses.

Literature review

31

Any one of these analytical methods is a feasible option to a designer, however, non-

linear effects, and in some situations kinematic interaction, should be incorporated into a

dynamic analysis. This is not captured in most of the existing design codes.

Literature review

32

Test set-up and methodology

33

Chapter 3

Test set-up and methodology

3.1 OVERVIEW

The full-scale dynamic testing described in this study consists of snap-back testing and free

vibration hammer tests on two single free-headed piles at a stiff Auckland residual clay site. Snap-

back testing also has the additional benefit of measuring the static response of the pile during the

pull-back phase of the test. Snap-back testing was carried out to measure and observe the inertial

response of single piles; including effects on surrounding piles, how the response changes over

subsequent tests and the behaviour under different levels of pile head mass. Localised soil

damage, the static response during the pull-back phase of the snap-back test and modal properties

from free vibration tests of the pile-soil system were also measured. The primary outcome of

snap-back testing was to provide a measure of non-linear stiffness and damping for the pile-soil

system. This section outlines pile details and layout, geotechnical site conditions, instrumentation

and data acquisition as well as snap-back test procedure including the testing program for the two

piles tested.

Test set-up and methodology

34

3.2 PILE DETAILS AND LAYOUT

Four steel pipe piles (referred to as Piles 1 – 4) were driven closed-ended into the Auckland

residual clay site using a 3000 kg drop hammer, as part of previous research (M.Sa’don, 2012);

full details of the pile set-up can be found in this reference. The piles had a centre to centre

spacing, s, of approximately 3.0 m (11.0 pile diameters, D). This was chosen to minimise

interaction effects between piles. Piles 1, 2 and 4 were driven to an embedment depth, z, of 6.5 m

(23.8 D), leaving the pile to extend approximately 1.0 m (3.66 D) above ground level (AGL); Pile

3 was driven to a depth of 6.75 m (24.7 D), extending 0.75 m (2.75 D) AGL. The piles have an

outside diameter, D, of 273 mm and a wall thickness, tw, of 9.27 mm, and a length, L, of 7.5 m

(27.5 D). The Young’s modulus, Ep, of the steel pipe pile is reported to be 200 GPa with a yield

bending moment, My, of 225 kNm. Pile details for Piles 3 and 4, the piles tested, are illustrated in

Figure 3-1. A pair of strain gauges were connected to Piles 3 and 4 above the ground surface to

provide a measure of the oscillatory pile response.

Figure 3-1: Pile details and instrumentation for (a) Pile 3; (b) Pile 4

Test set-up and methodology

35

3.3 PILE HEAD PREPARATION

Two custom-made mild steel brackets were connected to the pile head to support the steel tray

and lead masses. This configuration is adopted to simulate the mass of the superstructure

supported by the pile. A different steel tray and lead mass configuration was used for each pile

and are detailed in the following two subsections.

The steel brackets were designed with a yield stress of 350 MPa to sustain the dynamic loads

applied. A timber block from radiata pine was designed and placed in-between the steel brackets

to make good grip and contact with the test pile. The timber blocks and mild steel brackets were

carefully clamped by using eight pieces of M20 8.8 high strength friction bolts and nuts.

3.3.1 Pile 3 head details

The Pile 3 pile head configuration consisted of two 5 mm thick steel plates fillet welded to a base

plate, which was connected to the steel brackets with four M8 bolts; the sides were connected

with three long M12 4.6 bolts. Twenty four lead masses were used in the steel tray, with a

combined mass of 456.4 kg. The total mass attached to the pile (including collar and shackle) was

623.9 kg, with the pile extended 0.75 m above ground level. This layout is shown in Figure 3-2.

Figure 3-2: Pile head set-up for Pile 3

3.3.2 Pile 4 head details

The effect of altering the mass that was added to the pile was investigated for tests on Pile 4; with

the aim of achieving a greater natural period for the pile-soil system. To add to the cantilevered

Test set-up and methodology

36

pile response, Pile 4 was tested as it extended 1.0 m above ground level, 0.25 m greater than Pile

3. To hold more lead masses a new steel tray was designed and manufactured to sustain inertial

loads from all of the 50 lead masses available. The mild steel tray was conservatively designed for

a force in the steel tray equal to the maximum pull-back load (120 kN). The sides were again fillet

welded to the base plate, and the sides connected by drilling for up to six long threaded 4.6 M16

bolts. The thickness of steel tray was 16 mm which gave an advantage in terms of the extra mass

added to the pile in comparison with the 5 mm steel tray used for Pile 3. For practical reasons, the

heavy steel tray (140 kg) was cut in half and four 16 mm mild steel connector plates were used to

connect the two tray pieces together with 16 – 4.6 M16 counter-sunk cap screws in total. The

extra loadings meant that the tray and brackets were drilled and connected with four 4.6 M16

bolts. Drawings of the new steel tray manufactured are provided in Figure 3-3.

Three different levels of mass were investigated during testing; no added lead masses, 15 lead

masses and 50 lead masses. The respective masses attached to the pile head (including collar and

shackle) were: 324.1 kg, 609.4 kg and 1274.9 kg. All three arrangements are shown together in

Figure 3-4.

Figure 3-3: Drawings of steel tray manufactured for Pile 4 testing

Test set-up and methodology

37

Figure 3-4: Different pile head arrangements for Pile 4; (a) no added lead masses (324 kg); (b) 15 lead masses

(609 kg); (c) 50 lead masses (1275 kg)

3.4 GEOTECHNICAL SITE CONDITIONS

This section presents a summary of the results for soil tests carried out before pile driving by

M.Sa’don (2012) at the Auckland residual clay site, as well as testing carried out for the current

study. These tests are summarised below:

For the determination of the small strain stiffness of the soil:

o Wave activated stiffness (WAK) tests (Briaud and Lepert, 1990)

o Spectral analysis of surface waves (SASW) method (Heisey et al., 1982; Stokoe

and Nazarian, 1985)

o Seismic cone penetrometer tests (SCPT) (Robertson and Campanella, 1985)

To determine the undrained shear strength of the soil:

o Cone penetrometer tests (CPT)

o Shear vane tests

Laboratory testing to determine soil properties

3.4.1 Site location and description

The Auckland residual clay site is located in Albany; refer to Figures 3-5 and 3-6. Testing was

originally set up at this location due to free space for easier access and movement of testing

equipment. The highly variable clay is a product of in-situ weathering of Waitemata group

sandstones and siltstones (Pender et al., 2012b).

Test set-up and methodology

38

Figure 3-5: Aerial image of site location from Google Earth

Figure 3-6: Regional map of Auckland showing site location from Google Earth

Test set-up and methodology

39

3.4.2 Laboratory and undrained shear strength tests

This section summarises the following tests:

Laboratory tests; consisting of Atterberg limits and natural moisture content

determination

Undrained shear strength tests; involving shear vane tests and CPT testing

Results are summarised for testing before and during the present study.

3.4.2.1 Test results from previous research

A total of 14 different locations of soil samples were collected in close proximity to the four test

piles, at depths of 0.5 m and 1.0 m, using a hand auger. Figure 3-7 shows the locations of soil

samples; note that arrows refer to the direction of testing carried out at the site. All samples were

tested at the Geomechanics Laboratory at the University of Auckland. Testing consisted of

Atterberg limits and natural moisture content determination. During sampling, shear vane tests

were also performed at each borehole, at a shallow depth of around 1.0 m, to determine the

undrained shear strength, su-VaneShaer. Results of undrained shear strength from CPT testing, su-CPT;

determined as a function of cone resistance, qc, are also presented. A total of five soundings; four

at the pile locations and the fifth at the centre, were performed between ground level and 10 m

below ground level. A summary of the results for testing around Piles 3 and 4 are presented in

Table 3-1. CPT results at shallow depths only are presented.

Most of the soil samples taken from the Albany site are classified as inorganic silts and clays in

between medium and high plasticity. The Atterberg limit values are quite variable with results

scattered along the A-Line as shown in Figure 3-8. The natural water content (wN) was in the

range of 30 % to 40 % obtained from a conventional determination based on the loss of water

when soil is dried at a temperature of around 105oC. The liquid limit and plastic limit were in the

range of 40 % to 70 % and 25 % to 30 % respectively. Consistent with the visual description of

these soils as stiff to very stiff, the liquidity index values are less than 0.5. From the natural water

content and Atterberg Limit values recorded, the soil is classified as Auckland residual clay with

the values obtained agreeing well with previous published work (Pender et al., 2000 and Pender et

al., 2003). Most of the samples of soil taken from the Albany site are classified as inorganic silts

and clays between medium and high plasticity.

Test set-up and methodology

40

Figure 3-7: Location of soil sampling at Albany site (M.Sa’don, 2012)

Figure 3-8: Auckland residual clay based on the plasticity index and liquid limit (M.Sa’don, 2012)

3.4.2.2 Test results from current study

During the two stages of the testing program; 29/03/2012 (autumn) and 06/09/2012 (spring), soil

samples were taken around the test pile (Piles 3 and 4 respectively), and taken back to the

Laboratory to determine the natural water content, wN. Shear vane tests were also taken around

the test piles at shallow depths to determine the undrained shear strength of the clay, su-VaneShaer.

Tests were either taken prior to or following testing. A plan of the site showing shear vane and

Test set-up and methodology

41

water content tests is shown in Figure 3-9. Results are displayed in Tables 3-1 with test results

carried out by M.Sa’don (2012); note the same pile numbering system has been adopted for the

present study.

Reported values for the undrained shear strength and natural water content are generally less than

those reported through previous research. This result is expected as tests were taken at lower

depths where the soil stiffness is lower and the clay contains less moisture.

Table 3-1: Soil properties determined during current testing program, in comparison with results from previous

research

Reference Date Depth

(m)

Natural

water

content

Atterberg limit Plasticity

index

Liquidity

index

Undrained

shear strength

wN (%) LL

(%)

PL

(%)

PI LI su-

VaneShear

(kPa)

su-CPT

(kPa)

A Pile 3* 2009 0.50 22 35 20 15 0.16 136

90 A Pile 3* 2009 1.0 44 61 31 30 0.41 158

B Pile 3* 2009 0.50 32 47 25 22 0.30 132

B Pile 3* 2009 1.0 37 63 30 33 0.21 154

A Pile 4* 2009 0.50 39 67 31 36 0.22 125

100 A Pile 4* 2009 1.0 39 67 32 35 0.20 150

B Pile 4* 2009 0.50 34 55 29 26 0.22 147

B Pile 4* 2009 1.0 32 55 28 27 0.14 128

s1 Pile 3 29/03/2012 0.10 - - - - - 163 -

s2 Pile 3^ 29/03/2012 0.10 - - - - - 145 -

s3 Pile 3^ 29/03/2012 0.20 - - - - - 184 -

s4 Pile 4 06/09/2012 0.12 - - - - - 86.0 -

s5 Pile 4 06/09/2012 0.12 - - - - - 114 -

s6 Pile 4 06/09/2012 0.12 - - - - - 144 -

s7 Pile 4 06/09/2012 0.12 - - - - - 166 -

w1 Pile 3 29/03/2012 0.10 22 - - - - - -

w2 Pile 3 29/03/2012 0.1 20 - - - - - -

w3 Pile 4 06/09/2012 0.1 35 - - - - - -

w4 Pile 4 06/09/2012 0.1 25 - - - - - -

*Carried out by M.Sa’don(2012); ^Carried out after snap-back testing (for the present study)

Test set-up and methodology

42

Figure 3-9: Plan of site showing shear vane test and water content sample locations

3.4.3 Wave activated stiffness (WAK) tests (M.Sa’don, 2012)

The WAK (wave-activated stiffness [K]) test, developed by Briaud and Lepert (1990), is a load

test performed by hitting a spread footing with sledgehammer to measure the stiffness of the soil

beneath a footing. WAK test is a non-destructive test which was performed at the ground surface.

The experimental set up for WAK and SASW (spectral analysis of surface waves) is shown in

Figure 3-10. The test layout details are shown in Figure 3-11.

Figure 3-10: Experimental set-up for WAK and SASW testing (M.Sa’don, 2012)

Test set-up and methodology

43

Figure 3-11: Layout of test arrangement at Albany site (M.Sa’don.2012)

The results of the WAK test analysis is summarised in Table 3-2. From the data, the average shear

modulus, Gs and average shear wave velocity, Vs of the soil is 40 MPa and 152 m/s respectively.

The average recorded maximum depth was calculated to be approximately 2.4 m.

Table 3-2: Auckland residual clay properties under small strain from WAK test analysis (after M.Sa’don, 2012)

Test point Vertical stiffness,

Kv (kN/mm)

Shear modulus,

Gs (MPa)

Shear wave

velocity, Vs (m/s)

Max depth, z (m)

WAK 1 0.5m

plate

30 42 157 2.6

WAK 2 0.5m

plate

32 44 162 2.5

WAK 3 0.5m

plate

34 48 167 2.4

WAK 4 0.5m

plate

23 33 139 2.6

WAK 5 0.5m

plate

25 35 144 2.6

WAK 5 1.0m

plate

49 34 142 1.6

Average 32 40 152 2.4

Test set-up and methodology

44

3.4.4 Seismic cone penetrometer tests (SCPTs) (M.Sa’don, 2012)

SCPT’s were conducted at two locations of pile driving to a 4.0 m depth with 1.0 metre intervals.

The test consists of measuring the travel times of body waves between a seismic shear wave

source activated at different depths and an array of geophones. The tests were carried out to

determine the shear wave velocity and shear modulus of the soil under small strain. The shear

wave velocity from SCPTs and the calculated shear modulus is presented in Table 3-3.

Table 3-3: Auckland residual clay properties under small strain from SCPT test analysis (after M.Sa’don, 2012)

Location Shear wave velocity,

Vs (m/s)

Shear modulus, Gs

(MPa)

Depth, z (m)

Pile 3

161 44 1 – 2

140 33 2 – 3

162 45 3 – 4

Pile 4

164 45 1 – 2

155 41 2 – 3

146 36 3 – 4

3.4.5 Spectral analysis of surface waves (SASW) tests

The SASW tests were performed to determine the shear wave velocity and shear modulus of the

Auckland residual clay. This section summarises the SASW testing methodology and presents

SASW test results from previous research (M.Sa’don, 2012) and the present study.

3.4.5.1 SASW testing methodology

The test set-up for SASW testing is shown in Figure 3-12. A sledgehammer is used to hit a square

metal plate on the ground surface to provide a vertical excitation. The surface, or Rayleigh, waves

produced as a result of the impulse were monitored by geophones placed in a line at various

distances from the metal plate. For past research (M.Sa’don, 2012), two vertical accelerometers

(V3 and V4; refer to Figure 3-10) were used as the recording devices.

For a horizontally layered soil profile, Rayleigh wave velocity will vary with frequency (Heisey et

al., 1982). The variation of velocity with frequency is defined as wavelength and a plot of velocity

versus wavelength gives a dispersion curve. A dispersion curve is developed from phase

information of the cross power spectrum. The cross power spectrum is used to provide the relative

phase between the two signals at each frequency in the range excited during the SASW test.

Test set-up and methodology

45

Figure 3-12: Schematic of SASW test set-up

The cross power spectrum, Pxy, is the product of the linear spectrum used in analysing the two

signals recorded (Sx and Sy) and calculated from the following relationship:

(3-1)

where Sx is the linear spectrum of the first signal and Sy* is the complex conjugate of the linear

spectrum of the second signal.

From the calculated cross power spectrum, Pxy, the relative phase of the cross power spectrum

can then be determined, which represents the phase difference of the two recorded signals:

(

) (3-2)

The Rayleigh velocity, (VR), and wavelength, (λR), associated with a given frequency can be

calculated by the following formulas:

(3-3)

(3-4)

where x is the distance between the receivers and φ is the phase difference for a given frequency,

f, determined from the cross power spectrum of the two signals. This process is then repeated for

every frequency to form a dispersion curve. Once a dispersion curve is obtained, the velocities are

assigned to different depths by applying a wavelength criterion to the site. Signal phase

components from one line of SASW tests at a range of frequencies are shown in Figure 3-13.

Table 3-4 shows calculations for Rayleigh's wave velocity VR, which gives phase differences, φ,

against distance, x (8 m), at peak frequencies recorded. The VR value is approximately 10 percent

less than that of the shear wave’s velocity, Vs. The effective sampling depth for each wavelength

Test set-up and methodology

46

is considered to be equal to a fraction of the wavelength obtained. It has been recommended that

1/2 – 1/3 of the wavelength is representative as the effective sampling depth (Stokoe and

Nazarian, 1985).

Table 3-4: Shear wave velocity computation from signal wave components of SASW tests

f (Hz) φ (degrees) λR (m) z=λR/2 (m) VR (m/s) Vs=1.1VR(m/s)

13.0 184 15.6 7.82 203 223

17.4 359 8.02 4.01 139 153

32.8 721 4.00 2.00 131 144

41.5 900 3.16 1.58 131 144

Figure 3-13: Phase difference between two geophone recordings at a range of frequencies for one SASW test

3.4.5.2 Results from previous research

The results obtained from previous SASW tests are tabulated in Table 3-5. The shear modulus of

Auckland residual clay, Gs, was calculated using Gs = Vs2/ρs; where ρs is the mass density taken to

be 17 kg/m3 from M.Sa’don (2012). The value of Gs is the shear modulus at a very small strain

measured in a short period of time. Note that multiple tests were carried out over a relatively

shallow sampling depth, hence the range of results have been presented.

0 50 100 150-200

-150

-100

-50

0

50

100

150

200

Frequency (Hz)

Phase d

iffe

rence (

degre

es)

Test set-up and methodology

47

3.4.5.3 Results from current study

The shear wave velocity has been determined at four different sampling depths and is related to

the shear modulus using Gs = Vs2/ρs. Results are summarised in Table 3-5, with the range of test

results from previous research.

Table 3-5: Summary of SASW tests at Albany on 29/03/2012, in comparison with previous testing

Depth, z (m) Shear wave velocity, Vs (m/s) Shear modulus, Gs (MPa)

1.58 144 36.0

1.99 144 36.0

4.01 153 40.8

7.82 223 86.2

0.5 – 2.5* 154 – 171 40 – 49

*Range of six different sets of SASW tests carried out by M.Sa’don (2012)

3.4.6 Summary of stiffness tests under small strain

A summary of small strain stiffness site investigation data from previous research (M.Sa’don,

2012) and the current study is presented in Table 3-6. The shear modulus has been computed at

greater depths for the current study. From the ground surface to 4.0 m, generally a lower shear

modulus was found when comparing with test results from previous research.

Table 3-6: Summary of Auckland residual clay properties under small strain from the present study and

previous in-situ testing

Test Depth, z (m) Shear wave velocity,

Vs (m/s)

Shear modulus, Gs

(MPa)

WAK* 0.5 – 2.6 139 – 167 33 – 48

SCPT* 1.0 – 4.0 140 – 164 33 – 45

SASW* 0.5 – 2.5 154 – 171 40 – 49

SASW 1.6 – 2.0 144 36.0

SASW 4.0 153 40.8

SASW 7.8 223 86.2

*Denotes site investigation data from previous research (M.Sa’don, 2012)

Additional SASW tests were carried out at Albany on 29/03/2012 at the commencement of the

testing program for the present study so that small strain stiffness data could be available which

would be more representative of the site conditions than small strain stiffness data from previous

research. This data was also assumed to be representative of conditions during the second stage of

the testing program on 06/09/2012.

Test set-up and methodology

48

3.4.7 Representative soil profile from site investigation data

A representative soil profile from site investigation data is produced in Figure 3-14. SASW

testing from the present study is utilised in the determination of soil stiffness as a function of

depth below ground level (BGL), with the single distribution used for both Piles 3 and 4. The

undrained shear strength is based on CPT testing carried out previously at the Albany site

(M.Sa’don, 2012). Full CPT data for each pile can be found in this reference.

Figure 3-14: Representative soil profile from site investigation data

3.5 INSTRUMENTATION AND DATA COLLECTION

This section outlines instrumentation used to measure the response during testing of Piles 3 and 4

as well as detailing gap measurement and observation methodologies. An overview of the

instrumentation is summarised as follows (refer to Figure 3-1):

Linear variable displacement transducers (LVDTs) to measure pile displacement

A pair of four-armed strain gauges to measure pile bending

2g/10g accelerometers to measure accelerations

Four geophones to measure surface waves at ground level

Test set-up and methodology

49

3.5.1 Pile 3 instrumentation

One pair of four-armed strain gauges above ground level were utilised during testing of Pile 3, the

pile extending 0.75m above ground level. This meant that the bending moment on the pile could

not be measured; however, when not calibrated the strain gauges still provide a good measure of

the oscillatory response of the pile which is valuable for testing. The strain gauges could also be

later calibrated after testing to measure the force acting on the pile. Two linear variable

displacement transducers (LVDTs) were connected to the test pile, as shown in Figure 3-15. A

LVDT and 2g Accelerometer were connected to each of the piles not participating in Pile 3 testing

to assess interaction effects from the snap-back of the test pile. Accelerometers were not equipped

to the test pile because accelerations of the test pile were previously found to exceed 10g. These

instruments were used to measure the accelerations during the snap-back and the LVDTs were

used to measure the displacement of the pile above the ground level. The LVDTs were attached

using small steel frames that were clamped to static steel reference beams spanning between the

piles. The reference beams were fixed to the ground at approximately half the distance to adjacent

piles, a plan of the set up is shown in Figure 3-16. The load applied during the pull-back phase of

the snap-back tests was measured using a load cell with a capacity of 120 kN, connected between

the double acting hydraulic ram and steel collar attached to the test pile.

Figure 3-15: External instrumentation attached to the test pile (Pile 3)

Test set-up and methodology

50

Figure 3-16: Plan of Albany site showing reference beam layout and instrumentation for Pile 3 testing

3.5.2 Pile 4 instrumentation

One pair of strain gauges above ground level, not calibrated, was used during Pile 4 testing. As

with Pile 3, this was used as a measure of the oscillatory response of the pile, whilst also being

able to be later calibrated to measure the force on the pile. Again, two LVDTs were set up on the

steel reference beams and set up to the test pile. Three 10g 3D piezoelectric accelerometers were

set up on the ends of the reference beams and the steel bracket of the test pile to measure the

relative accelerations in the snap-back direction; a method of assessing any interaction between

the test pile and the reference beam fixities during snap-back tests. The instrumentation attached

to the test Pile 4 is shown in Figure 3-17. A plan layout of the site is provided in Figure 3-18.

Four geophones were set-up on the Albany site for Pile 4 testing to measure the surface motion

that passes through the clay site during the snap-back tests. The geophones were arranged at

various distances and orientations from Pile 4 to assess the level of radiation damping in the soil.

The geophones were set up on a mound of workable/moist clay facing the test pile and aligned to

the horizontal using an inclinometer. Three geophones are aligned directly in the line of the snap-

back at distances of 3, 5 and 7 m south from the test pile. The fourth geophone was set up 4 m

from the test pile at an angle of 45 degrees to the other geophones (southwest). Images taken of

the geophone arrangement are shown in Figure 3-19; the geophone locations are also confirmed in

Figure 3-18.

Test set-up and methodology

51

Figure 3-17: External instrumentation attached to the test pile (Pile 4)

Figure 3-18: Plan of Albany site showing reference beam and instrumentation layout for Pile 4 testing

Test set-up and methodology

52

Figure 3-19: Images of the four geophones used for Pile 4 testing

3.5.3 Gap monitoring around test pile

An important part of snap-back testing is monitoring the pile-soil gaps that develop around the

test pile during the pull-back and following the snap-back tests. This importance is due to the

significant impact this non-linear behaviour can have on the static and dynamic response of the

pile. Photos are taken of the gap developed behind the pile during the pull-back; for safety reasons

this gap is not measured, but this can be later done using the image. Following the snap-back,

residual gaps can develop around the pile. These are typically in line with the snap-back either in

front or behind the test pile. A flat measuring tape is used to measure the width of any gaps at the

front or behind the test pile, as well as the extent of the gap around the circumference of the pile.

In addition, photos are also taken shown residual damage around the test pile.

To measure the gap depth beneath the ground surface, the measuring tape is lowered into the gap

until significant resistance is met; this is assumed to be the bottom of the gap. The length of tape

that went beneath the ground surface is then measured as the gap depth. This measurement is

repeated on the other side of the pile if a gap has formed there as well. The cohesive nature of

clay means that it is difficult to assess whether the bottom of the gap has been reached, or the

object is simply passing through a thin gap at depth between the pile and clay. Care was taken that

measurements were recorded by the same person using consistent technique so results were

comparable. Figure 3-20 below is presented to show the typical gapping behaviour observed and

measured during testing. Figure 3-21 shows a schematic view of the measurement process.

Test set-up and methodology

53

Figure 3-20: Image of gapping around Pile 4 following a 120 kN snap-back at Albany

Figure 3-21: Schematic view of the gap measurement process

Test set-up and methodology

54

3.6 DATA PREPARATION

3.6.1 Data acquisition system

Response signals produced during testing were recorded using CompactDAQ_V14 (Beskhyroun,

2012; Mathworks, 2012). For the free-vibration hammer and snap-back tests, the system recorded

each channel with a sampling rate of 2000 readings per second; for the pull-back phase of snap-

back tests a sampling rate of 10 Hertz was used. The instrumentation that was required to be

calibrated was done so using CompactDAQ_V14. The LVDTs and load cell were calibrated

manually and these were checked against values provided by the manufacturer. These calibration

factors were then utilised in the data acquisition process. The relative response of accelerometers

and geophones was of importance for these separate sets of equipment, so the raw reading of volts

(calibration factor of unity) was recorded. As discussed earlier, the strain gauges were not

calibrated before testing, as they could be used for the free-vibration response and also be

calibrated as a measurement of force. The readings from the instrumented hammer were not

utilised, instead it was used to provide a low force level single excitation to the pile, measured

using other instrumentation. All readings were taken from a Compact DAQ box, connected to a

digital-analogue converter, before delivering data to CompactDAQ_V14 on the computer running

on site. Power to this recording system was provided by a 100 KVA (80 KW) diesel generator.

Figure 3-22 shows the data acquisition set up at the Albany site; a schematic of this process is

presented in Figure 3-23. MATLAB (Mathworks, 2012) was used for all data presentation and

analysis of test data in this thesis.

Figure 3-22: Data acquisition set up at the Albany site (during Pile 3 testing)

Test set-up and methodology

55

Figure 3-23: Schematic of data acquisition process on site

3.6.2 Pile 3 test data preparation

Each individual recording (versus time) carried out in CompactDAQ_V14 during testing was

saved as a text file and imported to MATLAB for analysis. A 30 Hz averaging Butterworth low-

pass filter (LPF) was used to remove the high frequency noise from the response, providing a

cleaner response.

Generally the un-calibrated response of the strain gauge on Pile 3 was slightly cleaner than that of

the two LVDT’s; because the readings from the LVDTs need to be converted between digital and

analogue twice, creating more noise. However, the strain gauge did not provide a measure of

displacement; so the bottom LVDT was used for all displacement plotting. This provided a

sufficiently clean response. Typically, the entire open time domain is not of interest; for example,

only one of many blows is required for a hammer test. The data is trimmed on MATLAB by

creating new vectors based on the specified time range. The entire response of a single hammer

blow has been considered; however, the large pull-back peak has been excluded. The recordings

are not zeroed automatically during data acquisition so an inbuilt detrend function in MATLAB is

applied to centre the trimmed section of response about the time axis. Low frequency effects were

evident for some responses, where the response would deviate from its centre at zero

displacement as it moves along the time axis. A low frequency Butterworth high-pass filter (HPF)

was used to modify the response so it is centred about the time axis throughout. In order to zero

the section of response about the time axis of interest, trimming had to be carried out first.

Filtering must be carried out last when the response has been trimmed and zeroed, otherwise it

will be detrimental to the response. The pull-back peak of the snap-back was not considered in the

Test set-up and methodology

56

response as its displacement was significantly greater than the rest of the response, distorting the

response when zeroing and filtering was applied.

The hysteretic response of the pile was assessed by calibrating the four-arm strain gauge above

the ground level for force during the pull-back with the load cell force. The ratio between the

mass and load collar lever arms to strain gauge was then applied to the strain gauge readings to

provide a measure of force during the snap-back, which was relative to the force applied by the

load collar during the pull-back. Noise filtering was required for both the strain gauge reading and

the LVDT displacement reading.

3.6.3 Pile 4 test data preparation

Data was dealt with on MATLAB in a similar way to methods outlined in the Pile 3 section; with

trimming, zeroing and noise filtering. The data analysis techniques were however, investigated

more rigorously in the Pile 4 data analysis. Note that the response was zeroed at the start of each

new test automatically during data acquisition, but the portion of the response of interest still

needed to be re-zeroed about the time axis using the inbuilt MATLAB function. The first reading

before the tare was carried out was outputted to the text file as this is useful when identifying

residual effects. A standard 40 Hz LPF was used to remove noise instead of the 30 Hz LPF used

for Pile 3. This filter was used because the unfiltered response for the LVDTs was cleaner for Pile

4 and also because the higher frequency filter has less effect on the response. The strain gauge for

Pile 4 was not producing signals as clean as those found for Pile 3. Again, the bottom LVDT was

used as it had a cleaner response by inspection. The steel frame arrangement meant that LVDTs

were set up at an angle to the horizontal; whilst the longer cantilever section meant that the load

collar applied the pull-back force at an angle to the horizontal as well. Both produced less than a

5% difference if the readings were taken about the horizontal, so this was ignored.

The signals recorded by the four geophones during snap-back tests provided a new set of data

available during the testing of Pile 4. Each response was filtered; to remove any localised signal

increases due to noise, and zeroed immediately before the snap-back; to ensure the signals

between each geophone were relative to each other.

3.7 TEST PROCEDURE AND EQUIPMENT

There are two primary test set-ups during testing of single piles at Albany: (1) Free-vibration tests

are carried out on a single pile by applying blows to the steel bracket of the pile with an

instrumented hammer; (2) Snap-back tests are carried out by pulling the test pile towards a

reaction pile, to a target force, and then releasing the pile and measuring the response.

Test set-up and methodology

57

3.7.1 Free vibration hammer test details

Free vibration tests were carried out to determine the fundamental natural frequency of the pile-

soil system. An instrumented sledgehammer (Dytran model 5803A) was used to hit the steel

bracket, in the direction of the snap-back, and the response was recorded. Multiple (three to five)

hammer blows, with sufficient time between each to let the pile stop vibrating, were applied to the

test pile for each test to provide multiple responses for data analysis. Figure 3-24 shows the

operator performing a free-vibration test on Pile 3 at the Albany site. The operator attempted to

use the same technique, with both force, location of the blow and timing between blows, across

all tests for consistency.

Figure 3-24: Operator performing a free vibration test using the instrumented sledgehammer

3.7.2 Snap-back test details

The equipment required to perform snap-back tests is relatively simple, a schematic of the set-up

is shown in Figure 3-25. At the Albany site, snap-back testing required two load collars connected

to the test pile and the reaction pile. A double acting hydraulic ram was used to provide the force

to pull the test pile. The pull-back force was measured with a 120 kN capacity load cell connected

between the hydraulic ram and the test pile. A shackle with a 120 kN factored capacity was

connected between the load cell and the test pile collar to provide the quick-release mechanism,

activated using a long straight crow-bar. A timber block was placed below the shackle so it did

Test set-up and methodology

58

not provide interference, as it released and hit the ground surface, to the signals recorded during

the dynamic response. Figure 3-26 shows the snap-back testing set-up during the commencement

of the pull-back phase of a Pile 3 test at the Albany. Figure 3-27 shows that the quick-release

mechanism does not interfere with the response of the pile. Snap-back tests have been shown to

be able to sufficiently replicate earthquake response history at a relatively low cost (M.Sa’don,

2010; Pender et al., 2011; M.Sa’don, 2012; Pender et al., 2012a).

Figure 3-25: Schematic illustrating snap-back set-up and equipment required

Figure 3-26: Snap-back testing set up on Pile 3 at the Albany site

Test set-up and methodology

59

Figure 3-27: Quick-release mechanism following activation, showing it does not interfere with the response of the

pile

3.8 TEST PROGRAM

The following two sections provide details of the snap-back tests performed on Piles 3 and 4;

detailing the reaction pile and the magnitude of pull-back forces.

3.8.1 Pile 3 test program

The testing program for Pile 3 was carried out over one day on 29/03/2012 in the spring season.

Snap-back tests were carried out at a range of final pull-back forces, utilising Pile 1 as the reaction

pile for all tests. Free vibration hammer tests and gap measurements and observations were

carried out at the start of testing and following each snap-back test. At the end of testing, hammer

tests were carried out on all four sides of the steel bracket to assess any differences in the natural

frequency of the pile in each direction. Pull-back tests are carried out before the snap-back test, to

bring the pile to its target snap-back release force. The sequence of snap-back tests is provided

below:

7.5 kN snap-back 1

15 kN snap-back 1

30 kN snap-back 1

60 kN snap-back 1

90 kN snap-back 1

120 kN snap-back 1

Test set-up and methodology

60

120 kN snap-back 2

90 kN snap-back 2

60 kN snap-back 2

30 kN snap-back 2

15 kN snap-back 2

7.5 kN snap-back 2

Note: hammer test, pull-back test and gap measurement details are omitted from the sequence

above.

3.8.2 Pile 4 test program

The testing program for Pile 4 was carried out over one day on 06/09/2012. As mentioned earlier,

three levels of pile head masses were investigated during testing, at two different snap-back force

levels. To assess the change in natural period from snap-back tests, a hammer free vibration test

had to be carried out when the pile head mass was changed, as well as after the snap-back test was

carried out. As with Pile 3 tests, gap measurements and observations were carried out at the start

of testing, and after each snap-back test. The sequence of snap-back tests is as follows:

10 kN zero lead masses (324 kg pile head) snap-back 1

10 kN 15 lead masses (609 kg) snap-back 1

10 kN 50 lead masses (1275 kg) snap-back 1

120 kN zero lead masses (324 kg) snap-back 1

120 kN 15 lead masses (609 kg) snap-back 1

120 kN 50 lead masses (1275 kg) snap-back 1

120 kN 50 lead masses (1275 kg) snap-back 2

120 kN 15 lead masses (609 kg) snap-back 2

120 kN zero lead masses (324 kg) snap-back 2

Recall the pull-back, hammer and gap measurement details are omitted from the list. Note the

second 120 kN snap-back with a 1275 kg pile head is the only snap-back test where the mass has

remained unchanged from the previous snap-back, so no hammer test was carried out before the

snap-back. For each new level of snap-back force, the 324 kg pile head was tested first; otherwise

the non-linear response would not be as clear if a larger mass was tested beforehand.

Static pile response from full-scale field tests

61

Chapter 4

Static pile response from full-scale

field tests

4.1 OVERVIEW

This chapter summarises the full-scale static response through force-displacement relationships of

two piles (Piles 3 and 4) at a residual clay site in Albany. The residual pile displacement

following individual tests and the results from gap measurements taken during different stages of

testing is also presented.

The static response was assessed during the pull-back phase of snap-back tests, by comparing the

displacement of the test pile versus the force applied to the pile at the load collar; this gives a

measure of the static pile head stiffness. Piles 3 and 4 were tested using Piles 1 and 2 as the

reaction pile respectively. The first phase of the testing program involved tests on Pile 3 at the site

in Albany; the load was applied to Pile 3 at an elevation of 0.3 m above ground level (AGL) and

Static pile response from full-scale field tests

62

displacement measured 0.25 m AGL. The order and magnitude of applied pull-back forces were

as follows:

7.5 kN

15 kN

30 kN

60 kN

90 kN

120 kN

120 kN

90 kN

60 kN

30 kN

15 kN

7.5 kN

For Pile 4 testing, the load was applied at an elevation of 0.65 m AGL; with the displacement

measured at an elevation of 0.2 m AGL. Recall from phase two of the testing program the

following order of pull-back tests were carried out on Pile 4:

10 kN

10 kN

10 kN

120 kN

120 kN

120 kN

120 kN

120 kN

120 kN

All forces were low enough such that the pile did not yield. The displacement measured from the

lower LVDT was utilised in these analyses. MATLAB (Mathworks, 2012) was used in all the

data analysis and presentation for this thesis.

Static pile response from full-scale field tests

63

4.2 PULL-BACK FORCE-DISPLACEMENT RESPONSE

This section is split up into two main parts, where the static response of Piles 3 and 4 is

considered separately. The static response is illustrated through force-displacement relationships

which provide a measure of the static pile head stiffness. Pull-back tests are categorised as low

force (less than 60 kN target pull-back force) and high force (greater than 60 kN pull-back force).

The accumulative residual pile displacement developed following each pull-back (and snap-back)

test is also presented for Pile 3.

4.2.1 Pile 3 pull-back tests

The force displacement curves for the low force pull-back tests on Pile 3, that is the magnitudes of

7.5, 15 and 30 kN, are displayed in Figure 4-1. There is a significant separation between the two

series of lower pull-back loads, which are a result of the two series of high force pull-back tests

carried out in between these two sets of pull-back tests. During testing the pile-soil gap depth on

the side of the pile under compression during the pull-back was observed to progressively grow

with each pull-back (and snap-back) test. The increased gap depth results in less soil contact with

the pile, and hence a softer response is evident for the second series of low force pull-back tests.

Due to extensive testing already carried out on Pile 3, there was a visible gap on the compression

side of the pile before testing for the current study commenced. The overall stiffness change

between successive low force pull-back tests is not significant when compared with the separation

between the two series of tests; thus high force pull-back tests have a much greater effect on gap

growth.

Looking at the behaviour of the individual pull-back tests in Figure 4-1, there is a relatively stiff

response during the early (low) levels of loading, and as the force applied to the pile increases, the

stiffness of the response starts to decrease. This softening occurs through one of two mechanisms:

1) Soil yielding in compression in front of the pile

2) Soil detaching from behind the pile as it cannot support tensile stresses

This effect is less evident for the second series of pull-back tests, which have a large gap depth

and hence the initial stiffness is much softer at the commencement of the pull-back tests. The high

force level tests carried out before the second series pull-back tests appear to limit their

capabilities of causing further non-linear soil response.

Static pile response from full-scale field tests

64

Note that discontinuities in the force displacement curves and the rapid stiffness reduction at the

end of the pull-back are due to the manual application of load during testing.

Figure 4-1: Force displacement curves for low pull-back forces on Pile 3 at Albany

Figure 4-2 displays the force displacement response for the high pull-back forces of 60, 90 and

120 kN. The order these were carried out in during testing is evident from the plot below. The

decrease in initial stiffness between tests is due to the growing gap depth between the soil and the

outside of the pile. The maximum pull-back force of 120 kN causes the largest reduction in the

initial stiffness of subsequent pull-back tests.

It is interesting to note that although there is significant softening during the early stages of

loading across all of the higher force pull-back tests (60, 90, 120 kN); the response at later stages

stiffens and tends to follow a relatively constant stiffness, or linear force displacement

relationship. This is more evident for the second series of pull-back tests. A constant stiffness

implies no soil non-linearity, either through soil deformation or gapping between the pile shaft

and surrounding soil.

The progressive gap depth growth that was observed during testing has the effect of lowering the

effective ground level; illustrated in Figure 4-3. This means that there will be a greater

cantilevered length of the pile extending above the effective ground level, thus a much greater

0 2 4 6 8 10 120

5

10

15

20

25

30

35

Displacement (mm)

Forc

e (

kN

)

7.5kN pull-back 1

7.5kN pull-back 2

15kN pull-back 1

15kN pull-back 2

30kN pull-back 1

30kN pull-back 2

Static pile response from full-scale field tests

65

contribution of linear cantilever displacement to the overall measured displacement. The deflected

shape of a cantilever in bending will result in less interaction along its length with the adjacent

compressive gap, than if it had a linear deflected shape. Thus, the influence on the response of the

compressive gap closing is not as significant. The stiffer soil encountered at these greater depths

will require higher stresses to be applied before non-linear behaviour occurs. Hence as the gap

depth increases with subsequent pull-back tests, the force required to initiate non-linear soil

deformation increases. This delay of stiffness degradation is shown in Figure 4-2 between the first

series of tests in the order they were carried out (60 – 90 – 120 kN), with a relatively constant

stiffness up to the force of the previous pull-back test. At the end of the first series of tests the 120

kN pull-back has lowered the compressive gap significantly enough to prevent non-linear soil

deformation at the new effective ground level for the second series of tests, shown through a

predominately linear response in Figure 4-2. Whilst this stiff layer of clay at the effective ground

level remains in the elastic zone, one could model the set-up using a linear approximation by

Davies and Budhu (1986); the Elastic Continuum Model (ECM). In this model there is a fixed

ground level which allows for ground displacement and rotation, and the above ground level pile

deformations are added to get a total elastic stiffness. The low level of non-linearity during the

early stages of loading is attributed to detachment of the soil on the tension side of the pile, or a

small amount of yielding in front, lowering the resistance of the pile-soil system.

Figure 4-2: Force displacement curves for high force level pull-back tests on Pile 3 at Albany

0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

100

120

140

Displacement (mm)

Forc

e (

kN

)

60kN pull-back 1

60kN pull-back 2

90kN pull-back 1

90kN pull-back 2

120kN pull-back 1

120kN pull-back 2

Static pile response from full-scale field tests

66

Figure 4-3: Effective ground level and gap depth illustration

An issue with identifying trends in Figures 4-1 and 4-2 is the different magnitudes of force and

displacement between the tests. The force displacement response for the two sets of 7.5, 60 and

120 kN pull-back tests have been normalised by their maximum values and presented in Figure 4-

4. It should be noted that plotting the data in this way loses the timing of effects during the pull-

back, as the tests reach different maximum forces/displacements.

The normalised plot shows that the 7.5 and 60 kN pull-back tests maintain a higher stiffness

throughout, which is expected due to the reduced load levels compared to the 120 kN pull back.

The 120 kN pull-back tests appear to have an approximately secant stiffness to the earlier pull-

backs, with a clearly linear stiffness for a large portion of the test. This highlights the greater level

of non-linearity in the earlier pull-back tests. The second series of tests are shown to be softer than

their corresponding first test. For the second series of tests, the pull-backs are shown to

progressively (120 → 60 → 7.5 kN) increase in stiffness due to a decreasing magnitude of

force/displacement reached. All of these second tests have a much more linear response than the

first series of tests, where gap growth causes the cantilever response to govern the overall

response.

Static pile response from full-scale field tests

67

Figure 4-4: Normalised force displacement relationship for 7.5, 60 and 120 kN pull-back tests

4.2.1.1 Accumulated residual pile displacement

Because the pile was released for the dynamic response after the pull-back, no data is obtained for

the static unloading response of the pile-soil system. Instead, data is presented for the

accumulative residual displacement following the dynamic snap-back unloads. During the data

analysis, the data is subtracted by its initial value so it starts at the origin; hence any residual

displacements between tests have been lost thus far. Although any residual displacement of the

pile could occur because of non-linear soil behaviour during the pull-back or snap-back phases,

the residual displacements are presented in this chapter.

The plot in Figure 4-5 shows the residual displacement of Pile 3 that has accumulated between

successive tests (12 in total). It is expected that as soil behind the pile detaches from the pile

during the pull-back, as the soil cannot support tensile stresses, the horizontal stresses in the soil

mass cause it to move into the tension gap. Thus after the pile is released it settles further in the

pull-back direction; illustrated in Figure 4-6. Note the steepest slope of the curve is around the

middle of testing, which coincides with the highest pull-back forces of 120 kN. After the second

30 kN pull-back (and snap-back), the tension gap may not have opened to a sufficient depth to

allow this movement of soil during the pull-back, illustrated through the plot showing no extra

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Displacement/maximum displacement

Forc

e/m

axim

um

forc

e

7.5kN pull-back 1

60kN pull-back 1

120kN pull-back 1

120kN pull-back 2

60kN pull-back 2

7.5kN pull-back 2

Static pile response from full-scale field tests

68

residual displacement for the last two pull-backs. The small gap growth will be due to the

predominately linear cantilever deformation that was evident during the force displacement

responses.

Figure 4-5: Accumulative residual displacement of Pile 3 versus pull-back test magnitude

Figure 4-6: Displacement and gapping of soil behind pile during pull-back, due to horizontal earth pressures

0 7.5 15 30 60 90 120 120 90 60 30 15 7.50

0.5

1

1.5

2

2.5

3

3.5

4

Pull-back test magnitude (kN)

Accum

ula

tive r

esid

ual dis

pla

cem

ent

(mm

)

Static pile response from full-scale field tests

69

4.2.2 Pile 4 pull-back tests

The force displacement response of Pile 4 during pull-back tests is presented in Figures 4-7 and 4-

8 for 10 kN and 120 kN tests respectively. Note that two pull-back tests were carried out for the

1275 kg pile head 10 kN force level because the first snap-back test had to be disregarded because

the crow-bar hit the reference beam during the quick-release of the shackle. The way that all of

the 10 kN tests nearly collapse onto each other with a similar stiffness throughout (Figure 4-7),

supports observations that no residual gapping took place around Pile 4 during these tests. The

slight change in initial stiffness is more likely due to soil that has deformed but not gapped during

previous pull-back tests, although some gapping beneath the ground surface may have developed.

The significant discontinuity in the 324 kg pull-back test is due to the nature of the manual load

application to the test pile. A back-bone curve is created when modelling such a response. No

gapping was observed behind the pile during the pull-back tests so it is presumed that the slight

change in stiffness at later loading stages is due to soil yielding near the ground surface in front of

Pile 4.

Figure 4-7: Pull-back force displacement plots for 10 kN snap-back tests Pile 4

Figure 4-8 shows that a much greater level of non-linearity is present in the high force level test

series. There is a consistent separation between tests due to an increasing gap depth between tests.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

2

4

6

8

10

12

14

Displacement (mm)

Forc

e (

kN

)

324kg 10kN pull-back 1

609kg 10kN pull-back 1

1275kg 10kN pull-back 1

1275kg 10kN pull-back 2

Static pile response from full-scale field tests

70

Note that the first 120 kN zero added mass pull-back test contains the greatest change in

tangential (or secant) stiffness during the loading, this is because no gapping was present around

the pile before this test so the potential for an increase in non-linearity was at its greatest. A

predominately linear cantilever response has been produced for later tests, as discussed during

Pile 3 pull-back-test results, due to deep residual gapping present.

Figure 4-8: Pull-back force displacement plots for 120 kN snap-back tests Pile 4

4.3 PILE-SOIL GAP MEASUREMENTS AND

OBSERVATIONS

A residual gap can form between the pile and soil due to irrecoverable soil deformation when

loaded in compression, during the pull-back or snap-back tests. Horizontal stresses in the soil

apply a confining stress to the pile. When the pile is moved away from this area of soil, the

compressive stress in the soil can be eventually reduced to zero. Because soil cannot support

tensile stresses the soil in that area is no longer able to provide resistance to pile displacement and

a gap is formed between the pile and soil. Therefore gapping can also occur when the soil is

‘loaded in tension’, because of its inability to support tensile stresses.

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Displacement (mm)

Forc

e (

kN

)

324kg 120kN pull-back 1

609kg 120kN pull-back 1

1275kg 120kN pull-back 1

1275kg 120kN pull-back 2

609kg 120kN pull-back 2

324kg 120kN pull-back 2

Static pile response from full-scale field tests

71

4.3.1 Pile 3 gapping behaviour

Due to extensive testing already carried out on Pile 3 at the site in Albany, a residual compression

gap was visible at the ground surface in front of the pile; an illustration is shown in Figure 4-9.

Photos were taken after each test to monitor gap growth from the surface and measuring tape was

used to measure the width and circumference of the gap between the pile and surrounding soil. A

thin rod was lowered into the gap until it reached the bottom of the gap to measure the gap depth.

Figure 4-9: Image looking east showing existing gapping on Pile 3 at Albany before testing on 29/03/2012

Figure 4-10: Gap developed behind the Pile 3 during the second 90 kN pull-back test at Albany

Static pile response from full-scale field tests

72

Although significant gapping was observed between the pile and soil on the tension side of the

pile during the pull-back tests; see Figure 4-10, following the release of the pull-back forces

(snap-back phase) there was no clear residual gapping on the tension side of the pile. The soil on

this side of the pile showed signs of slight heaving at the ground surface from the snap-back of

the pile and previous testing. This heaving observations difficult and is illustrated in Figure 4-11.

It was expected that some residual gapping would develop following the snap-back.

Figure 4-11: Residual gap, that could not be accurately measured due to excessive soil deformation, behind the

tension side of Pile 3 following the second 120 kN snap-back

Gap measurements were able to be taken for the compression side of Pile 3, these were taken at

various stages during testing and are summarised in Table 4-1. There is a clear trend found from

the measurements reported in Table 4-1. The gap on the compression side of Pile 3 generally

grows as testing progresses. This trend is not so evident in the gap width measurements, and the

gap depth measurement following the 2nd

120 kN snap-back force. It should be noted that

although the gap width may remain constant, the pile does not necessarily return to its original

position due to encroaching of the soil behind the pile (tension side) that has detached from the

pile; this has shown to be the case earlier in Figure 4-5. The maximum measured gap depth was

2.5 pile diameters, and detached over half of the circumference of the pile at the ground surface.

It can be concluded that there is a significant amount uncertainty in this measurement procedure

and that measurement techniques need to be improved to obtain more meaningful results. Figure

4-12 presents a comparison between the gap at the surface before testing, and the gap following

the second 120 kN snap-back test. Although the images show the pile from different angles, it is

Static pile response from full-scale field tests

73

evident that the gap has grown, most significantly around the circumference as opposed to the size

of the gap width at ground level, on the compression side of the pile from testing on 29/03/2012.

Table 4-1: Summary of gap measurements on the compression (north) side of Pile 3 at Albany

Stage of testing/

Measurement*

Gap depth (mm) Gap width (mm) Gap circumference

(mm)

Before testing 580 (2.12) 20 (0.0733) 330 (0.385)

After 1st 120 kN snap 645 (2.36) 20 (0.0733) -

After 2nd

120 kN snap 600 (2.20) 23 (0.0842) -

After testing 670 (2.45) 20 (0.0733) 430 (0.501)

*bracketed values () denote non-dimensional quantity; 2nd

and 3rd

column normalised by pile diameter, 4th

column normalised by pile circumference

Figure 4-12: Gap growth development around Pile 3, (a) before testing; (b) following second 120 kN snap-back

4.3.2 Pile 4 gapping behaviour

More frequent gap measurements and observations were taken during Pile 4 testing, as it was

found to be of particular importance if trying to capture the response in a numerical analysis. Gap

measurements were also taken on both sides of the pile, which was not carried out during Pile 3

testing. There was no residual gapping at ground surface observed before the start of testing on

06/09/2012. The 10 kN snap-back tests at each level of mass were carried out first, and no

gapping developed following these tests either. Clearly, soil deformations during the 10 kN pull-

back and snap-back release were not significant enough to cause notable residual soil

deformation. An image of the pile-soil contact in front and behind the pile (soil in front is

compressed during the pull-back phase of snap-back tests) is shown in Figure 4-13, illustrating

Static pile response from full-scale field tests

74

that a notable gap had not developed up to this point in testing. Figure 4-14 shows that gaps

developed behind the pile during the pull-back tests of the 120 kN snap-back test series, and

residual gaps after the snap-back test.

Figure 4-13: No notable gap developed around Pile 4 following 10 kN snap-back series, (a) in front/north side of

pile; (b) behind/south side of pile

Figure 4-14: Gap developed around Pile 4 during the 324 kg, 120 kN snap-back test one, (a) behind pile (south

side) at the end of the pull-back test; (b) in front of pile (north side) after snap-back test

Static pile response from full-scale field tests

75

Gap measurements were taken after the completion of snap-back tests. The gap depth, width and

circumference either side of the pile were of interest. The gap circumference, or girth, was

difficult to define and soil contact at the sides of the pile was not considered as important as

monitoring soil contact in front and behind. The gap was noted to cover approximately the entire

circumference of the pile on the front side, but coverage on the other side was not defined. All gap

measurements taken during testing are summarised in Table 4-2.

Table 4-2: Gap measurements taken during Pile 4 testing on 06/09/2012

Stage of testing

(after snap-

back)

In front of pile (north side) Behind pile (south side)

Width Depth Girth* Width Depth Girth*

Start of testing 0 0 0 0 0 0

10kN_1 0 0 0 0 0 0

10kN_2 0 0 0 0 0 0

10kN_3 0 0 0 0 0 0

120kN_1

10

(0.0367) 475 (1.74) 429 (0.5)

2

(0.00732) 530 (1.94) -

120kN_2

10

(0.0367) 605 (2.22) -

10

(0.0367) 755 (1.77) -

120kN_3

15

(0.0549) 705 (2.58) -

10

(0.0367) 705 (2.58) -

120kN_4

15

(0.0549) 885 (3.24) -

10

(0.0367) 835 (3.06) -

120kN_5

15

(0.0549) 755 (2.77) -

12

(0.0440) 855 (3.13) -

120kN_6

15

(0.0549)

1085

(3.97) -

15

(0.0549) 855 (3.13) -

*circumference measurements not taken except in front of pile after first 120 kN snap-back test; bracketed

values () denote non-dimensional quantity; 2nd

and 3rd

column normalised by pile diameter, 4th

column

normalised by pile circumference

A thin metal tape was used to measure the gap widths and depths; the section was less than one

millimetre thick and was able to slide against the pile shaft to the bottom of the gap whilst

remaining rigid. This was a more accurate tool than the thin rod used during Pile 3 testing, as the

thinner section would allow it to reach more realistic gap depths. There was still significant

uncertainty in the gap measurements at the current site. Gap depths reached saturated clay,

Static pile response from full-scale field tests

76

although not beneath the water table itself (reported to be at a depth of 5 m in Figure 3-14); it was

difficult to distinguish how much soil pile contact was present, and whether this should be

considered as a gap. The cohesive nature of clay combined with the high possibility of narrow

gaps at large depths may have resulted in the tape not reaching the full gap depth, giving

conservative gap measurements. The tape was pushed down alongside the pile shaft with a

reasonable amount of force until the tape would not go further. It was also possible that the tape

was pushed down past the bottom of the gap, giving overestimated gap depths. This uncertainty is

the nature of the non-linear testing carried out.

Gap width and depth measurements consistently increase on both sides of the pile once the 120

kN snap-back series starts. There is one measurement for each side of the pile where the gap

depth measurement reduced from the previous reading. As in 4.3.1, the significant uncertainty in

these measurements is the likely reason for deviation. The increasing measurements after each

new 120 kN snap-back test is expected as further non-linear soil deformation during pull-back and

snap-back tests results in further residual gapping around the pile. It should be noted again that

although the trends evident in the gap width and depth measurements seem reasonable, the

magnitude of these values are not necessarily correct.

4.4 SUMMARY

The full-scale single pile static lateral response of Pile 3 and Pile 4 was measured by pulling the

test piles against reaction Piles 1 and 2 respectively The following observations were made during

field tests in stiff Auckland residual clay that agree with findings in the Literature Review (2.3.4):

Soil behind the pile detached from the pile, and gapping occurred, during the pull-back of

the pile as soil was unable to support tensile stresses to resist lateral pile movement.

After the snap-back release of the pile residual gaps were present between the pile and the

soil in front of the pile, loaded in compression during the pull-back. This was due to

irrecoverable soil deformation that removed the initial horizontal pre-stresses acting on

the pile from the soil.

From full-scale pull-back tests on Pile 3 at Albany:

The residual gap depth in front of the pile (compression side) before testing extended

from 0.58 m to 0.67 m following testing.

This gap growth contributed to significant cantilever action of the test pile during

subsequent pull-back tests. This resulted in a predominately linear response up to later

Static pile response from full-scale field tests

77

stages of loading, where ground displacement enables further non-linear soil response to

occur.

A decrease in the initial stiffness between tests confirmed an increase in residual gap

growth has occurred

Non-linear response during the initial stages of loading was attributed to soil detachment

at the back of the pile, or soil yielding in front of the pile, lowering the stiffness of the

pile-soil system.

The pile was found to accumulate residual displacement in the direction of the pile pull-

back after each pull-back and release. Horizontal stresses that were reduced in the soil as

it detached from behind the pile during the pull-back, has caused the soil to move into the

tension gap, thus displacing the pile following its release.

From full-scale pull-back tests on Pile 4 at Albany:

Rigorous pile-soil gap measurements and observations were carried out on both sides of

Pile 4. Gaps did not form around the pile until the 120 kN snap-back series; a maximum

gap width of 15 mm was recorded either side of the pile, and a maximum depth of 1085

mm was recorded on the side of the pile in the direction of the pull-back load. A thin

metal tape was used to take measurements, although significant uncertainty was present

in depth measurements due to a lack of visibility beneath the ground surface, the cohesive

nature of clay as well as any clay saturation effects.

Pull-back test results supported gap observations as the 10 kN pull-back tests effectively

collapsed onto each other due to no residual gapping occurring at these low force levels.

The first 120 kN snap-back test produced the greatest change in stiffness as the largest

change in gap growth occurred during this test. As with Pile 3, a largely linear cantilever

response was evident in later pull-back tests because of the large residual gap depth

present between Pile 4 and the surrounding soil.

Static pile response from full-scale field tests

78

Dynamic pile response from full-scale field tests

79

Chapter 5

Dynamic pile response from full-

scale field tests

5.1 OVERVIEW

The full-scale dynamic lateral response of Pile 3 and Pile 4 in stiff clay has been analysed by

carrying out snap-back tests, where the test pile is released from its desired pull-back force and its

response is measured.

The mass of Pile 3 was supplied by 456 kg of lead weighs, in addition to the specifically designed

steel tray and bracket at the pile head, the load collar, and the pile itself. Pile 3 extended 0.75m

above ground level. Pile 4 had three different quantities of lead masses added to the new steel

bracket and tray arrangement attached to the pile head; zero lead masses (total pile head mass

including bracket, tray and pile collar of 324 kg), 15 (609 kg) and all of the 50 lead masses

available (1275 kg). The comparative dynamic response between each was investigated, with the

aim of increasing the natural period of the pile. To help with this, Pile 4 was chosen because its

Dynamic pile response from full-scale field tests

80

cantilevered section extends 1.0 m above ground level, 33% further above ground level than Pile

3. Dynamic forces applied to the pile did not cause any yielding of the pile.

Dynamic tests are categorised into hammer free vibration tests, low force (less than 60 kN) snap-

backs and high force (60 kN and greater) snap-backs. The natural frequency of the pile is

determined by converting the response to the frequency domain; the hammer is assumed to give

the natural elastic frequency. The damping ratio is calculated in the time domain and is used to

represent the level of damping exhibited by the pile. Strain gauges are utilised to generate the

hysteresis loops produced during snap-back tests. Recall from the testing program the order and

magnitude of snap-back tests, for testing on 29/03/2012 for Pile 3:

7.5 kN

15 kN

30 kN

60 kN

90 kN

120 kN

120 kN

90 kN

60 kN

30 kN

15 kN

7.5 kN

and for testing on 06/09/2012 for Pile 4:

10 kN (324 kg pile head mass)

10 kN (609 kg)

10 kN (1275 kg)

120 kN (324 kg)

120 kN (609 kg)

120 kN (1275 kg)

120 kN (1275 kg)

120 kN (609 kg)

120 kN (324 kg)

Relative accelerations between the test Pile 4 and reference beams, as well as other pile

accelerations during Pile 3 testing was considered to assess interaction effects within the pile

Dynamic pile response from full-scale field tests

81

group. Four geophones were placed on the ground in the direction of the snap-back at various

distances from Pile 4. The compression wave signals picked up from each geophone during the

snap-back tests were used to assess the level of elastic radiation damping in the residual clay soil.

This chapter is separated into three main sections; the dynamic pile behaviour in the frequency

domain (5.2), the time domain (5.3) and the hysteretic response of each pile (5.4). MATLAB

(Mathworks, 2012) was used in all the data analysis and presentation for this thesis.

5.2 RESPONSE IN THE FREQUENCY DOMAIN

This section presents peak frequencies determined by taking the Fast Fourier Transform (FFT) of

the displacement response in the time domain, for hammer tests and snap-back tests on Piles 3

and 4. For comparison purposes the frequency computed between individual cycles in the time

domain is also presented here, to validate the peak frequencies determined from the inbuilt FFTs

carried out in MATLAB.

5.2.1 Peak frequencies from the Fast Fourier Transform (FFT)

Hammer tests and snap-back tests provide data for the displacement time response of the pile. For

both Piles 3 and 4 the displacement readings from the lower LVDT were trimmed (to separate the

section of the response of interest), detrended (to bring the response about zero displacement) and

smoothed by applying a low-pass filter (LPF; to remove noise) on MATLAB. The Fast Fourier

Transform (FFT) of the displacement signal, given the sampling rate of 2000 readings per second

for dynamic tests, is used to convert from the time to the frequency domain, and enables the

natural frequency (or frequencies) of the system to be established.

5.2.1.1 Natural elastic frequency from free-vibration hammer tests

The low force applied by the hammer to the test pile is assumed to give the natural elastic

frequency for the pile. There is one distinct peak in frequency evident in the free-vibration

hammer response for both Piles 3 and 4 and this is the natural frequency, shown in Figures 5-1

and 5-2. The displacement response in the time domain and frequency domain is presented in

both plots.

The large first peak displacement in the time domain for the Pile 3 hammer test is due to the

consideration of the first response cycle. This first peak has been excluded from the analysis for

Pile 4 as it was suspected that there may still be hammer contact with the pile head. The

difference has a negligible effect on the frequency computed for the system.

Dynamic pile response from full-scale field tests

82

Figure 5-1: Response in time and frequency domain from hammer test following first 30 kN snap-back on Pile 3

Figure 5-2: Response in time and frequency domain from hammer test following first 120 kN snap-back on Pile 4

with 609 kg pile head

14.8 15 15.2 15.4 15.6 15.8 16

-0.4

-0.2

0

0.2

Time (s)

Dis

pla

cem

ent

(mm

)

0 2 4 6 8 10 12 14 16 18 200

5

10

15x 10

-3

Frequency (Hz)

FF

T -

dis

pla

cem

ent

am

plit

ude

Peak; 12.2 Hz

13.2 13.4 13.6 13.8 14 14.2 14.4

-0.2

0

0.2

Time (s)

Dis

pla

cem

ent

(mm

)

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8x 10

-3

Frequency (Hz)

FF

T -

dis

pla

cem

ent

am

plit

ude

Peak; 11.1 Hz

Dynamic pile response from full-scale field tests

83

The natural elastic frequency is of great importance because it defines the fundamental modal

properties of the pile-soil system. Hammer tests are carried out following the snap-back to assess

changes in the soil stiffness around the pile. Although several hammer blows were applied for

each test, similar responses between blows meant that only one free-vibration response was

analysed for each test.

5.2.1.1.1 Pile 3 natural frequency

Figure 5-3 presents a bar chart summary of elastic frequencies computed for all during testing on

Pile 3. Data is presented in Hertz, and ordered chronologically with testing. There is a general

trend evident in Figure 5-3, indicating that the elastic frequency of the pile-soil system decreases

as the testing progresses. This has been attributed to the gap around the pile growing as the soil

deforms under different snap-back test forces. Pile 3 has a natural elastic frequency of 13.2 Hz

(0.076 s) at the start of testing, this decreases to 10.8 Hz (0.093 s) after the second 120 kN snap-

back, the minimum frequency reached. The frequency is shown to increase slightly as the snap-

back force decreases for the second series of tests. There is some uncertainty in these values as the

frequency is shown to increase slightly after the first 30 kN and 60 kN snap-back tests,

disagreeing with the outlined general trend.

Figure 5-3: Natural elastic frequencies determined from FFT hammer response of Pile 3

7.5 15 30 60 90 120 120 90 60 30 15 7.50

2

4

6

8

10

12

14

Snap-back test magnitude (kN) relative to hammer tests

Natu

ral ela

stic f

requency (

Hz)

Dynamic pile response from full-scale field tests

84

Hammer tests were carried out on the north side of the pile throughout testing, the side of the pile

that the soil was loaded into during the pull-back tests. After testing, following the second 7.5 kN

pull-back force, hammer blows were applied to all four sides of the pile (steel bracket) to assess

the natural period in different directions. The natural frequencies in each direction are presented

in Table 5-1.

Table 5-1 shows a consistent natural frequency in the north-south direction and the east-west

direction. The lower natural frequency in the north-south direction is due to the development of

gapping in that direction from testing. There were no gaps noted on the east and west sides of the

pile during testing, which has resulted in a much greater stiffness in that direction and hence

greater frequency; this shows that the soil directly in line with the loading direction has a much

greater effect on the stiffness than the soil, or contact, either side of the pile. A modal analysis

was carried out in Ruaumoko 3D (Carr, 2004) on Pile 3, with no residual gapping around the pile.

The natural frequency was found to be 18.9 Hz, or 0.0529 s. The frequency of around 13 Hz

computed during testing is still much smaller, where there is significant gapping in the

perpendicular direction, indicating the soil contact on the sides of the pile does influence the

natural period, or frequency.

Table 5-1: Natural frequency from hammer tests carried out in four directions following testing on Pile 3

Direction Natural frequency (Hz)

North (principal) 10.9

South 10.8

East 13.0

West 12.9

5.2.1.1.2 Pile 4 natural frequency

Figure 5-4 presents natural pile frequencies determined from hammer testing on Pile 4. Data is in

Hz and is presented in a bar chart form, with results plotted on the horizontal axis in the order

they were carried out during testing (refer to 3.8 or 5.1). Hammer tests were carried out before

and after snap-back tests due to the pile head mass variation during testing.

Peak frequencies are found to decrease as the mass on the pile head is increased, and following

snap-back tests as the stiffness of the pile is reduced as the gap depth increases. The effect of pile-

soil stiffness can be seen on the hammer plot as tests are carried out either side of the snap-back.

The bar chart is colour co-ordinated with pile mass so bars of the same colour later on in testing

Dynamic pile response from full-scale field tests

85

are comparable in terms of stiffness effects on frequency. Note these findings are consistent with

the SDOF formula of frequency, f:

√

(5-1)

where m is the mass and K is the stiffness of the pile-soil system; 1/2π converts between radians

per second and Hertz.

The minimum natural elastic frequency computed from Pile 3 testing was 11 Hz. As expected, a

smaller frequency was computed for the two higher mass levels on Pile 4; 10 Hz and 7 Hz for the

609 and 1275 kg respective pile head mass levels. The elastic frequency at the start of testing for

Pile 3 was 13 Hz, meaning a change in frequency of 2 Hz has occurred during testing as a result

of pile-soil stiffness reduction. Greater changes in frequency for each individual mass level have

occurred across testing for Pile 4, evident from Figure 5-4. This is because there was no residual

gapping around the pile at the start of testing, enabling greater increases in gap growth to occur.

The range of masses tested has also increased the range of frequencies computed to around 14 Hz.

Figure 5-4: Natural elastic frequencies determined from FFT hammer response of Pile 4

0 2 4 6 8 10 12 14 16 180

2

4

6

8

10

12

14

16

18

20

Hammer test number

Natu

ral ela

stic f

requency (

Hz)

324 kg mass on pile head

609 kg mass on pile head

1275 kg mass on pile head

Dynamic pile response from full-scale field tests

86

5.2.1.2 Snap-back response in frequency domain

This section covers the snap-back response in the frequency domain and outlines the methodology

developed for separating the inelastic and elastic portions of high force level snap-back tests in

the frequency domain. Peak frequency data for each pile is also presented.

5.2.1.2.1 High force level snap-back separation using high-pass filters (HPFs) in MATLAB

Low force level snap-back tests (7.5, 10, 15, 30 kN) produced a similar response in the frequency

domain to hammer tests. Conversely, for high force level snap-back tests (60, 90, 120 kN) a

Multi-Degree-of-Freedom (MDOF) system becomes evident from the FFT frequency domain

response. This has been attributed to the inelasticity of the response, the impact effects of the

snap-back from a large pull-back force. For Pile 3, non-linear soil behaviour governs the response

and there is a lower softened frequency, as well as a natural elastic frequency evident, see Figure

5-5. The inelastic frequency dominates the response as indicated by the much larger amplitude

peak in the FFT compared to the elastic frequency. The elastic frequency peak of 12.2 Hz

coincides with the elastic natural frequency from hammer tests; refer to Figure 5-1.

The non-linear influence on Figure 5-5 is apparent when compared to the more consistent free

vibration hammer response and the single dominant frequency peak of the FFT in Figure 5-1.

Because the non-linear response during the snap-back causes soil softening as it yields, the

frequency decreases. Also, as the gap depth increases during the snap-back the length of the pile

cantilever section effectively increases, lowering its stiffness, and again decreasing the frequency.

It is assumed non-linear response is confined to the frequencies that are lower than the elastic

frequency of that response. The cut-off frequency is defined as the red vertical line in Figure 5-5,

between the inelastic and elastic frequency peaks.

Dynamic pile response from full-scale field tests

87

Figure 5-5: Snap-back response of Pile 3 from first 90 kN pull-back force and corresponding FFT indicating cut-

off frequency

The Pile 4 response is slightly more complicated than the Pile 3 response because of the three

different mass levels which create different amounts of inertial forces during the snap-back. This

seems to have a much greater effect on the response in the frequency domain than the varying

inelastic force levels used on Pile 3 (recall 60 kN, 90 kN and 120 kN snap-backs were carried

out). Where no lead masses have been added to Pile 4, 324 kg pile head mass, there is only one

clear peak, assumed to be an inelastic peak, shown in Figure 5-6. The small bump on the FFT

response in Figure 5-6 is indicated as an elastic peak as it is in the range of the elastic frequencies

computed from the two corresponding hammer tests carried out either side of the snap-back test.

The response of the 609 kg pile head in Figure 5-7 shows two distinctly different peak

frequencies; however, the largest amplitude peak coincides with the elastic frequency of the pile,

determined from hammer tests, shown in Figure 5-2. The 1275 kg mass pile response in Figure 5-

8 shows a clear inelastic peak, with a small elastic bump. It should be noted that the unfiltered

response is shown for these snap-back tests, this is necessary for the inclusion of the pull-back

peak in the response. This was not possible for Pile 3 data because the LVDT readings were

significantly noisier.

5.8 5.9 6 6.1 6.2 6.3 6.4 6.5 6.6

-2

-1

0

1

2

Time (s)

Dis

pla

cem

ent

(mm

)

0 5 10 15 20 25 30 35 400

0.01

0.02

0.03

Frequency (Hz)

FF

T -

dis

pla

cem

ent

am

plit

ude ElasticInelastic

Peak 1; 7.75 Hz

Cut off; 11.2 Hz

Peak 2; 12.2 Hz

Dynamic pile response from full-scale field tests

88

Figure 5-6: 324 kg pile head 120 kN snap-back 1 response in time and frequency domain

Figure 5-7: 609 kg pile head 120 kN snap-back 1 response in time and frequency domain

17.6 17.7 17.8 17.9 18 18.1 18.2 18.3 18.4 18.5

-10

0

10

20

30

Time (s)

Dis

pla

cem

ent

(mm

)

0 2 4 6 8 10 12 14 16 18 200

0.1

0.2

Frequency (Hz)

FF

T -

dis

pla

cem

ent

am

plit

ude

Inelastic peak;

11.7 Hz

Elastic peak;

14.9 Hz

36.55 36.6 36.65 36.7 36.75 36.8 36.85 36.9 36.95

-10

0

10

20

30

Time (s)

Dis

pla

cem

ent

(mm

)

0 2 4 6 8 10 12 14 16 18 20

0.06

0.08

0.1

0.12

Frequency (Hz)

FF

T -

dis

pla

cem

ent

am

plit

ude

Elastic peak;

10.4 Hz

Inelastic peak;

7.87 Hz

Dynamic pile response from full-scale field tests

89

Figure 5-8: 1275 kg pile head 120 kN snap-back 1 response in time and frequency domain

Considering each of the Pile 4 120 kN snap-back plots, it is interesting that the inelastic frequency

governs for the high and low mass levels, however for the medium mass level, the elastic

frequency is more apparent. These findings are consistent with the second series of 120 kN snap-

backs carried out after the three responses presented here (not shown). There was an issue of

stability when 15 lead masses (609 kg pile head mass) were added to the steel tray, such that the

lead masses moved around significantly during the 120 kN snap-backs. A before and after

comparison of this is shown in Figure 5-9; 50 lead masses (1275 kg pile head mass) were heavier

and produced a more stable arrangement during testing. The movement of the 15 lead masses

during the snap-back may be a contributing factor in the inconsistent responses computed for the

medium mass level. The 33% increase in cantilever length extending above ground level may be a

contributing factor to both peak frequencies being less clear than those for Pile 3.

15.7 15.8 15.9 16 16.1 16.2 16.3-10

0

10

20

30

Time (s)

Dis

pla

cem

ent

(mm

)

0 2 4 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

Frequency (Hz)

FF

T -

dis

pla

cem

ent

am

plit

ude

Elastic peak;

6.93 Hz

Inelastic peak;

4.35 Hz

Dynamic pile response from full-scale field tests

90

Figure 5-9: 15 lead mass (609 kg) pile head (a) before 120 kN snap-back 1; (b) after 120 kN snap-back 1

A high-pass filter (HPF) was applied to these high force snap-back responses with a cut-off

frequency to the left of the elastic peak frequency. This removed all lower inelastic frequencies,

extracting the elastic response. This filter is utilised in the time domain to attribute the

displacement-time response, and damping, between elastic and inelastic. The inelastic response is

obtained by subtracting the elastic response from the original response. In summary, for high

force snap-backs the following methodology was used (order is important):

1. Trim response (extract section of response of interest)

2. Detrend (zero response)

3. Low-pass filter; order = 4, cut-off frequency = 30 – 40 Hz (remove noise) [Original

Response]

4. High-pass filter; order =4, cut-off frequency = variable [Linear Response]

5. Original Response – Linear Response => Non-linear Response

Low force level snap-backs and hammer tests only require the first three steps to be carried out, as

they have been shown to produce predominately a linear response in the frequency domain. For

Pile 4, the large variation in mass and gap depth mean that the cut-off frequency is determined on

a case by case basis for each snap-back test.

5.2.1.2.2 Pile 3 snap-back peak frequencies

Pile 3 peak frequencies are presented as elastic and inelastic frequencies (Hz) in Figure 5-10. The

elastic frequencies computed from snap-back tests are not presented as the natural pile-soil

Dynamic pile response from full-scale field tests

91

frequencies because non-linear effects become more apparent with the larger forces that are

involved in the pull-back and release. Hence hammer tests are a more effective means of

determining the natural period.

The inelastic frequencies computed from the high snap-back forces decrease as a result gap

growth during testing, and increasing snap-back magnitude. These inelastic frequencies are in the

order of 5 – 10 Hz, much smaller than the elastic frequencies because they capture non-linear

effects such as softening of the soil at larger strains. A minimum frequency of 4.5 Hz is reached

for the second 120 kN snap-back; the inelastic frequency increases after this suggesting the size of

the snap-back has a greater influence than the stage of testing (how many snap-backs were carried

out prior to the current snap-back test).

Figure 5-10: Peak frequencies determined from FFT snap-back response of Pile 3

5.2.1.2.3 Pile 4 snap-back peak frequencies

Figure 5-11 presents the peak elastic and inelastic frequencies from the snap-back response of Pile

4 in the frequency domain. Similarly for the corresponding hammer plot in Figure 5-4, results are

plotted on the horizontal axis in the order they were carried out in during testing and the bar chart

is colour co-ordinated with pile mass so bars of the same colour later on in testing are comparable

in terms of stiffness effects on frequency.

0 7.5 15 30 60 90 120 120 90 60 30 15 7.50

2

4

6

8

10

12

14

Snap-back magnitude (kN)

Ela

stic/inela

stic p

eak f

requency (

Hz)

Elastic frequency

Inelastic frequency

Dynamic pile response from full-scale field tests

92

It should be noted that the elastic frequencies from the snap-back tests generally coincide with

those computed from the hammer tests. Peak frequencies are found to decrease as the mass on the

pile head is increased, and following snap-back tests as the stiffness of the pile is reduced as the

gap depth increases. A 2 Hz inelastic frequency was computed for the 1275 kg pile head final 120

kN snap-back test.

These snap-back frequencies are important when determining the cut-off frequency for the elastic

response, thus the pull-back peak was not considered in their computation because the HPF that

utilises the cut-off frequency is not compatible with the pull-back peak.

Figure 5-11: Peak frequencies determined from FFT snap-back response of Pile 4

5.2.2 Frequency between cycles in the time domain

The time between response cycles in the time domain is inverted to give a localised frequency of

the response for Piles 3 and 4, and compared with results from FFT analysis in the frequency

domain.

0 10 10 10 120 120 120 120 120 1200

2

4

6

8

10

12

14

16

18

20

Snap-back magnitude (kN)

Ela

stic/inela

stic p

eak f

requency (

Hz)

324 kg mass - elastic frequency

609 kg mass - elastic frequency

1275 kg mass - elastic frequency

Inelastic frequency

Dynamic pile response from full-scale field tests

93

5.2.2.1 Pile 3 individual cycle frequency

The time between successive peak displacements (half cycles) for three different tests is shown in

Table 5-2. A hammer test, low force snap-back and high force snap-back have been considered.

The time between peaks vary from around 0.03 to 0.07 seconds; for whole cycles (two half

cycles) this corresponds to frequencies in the order of 7 to 17 Hz. The 30 kN snap-back and

hammer test predominately produce frequencies in the elastic range; 11 – 13 Hz. This is expected

as the FFT of these low force snap-backs and hammer tests showed natural frequencies in this

range; see Figures 5-3 and 5-10. Note that low frequencies, or high periods, were earlier attributed

to inelastic response and these are evident in the early cycles of the 90 kN snap-back, shown in

Table 5-2. This suggests inelastic behaviour confined to these frequencies occurs during the early,

or large, displacement cycles.

For all of the three tests the time between peaks has the overall trend of decreasing across cycles,

although some localised increases in time are present. The decreasing nature of the time between

peaks is attributed to the greater stiffness at lower load levels, shown in Figure 5-12.

Table 5-2: Time between successive peaks of half cycles and extrapolated whole cycle frequencies for three

dynamic tests on Pile 3

Hammer test following second

60 kN snap-back

Second 30 kN snap-back First 90 kN snap-back

Time (s) Frequency

(Hz)

Time (s) Frequency

(Hz)

Time (s) Frequency

(Hz)

0.0600 8.33 0.0430 11.6 0.0730 6.85

0.0430 11.6 0.0620 8.06 0.0670 7.46

0.0545 9.17 0.0450 11.1 0.0630 7.94

0.0445 11.2 0.0465 10.8 0.0300 16.7

0.0430 11.6 0.0470 10.6 0.0520 9.62

0.0455 11.0 0.0430 11.6 0.0430 11.6

0.0395 12.7 0.0435 11.5 0.0465 10.8

0.0430 11.6 0.0445 11.2 0.0410 12.2

0.0415 12.0 0.0440 11.4 0.0460 10.9

0.0455 11.0 0.0395 12.7 0.0410 12.2

0.0370 13.5 0.0425 11.8 0.0365 13.7

- - 0.0435 11.5 0.0450 11.1

- - - - 0.0315 15.9

Dynamic pile response from full-scale field tests

94

Figure 5-12: Load-deformation plot illustrating stiffness change at different levels of soil deformation

5.2.2.2 Pile 4 individual cycle frequency

The local frequency between cycles for Pile 4 was investigated for the three types of tests carried

out; hammer, low force 10 kN snap-back and high force 120 kN snap-back. Table 5-3 presents

these results, with the peak frequency (or frequencies) in the first row(s) for comparison. The

pull-back peak for snap-back tests has been included here, hence the unfiltered response was

considered. Note the hammer ‘Cycle 1’ actually refers to the second cycle as the hammer may

still be in contact with the pile during this period, and the snap-back ‘Cycle 1’ is the pull-back

peak.

Although the 10 kN low force snap-backs produced 21 cycles, the higher force and mass levels

produced significantly less, down to a minimum of 6 cycles for the 609 and 1275 kg pile head

masses. This supports what was seen in the time domain in Figures 5-6 to 5-8, where the response

was more varied and different frequencies seemed to have a greater effect, as the mass and force

level increased. This has resulted in fewer cycles produced as reported in Table 5-3.

For the hammer test, the 10 kN snap-backs and 120 kN snap-backs there is a shift in frequency

versus cycle number for each. This is more apparent as the force is increased, where the hammer

has the lowest force and the 120 kN snap-back the greatest. Generally, lower frequencies are

computed earlier in the response and higher frequencies are computed later on as the system

stiffens after repeated cycles, presumably because smaller displacement cycles occur in the soil

later on in the response, or an increased contact between soil and pile develops. The agreement

between FFT peak frequency values and those between cycles was more difficult to observe for

the high force 120 kN snap-backs because of the inelastic and elastic frequencies evident in the

response. It is interesting that a shift in the hammer frequency was found as this was presumed to

be elastic. There must be a very low level of gapping, or yielding, developed near the ground

level. The pull-back peak of the 10 kN snap-back tests appear to contain an element of inelasticity

Dynamic pile response from full-scale field tests

95

as the first cycle is notably shorter in frequency than later cycles. The FFT frequencies reported

earlier seem to model the average frequency picked up mid-way into the response, which seems to

be a good approximation of the fundamental frequency given the variability in cycle to cycle

frequencies.

Table 5-3: Comparison of frequency between individual response cycles and FFT frequency for Pile 4

Frequency

(Hz)

609kg

120kN_2

hammer

324kg

10kN_1

snap

609kg

10kN_1

snap

1275kg

10kN_1

snap

324kg

120kN_1

snap

609kg

120kN_1

snap

1275kg

120kN_1

snap

Elastic

frequency

11.09

17.50

13.85

8.70

14.92

10.44

6.93

Inelastic

frequency

- - - - 11.77

7.87

4.35

Cycle 1 10.47 15.38 13.16 7.52 10.00 9.05 5.24

Cycle 2 10.53 17.39 13.61 8.40 11.76 11.43 3.85

Cycle 3 10.70 16.95 12.90 8.44 12.20 13.16 3.80

Cycle 4 10.99 17.24 13.70 8.55 11.90 12.90 6.19

Cycle 5 11.05 18.18 13.79 8.47 11.98 10.81 6.78

Cycle 6 11.11 17.86 12.82 8.81 12.42 10.15 6.60

Cycle 7 11.30 17.39 13.42 9.39 12.74 - -

Cycle 8 11.30 17.09 14.81 8.89 12.99 - -

Cycle 9 11.30 18.18 13.99 8.62 12.99 - -

Cycle 10 10.87 19.23 13.25 8.77 13.25 - -

Cycle 11 11.70 17.24 13.33 8.40 13.33 - -

Cycle 12 13.07 17.70 14.71 8.58 - - -

Cycle 13 11.49 18.87 14.81 8.58 - - -

Cycle 14 11.36 17.86 12.74 9.43 - - -

Cycle 15 11.70 19.05 13.99 9.17 - - -

Cycle 16 10.99 18.87 13.89 8.62 - - -

Cycle 17 11.70 17.86 12.74 8.70 - - -

Cycle 18 - 18.02 14.81 9.01 - - -

Cycle 19 - 18.52 14.49 9.43 - - -

Cycle 20 - 20.62 13.33 9.01 - - -

Cycle 21 - 18.69 13.42 8.58 - - -

Dynamic pile response from full-scale field tests

96

5.3 RESPONSE IN THE TIME DOMAIN

This section outlines two different techniques for the collection of damping ratio data, and

presents results for each pile:

1) Damping is calculated on an individual cycle basis by utilising the logarithmic decrement

method (Thompson, 1988) between adjacent displacement peaks, and;

2) The overall system damping is determined by fitting exponential envelopes from the

under-damped displacement solution for a viscously damped Single-Degree-of-Freedom

(SDOF) system (Chopra, 2006).

The high force snap-back tests result in the response being unable to be characterised by a single

system damping, or frequency. Two different methods are employed to split the response into two

parts so that damping could be attributed as elastic or inelastic:

a) Inspection of the time domain – for 1) and 2)

b) Considering the FFT of the high force snap-backs in the frequency domain and applying

filtering to the response in the time domain (5.2) – for 1) only

The following additional data is also presented for Pile 4:

Sensitivity analysis on different levels of noise filtering

Sensitivity analysis on the SDOF displacement prediction response

Relative accelerations between Pile 4 and its reference beams to assess the occurrence of

any interaction effects

Surface wave readings from geophone signals, to assess the level of elastic radiation

damping in the soil

5.3.1 Logarithmic decrement method (Thompson, 1988)

This section introduces the logarithmic decrement method and presents damping ratio data

computed using the logarithmic decrement method for hammer, low force snap-back and high

force snap-back tests. This section is characterised by high force snap-back test data being split

between the elastic and inelastic damping by applying high-pass filters (HPFs) to the response.

The lateral dynamic response of Piles 3 and 4 in the time domain is primarily assessed by the

level of damping exhibited for each system. Damping is what causes the response of structures to

decay with time, and always exists. Equivalent viscous damping is used to idealise all of the

different sources of damping on a structure mathematically, resulting in exponential decay

Dynamic pile response from full-scale field tests

97

(Chopra, 2006). It is more convenient to express damping in terms of the damping ratio, ζ (zeta),

for a Single-Degree-Of-Freedom (SDOF) structure:

√ (5-2)

where ζ is the damping ratio (usually expressed as a percentage), c is the damping coefficient, m

is the mass and K is the stiffness.

The logarithmic decrement method (Thompson, 1988) utilises the relative magnitude of two

adjacent peaks of the free vibration response to determine a value of damping for the pile-soil

system. For low levels of damping (typically the case) the following term may be neglected:

√ (5-3)

Using this simplification, the logarithmic decrement method is given by:

(

)

(5-4)

where x1 and x2 are the displacement amplitudes of successive peaks, illustrated in Figure 5-13.

The approximation in equation (5-3) is assumed to be valid for a damping ratio of up to 50% for

this study, where a 10% error is present, above this the term must be accounted for in the damping

ratio computation.

Figure 5-13: Graphical illustration of peaks used in the logarithmic decrement calculation for damping

14.8 14.85 14.9 14.95 15 15.05 15.1 15.15 15.2

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

Time (s)

Dis

pla

cem

ent

(mm

)

x1x2

Dynamic pile response from full-scale field tests

98

Damping is attributed between inelastic and elastic for high-force snap-back tests in either the

frequency domain (5.2), or as later discussed in 5.3.2, the time domain. Utilising the frequency

domain to attribute damping between inelastic and elastic, a filtering method is carried out on

high force snap-back tests, as per analysis in the frequency domain (5.2), the following steps are

taken:

1. Trim response (extract section of response of interest)

2. Detrend (zero response)

3. Low-pass filter; order = 4, cut-off frequency = 30 – 40 Hz (remove noise) [Original

Response]

4. High-pass filter; order =4, cut-off frequency = variable [Linear Response]

5. Original Response – Linear Response => Non-linear Response

5.3.1.1 Pile 3 damping ratio data

Using the logarithmic decrement method, the elastic damping ratios determined from the hammer

tests, low force snap-backs and elastic filtered high force snap-backs carried out on Pile 3 are

shown in Figure 5-14. The damping is plotted against the magnitude of the first displacement

peak from which the damping ratio is calculated.

This scatter plot in Figure 5-14 shows a dense grouping of damping ratios in the 0-10% range.

This group is at low first peak displacements, less than 0.25 mm. Most of the elastic data is

lumped in this area of the plot, which is expected as elastic behaviour occurs at lower

displacements. As the first peak displacement increases, the damping ratio generally increases.

Hammer tests and low snap-back data reach maximum first peak displacements of 0.5 – 0.75 mm,

with some damping outside the elastic 0-10% range. This deviation is due to the noise and other

frequency effects associated with the response. High force snap-backs that have been high-pass

filtered to extract the elastic response provide data for much greater first peak displacements.

Generally, there is not a significant increase in damping of these data points that reach a

maximum displacement of 2.5 mm. The reduction in the rate of increase of damping ratio with

first peak displacement has been illustrated with a cube-root trend line to approximate the

relationship between damping and displacement. Note that the high force snap-backs that

contribute significantly to this relationship have been manipulated with high-pass filters, resulting

in less confidence than the low force snap and hammer tests which have predominately been

filtered for noise only. If the noise filtered response still moves about the horizontal axis due to

low frequency effects, a low frequency HPF is used to bring the response back up to zero

displacement.

Dynamic pile response from full-scale field tests

99

Figure 5-14: Elastic damping of Pile 3 from dynamic testing at Albany

The damping corresponding to the inelastic portion of the high force snap-backs is plotted in

Figure 5-15. Inelastic first peak displacements reach much greater amplitudes than the

corresponding elastic damping values shown in Figure 5-14, which is expected as more non-

linearity occurs at greater strains. This coincides with greater damping ratios at these higher

displacements. Again, there is a cluster of damping values around the 10% value at low first peak

displacements. Although not as significant as in Figure 5-14, this high density area of data points

at low displacements implies that inelasticity is also having an effect on the response at lower

displacements. Soil at the bottom of the gap can experience yield at low pile displacements, but,

soil detachment behind the pile is the more likely reason for this supposed non-linearity at small

displacements. This occurrence was evident from the static response of the pile; however, it

disagrees with findings in Table 5-2, where inelastic data was found to be confined to early large

displacement peaks by analysing the frequency between cycles. This suggests that the inelastic

damping data might be flawed due to the inelastic damping computed at low levels of

displacement. It should be noted that the data in Table 5-2 is for the combined response, so elastic

behaviour may be more dominant over any inelastic effects at later stages of the response.

The larger first peak displacements for the inelastic response produce much higher damping

ratios; although these are significantly scattered. A square-root trend line is used to approximate

0 0.5 1 1.5 2 2.50

10

20

30

40

50

60

70

First peak displacement amplitude, x1 (mm)

Dam

pin

g r

atio (

%)

Hammer tests

Low force snap-backs (7.5, 15, 30 kN)

Elastic-filtered high force snap-backs (60, 90, 120 kN)

Cube-root trend line

25x11/3; R2 = 0.650

Dynamic pile response from full-scale field tests

100

the relationship between damping and first peak displacement amplitude, a similar relationship to

the elastic damping ratio plot in Figure 5-14; even though a linear trend line could produce a

similar quality fit. Note that the term in Equation (5-3) has been accounted for where the damping

ratio has exceeded 50% (10% error – percentage difference – at this level of damping).

Figure 5-15: Inelastic damping of Pile 3 from high force snap-back tests carried out at Albany

5.3.1.2 Pile 4 damping ratio data

The first elastic-inelastic damping data collection technique for high force 120 kN snap-back tests

carried out on Pile 4 is shown in Figures 5-16 and 5-17. Note the elastic-filtered damping values

on Figure 5-16 include those computed from the 10 kN snap-back tests. Hammer data is presented

later in 5.3.2; combined with damping ratios determined using the exponential envelope fitting

technique for comparative purposes. Here it can be seen that very large elastic damping ratios are

computed for the elastic response of the 120 kN snap-backs. This highlights issues with the

uncertainties of carrying out these significant HPFs, and the practical application of damping of

this level should be approached with care, from the perspective of a design engineer. For the

10%+ damping ratios, mass appears to be proportional to damping, which is in disagreement with

equation (5-2).

0 1 2 3 4 5 60

10

20

30

40

50

60

70

First peak displacement amplitude, x1 (mm)

Dam

pin

g r

atio (

%)

Inelastic-filtered high force snap-backs (60, 90, 120 kN)

Square-root trend line

25x11/2; R2 = 0.938

Dynamic pile response from full-scale field tests

101

Similarly high levels of damping are found for the inelastic filtered response for each mass level

in Figure 5-17, with three distinct mass level groupings of these high damping values. The large

peak displacements shown on both Figures 5-16 and 5-17 are as a result of the 324 kg pile head

mass being disrupted less by the HPFs applied to it. This may be because only the pull-back peak,

which is not considered here, was found to contain significant amounts of inelasticity; determined

from inspection of the response in the time domain (5.3.2).

Larger damping values are also computed at lower displacement cycles for both plots. As found

with the Pile 3 analysis, small damping values are also computed for the inelastic response. A

cubed and square root function was fitted to both corresponding plots produced in the

corresponding Pile 3 section; this does not seem as feasible with the current Pile 4 data, although

this may be due to an inappropriate displacement scale for the two higher mass levels. Instead,

there is a cluster of 0 – 10% damping, with larger damping values grouped by mass.

Figure 5-16: Pile 4 10 kN snap-back damping data with elastic filtered 120 kN snap-back damping data

0 2 4 6 8 10 12 14 160

5

10

15

20

25

30

35

40

45

First cycle displacement, x1 (mm)

Dam

pin

g (

%)

324 kg mass on pile head

609 kg mass on pile head

1275 kg mass on pile head

Dynamic pile response from full-scale field tests

102

Figure 5-17: Pile 4 inelastic filtered 120 kN snap-back damping data

5.3.2 SDOF displacement solution (Chopra, 2006)

This section presents the SDOF displacement solution and the exponential envelopes that define

the system damping. Results for hammer tests, low force and high force snap-back tests are

presented for Pile 4 only. Also, a different method is employed to separate damping between

elastic and inelastic for high-force snap-back tests, where an assessment is made in the time

domain.

The logarithmic decrement method has shown to produce variable damping data and as a result, a

different technique was employed to characterise the damping of the pile-soil system for Pile 4.

For an equivalent-viscously damped Single-Degree-of-Freedom (SDOF) system subject to an

initial displacement and/or velocity, the under-damped displacement solution from the equations

of motion is given by (Chopra, 2006):

[

] (5-5)

where u(t) is the displacement at time t, (0) is the initial velocity, ζ is the damping ratio, ωN is

the natural frequency of the system in rad/s, and ωD is the damped frequency. The relationship

0 5 10 15 20 250

10

20

30

40

50

60

First cycle displacement, x1 (mm)

Inela

stic f

iltere

d d

am

pin

g (

%)

324 kg mass on pile head

609 kg mass on pile head

1275 kg mass on pile head

Dynamic pile response from full-scale field tests

103

between the damped frequency (computed from the FFT of the test data response) and un-damped

natural frequency is as follows:

√ (5-6)

Thus damping extends the natural period (or decreases natural frequency) of the system. An initial

displacement needed to be defined for the displacement solution, with a static displacement

available at the pull-back peak displacement of snap-back tests. This meant that the unfiltered

response had to be considered for the snap-back tests, with the lower LVDT providing a

sufficiently clean response for this analysis. The displacement solution was fitted to the snap-back

response on MATLAB by inputting the natural frequency from the FFT (converting to rad/s from

Hz by multiplying by 2π) and calculating the un-damped natural frequency, and modifying the

damping ratio until a reasonable fit was found. The pull-back peak and high force snap-back tests

contain two separate inelastic and elastic frequencies; meaning a SDOF approximation could not

accurately model the entire response.

Note that the exponential function governs the decay of the displacement solution which is the

key outcome for this data analysis technique; hence the envelopes created by the exponential

function were plotted by themselves to find the level of system damping, which was successfully

carried out on the hammer responses, utilising the peak displacement of the second peak (the

hammer is likely still in contact with the pile during the first peak so this part of the response is

ignored).

As mentioned above there are issues when attempting to model the pull-back peak of the low

force snap-back and the more significant impact effects associated with the high force snap-back,

which result in an apparent Multi-Degree-of-Freedom (MDOF) system. From inspection of the

individual damping and frequency data between cycles, as well as the total response in the time

and frequency domain, it appeared that the pile-soil system is a two degree of freedom system,

and that the inelastic degree of freedom is present at the start of the response, with the elastic

degree of freedom present later on. Hence, damping envelopes were fitted to the low force snap-

back response after the pull-back, and for the high force snap-back separate envelope pairs were

fitted at the start and end of the response, dividing the response into two separate SDOF systems

in the time domain so that the SDOF system damping could be computed for each of the elastic

and inelastic parts. Thus a different system damping for the inelastic and elastic responses is

obtained. This is discussed further in the following section.

Due to the adverse effects HPFs were found to have on the data; this methodology was also

applied to split the individual cycle damping (logarithmic decrement method) between inelastic

Dynamic pile response from full-scale field tests

104

and elastic. This is an alternative to applying filters to the response (by analysing the frequency

domain) and has the advantage that only the raw unfiltered response is considered.

5.3.2.1 Pile 4 response characteristics

A detailed look into the response of Pile 4 for the three different dynamic tests (10 kN low force

snap-backs, 120 kN high force snap-backs and hammer tests) under the three different levels of

pile head mass (324 kg, 609 kg and 1275 kg) is carried out in this section by juxtaposing the

response with the SDOF displacement solution presented earlier. Damping and frequency data

between cycles is also presented to assist in determining where the inelastic response finishes and

elastic response starts for high force level snap-back tests.

Figures 5-18, 5-20 and 5-21 show the exponential envelopes and displacement prediction

comparisons with a hammer, 10 kN and 120 kN snap-back. Figure 5-18 illustrates that only one

symmetrical pair of damping envelopes are required to model the entire noise-filtered free

vibration response produced from the instrumented hammer tests, the final hammer for the 609 kg

mass level is shown. A damping ratio of 11% was found to satisfy the shape of the data. Two

subplots are shown together; the bottom plot shows the effect of the direction of hammer blow

later on in the free vibration response, where the pile starts drifting permanently in one direction,

by comparing the overall response with the trimmed response. The trimmed response has

removed the first five hammer peaks; hence the response is zeroed about the new residual pile

displacement. The same 11% damping envelopes fit this trimmed response (scaled to fit the first

peak displacement), so although the overall response deviates away from the envelope at later

stages of the response, the same 11% damping is shown to correctly define the ‘elastic system

damping’ of Pile 4 (at this stage of testing with a 609 kg pile head).

Several blows are carried out for each test and Figure 5-19 confirms that the pile has a small

amount of permanent deformation that has developed after each individual hammer blow, where

some of this is recovered later on in the time domain. This was previously not realised with what

was assumed an elastic free vibration pile response. The hammer blows carried out are not a high

load level, but clearly a minor amount of inelasticity still develops in the surrounding soil,

through either gapping or yielding. The snap-back test involves releasing the pile from a large

displacement in the same direction that the hammer blows are carried out. The large impact

effects on the soil may have resulted in weakened soil behaviour in that direction for hammer

tests.

Dynamic pile response from full-scale field tests

105

Figure 5-18: Damping envelopes for hammer test following 120 kN snap 2 with 609 kg pile head

Figure 5-19: Unfiltered hammer test (3 blows) on open time domain following second 120 kN snap-back with 609

kg added to Pile 4

9.4 9.5 9.6 9.7 9.8 9.9 10 10.1-0.4

-0.2

0

0.2

0.4

Time (s)

Dis

pla

cem

ent

(mm

)

Overall response

Test data

11% damping envelopes

9.7 9.8 9.9 10 10.1 10.2

-0.05

0

0.05

Time (s)

Dis

pla

cem

ent

(mm

)

Trimmed response

Trimmed test data

11% damping envelopes

Hammer blow direction

0 2 4 6 8 10 12 14 16 18-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

Time (sec)

Dis

pla

cem

ent

(mm

)

Dynamic pile response from full-scale field tests

106

The 10 kN snap-back test in Figure 5-20 for the 324 kg pile head mass shows that the SDOF

displacement prediction commencing at the pull-back, has difficulties in modelling the entire

snap-back response. This is due to two reasons; (1) the pull-back peak has a much greater

displacement than the other peaks so there are impact effects that cannot be modelled by the

SDOF approximation and (2) the pile displacement in the negative direction of the plot is smaller

in magnitude than the positive cycles. A 6% system damping value has been imputed into the

displacement prediction equations and its corresponding envelope, but clearly a worthwhile

system damping value is one that neglects the pull-back peak, using its individual damping value

as the inelastic damping for that system, and models the remainder of the response as a SDOF

elastic response. Two envelopes are fitted to the second and third peaks of the response to find an

elastic system damping of 5%. It should be noted that the same symmetrical envelope pair is not

used (this was done for hammer tests), due to the greater response in the positive direction. This is

not unexpected, when the unsymmetrical nature of snap-back testing is considered.

Figure 5-20: Damping envelopes and displacement prediction for 10 kN snap-back with 324 kg pile head

The lower force level of the 10 kN snap-back, compared with a 120 kN snap-back, may result in

less impact effects from the snap-back. However, the large strains developed during the pull-back

may have resulted in excessive residual gapping between the compressed soil after the pile

release, hence softer behaviour in the one direction. As with the hammer, some residual pile

10.5 10.6 10.7 10.8 10.9 11 11.1 11.2

-1

-0.5

0

0.5

1

Time (s)

Dis

pla

cem

ent

(mm

)

Test data

SDOF displacement prediction

Damping envelopes

Bottom elastic damping envelope

Top elastic damping envelope

Dynamic pile response from full-scale field tests

107

movement is developed in the negative direction later on in the response, and recovered slowly

after the cyclic response of the pile has stopped, but is presumed to not affect the damping

solution. The recovery of the pile is consistent with the observed increase in frequency between

subsequent cycles, which may represent some pile-soil contact recovery as the pile returns to its

residual position.

The displacement solution in Figure 5-21 is set up to model only the inelastic portion of the high

force 120 kN snap-back response, with 609 kg added to the pile head, because the elastic peak

displacements are small in comparison and the two extreme response behaviours, heavily damped

inelastic and lightly damped elastic, mean that an average fit cannot be made to both. The large

variance in frequency developed between the first three peaks, the inelastic response, results in the

displacement prediction moving out of phase with the 120 kN snap-back test. The 40% inelastic

system damping envelopes do however model the test data during the first three peaks accurately.

Elastic envelopes are fitted after the first three peaks, to the fourth and fifth peaks, to determine

the elastic system damping of the response. The large impact effects involved in the 120 kN snap-

back response result in the most significant pile movement in the negative displacement direction

in Figure 5-21, in comparison to the movement developed during the hammer tests and low force

10 kN snap-back tests. The unsymmetrical behaviour, evident during the elastic cycles, has

resulted in the need for two different levels of damping to be used for the pair of exponential

envelopes that define the elastic system damping for the system. For this case a 9% damping ratio

has been inputted into the top envelope, and a 17% damping ratio has been used for the bottom

envelope; the average of these is taken to given an elastic system damping of 13% for this snap-

back test. Note that the weakened soil behind the pile that has shifted during the pull-back may

also be a contributing factor to the pile movement in the negative direction, shown to be the case

earlier in Figure 4-5.

The slight deviation of the second peak from the bottom elastic exponential envelope suggests

that the fourth peak in the response which was presumed to be elastic may still contain a small

amount of inelasticity. For the 10 kN snap-back test with a 609 kg pile head mass (not shown),

the first three peaks had to be ignored for the elastic response, this disagrees with the other two

mass levels and was presumed to be a result of the chaotic nature of the 15 lead mass

arrangement, illustrated previously in Figure 5-9.

Dynamic pile response from full-scale field tests

108

Figure 5-21: Damping envelopes and displacement prediction for 120 kN snap-back with 609 kg pile head

Table 5-4 presents local damping and frequency data between cycles to assist with the

determination of the inelastic-elastic separation in the response for high force 120 kN snap-back

tests. Frequency between cycles is computed in the time domain (5.2.2) and damping is calculated

using the logarithmic decrement method (5.3.1). There was a distinct shift in the 120 kN snap-

back 1 for the 1275 kg pile head that highlight an inelastic to elastic shift in the response after

three peaks, and a shift after only one peak for the 324 kg pile head, shown in Table 5-4.

For all levels of added mass the individual damping was found to deviate later on in the response

which is due to the pile movement in the negative displacement direction. Low frequency high-

pass filters (HPFs) were used in the analysis of Pile 3 to bring the displacement back to centre on

zero displacement where low frequency effects were present in the response, with the sacrifice of

having to manipulate the response with inbuilt filters on MATLAB. This was not carried out on

Pile 4 regardless as low frequency HPFs were not effective in bringing the response back to zero

displacement.

36.55 36.6 36.65 36.7 36.75

-20

0

20

40

Time (s)

Dis

pla

cem

ent

(mm

)Overall response

36.7 36.8 36.9 37 37.1 37.2 37.3 37.4

-1.5

-1

-0.5

0

0.5

Time (s)

Dis

pla

cem

ent

(mm

)

Later cycles of response

Test data

SDOF displacement prediction

Damping envelopes

Bottom elastic damping envelope

Top elastic damping envelope

Dynamic pile response from full-scale field tests

109

Table 5-4: Damping and frequency data between peaks for the first series 120 kN snap-backs on Pile 4 that were

used to help assess the inelastic-elastic response division

324 kg pile head mass 609 kg pile head mass 1275 kg pile head mass

Damping

ratio between

successive

peaks (%)

Frequency

between

successive

peaks (Hz)

Damping

ratio between

successive

peaks (%)

Frequency

between

successive

peaks (Hz)

Damping

ratio between

successive

peaks (%)

Frequency

between

successive

peaks (Hz)

16.1 10.0 35.6 9.05 40.0 5.24

11.6 11.8 29.1 11.4 *48.5 3.85

10.3 12.2 26.5 13.2 42.6 3.80

12.1 11.9 21.2 12.9 1.80 6.19

12.0 12.0 9.14 10.8 20.2 6.78

11.8 12.4 11.5 10.2 0.72 6.60

11.8 12.7 - - - -

12.3 13.0 - - - -

9.61 13.0 - - - -

9.37 13.3 - - - -

7.53 13.3 - - - -

*adjusted for the term in equation (5-3)

High frequency HPFs were required when separating the elastic response and inelastic responses

using inbuilt filters on MATLAB, the first data collection method utilised in 5.3.1. Figure 5-22

shows the effect of this filtering technique on a high force 120 kN snap-back test.

The effect of a HPF increases when the cut-off frequency increases. A large cut-off frequency is

required when removing the elastic response from the system. Figure 5-22 in the time domain

shows the elastic response is flipped upside down in comparison to the original response and

similar magnitude peaks are produced for the first few cycles, before a low magnitude

displacement oscillation continues. It is difficult to be sure where these peaks come from, which

is a significant disadvantage of using this technique. When subtracting the elastic response from

the overall response to get the inelastic response, the half period phase difference of the elastic

response results in greater magnitude inelastic peaks compared with the original response.

In the frequency domain, the elastic HPF has removed lower inelastic frequencies as expected. In

comparison to the original response; the FFT amplitude generally decreases across the entire

frequency domain for the elastic response, and increases for the inelastic response. The inelastic

peak frequency amplitude increases only slightly for the inelastic response, and shows a slight

Dynamic pile response from full-scale field tests

110

shift towards the elastic peak frequency range. Although there may be some overlay of inelastic

and elastic effects in the original response in the time domain, it is a more desirable technique to

split the response into these two portions in the time domain as there is no adverse effect on the

response itself, and the data in Table 5-4 shows a clear distinction can be made.

Figure 5-22: Effect of filtering technique to extract elastic/inelastic responses on 1275 kg 120 kN snap-back 1

5.3.2.2 Pile 4 damping ratio data

This section presents elastic and inelastic system damping determined by fitting exponential

envelopes to the response where applicable, for hammer, 10 kN low force snap-back, and 120 kN

high force snap-back tests. For snap-back tests, inelasticity was found to be confined to the first

few cycles of the response, to summarise the results of the inelastic-elastic divide in the time

domain from the previous section:

The low force 10 kN snap-backs and the 120 kN 324 kg pile head have inelasticity in the

first pull-back peak only – thus the logarithmic damping of that peak is reported as the

inelastic system damping and the rest of the response is fitted with exponential envelopes

to determine elastic system damping.

15.7 15.8 15.9 16 16.1 16.2 16.3 16.4 16.5

-10

-5

0

5

Time (s)

Dis

pla

cem

ent

(mm

)

0 5 10 15 200

0.05

0.1

Frequency (Hz)

FF

T -

dis

pla

cem

ent

am

plit

ude

Original response

Elastic response

Inelastic response

Elastic peaks

Inelastic peaks

Dynamic pile response from full-scale field tests

111

The low force 10 kN, 609 kg snap-back contained some inelastic effects in the first three

peaks, the pull-back peak was still reported as inelastic system damping however elastic

envelopes were fitted from the forth peak to the end of the response.

The high force 120 kN, 609 and 1275 kg pile heads predominately contained inelasticity

in the first three cycles, thus inelastic envelopes were fitted over these cycles to determine

the inelastic system damping; a separate pair on envelopes were fitted to the remainder of

the response to determine the elastic system damping.

This section is characterised by the usage of the time domain to make these inelastic and elastic

divisions; logarithmic damping is also presented here as it is distributed between the inelastic and

elastic regions in the time domain; it is also used to provide a comparison with damping

determined using the exponential envelope fitting technique.

5.3.2.2.1 Hammer damping ratio data

Damping ratios computed for all instrumented hammer free vibration tests is presented in Figure

5-23. Damping ratios are computed from cycle to cycle peak amplitudes using the logarithmic

decrement method, and by fitting exponential envelopes to the response to give the elastic system

damping. The displacement of the successive peak cycles that damping is calculated from, x1 and

x2, was found to be independent of the damping ratio, ζ, for hammer tests so damping is instead

presented against the stage of testing (refer to 3.8 or 5.1). The damping ratio is a function of mass

from the following relationship defined earlier:

√ (5-2)

For results to be comparable between tests of the same level of mass, the plot includes an

appropriate legend. From equation (5-2) it is expected that for a constant pile head mass the

damping ratio increases for subsequent tests, due to a reduction in stiffness from loss of soil

contact around the pile. For the hammer tests carried out during the 10 kN and first series of 120

kN snap-backs, it is expected that as the level of mass increases between hammer tests, there is a

decrease in the damping ratio, provided this is not offset by a decrease in stiffness. For tests

carried out during the second series of 120 kN snap-backs, the level of mass decreases between

tests so it is expected that a damping ratio increase is observed.

The system damping data points generally follow these predictions in Figure 5-23. Damping

ratios computed for the two lower mass levels cause the most disagreement to this trend.

Relatively low damping (considering it has the lowest mass) is computed for the 324 kg pile head.

For the medium mass level 609 kg pile head, high variability is evident in both the exponential

Dynamic pile response from full-scale field tests

112

envelope system damping and individual logarithmic decrement method damping. This deviation

has been found to be typical for this mass level and was previously attributed to the loose lead

mass arrangement in the pile head (Figure 5-9). Inconsistent results for the low mass level (324

kg) suggest that it may be due to the mass added to the pile head. The lower proportion of mass at

the pile head compared with the mass along the length of the pile has a considerable effect on

whether those systems can be treated as equivalent SDOF systems (which was assumed in (5-2)).

Individual cycle damping values produce a large variance away from the exponential system

damping for all hammer tests. The unsymmetrical behaviour later on in the response (5.3.2.1) is

the likely cause. Figure 5-24 – 5-26 present the individual cycle damping versus cycle number in

the response, for each mass level. It is evident that consistent damping is computed for the first

half of the response, and then later on deviation occurs. Some particularly large values were

computed for the 609 kg pile head. These were ignored in Figure 5-23 as they are significantly

flawed and not representative of an elastic hammer damping ratio. Note the logarithmic

decrement method was employed using peaks further away in the response from the first

subsequent peak displacement to generate more accurate damping from the data, however, similar

values were computed to using successive peaks. The exponential damping technique is an

important tool as it is able to account for the varied nature of the response.

Figure 5-23: Damping ratios computed from hammer tests on Pile 4; using the logarithmic decrement method

and exponential system damping envelopes

0 2 4 6 8 10 12 14 160

5

10

15

20

25

30

Hammer test number

Dam

pin

g (

%)

324 kg mass on pile head

609 kg mass on pile head

1275 kg mass on pile head

system damping for each test

Dynamic pile response from full-scale field tests

113

Figure 5-24: Cycle damping ratio versus cycle number for hammer tests on 324 kg pile head

Figure 5-25: Cycle damping ratio versus cycle number for hammer tests on 609 kg pile head

0 5 10 15 20 250

2

4

6

8

10

12

14

16

18

20

Cycle number

Dam

pin

g r

atio (

%)

Damping ratio for 324 kg pile head mass

10kN hammer 1

10kN hammer 2

120kN hammer 1

120kN hammer 2

120kN hammer 3

120kN hammer 4

0 2 4 6 8 10 12 14 16 180

5

10

15

20

25

30

Cycle number

Dam

pin

g r

atio (

%)

Damping ratio for 609 kg pile head mass

10kN hammer 1

10kN hammer 2

120kN hammer 1

120kN hammer 2

120kN hammer 3

120kN hammer 4

Dynamic pile response from full-scale field tests

114

Figure 5-26: Cycle damping ratio versus cycle number for hammer tests on 1275 kg pile head

5.3.2.2.2 Low force 10 kN snap-back damping ratio data

The damping ratios computed for the unfiltered low force 10 kN snap-back tests is shown in

Figure 5-27, plotted against the first peak displacement. The pull-back peaks are identified as they

are defined as the inelastic system damping for these tests. From Figure 5-27, the elastic system

damping values, which do not include the pull-back peaks, appear to model the centre of the

logarithmic decrement damping clusters for each mass level. Also, the 609 kg pile head has the

most deviation in both individual cycle damping and system damping; where it has a smaller

damping ratio than the largest mass level, the 1275 kg pile head. This is in disagreement with

equation (5-2).

The assumption that the system inelasticity is confined to the large cycle displacement and large

damping pull-back peaks seems consistent with the results shown on Figure 5-27, with the

possible exception of the 609 kg mass pile head which has large damping in one or two

subsequent cycles. The majority of the elastic damping is at a damping ratio of approximately 5%,

with deviations between 0 and 10%. To investigate whether this is related to the deviation of the

response away from the zero displacement horizontal axis, Figure 5-28 relates the individual

damping ratio to the cycle number, including the pull-back peak.

0 5 10 15 20 250

2

4

6

8

10

12

14

16

18

20

Cycle number

Dam

pin

g r

atio (

%)

Damping ratio for 1275 kg pile head mass

10kN hammer 1

10kN hammer 2

120kN hammer 1

120kN hammer 2

120kN hammer 3

Dynamic pile response from full-scale field tests

115

Figure 5-27: Damping ratios computed from 10 kN snap-back tests on Pile 4; using the logarithmic decrement

method and exponential system damping envelopes

Figure 5-28: Cycle damping ratio versus cycle number for low force 10 kN snap-back tests on Pile 4

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

5

10

15

20

25

First cycle displacement, x1 (mm)

Dam

pin

g (

%)

324 kg mass on pile head

609 kg mass on pile head

1275 kg mass on pile head

pull-back peak damping

system damping

0 5 10 15 20 25 300

5

10

15

20

25

Cycle number

Dam

pin

g r

atio (

%)

10kN snap 1 324kg mass

10kN snap 1 609kg mass

10kN snap 1 1275kg mass

Dynamic pile response from full-scale field tests

116

Figure 5-28 shows very consistent damping is produced from these three 10 kN snap-back tests,

where only the last few damping ratios deviate away from a relatively horizontal line of constant

damping. The fact that the 15 lead masses (609 kg) pile head produces larger damping is

unexpected, but modal effects from the loose lead mass arrangement highlighted in Figure 5-9

must have a significant effect.

5.3.2.2.3 High force 120 kN snap-back damping ratio data

Figures 5-29 and 5-30 present damping data using the method of splitting the inelastic and elastic

components in the time domain, as opposed to the frequency domain carried out earlier (5.3.1).

Damping data is found between cycles using the logarithmic decrement method, as well as the

inelastic and elastic system damping ratios by fitting exponential damping envelopes to each

portion of the response.

Figure 5-29: Elastic damping ratios computed in the time domain from 120 kN snap-back tests on Pile 4

The individual elastic cycle damping in Figure 5-29 is centred at around 10% for this 120 kN

snap-back force level, which is greater than the 5% damping for low force 10 kN snap-backs and

hammer tests presented earlier. This, and the greater deviation of damping away from 10%, is

presumably due to the chaotic nature and impact effects of the high force 120 kN snap-back tests

affecting the response at later cycles. There is less variance in the 324 kg mass response, which

0 5 10 15 20 250

5

10

15

20

25

First cycle displacement, x1 (mm)

Ela

stic d

am

pin

g (

%)

324 kg mass on pile head

609 kg mass on pile head

1275 kg mass on pile head

elastic system damping

Dynamic pile response from full-scale field tests

117

had less impact effects; inelasticity was only found in the first peak, and a more symmetrical

response than the higher mass levels. The unsymmetrical nature of the response increased with

increasing mass levels. The unusually high level of inelasticity evident later in the response of the

medium mass level of 609 kg has resulted in the greatest elastic system damping for all tests. It is

expected that this level of damping should lie in between the system damping for the other mass

levels to fit the relationship in equation (5-2). It should be noted that a relatively low level of

elastic system damping for the 324 kg mass level makes this difficult.

Figure 5-30: Inelastic damping ratios computed from 120 kN snap-back tests on Pile 4 in the time domain

The greater impact and inelastic effects with the high mass levels becomes evident in the inelastic

damping computed in Figure 5-30. Here, the greater the mass, the higher individual and system

damping computed. The unsymmetrical nature of the snap-back tests is more notable later on in

the response, which is why the earlier inelastic response has more consistent damping than the

later elastic response when splitting in the time domain. The inelastic system damping for the 324

kg pile head is assumed to be the individual pull-back peak damping as inelasticity is only evident

in the first peak. Both Figures 5-29 and 5-30 make more intuitive sense than the frequency

domain splitting alternatives, with regards to only low levels of elastic damping and only high

levels inelastic damping computed; which is observed when looking at the response in the time

domain. The exponential system damping envelopes are advantageous in being able to define the

0 10 20 30 40 50 600

10

20

30

40

50

60

70

First cycle displacement, x1 (mm)

Inela

stic d

am

pin

g (

%)

324 kg mass on pile head

609 kg mass on pile head

1275 kg mass on pile head

inelastic system damping

Dynamic pile response from full-scale field tests

118

inelastic or elastic systems with one damping value, as opposed to many individual cycle to cycle

values. This technique would not be possible when splitting the response in the frequency domain

given the varied nature of the inelastic and elastic responses when HPFs are applied.

One weakness of Figures 5-29 and 5-30 is that it is difficult to assess stiffness effects on the

damping computed in terms of timing during testing; this can be assessed in Figure 5-31, where a

bar chart of damping versus test number, in chronological order, is presented. Excluding relative

inconsistencies between the 324 and 609 kg pile head responses, an inverse damping-mass

relationship is evident across the separate 10 kN and 120 kN snap-back tests in Figure 5-31. This

is not the case for inelastic 120 kN snap-back damping, as a greater mass produces more impact

effects and higher damping. Comparing between the first and second 120 kN snap-back series, a

general increase in inelastic damping as testing progresses is evident, which is expected given the

softening of the pile-soil system as testing progresses. This is not the case for the two higher mass

levels for elastic damping, which may have something to do with these impact effects producing a

more unsymmetrical response for later elastic cycles. This possibility is explored in Figure 5-32,

where the individual cycle damping versus cycle number for all high force 120 kN snap-back tests

is plotted. Figure 5-32 presents damping for inelastic as well as elastic cycles, the entire response.

Figure 5-31: Exponential system damping for all snap-back tests, illustrating snap-back order

0 10 10 10 120 120 120 120 120 1200

5

10

15

20

25

30

35

40

45

50

Snap-back magnitude (kN)

Ela

stic/inela

stic d

am

pin

g (

%)

324 kg mass - elastic damping

609 kg mass - elastic damping

1275 kg mass - elastic damping

Inelastic damping

Dynamic pile response from full-scale field tests

119

The scale on the horizontal axis of Figure 5-32 shows that the snap-back response is highly

chaotic with damping computed on less than half the number of cycles it was for low force 10 kN

snap-back tests and hammer tests. A large variation is expected during the transition from the

inelastic cycles to the elastic cycles. The elastic response starts at the fourth peak for the two high

mass levels, and the second peak for the low mass level. The low mass level clearly has the most

consistent damping, with some variance later on due to asymmetry in the response. The elastic

cycles of the 1275 kg second 120 kN snap-back are of a similar nature, however elastic cycles for

the remaining three high mass 120 kN snap-back tests, are of a highly varied nature throughout.

Overall, high force 120 kN snap-back tests, particularly for the two high mass levels, have

significant asymmetry in the entire elastic portion of the response. These effects are more

considerable than those in the lower force level tests (10 kN snap-back and hammer) where an

unsymmetrical response is only developed significantly later on in the response.

Figure 5-32: Cycle damping ratio versus cycle number for high force 120 kN snap-back tests on Pile 4

5.3.3 Sensitivity analysis on noise filtering

Low-pass frequency noise filters (LPFs) are applied to the dynamic response in the time domain

to remove high frequency noise and produce a clean signal. This also enables accurate levels of

damping to be computed from the response, which is not influenced by local fluctuations in

0 2 4 6 8 10 120

5

10

15

20

25

30

35

40

45

50

Cycle number

Dam

pin

g r

atio (

%)

120kN snap 1 324kg mass

120kN snap 1 609kg mass

120kN snap 1 1275kg mass

120kN snap 2 1275kg mass

120kN snap 2 609kg mass

120kN snap 2 324kg mass

Dynamic pile response from full-scale field tests

120

response due to noise. There is a balance between tidying the data with a sufficient frequency

LPF, but not over-filtering the response and altering the data. To investigate this, three different

levels of LPFs were compared to the unfiltered response, in the time and frequency domain, of the

first 324 kg pile head 120 kN snap-back test, see Figure 5-33.

No noteworthy effect on the response in the frequency domain of Figure 5-33 is evident;

however, a delay of the response in the time domain is apparent when filtering is employed. The

40 Hz filter was chosen as it cleans up localised noise effects on the response, without causing a

significant delay in the response or changing the peak amplitudes significantly. Note the filter

used is an averaging filter so the responses all start at zero displacement, even though the true

displacement starts at the pull-back displacement before release. This is why an unfiltered

response is desirable when considering the pull-back peak; not only does the peak displacement

change, the cyclic behaviour changes in the time domain as the response commences at zero

displacement. It should be noted that this is a particularly clean unfiltered response with large

displacements; often a 40 Hz filter is required to remove local noise, which is particularly evident

at small displacements.

Figure 5-33: Noise filtering effects on the response of the first 120 kN snap-back with a 324 kg pile head

17.6 17.65 17.7 17.75 17.8 17.85 17.9 17.95

-10

0

10

20

30

Time (s)

Dis

pla

cem

ent

(mm

)

10 20 30 40 50 60

0

0.1

0.2

Frequency (Hz)

FF

T -

dis

pla

cem

ent

am

plit

ude

unfiltered 120kN snap 1 - 324kg

20Hz low pass filter

40Hz low pass filter

60Hz low pass filter

Dynamic pile response from full-scale field tests

121

5.3.4 Sensitivity analysis on SDOF displacement prediction

Key parameters used in the SDOF displacement prediction equation (5-5) and the corresponding

exponential damping envelopes, given by the term outside the brackets of equation (5-5), is the

damped natural frequency (also used to calculate the un-damped natural frequency) and damping

ratio for the SDOF system. Both parameters vary between responses, in terms of test type, stage

of testing and mass level. A damping ratio of 13% and the (inelastic) damped natural frequency of

12 Hz were used to model the ‘overall’ response of the first 324 kg mass 120 kN snap-back test,

even though inelasticity was contained in the pull-back peak and the response was elastic

thereafter, meaning it is not a true SDOF system. Key parameters of damping ratio and frequency

were varied by 50%, and compared with the base model as well as the 120 kN snap-back test,

shown in Figure 5-34.

Figure 5-34: Sensitivity analysis on key parameters of damping ratio and damped natural frequency for the

SDOF displacement prediction model and corresponding damping envelopes

Looking at the damping envelopes, both 50% increases in key parameters of damping ratio and

natural frequency produce the same change in the damped free vibration shape. This is because

both terms are proportionally contained in the exponential term. An increase in these terms

increases the negative exponential by the same amount, resulting in a more highly damped

response, as one would expect. Additionally, the increase in frequency alters the phase of the

17.6 17.65 17.7 17.75 17.8 17.85 17.9-30

-20

-10

0

10

20

30

Time (s)

Dis

pla

cem

ent

(mm

)

120kN snap 1 - 324 kg

12Hz, 13%

18Hz, 13%

12Hz, 20%

Dynamic pile response from full-scale field tests

122

response, completing three cycles in the time it takes the original response to complete two,

consistent with a 50% increase. Note also the three models fail to capture the test behaviour

during the pull-back release, shown at the 17.6 s start time, as it takes longer for the pile to reach

its maximum negative displacement than it does for the displacement prediction models. This

could be due to a flaw in the quick release of the pile or modal effects as the displacement is

measured at a significant distance from the pile head mass.

5.3.5 Reference beam accelerations relative to test pile

3D Piezoelectric accelerometers were placed on the steel bracket and the ends of the reference

beams closest to the test pile (Pile 4), to measure accelerations in the snap-back direction. This set

up was adopted so the influence of the reference beam interaction on LVDT readings, which are

supported by the reference beams, could be determined. Thus the relative accelerations between

test pile and reference beam ends, where they are fixed to the ground, are important. The

accelerations produced during the 1275 kg pile head 120 kN snap-back test one is shown in

Figure 5-35.

The 10 g accelerometer reading limit is exceeded on the test pile for multiple readings, illustrating

why accelerometers at this limit are not vital instrumentation for snap-back testing. This means

that the absolute maximum acceleration recorded on the west end of the reference beam, of 1.37

g, cannot be related to test pile accelerations. A lower force level snap-back test was considered

so a maximum test pile reading within the 10 g limit could be obtained. The accelerations

produced during the 1275 kg pile head 10 kN snap-back test is shown in Figure 5-36.

The absolute maximum test pile acceleration during the 1275 kg pile head 10 kN snap-back from

Figure 5-36 is 2.66 g, within the 10 g limit. The absolute maximum acceleration on the west

reference beam is 0.199 g; this corresponds to a relative acceleration of 7.45% compared with

maximum test pile acceleration. This is an upper bound on the possible error that could be

introduced into the LVDT readings, one which has been accepted for the field testing carried out.

It is worth noting the time delay in the arrival of the maximum reference beam acceleration,

compared with the almost instantaneous reading for the 120 kN snap-back test in Figure 5-35.

The impact effects associated with the 10 kN snap-back test are significantly less, which must

result in superposition of elastic waves in the soil producing the maximum ground acceleration at

the reference beam fixities, as opposed to what appears to be an impact wave triggering the

maximum reference beam acceleration during the initial stages of the 120 kN snap-back test.

Dynamic pile response from full-scale field tests

123

Figure 5-35: Accelerometer readings from 120 kN 1275 kg snap-back 1

Figure 5-36: Accelerometer readings from 10 kN 1275 kg snap-back

15.5 16 16.5 17-10

-8

-6

-4

-2

0

2

4

6

8

10

Time (sec)

Accele

ration (

g)

Test pile

West reference beam 2.1m

East reference beam 2.2m

Maximum acceleration = -1.37g

18 18.2 18.4 18.6 18.8 19 19.2 19.4 19.6-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

Time (sec)

Accele

ration (

g)

Test pile

West reference beam 2.1m

East reference beam 2.2m

Maximum test pile acceleration

Maximum reference beam acceleration

-0.199g

2.66g

Dynamic pile response from full-scale field tests

124

5.3.6 Ground motion decay

Four geophones were placed horizontal to the ground at various distances from the test pile, to

record compression-equivalent waves at the ground surface, assumed to be Rayleigh waves, and

provide a measure of the elastic radiation damping at the Albany test site. The geophone set-up is

illustrated in Figure 5-37. Geophones one, two and three were placed in the direction of the snap-

back at respective distances of 3, 5 and 7 m south of Pile 4, the test pile. Geophone four was place

4 m southeast of Pile 4, at an angle of 45 degrees to the line of the other geophones.

Figure 5-37: Geophone set-up for Pile 4 testing

The relative size of the peaks compared with that of the closest geophone is important, so the

signal strength can be plotted versus distance from the test pile to assess what level of radiation

damping is present. Thus signals have been noise filtered to remove localised increases in

response, and zeroed just before the first wave from the snap-back arrives so signals are relative

to each other. Figures 5-38 – 5-40 present the geophone signals for the 324 kg 10 kN snap-back,

609 kg 120 kN snap-back and 1275 kg 120 kN snap-back tests, series one.

The geophones are placed at a sufficient distance from the released test pile (and reaction pile) so

that only elastic soil response is considered. The low force low mass response in Figure 5-38

produces a consistent sinusoidal response for all geophones, with the peaks of each relatively in

phase with one another. There are some superposition effects that develop in the response as the

magnitude of the first peak is exceeded by some subsequent peaks.

Dynamic pile response from full-scale field tests

125

Figure 5-38: Geophone response signals during 10 kN snap-back

Figure 5-39: Geophone response signals during 120 kN snap-back (1)

10.5 10.55 10.6 10.65 10.7 10.75

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

Time (s)

Geophone s

ignal (V

)

Noise filtered and zeroed geophone response in time domain - 10kN snap 1; 324kg

geophone 1

geophone 2

geophone 3

geophone 4

36.55 36.6 36.65 36.7 36.75

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time (s)

Geophone s

ignal (V

)

Noise filtered and zeroed geophone response in time domain - 120kN snap 1; 609kg

geophone 1

geophone 2

geophone 3

geophone 4

Dynamic pile response from full-scale field tests

126

Figure 5-40: Geophone response signals during 120 kN snap-back (2)

Figures 5-39 and 5-40 produce a more sporadic response for the higher force and mass levels.

Each geophone response for these two tests contains varying frequencies and peak amplitudes.

The impact effects of the snap-back for these high force levels must result in disruption to the

previously consistent response. For the 1275 kg pile head mass test, the subsequent geophone four

peak signal is the greatest magnitude signal for that test. The response of the reaction pile could

also send waves to cause further disruption to the response.

The significant superposition effects present in the responses in Figures 5-38 – 5-40 suggest that

the first undisrupted peak, shown in plots, is of interest in terms of assessing the radiation

damping in the soil. For an under-damped system it would not fit theory if the response was

greater at later stages in the time domain.

The first peak signal amplitudes for each geophone are plotted versus the geophone distance from

the test pile for all snap-back tests in Figures 5-41 – 5-43. Note the different scale on the vertical

axis for the 10 kN snap-back tests, because much lower signals were recorded for the low force

level compared with high force level tests.

15.65 15.7 15.75 15.8 15.85 15.9

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Time (s)

Geophone s

ignal (V

)

Noise filtered and zeroed geophone response in time domain - 120kN snap 1; 1275kg

geophone 1

geophone 2

geophone 3

geophone 4

Dynamic pile response from full-scale field tests

127

Figure 5-41: Geophone first peak signal versus distance from test pile for 10 kN snap-back tests

Figure 5-42: Geophone first peak signal versus distance from test pile for 120 kN snap-back tests series one

3m 5m 7m 4m, 45 degrees0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Distance from test pile

Geophone s

ignal (v

olts)

324 kg mass 10kN snap 1

609 kg mass 10kN snap 1

1275 kg mass 10kN snap 1

3m 5m 7m 4m, 45 degrees0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Distance from test pile

Geophone s

ignal (v

olts)

324 kg mass 120kN snap 1

609 kg mass 120kN snap 1

1275 kg mass 120kN snap 1

Dynamic pile response from full-scale field tests

128

Figure 5-43: Geophone first peak signal versus distance from test pile for 120 kN snap-back tests series two

Generally from Figures 5-41 – 5-43, the rate of signal decrease is greatest between the first and

second geophones, with a lower loss in signal between the second and third geophones (note

equal distances between three geophones). The fourth geophone signal typically lies between the

magnitude of the second and third geophones. The fourth geophone is closer to the test pile than

the second geophone, so the reduced signal amplitude must be the result of more surface waves

travelling in the principal snap-back direction. For each plot, the larger masses produce smaller

signal strengths, and hence are more heavily damped.

All geophone signals are normalised by the closest geophone signal peak for each test, and plotted

together in Figure 5-44. Figure5-44 allows the relative damping to be assessed between each test.

Three separate groups of mass are evident in the plot, characterised by line colour. It confirms the

earlier finding that the heavier pile mass, the greater the level of radiation damping in the soil,

shown through a more rapid decay in the normalised first peak signals.

For the 324 and 609 kg pile head masses, the 10 kN snap-back test exhibits the greatest level of

damping, where force level is characterised by line style. For the 324 and 1275 kg pile head

masses, the first series of 120 kN snap-back tests produce greater damping than the corresponding

second series 120 kN snap-back test. Although less impact effects were evident for earlier tests,

presumably due to a shallower gap depth, it is the shallower gap depth itself that is the more likely

3m 5m 7m 4m, 45 degrees0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Distance from test pile

Geophone s

ignal (v

olts)

1275 kg mass 120kN snap 2

609 kg mass 120kN snap 2

324 kg mass 120kN snap 2

Dynamic pile response from full-scale field tests

129

reason for increased damping for earlier tests. There was no gap evident around the pile during

the 10 kN snap-back tests, which means the pile is oscillating against a greater surface area of

soil, that is also closer to the ground surface. This would allow a greater volume of soil to radiate

compression waves that have an influence at the ground surface and hence a greater level of

damping. The significant impact effects associated with the higher force 120 kN snap-back tests

may also have resulted in strong surface wave signals that were more difficult to dissipate through

radiation damping in the soil.

Figure 5-44: Normalised geophone first peak signals versus distance from test pile for all snap-back tests

Different radiation damping models in Figure 2-4, that account for plane-strain body waves

(compression-extension, VLa, and shear waves, Vs), are considered based on the findings of the

geophone results. The major limitation in this assessment is that geophones were set up on the

ground surface. Gazetas and Dobry (1984), in their radiation damping model formulation, state

that at very shallow depths, surface waves are generated instead of, or in addition to, plane-strain

body waves. These surface waves propagate with velocities closer to Vs than VLa. Thus near the

ground surface, they approximate waves to be travelling with velocity Vs in all four quarter planes

of their model shown in Figure 2-4 (c). Results from geophone tests suggest that 2D wave travel

at ground surface is more sophisticated than the radial independence approximation made by

Gazetas and Dobry, for these body wave models. To gain more understanding of the applicability

3m 5m 7m 4m, 45 degrees0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Distance from test pile

Norm

alis

ed g

eophone s

ignal

324kg 10kN 1

609kg 10kN 1

1275kg 10kN 1

324kg 120kN 1

609kg 120kN 1

1275kg 120kN 1

1275kg 120kN 2

609kg 120kN 2

324kg 120kN 2

Dynamic pile response from full-scale field tests

130

of the models in Figure 2-4, geophones would somehow need to be set-up beneath the ground

surface. It would be easier to gain more of an understanding of the different surface waves present

by rotating the geophones 90 degrees, facing away from the test pile, in order to record surface

waves perpendicular to the snap-back direction.

Figure 2–4: Radiation damping of a horizontally vibrating pile (a) Berger et al. (1977); (b) Novak et al. (1978);

and (c) Gazetas and Dobry (1984)

5.4 HYSTERETIC PILE RESPONSE

This section presents an overview of the strain gauge calibration to the pull-back force applied at

the load collar, and utilising this measurement of force during the snap-back, hysteretic force-

displacement plots are provided for both Piles 3 and 4 at different levels of release force. The Pile

3 pull-back force and calibrated strain gauge snap-back force versus displacement, is also

presented with the displacements of the other piles not participating in testing (Piles 2 and 4), to

assess any interaction between piles.

5.4.1 Strain gauge calibration

The pull-back phase of testing is used to calibrate the strain gauges so they output a force, which

can then be utilised during the snap-back phase of the pile to produce force displacement curves.

Strain gauge versus load cell readings for a variety of pull-back tests on Pile 3 is shown in Figure

5-45. The readings are normalised by their maximum values so that they can be combined on the

same plot. Strain gauge readings during the static phase of testing are presented in the dynamic

section of this thesis as they are only relevant to producing the hysteretic response and are not

used to describe the static response.

(a) (b) (c)

Dynamic pile response from full-scale field tests

131

During the early stages of loading there is a large variation in the calibration factor between the

strain gauge reading and load cell reading, evident in Figure 5-45. After this a relatively constant

calibration factor between the two readings is found. The initial tightening of the load collar

around the test or reaction pile may be responsible for this. The 60 kN pull-back varies more than

the 15 and 120 kN pull-back tests, presumably due to the response not being quite as clean as the

others. The average calibration factor is taken during the relatively constant section of the

calibration factor vector; the middle to later stages of the pull back.

Figure 5-45: Calibration factor variation between strain gauge and load cell pull-back force for Pile 3

To investigate the effect of taking the average calibration factor, the force displacement response

during the pull-back can be compared with the force re-calculated using the average calibration

factor from the strain gauge. The results are in non-dimensional form for the aforementioned pull-

back forces and are displayed in Figure 5-46. Because the load cell cannot provide meaningful

data during the snap-back, the pull-back response needs to be used as a comparison. The solid

lines represent the response predicted by applying the average calibration factor to the strain

gauge readings, the dotted lines are the direct readings from the load cell.

From Figure 5-46, the strain gauge predicted response is generally more accurate at later stages of

the response, which is expected because this is the region from which the calibration factors were

calculated. The 15 and 120 kN pull-back predictions are slightly too stiff, whilst the 60 kN pull-

back predictions vary during the pull-back more significantly. The reason for these variations is

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

Force/maximum force

Str

ain

gauge/m

axim

um

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-500

0

500

1000

1500

Force/maximum force

Calibra

tion f

acto

r

15kN pull-back 1

60kN pull-back 1

120kN pull-back 1

Dynamic pile response from full-scale field tests

132

apparent in Figure 5-45, where the calibration factors vary throughout the response, particularly

for the 60 kN pull-back. Since the strain gauge is set up to measure a bending moment, the

response of the soil may actually have a significant effect on the output readings. The bending

moment in the pile is a function of the stiffness in the soil. Because the soil response is non-linear;

the bending moment does not have a linear relationship with the applied force. Thus, there may be

similar errors in the snap-back response, as predicted by the force calibrated strain gauges.

Because the strain gauges are instrumented to measure moment, once the pile is released and

inertial forces control the response of the system, the strain gauge readings will no longer be

applicable to the pull-back force measured from the load cell. Thus, the ratio of the lever arms to

the load collar and lead mass from the strain gauge is multiplied with the old calibration factor, to

obtain a new calibration factor for the snap-back response.

Figure 5-46: Pile 3 comparison between force displacement response using load cell, and the force calculated

using the average calibration factor

5.4.2 Pile 3 hysteretic response

Both 120 kN and the second 90 kN snap-back hysteresis response for Pile 3 is shown in Figure 5-

47. All three responses follow a similar shape – a large increase in inertial forces is evident as the

pile accelerates in the negative direction during its first half cycle; the pile then rebounds near the

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Displacement/maximum displacement

Forc

e/m

axim

um

forc

e

calibrated strain gauge - 15 kN

load cell - 15 kN

calibrated strain gauge - 60 kN

load cell - 60 kN

calibrated strain gauge - 120 kN

load cell - 120 kN

Dynamic pile response from full-scale field tests

133

origin, before a sharp change in direction as the force at the strain gauge changes and becomes

negative, hence the pile bends in the opposite direction. The pile continues in the original negative

snap-back direction, and then a reversal in both force and displacement brings the pile back to its

original position where it oscillates until damping stagnates the pile. It should be noted that

because the strain gauge is instrumented to measure bending moment, the direction the pile bends

at the strain gauge location dictates the sign of the force. A change from positive to negative force

readings from the strain gauge is expected as the pile moves and bends in each direction during

the snap-back.

Figure 5-47: Pull and snap-back response for both of the 120 kN and the second 90 kN tests on Pile 3

There is a significant delay in this expected change of strain gauge sign, represented as a change

in the bending moment direction within the pile, as the pile changes direction, shown in Figure 5-

47. With a large gap depth at this stage of the testing, the length of the cantilever portion of the

pile is very significant. This may result in the response at the effective ground level (bottom of the

gap) taking a considerable time to influence the strain gauge near the top of the pile. The sign on

the strain gauge shows only two changes in the bending force produced (compression or tension

on one half of the section), compared with four changes in direction of the pile, before the pile

enters small hysteresis loop near the origin. This does seem unusual but could be due to dynamic

effects or higher order mode shapes. The mass of the lead weights and steel bracket at the pile

-5 0 5 10 15 20 25 30 35 40-60

-40

-20

0

20

40

60

80

100

120

Displacement (mm)

Str

ain

gauge (

kN

)

120 kN snap-back 1

120 kN pull-back 1

120 kN snap-back 2

120 kN pull-back 2

90 kN snap-back 2

90 kN pull-back 2

Dynamic pile response from full-scale field tests

134

head make up only 56 % of the total pile weight for Pile 3. The significant weight along the

length of the pile means that this is not the best representation of a single degree of freedom

system and higher modal effects may be what are causing this response. Investigating the effects

of the added mass at the head of the pile was carried out during Pile 4 testing.

The relatively small hysteresis loop compared with the size of the initial forces/deformations is

due to the nature of the snap-back test. Mass shaker induced responses start with low levels of

force and displacement, whereas the snap-back starts at a relatively large force and displacement

which was generated during the pull-back phase. The hysteresis loops for four different snap-back

tests are shown in Figure 5-48. A major disadvantage of snap-back testing is evident from Figure

5-48; the hysteresis loops for snap-back testing are not as clean as those produced from using an

eccentric mass shaker. A hysteresis loop produced using a mass shaker on a single pile at the site

in Albany is shown in Figure 5-49 (M.Sa’don, 2012).

Of the hysteresis loops in Figure 5-48, the 60 kN snap-back produces the least hysteretic

response; there is significant ‘ratcheting’ of the pile in the original snap-back direction, without

much change in force. The ‘ratcheting’ of the pile is evident in all of these snap-back tests and is

one of the reasons for the poor hysteretic response. The soil on the side of the pile that this

‘ratcheting’ affect occurs on coincides with the side that the snap-back of the pile is released

towards initially, which could also result in greater softening due to impact damage from the pile.

The horizontal earth pressure acting against the pile can cause some movement of the clay before

a gap is formed between the pile and soil during the pull-back of the pile; refer to Figure 4-6. This

may also result in cyclic movements of the pile towards this side, because the clay on the side of

the pile that has gapped during the pull-back is less stiff than the soil on the compression side of

the pile during the pull-back.

From the hysteresis loops presented in Figure 5-48, the 120 kN snap-back produces the best result

for analysis. Both 120 kN snap-back hysteresis loops are shown together in Figure 5-50, with an

operational stiffness defined for each. The operational stiffness (Pender et al., 2012b) is a

convenient means of describing the hysteretic response with a single stiffness, where the stiffness

is constantly changing at different levels of displacement and hysteretic cycles. A straight line is

connected at the positive and negative extremities of the hysteresis loop, with its’ slope equal to

the operational stiffness of that particular response.

Dynamic pile response from full-scale field tests

135

Figure 5-48: Hysteresis loops for various snap-back tests on Pile 3 at Albany

Figure 5-49: Eccentric mass shaker hysteresis loops at high and low force levels on Pile 4 at Albany (M.Sa’don,

2012)

0.2 0.4 0.6 0.8 1 1.2

-8

-6

-4

-2

0

2

4

6

8

Displacement (mm)

Str

ain

gauge (

kN

)

60 kN snap-back 1

120 kN snap-back 1

90 kN snap-back 2

30 kN snap-back 2

Dynamic pile response from full-scale field tests

136

The hysteretic response of the snap-back has proved to be inconsistent, with the second 120 kN

snap-back test not providing a hysteresis loop as good as the first 120 kN snap-back test. It is

interesting to note that the second 120 kN snap-back has a slightly higher operational stiffness

than the first 120 kN snap-back. The ‘ratcheting’ nature of the snap-back hysteresis loops do

make it hard to define an operational stiffness for the pile-soil system, so there may be some error

in the selections in Figure 5-50.

Figure 5-50: Two 120 kN snap-back hysteresis loops with operational stiffness defined for each

5.4.2.1 Pile group interaction

The pile layout was selected at the Albany site to avoid interaction between the piles during

testing. A spacing of 3m between adjacent piles was chosen. It should be noted that whilst there

may be sufficient pile spacing, there are reference beams fixed to the ground between the piles

that hold the LVDTs in place on the various piles. Thus LVDT readings for the two piles not

participating in testing are only reading the displacement of the pile relative to the reference

beam. Hence with this analysis alone, it is not known whether interaction is significant or not. The

force readings from the load cell and strain gauge on Pile 3 (test pile) during the second 120 kN

pull-back and snap-back respectively are plotted against the displacement of each of the piles not

participating in testing (Piles 2 and 4), see Figure 5-51. The displacements of these piles are

0.2 0.4 0.6 0.8 1 1.2 1.4

-10

-8

-6

-4

-2

0

2

4

6

8

Displacement (mm)

Str

ain

gauge (

kN

)

120 kN snap-back 1

120 kN snap-back 2

Operational stiffness of snap-back 1

Operational stiffness of snap-back 2

Dynamic pile response from full-scale field tests

137

normalised with the maximum displacement of the test pile at the end of the pull-back, as it is the

relative displacement with the test pile that is important.

The horizontal axis values are multiplied by 10-3

, hence the computed displacements of the other

piles are small relative to that of Pile 3, the test pile. There is significant noise associated with the

responses of Piles 2 and 4. This is because the magnitudes of their displacements are very small.

Pile 2 is diagonally opposite the test pile, whereas Pile 4 is adjacent to the test pile. This results in

much greater displacements for Pile 2. This is because the direction of soil movement during the

pull and snap-back is perpendicular to Pile 4, but not Pile 2, being diagonally opposite. There is a

gradual increase in displacement of Piles 2 and 4 during the pull-back of the tests pile. During the

snap-back, there is a sharp increase in the displacement of Pile 2, during the initial rebound into

the tension-gapped side of the soil. There is little response from Pile 4 during the snap-back. The

maximum relative displacement of Pile 2 is approximately 10-2

, which is still small compared

with the displacement of the test pile. The reference beams need to be fixed further away from the

test pile to avoid interference with the displacement readings, if one wishes to draw conclusions

from these results alone.

Figure 5-51: Force on test pile during pull and snap-back versus displacement on Piles 2 and 4 not participating

in testing

-10 -8 -6 -4 -2 0 2 4

x 10-3

-60

-40

-20

0

20

40

60

80

100

120

140

Displacement/maximum test pile displacement

Forc

e o

n t

est

pile

(kN

)

Pile 2 pull-back

Pile 2 snap-back

Pile 4 pull-back

Pile 4 snap-back

Dynamic pile response from full-scale field tests

138

It was noted in 5.3.5 that there was a relative reference beam response of 7.5% compared with test

Pile 4, assumed to be negligible. Hence negligible pile interaction effects evident in Figure 5-51

holds true because the reference beam response does not significantly affect the readings

presented, given the similar reference beam layout for tests on Piles 3 and 4.

5.4.3 Pile 4 hysteretic response

The hysteresis responses for all first series snap-back tests on Pile 4 have been considered, along

with comparable load cell force pull-back tests. Low force 10 kN tests are shown in Figure 5-52

with a separate Figure 5-53 presenting a plot focusing on the hysteresis loops and the operational

stiffness of the soil. The low force level produces much cleaner hysteresis loops than the high

force level hysteresis loops presented for Pile 3, where the relative displacement of the low force

hysteresis loops are larger in comparison to the pull-back displacement, shown in Figure 5-52.

Similar effects were seen for the displacement-time response, which has been attributed to the

influence of impact effects on the response, which are more significant for the large pull-back

displacements/forces.

Figure 5-52: Snap-back hysteresis responses for low force level tests Pile 4

It can be seen in Figure 5-53 that all three low force 10 kN tests have approximately the same

operational stiffness, using the 324 kg pile head test as the operational stiffness model. This is not

-1 -0.5 0 0.5 1 1.5-8

-6

-4

-2

0

2

4

6

8

10

12

14

Displacement (mm)

Str

ain

gauge (

kN

)

324kg 10kN snap-back 1

324kg 10kN pull-back 1

609kg 10kN snap-back 1

609kg 10kN pull-back 1

1275kg 10kN snap-back 1

1275kg 10kN pull-back 1

Dynamic pile response from full-scale field tests

139

unexpected because there was no observed gapping during or after any of these tests. Consistent

with findings in the time domain, the hysteresis loop for the 609 kg pile head is the least clear on

this plot with relatively lower peak displacement reached during the hysteretic cycles.

Figure 5-53: Hysteresis loops with constant operational stiffness defined for each low force level test

High force 120 kN snap-back hysteresis responses are shown in Figure 5-54, with Figure 5-55

focusing on the hysteresis loops produced these tests and corresponding operational stiffness’.

Much smaller hysteresis loops are produced in Figure 5-54, relative to the size of the initial pull-

back force/displacement, in comparison with low force tests. The large cycles occurring before a

defined hysteresis loop is present could be the result of highly inelastic impact effects governing

the behaviour of the response. This is assumed to be the case because these large cycles were not

present during the low force 10 kN snap-back hysteretic response. The 609 kg mass level

hysteretic response has not produced clear hysteresis loops, so only an operational stiffness for the

other two mass levels were able to be defined (Figure 5-55). The hysteresis loops are not as clean

as the low force 10 kN ones, with a ‘racheting’ effect towards the presumably softer tension side,

due to the large gap developed during the pull-back loading to the target snap-back force.

The fact that hysteresis loops are produced in later cycles for both low and high force tests mean

that by definition all tests still contain a level of inelasticity during these low cycle displacements.

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6-8

-6

-4

-2

0

2

4

6

Displacement (mm)

Str

ain

gauge (

kN

)

324kg 10kN snap-back 1

609kg 10kN snap-back 1

1275kg 10kN snap-back 1

Operational stiffness

Dynamic pile response from full-scale field tests

140

Figure 5-54: Snap-back hysteresis responses for high force level tests Pile 4

Figure 5-55: Hysteresis loops with operational stiffness defined for first series high force level snap-back tests

-15 -10 -5 0 5 10 15 20 25 30 35 40-60

-40

-20

0

20

40

60

80

100

120

Displacement (mm)

Str

ain

gauge (

kN

)

324kg 120kN snap-back 1

324kg 120kN pull-back 1

609kg 120kN snap-back 1

609kg 120kN pull-back 1

1275kg 120kN snap-back 1

1275kg 120kN pull-back 1

0 0.5 1 1.5 2 2.5-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Displacement (mm)

Str

ain

gauge (

kN

)

324kg 120kN snap-back 1

609kg 120kN snap-back 1

1275kg 120kN snap-back 1

Operational stiffness

Dynamic pile response from full-scale field tests

141

The operational stiffness defined for the first and last series one 120 kN tests (Figure 5-55) show a

significant level of softening has occurred between the first series tests. These values are reported

in Table 5-5, with the initial stiffness during the pullback test for comparison. The operational

stiffness is presented in units of kN/mm and in non-dimensional form.

The initial stiffness and operational stiffness both decrease between tests (Table 5-5), with a large

difference between the stiffness of the two 120 kN snap-back tests shown. By scaling the

operational stiffness with the initial stiffness, the effect of the residual gaps present around Pile 4

are removed and only the new gap growth or yielding during the pull-back tests and snap-back

tests is considered. In Table 5-5, the normalised operational stiffness’ are much closer than the

corresponding dimensional values because the gap growth developed throughout testing is

removed from the normalised term. The 324 kg, 120 kN snap-back test has the lowest ratio

because it is the first 120 kN snap-back test carried out, where significant gap growth took place

because no gapping had been observed up to that point in testing.

Table 5-5: Operational stiffness in units of kN/mm and non-dimensionalised by the static (pull-back) initial

stiffness

Snap-back test Initial stiffness

(kN/mm)

Operational stiffness

(kN/mm)

Operational stiffness /

Initial stiffness

10kN_all 12.8 7.19 1.78

324kg_120kN_1 11.1 6.66 1.67

1275kg_120kN_1 6.54 3.73 1.75

5.5 SUMMARY

The dynamic lateral response of Piles 3 and 4 was measured from instrumented hammer free-

vibration tests and snap-back tests (considered separately as low and high force snap-back tests).

Comparisons were made between each in the time and frequency domain, and the force

displacement hysteretic response was also considered.

From the response in the frequency domain:

For Pile 3, there was an existing gap on the compression side of the pile, resulting in a

natural elastic frequency of 13.2 Hz for the pile-soil system, computed from free vibration

instrumented hammer tests. The pile-soil gap depth progressively grew during snap-back

testing, and the natural frequency decreased to 10.8 Hz by the end of testing.

Dynamic pile response from full-scale field tests

142

For Pile 4, a much greater range in natural frequencies was computed than those from Pile

3 testing. The natural elastic frequency from hammer tests varied from 19.1 Hz at the start

of testing, where no residual gapping between the pile shaft and soil was present and no

lead mass was added to the pile head (324 kg), to 6.99 Hz, following the second 120 kN

snap-back test with 50 lead masses added to the pile (1275 kg) and significant gapping

developed around Pile 4.

Snap-back tests were categorised as high force (60, 90, 120 kN) and low force (7.5, 10,

15, 30 kN) tests in the frequency domain, by taking the Fast Fourier Transform (FFT) of

the response. This was based on high force level tests containing elastic and inelastic peak

frequencies. From this analysis, elastic and inelastic responses were separated on

MATLAB for high force tests. This enabled damping data in the time damping data to be

attributed as elastic or inelastic.

The frequency between cycles for all dynamic tests (hammer, low force and high force

snap-back tests) was also assessed, and it was found that even a small amount inelasticity

is evident in all tests, shown through an increase in frequency as the pile-soil system

stiffens during subsequent cycles.

From the response of Pile 4 in the time domain:

The high force 120 kN snap-back tests’ inelastic and elastic components were separated

by looking at the response in the time domain, as opposed to separation on MATLAB.

Carrying this out over the time domain is suggested as filtering based on the response in

the frequency domain significantly alters the response in both domains.

Damping was calculated using the logarithmic decrement method and by fitting SDOF

exponential envelopes to the response to determine the ‘system damping’ of different

tests. The exponential envelopes were important as unsymmetrical pile response evident

in all three types of dynamic tests affected cycle to cycle damping calculated using the

logarithmic decrement method, but not the ‘system damping’ values computed.

Significant inelasticity was generally evident in the pull-back peak of the 10 kN snap-

back tests and low mass 120 kN snap-back tests, and the first three cycles of the two

higher mass level 120 kN snap-back tests (separation in the time domain). This required

that two different sets of envelopes were fitted for the elastic and inelastic responses, to

give the elastic and inelastic ‘system damping’.

Including the pull-back peak is beneficial as it contains inelastic impact effects which are

an important nature of snap-back testing. For the inclusion of the pull-back peak a clean,

unfiltered response is desirable.

Dynamic pile response from full-scale field tests

143

Elastic system damping, of around 5%, was often found to increase for decreasing mass

levels, and as testing progressed due to increased gap depths and a resulting reduction in

pile-soil stiffness. This agrees with the mathematical definition of damping ratio. There

were deviations for the two lower mass levels (324 and 609 kg), which was attributed to

the significant contribution of the distributed pile mass to the overall mass at the pile

head. Thus it is suggested that larger mass levels are predominately tested in future. This

corresponds to a maximum frequency of around 10 Hz.

The inelastic system damping for the high force 120 kN snap-back tests was found to

increase with increasing mass levels, due to highly inelastic impact effects that become

more prominent. A maximum system damping ratio of 50% was computed for the high

mass level (1275 kg); a result of large displacements and hence significant impact effects.

Note this damping is computed during the early cycles only and is not representative of

an elastic level of damping that should be associated with these pile-soil systems.

The relative accelerations between test pile and the reference beam ground fixities, which

support the LVDT’s, were found to be 7.45%. This is an upper bound on the possible

error introduced to LVDT readings, and is acceptable for the field testing undertaken.

This result was applied to pile group interaction tests during Pile 3 testing, and found that

no significant interaction between piles occurs during testing.

Geophone first peak signals were plotted versus distance from the test pile to assess the

level of elastic radiation damping from ground surface wave readings. Normalising the

signals by the response of the closest geophone allowed the relative damping to be

compared between tests of different force and mass levels. The earlier and lower force

tests were found to have the highest level of damping, and this was attributed to the

reduced gap depth providing a greater volume of soil to dissipate energy. Higher mass

levels were also found to provide more radiation damping.

From the hysteretic pile response:

For Pile 3, snap-back testing was found to produce poor hysteresis loops compared with

eccentric mass shaker tests carried out by M.Sa’don (2012); with the highest snap-back

forces of 120 kN providing a reasonable hysteretic response. The strain gauge in between

the ground surface and the load collar was calibrated to measure the applied force to the

system during the snap-back.

The snap-back responses were found to have a ‘ratcheting’ movement in the direction of

the snap-back release. This was attributed to the pile vibrating against the soil that was

imparted with large impact damage following the initial cycle of the snap-back release. It

is also possible that the clay on this side of the pile may have moved, and hence become

Dynamic pile response from full-scale field tests

144

less dense and softer, due to reducing lateral earth pressures in the soil as the pile moves

away during the pull-back test.

The hysteretic response for low force level snap-back tests were much cleaner than high

force snap-back tests due to significant impact effects for the latter. The relative

displacement of the hysteresis loops to pull-back displacement was also much greater for

low force level tests.

Hysteresis loops evident at low displacement cycles for low and high force tests mean

that there is some inelasticity occurring during the presumed elastic response.

Numerical modelling of lateral pile response

145

Chapter 6

Numerical modelling of lateral

pile response

6.1 OVERVIEW

This chapter documents the development of numerical pile models in Ruaumoko 3D to replicate

the following responses from full-scale field experiments carried out:

Hammer tests (natural period) – modal response

Pull-back phase of snap-back tests – pushover response

Snap-back and hammer tests – dynamic response

Additionally sensitivity analyses were carried out on the following, by varying key parameters:

Modal response

Pushover response

Gap predictions of pushover model

Numerical modelling of lateral pile response

146

Dynamic response

Ruaumoko is a structural analysis program developed by Carr (2004) capable of inelastic

response history analysis in two and three dimensions. Structures are inputted into the program as

data files, through text files written by the user. Single Piles 3 and 4 were modelled using a

Winkler Spring model (Vesic, 1961; Matlock, 1970; Reese and Welch, 1975; Matlock et al.,

1978; Gazetas and Dobry, 1984; Wotherspoon, 2009). A layout of the Winkler Spring model is

provided in Figure 6-1. Vertical beam elements are connected between a line of nodes along the

pile to represent the pile. Two dimensional horizontal springs and dashpots are connected to

nodes along the length of the pile to represent soil stiffness and damping. Mass was defined for

the modal and dynamic responses and added based on the tributary pile length at each node. An

extra node was included above the pile and defined with the pile head mass added to the pile

during testing. Note out of plane actions are restrained in the modelling approach.

Figure 6-1: (a) Field testing set-up; (b) Numerical Winkler Spring model representation

Detachable springs were used to model the zero tensile stress resistance provided by soil, and any

residual gapping around the pile before testing. The springs were also defined with a preforce to

represent horizontal earth pressures within the soil under zero lateral strain. For the dynamic

response, material specific damping was required so that elastic soil damping could be confined to

Numerical modelling of lateral pile response

147

the dampers and the structural damping of the pile/cantilever could be defined separately. The

level of loading was consistent with that carried out in the field, so no yielding of the pile was

expected; hence no hysteresis rule was defined.

The loading was applied using a shape function, which captured the pull-back phase for pushover

modelling. For the dynamic response, the snap-back was incorporated at the end of the pushover,

and the free vibration hammer response was also considered.

6.2 MODAL RESPONSE

The modal response was assessed using the natural period computed from the modal analysis

carried out by Ruaumoko. This was compared with the elastic natural period from the

instrumented hammer tests carried out in the field.

6.2.1 Model development in Ruaumoko 3D

As the natural period is of interest only the mass and elastic stiffness of the pile-soil system need

to be defined. The free-vibration model developed for the pile-soil system is shown in Figure 6-3.

The lead and steel bracket weights were lumped at nodes in the positions of their respective centre

of masses, and the steel pile weight was lumped at nodes along the pile, based on the tributary

length of each node. Beam elements were used to represent the pile, with the stiffness of the steel

tube piles used in testing. Spring members were used to represent soil stiffness and defined at a

spacing of 0.05 m, to the pile embedment depth (6.75 and 6.50 m respectively for Piles 3 and 4).

The stiffness of the springs was defined using the modulus of subgrade reaction from Vesic

(1961), from 2.2:

√

(2-1)

The Young’s modulus for the soil, Es, was calculated from the representative soil profile in Figure

3-14. Equation (2-1) was developed from the beam on elastic foundation case; where 1.3 is the

constant for total resistance and 0.65 is applied to springs on either side of the pile. Modification

factors have been applied to this equation in past studies (Carter (1984), Ling (1988) and Ashford

and Juirnarongrit (2003)) to acknowledge that there is soil contact on both sides of the pile, but

not all around the pile when subjected to lateral loading; and during which friction develops on

the sides of the pile. For the present study, no scaling has been applied for Pile 3; however, a

scaling factor of 0.5 was applied for Pile 4, resulting in a constant of 0.325.

Numerical modelling of lateral pile response

148

Multiplying the modulus of subgrade reaction by the tributary length of the spring, gives the

stiffness for that spring, K, in kN/m. Stiffness could be assigned for a model containing springs on

one side of the pile model, however, this model is going to be developed for loading in two

directions. Consequently the stiffness was computed based on a factor of 0.65 and assigned to

each of the springs either side of the pile.

Instrumented hammer tests discovered that the natural period increases following snap-back tests.

This is due to an observed gap forming between the soil and the pile during field testing, and the

depth that this gap extends below the ground surface. Residual gaps were accounted for in the

model by defining the springs with a slackness hysteresis. The slackness hysteresis has a bi-linear

force-deformation relationship, however, allows the user to define a displacement ‘gap’ in tension

and/or compression. This results in the member having zero stiffness in that direction until the

gap has been overcome, see Figure 6-2. This is typically used to model diagonal braced systems

where yield can cause members to stretch, leading to slackness in the bracing system. A

compression gap was applied to both springs at the ground surface and the magnitude (or width of

the gap) was tapered down linearly to the depth that accomplished a natural period that agreed

with corresponding hammer tests. A large gap was also defined on the tension side due to an

assumed zero tensile strength of soil. Note that the compressive spring gap (Gap +) used to

represent the residual pile-soil gap is actually defined in the negative direction in Ruaumoko. This

is due to the different sign convention adopted for this thesis (positive is compression for this

thesis; positive is tension in Ruaumoko).

Figure 6-2: Bi-linear slackness hysteresis used to represent residual soil gap (after Carr, 2004)

Numerical modelling of lateral pile response

149

The compression gap introduces a new effective ground level below the ground surface with

respect to the modal response as the springs between these two levels have zero stiffness. This

effect is displayed in the free-vibration model in Figure 6-3. The compression gap was also

accounted for by removing springs that were within the extent of the gap, this produced the same

results that were obtained using the slackness hysteresis rule.

Figure 6-3: Model representation for modal analysis

6.2.2 Model comparison with Pile 3 hammer tests (natural period)

Table 6-1 presents a comparison between the gap depths and resulting natural periods used in the

different modal analyses, with those obtained from gap monitoring and hammer tests at various

stages during testing on Pile 3 at Albany on 29/03/2012. Since extensive testing had already been

carried out on Pile 3 at the Albany site, there was already a residual gap before testing had been

carried out. Note that different gap depths were often employed either side of the pile in

modelling; a deeper gap was used on the side of the pile which is pulled towards the soil during

the pull-back. Following the release of the pile during testing, only measurements were obtained

for this side of the pile, referred to as the compression side of the pile.

To ensure the correct gap depths were used in each model, the model was developed for an

inelastic pushover analysis (next section). The gap was then altered until satisfactory agreement

Numerical modelling of lateral pile response

150

with the corresponding test pull-back was obtained. The modal response and pushover response

were both used to obtain the gap depths in Table 6-1. The modal analysis is carried out prior to

the pushover analysis, so the gaps used in the model and computed natural period corresponded to

the gap measurements and hammer tests carried out at the end of the previous pull-back.

Table 6-1: Comparison of measured gap depths and natural periods from field testing on Pile 3 at Albany site on

29/03/2012 with modal analyses on Ruaumoko

Stage of testing Measured gap

depth (m)

Gap depths used

in subsequent

model on each

side of pile (m)

Natural elastic

period from

hammer tests (s)

Fundamental

period from

subsequent modal

analysis (s)

Start of testing 0.58 0.55 both sides 0.0755 0.0802

Following 1st 7.5

kN pull-back

- 0.55 both sides 0.0822 0.0802

Following 1st 15

kN pull-back

- 0.60, 0.55 0.0830 0.0816

Following 1st 30

kN pull-back

- 0.60, 0.55 0.0808 0.0816

Following 1st 60

kN pull-back

- 0.60, 0.55 0.0800 0.0816

Following 1st 90

kN pull-back

- 0.60, 0.60 0.0854 0.0831

Following 1st 120

kN pull-back

0.65 0.80, 0.60 0.0830 0.0876

Following 2nd

120 kN pull-back

0.60 0.90, 0.65 0.0930 0.0914

Following 2nd

90

kN pull-back

- 0.90, 0.65 0.0911 0.0914

Following 2nd

60

kN pull-back

- 0.95, 0.65 0.0921 0.0920

Following 2nd

30

kN pull-back

- 1.00, 0.65 0.0900 0.0926

Following 2nd

15

kN pull-back

- 1.05, 0.65 0.0897 0.0931

Following 2nd

7.5

kN pull-back

0.67 1.05, 0.65* 0.0920 0.0931*

*These values are carried forward assuming no gap growth develops following the 2nd

7.5 kN pull-back

Numerical modelling of lateral pile response

151

The modal analysis results indicate that the mass and elastic stiffness (at small strain) properties

of Pile 3 at Albany have been captured in Ruaumoko; with an increasing period similar to those

computed from free-vibration hammer tests. The gap depths used in modelling grew to depths that

significantly exceed those measured during testing. The thin rod used to measure the gap in the

field for Pile 3 may not have been able to reach the bottom of the gap as the gap between the pile

and soil may have been narrower than the measuring device over this extra depth used in

Ruaumoko. The varying nature of the natural periods computed from the hammer tests was likely

due to deviations in the data acquisition and data analysis stages of testing. The general increasing

trend of these test results is still evident. Since they are similarly matched with Ruaumoko

predictions, a growing gap depth is verified as the reason for the increase in natural period

between subsequent tests.

A modal analysis was carried out with full spring-pile contact up to ground level, to determine the

natural period of Pile 3 if no gaps were present around the pile. This analysis produced a period of

0.0529 s, or a frequency of 18.9 Hz, and is reported in 5.2.1.

6.2.3 Model comparison with Pile 4 hammer tests (natural period)

Table 6-2 presents a comparison for Pile 4 between gap depths and corresponding natural periods

computed during testing and from modal analyses on Ruaumoko. Because of the changing pile

head mass during testing, hammer tests were carried out before the commencement of pull-back

tests, so natural periods presented are comparable to the modal analysis carried out at the start of

the pushover analysis. Gap measurements are taken at the end of each snap-back test, so the gap

measurement from the previous test corresponds to those used in modal analysis. As with Pile 3

analysis, the modal analysis and the pushover response were used to determine an appropriate gap

depth to utilise in the model, on each side of the pile.

There was no visible residual pile-soil gap around Pile 4 at the start of testing. Hence the first few

pull-back and hammer tests provided a good opportunity to determine an appropriate level of

elastic spring stiffness to use in the model. For Pile 4, a scaling factor 0.5 was applied to the

modulus of subgrade reaction defined by Vesic (1961), in (2-1), to capture the elastic period and

initial stiffness of the pull-back response. No scaling was required for the modulus of subgrade

reaction for Pile 3. This has been attributed to the usage of gap depths in the Pile 3 model to

soften the response, as well as the timing of testing. Pile 3 was conducted following the dry

season, and Pile 4 following the wet season; with heavy rain in the weeks leading up to testing.

In general, the modelling approach has produced similar gap depths and natural periods to testing,

with an increasing gap depth and natural period throughout both. More frequent gap depth

Numerical modelling of lateral pile response

152

measurements during Pile 4 testing, in comparison to those taken during Pile 3 testing, has

provided a more detailed comparison with gap depths implemented in the numerical model. Table

6-2 conveys that typically a greater gap on side one (compression side) and reduced gap on side

two (tension side) has been used in the model, with respect to measured values. A greater

compression gap has been utilised in the model because two different hammer tests were carried

out between the measured gap depths and the commencement of the pushover test. There was

some non-linearity previously associated with hammer tests in Figure 5-19, so this needed to be

accounted for to capture the pushover response. The hammer test corresponding to the modal

analysis is the second of the two tests, once the new mass level has been set-up on the pile head.

The differences in gap depth between numerical model and field testing could also be attributed to

the uncertainty in gap depth measurements carried out in the field.

Table 6-2: Comparison of measured gap depths and natural periods from field testing on Pile 4 at Albany site on

06/09/2012 with modal analyses on Ruaumoko

Stage of testing Measured gap

depth from end of

previous test (m)

Gap depths used in

model (m)

Natural elastic

period from

hammer tests (s)

Fundamental

period from

modal analysis

(s) Side 1 Side 2 Side 1 Side 2

10 kN pull-back,

324 kg 1

0 0 0 0 0.0523 0.0529

10 kN pull-back,

609 kg 1

0 0 0 0 0.0731 0.0725

10 kN pull-back,

1275 kg 1

0 0 0 0 0.110 0.110

120 kN pull-back,

324 kg 1

0 0 0 0 0.0540 0.0529

120 kN pull-back,

609 kg 1

0.48 0.53 0.50 0.40 0.0861 0.0962

120 kN pull-back,

1275 kg 1

0.61 0.76 0.70 0.40 0.131 0.150

120 kN pull-back,

1275 kg 2

0.71 0.71 0.80 0.40 0.140 0.152

120 kN pull-back,

609 kg 2

0.89 0.84 0.85 0.40 0.0978 0.102

120 kN pull-back,

324 kg 2

0.76 0.86 0.90 0.40 0.0731 0.0757

Numerical modelling of lateral pile response

153

Initial modal analysis results indicated an overestimated natural period in comparison to hammer

tests. It is noted in 6.5.1 that the pushover model is insensitive to tension gap changes to the

model. A reduced tension gap was thus implemented to gain periods more comparable to hammer

tests. Some of the computed periods were still slightly greater than those found during testing.

Pile 3 testing involved carrying out hammer tests in four different directions on the pile; from

analysis in 5.2.1, it was concluded that the soil contact on the sides of the pile have a significant

effect on the computed natural periods. The side contact is not captured for the numerical analysis

in this study because pairs of springs at different depths were used to model soil contact with the

pile, capturing effects in the principal direction only. Thus a reduced tension gap was used to

model this side contact effect. No tension gap measurements were obtained during Pile 3 testing

so it was not known if any tension gap adjustments were made. From the pushover analysis

results, it can be assumed that the side contact does not have an effect on the pull-back response

during testing.

6.3 PUSHOVER RESPONSE

The models presented in the modal analysis section are developed for soil inelasticity so that they

could be subjected to a pushover analysis in Ruaumoko, and compared to full scale pull-back

tests.

6.3.1 Model development in Ruaumoko 3D

The pushover analysis was applied using a shape function defined in the model data file. A

linearly increasing force was applied at a rate of 12 kN per second, reaching a maximum value of

120 kN in ten seconds. This was the largest pull-back force applied during field testing. Once the

target force had been reached it was maintained for two seconds, before unloading at the same

rate to zero force. This load was applied to the node that was defined in the position of the load

collar, used to apply the pull-back force during field testing. This was done so that the pushover

response predicted by Ruaumoko was comparable to test data from the pull-back phases of the

snap-back tests. Displacement was also plotted at the position of the LVDTs utilised during

testing for this reason.

To incorporate the effects of initial stress in the soil, each soil spring was prestressed to account

for horizontal soil stresses created by the soil overburden pressure (Wotherspoon, 2009). The

compressive force, Fpre applied to each spring was calculated using:

(6-1)

Numerical modelling of lateral pile response

154

where γs is the unit weight of the soil, z is the depth from the ground surface to the tributary centre

of the spring, Lt is the tributary length of pile for the spring and K0 is the coefficient of earth

pressure at zero lateral strain, or ‘at rest’, assumed to be 1.0.

To replicate the pull-back pile response from field testing non-linear soil deformation is

accounted for in the pushover model. Geometric non-linearity has already been accounted for in

the slackness hysteresis model used in the modal analysis, refer to Figure 6-2. The residual gap

present around the pile is replicated with a gap in compression defined for the corresponding

spring; and the inability of soil to provide any tensile resistance is modelled by defining a large

gap of 1.0 m in tension for all springs, that would not be recovered by the deflecting pile. Once

the preforce was reduced to zero in the springs behind the test pile, the tensile gap would engage

and prevent any resistance from the springs, reducing their stiffness to zero.

P-y curves for static loading were developed from CPT data (M.Sa’don, 2012) and procedures by

Reese and Welch (1975) for stiff clay with no free water to model the non-linear load deformation

response of the springs. The pushover model to represent both Piles 3 and 4 was defined based on

the following curves for stiff clays:

(

)

(6-2)

(6-3)

{(

) } (6-4)

where p is the applied load in kN/m, y is the displacement in mm, pult is the maximum applied

load, y50 is the displacement at 50% of pult, D is the pile diameter, z is the depth at which the p-y

curves are being developed, γs is the average unit weight to z and su is the average undrained shear

strength to depth z. The strain at 50% of pult, ε50, was determined using recommendations from

Reese and Van Impe (2001) for stiff clays with no free water. The average undrained shear

strength was determined from CPT testing carried out by M.Sa’don (2012) at the Albany site.

These values were used to develop p-y curves at different depths; the p-y curves used for Pile 3 is

shown in Figure 6-4.

The load deformation response of the springs used in the pushover analysis, illustrated in Figure

6-5, is based on the initial stiffness, K, the yield force of the spring, Fy, and the bi-linear post yield

stiffness factor, r.

Numerical modelling of lateral pile response

155

Figure 6-4: P-y curves at representative depths developed from CPT data for the Albany Pile 3 model in stiff

clay

Figure 6-5: Non-linear hysteresis rule used for soil springs in pushover model

0 0.05 0.1 0.15 0.2 0.250

50

100

150

200

250

300

350

400

450

y (m)

p (

kN

/m)

-0.5 m

-1.5 m

- 3.0 m

-6.0 m

- 7.0 m

Numerical modelling of lateral pile response

156

The springs were defined with an initial stiffness corresponding to that determined in the modal

analysis section. Fy and r were determined for the five springs corresponding to the depths of their

respective p-y curves by modelling the load deformation response defined by the p-y curves, with

a bi-linear approximation, see Figure 6-5. Fy and r were calculated for the other springs in the

Ruaumoko model by using linear interpolation. The preforce at each spring is then added to the

yield force from the p-y analysis, to determine the yield force inputted into Ruaumoko, Fy. Note

that the change in tributary length between springs was accounted for in the linear interpolation

equations; the change in yield force is proportional to the change of tributary length, and the bi-

linear factor is independent of tributary length. The expected displacement range of the springs

was determined from the predicted ground displacement at the bottom of the gap using the Elastic

Continuum Model (ECM) by Davies and Budhu (1986). In this model the elastic response was

factored down to account for non-linear soil response. The expected ground displacement, and

hence the p-y response, is a function of the level of pull-back load, so adjustments were made for

each new pull-back test force level.

6.3.2 Model comparison with Pile 3 pull-back tests

The Pile 3 pushover model was developed with no scaling to the modulus of subgrade reaction (2-

1) and matched to corresponding pull-back tests under a non-linear static loading analysis in

Ruaumoko (pushover analysis), by altering the gap depth either side of the pile. The model gap

depths displayed in Table 6-1 are representative of the conditions following the previous pull-

back test. The model is also unloaded so soil conditions can be compared with conditions after the

pull-back is released during testing. There were 12 pull-back tests carried out on the 29/03/2012 at

Albany, these tests and corresponding models are displayed in Figures 6-6 to 6-9. In general, the

Ruaumoko pushover models provide a reasonable fit to pull-back test data.

Figure 6-6 and 6-7 contain the series one pushover models, for the low force and high force levels

respectively. The response from field pull-back tests is captured quite closely in Ruaumoko for

these tests. The elastic natural period of each model has been matched to hammer tests, so as

expected the initial stiffness has been correctly captured, in comparison to the test data. The

greatest level of non-linearity is developed during the early stages of loading, which can be seen

more significantly on the low force plot in Figure 6-6. The combination of springs detaching due

to zero tensile resistance defined through the tension gap and compression springs yielding cause

this initial stiffness to degrade during the early stages of loading. Generally, the level of preforce

(which controls gapping for tension springs) and the yield and post-yield stiffness defined in the

bi-linear force-displacement approximation for compression springs, are able to model this early

non-linear response.

Numerical modelling of lateral pile response

157

Figure 6-6: Ruaumoko pushover modelling for 7.5, 15 and 30 kN series one pull-back tests Pile 3

Figure 6-7: Ruaumoko pushover modelling for 60, 90 and 120 kN series one pull-back tests Pile 3

0 1 2 3 4 5 6 70

5

10

15

20

25

30

35

Displacement (mm)

Forc

e (

kN

)

30kN pull-back 1

30kN Ruaumoko model

15kN pull-back 1

15kN Ruaumoko model

7.5kN pull-back 1

7.5kN Ruaumoko model

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Displacement (mm)

Forc

e (

kN

)

120kN pull-back 1

120kN Ruaumoko model

90kN pull-back 1

90kN Ruaumoko model

60kN pull-back 1

60kN Ruaumoko model

Numerical modelling of lateral pile response

158

Figures 6-8 and 6-9 present the series two pushover tests carried out on Pile 3. The series two

tests contain a larger gap depth compared with field test measurements (Table 6-1). This

difference is more pronounced than the first series comparison with test data. This coincides with

the models appearing to deviate more significantly from test data, particularly during the later

stages of loading. At later stages of loading, the pile displacement has caused more springs to

yield and detach at depth (depending on whether the springs are in compression or tension

respectively), and the residual gap on the compression side of the pile (soil loaded in compression

during the pull-back) has closed, and often yielded as well. The springs near the bottom of the

residual gap have also undergone significant post-yield displacement. These factors tend to

highlight any deviance of the model or its approximations from the behaviour in the field,

resulting in these more significant deviations at later stages of loading in Figures 6-8 and 6-9.

This effect is seen most significantly in the force-displacement predictions for the second 120 and

90 kN pushover models, which have deeper gaps in combination with high levels of force,

resulting in excessive ground displacements.

The largely linear pile-soil behaviour seen during the pull-back tests at larger load levels was also,

for the most part, predicted by Ruaumoko. Springs at a large enough depth on each side of the

pile have either yielded, or detached, such that the softer springs that have yielded, and the

cantilever portion of the pile with a constant stiffness, primarily deform as the pile is loaded

further. Thus, the relative pile-soil stiffness has been captured. This cantilever deformation results

in further displacement at the top of the pile but not to the depth of the springs that haven’t

yielded or detached on the compression or tension sides of the pile, respectively. The recorded

displacement is actually a combination of post-yield compressive spring, detached zero stiffness

tensile spring and pile deformation. All of which have a constant stiffness. Although the post-

yield stiffness of the soil during field testing may not be exactly linear it is likely somewhat close

to this, suggested by the p-y curves in Figure 6-4, hence the overall pile-soil response is similarly

linear at larger load levels. The soil contribution to the linear behaviour of the pile was not noted

in Chapter 4, where static field test results are presented and discussed. As noted earlier in the

Chapter 4, the nature of the manual load application during testing has caused some

discontinuities in the test pull-back response. Significant deviations were removed by creating a

back-bone curve for this data in MATLAB (Mathworks, 2012), to provide realistic comparisons

with the models developed in Ruaumoko.

Numerical modelling of lateral pile response

159

Figure 6-8: Ruaumoko pushover modelling for 60, 90 and 120 kN series two pull-back tests Pile 3

Figure 6-9: Ruaumoko pushover modelling for 7.5, 15 and 30 kN series two pull-back tests Pile 3

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Displacement (mm)

Forc

e (

kN

)

120kN pull-back 2

120kN Ruaumoko model

90kN pull-back 2

90kN Ruaumoko model

60kN pull-back 2

60kN Ruaumoko model

0 2 4 6 8 10 120

5

10

15

20

25

30

35

Displacement (mm)

Forc

e (

kN

)

30kN pull-back 2

30kN Ruaumoko model

15kN pull-back 2

15kN Ruaumoko model

7.5kN pull-back 2

7.5kN Ruaumoko model

Numerical modelling of lateral pile response

160

During the unloading stage of these pushover models in Ruaumoko, the bi-linear springs unload

with an unload stiffness equal to their original stiffness. Due to post-yield deformations, this may

result in the force reducing to zero in the compression springs before the pile has been unloaded

to its residual position. When this occurs, the spring detaches due to the large tension gap defined

in the bi-linear spring properties table. This situation is illustrated in Figure 6-10. The result, after

unloading, is that the residual gap on the pile has increased to a greater depth. Due to post-yield

deformations the pile’s residual position is in the direction of the pull-back force application. This

produces less tension spring reattachment during the unload of the pile. Hence a deeper gap is

also developed on the tension side, also shown in Figure 6-10.

Figure 6-10: Graphical illustration of spring element behaviour in Ruaumoko

Note the sign convention used in Figure 6-10; the compression force is taken as positive, and

displacement is based on the local co-ordinates of the spring, where spring compression is taken

to be positive displacement. The gradual unloading of the pile is an approximation to what

actually occurs in the field, where the pile is released suddenly and a snap-back test carried out.

The Ruaumoko pushover model is not capable of being subject to a dynamic analysis so the

unload phase, and gapping behaviour, are not exactly comparable to field testing. A snap-back

test would cause repeated yielding in both directions, which one would assume corresponds to

greater gap growth, that is not captured during a static unload. The residual gaps predicted by the

Ruaumoko models are summarised in Table 6-3.

The gap predictions made by Ruaumoko after unload on the far-right column in Table 6-3 are in

excess of the gaps actually used for each Ruaumoko pushover analysis, and the measurements

taken during field testing. Gap predictions reach an order of 2 -3 times greater than the gaps

implemented by the pushover models on both sides of the pile.

Numerical modelling of lateral pile response

161

Table 6-3: Gap predictions by Ruaumoko in comparison with measured gap depths from field testing of Pile 3 at

Albany site on 29/03/2012, and gaps implemented in Ruaumoko

Stage of testing Measured gap depth

on side one

(compression) (m)

Gap depths used in

subsequent model on

each side of pile (m)

Gap depths after

unload in Ruaumoko

on each side of pile

(m)

Start of testing 0.58 0.55 both sides -

Following 1st 7.5 kN

pull-back

- 0.55 both sides 0.65, 0.55

Following 1st 15 kN

pull-back

- 0.60, 0.55 1.05, 0.6

Following 1st 30 kN

pull-back

- 0.60, 0.55 1.35, 0.8

Following 1st 60 kN

pull-back

- 0.60, 0.55 1.8, 1.15

Following 1st 90 kN

pull-back

- 0.60, 0.60 2.1, 1.4

Following 1st 120 kN

pull-back

0.65 0.80, 0.60 2.3, 1.65

Following 2nd

120 kN

pull-back

0.60 0.90, 0.65 2.35, 1.3

Following 2nd

90 kN

pull-back

- 0.90, 0.65 2.2, 1.05

Following 2nd

60 kN

pull-back

- 0.95, 0.65 1.95, 0.9

Following 2nd

30 kN

pull-back

- 1.00, 0.65 1.65, 0.7

Following 2nd

15 kN

pull-back

- 1.05, 0.65 1.4, 0.65

Following 2nd

7.5 kN

pull-back

0.67 1.05, 0.65* 1.05, 0.65

*These values are carried forward assuming no gap growth develops following the 2nd

7.5 kN pull-back

It is unlikely that a dynamic release (which is not carried out) would reduce the magnitude of

these gap predictions; an increase in gap predictions would be expected. Wotherspoon (2009)

carried out successful gap modelling using Ruaumoko to model cyclic quasi-static lateral loading

performed at Iowa State University (ISU). The level of preforce directly controls the gapping

Numerical modelling of lateral pile response

162

behaviour of the soil in tension, and hence indirectly controls the gapping behaviour of the soil in

compression. Therefore an increase in preforce would affect the displacement at which the tension

springs would detach; altering the overall response of the pile. Thus the gap depth predictions

could not be changed without affecting the pushover model predictions shown earlier in Figures

6-6 to 6-9. For these reasons the gap depth predictions were not investigated further until 6.5.1,

where a sensitivity analysis was carried out on the pushover model.

Gap depth measurements taken during testing were within zones of saturated clay. This clay was

cohesive and made measurements difficult. It is possible that:

1) Cohesion from the saturated clay prevented large gap growth, as predicted during

pushover modelling, from occurring during field testing. This cohesion, not accounted

for in the numerical model, could have maintained pile-soil contact at greater depths.

2) Alternatively, the gap growth suggested by the Ruaumoko pushover responses in Table

6-3 was actually experienced during testing. The saturated clay may have recovered these

large gap depths before the next pull-back test was carried out.

For the former, utilising bi-linear springs without any slackness (gapping capabilities) from a

certain depth could be used to account for a lack of gap growth beyond about one metre. Given

that the stiffness was captured well during modelling, it is more likely that 2) is the reason and

these large gap depths were in fact developed during full-scale testing.

6.3.3 Model comparison with Pile 4 pull-back tests

The full pile-soil contact during the first five pull-back tests was utilised in pushover modelling to

determine an appropriate scaling factor for the modulus of subgrade reaction of Pile 4, and

applied in later pushover models where significant gap growth had occurred during testing. As

mentioned in 6.2.3, a factor of 0.5 was used which differed to the factor of 1.0 used for Pile 3.

This was attributed to testing after the wet season, and that a pull-back test with no residual

gapping was not available for Pile 3 modelling. The 10 kN pushover models, all with no gapping

either side of the pile, are compared with pull-back tests in Figures 6-11 and 6-12. Note that two

10 kN pull-back tests were carried out for the 1275 kg pile head mass because of disruption to

instrumentation during the first 10 kN snap-back attempt for this mass level; additional gap

measurements or hammer tests were not carried out.

Although no gap growth was observed during testing some residual soil deformation must have

been present in these tests due to a faster reduction in the initial stiffness between tests; this is

most notable between the first and last three tests. The base model is used to model the first pull-

back test (324 kg pile head) in Figure 6-11, with the other 10 kN tests presented for comparative

Numerical modelling of lateral pile response

163

purposes. Some non-linearity due to spring yield is evident during later loading stages, although

not quite as significant as that exhibited by the corresponding 324 kg pull-back test. This effect

may also be exaggerated as the loading rate is reduced towards the end of the test. The

undesirable model behaviour during later stages of loading is due to the upper springs only just

reaching yield in the analysis, this effect could be reduced by adopting a smaller time step in the

analysis.

The base model was modified to provide a better response that captures the last three tests, in

Figure 6-12. The yield force specified in the top p-y curve (0.5 m depth) was reduced in order to

achieve a faster reduction in stiffness, which was evident during the last three pull-back tests. This

reduction in yield force could be accounting for some residual force present in the clay near

ground surface at commencement of the later pull-back tests. Figure 5-20 showed the 10 kN 324

kg snap-back test has a line of symmetry in the pull-back direction. This could have resulted in

initial deformations at the start of subsequent pull-back tests. Again, there is a slight delay in the

yield of this model, which could be a result of the 0.025 m tributary spring spacing adopted in the

model at the ground surface. Because there is no soil gap, the soil behaviour governs these early

responses, as opposed to the linear cantilever pile deformations controlling the response during

later tests when there is a large gap depth present around the pile.

Figure 6-11: Ruaumoko pushover modelling for the first 10 kN pull-back test on Pile 4

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

2

4

6

8

10

12

14

Displacement (mm)

Forc

e (

kN

)

324kg 10kN pull-back 1

324 kg Ruaumoko model

609kg 10kN pull-back 1

1275kg 10kN pull-back 1

1275kg 10kN pull-back 2

Numerical modelling of lateral pile response

164

Figure 6-12: Ruaumoko pushover modelling for the last three 10kN pull-back tests on Pile 4

Figures 6-13 and 6-14 display Pile 4 pushover models and corresponding high force level 120 kN

pull-back tests. The series one test modelling in Figure 6-13 requires the greatest range of

stiffness to be captured. The 324 kg 120 kN pull-back test one model contained no residual gaps.

Whereas the 1275 kg 120 kN pull-back test one model contained residual gaps of 0.8 and 0.4 m

on each side of Pile 4, developed as a result of the previous two pushovers. The initial loading

stages are captured well, however there is some deviation at larger loading stages as deeper soil

springs are active in the model.

The series two pull-back tests and models in Figure 6-14 are almost parallel, with only a small

increase in residual gap depths inputted into each. The models have been offset from each other

so that individual comparisons can be made on the same plot. The predominately linear response

indicates a reduced range of stiffness and hence non-linearity (developed) during the tests.

Looking at the pull-back tests, a small amount of non-linearity at the start of the test, presumably

tensile detachment, and a slight stiffening of the response at later loading stages need to be

captured in each model. The 1275 kg 120 kN pull-back test two pushover model exhibits a much

sharper localised increase in stiffness mid-way through the pushover analysis. This is a result of

the residual gap closing on the compression side of the pile (soil loaded in compression during the

pull-back test), before this soil/spring reaches yield and the system stiffness reduces again.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

2

4

6

8

10

12

14

Displacement (mm)

Forc

e (

kN

)

324kg 10kN pull-back 1

609kg 10kN pull-back 1

1275kg 10kN pull-back 1

1275kg 10kN pull-back 2

609/1275kg Ruaumoko model

Numerical modelling of lateral pile response

165

Similar pile-soil gaps were used between testing and the model, so it is assumed that repetitive

pull-back and snap-back tests carried out without a significant change in the pile-soil gap has

resulted in some residual deformation within this gap; that causes a softer response when this gap

is closed during pull-back tests. The disagreement between test and model was more significant

for the last two pull-back tests (609 and 324 kg) as the compression gap closes. To account for

this, a reduced yield force was defined for the top p-y curve (0.5 m depth) in these two pushover

models. This was a necessary adjustment as residual compression gaps were previously the only

means to account for previous pull-back/snap-back tests carried out prior to the current pushover

model. From Figure 6-14, a much more satisfactory comparison is evident for the last two models

when this adjustment is made.

Figure 6-13: Ruaumoko pushover modelling for the first series of 120 kN pull-back tests on Pile 4

0 5 10 15 20 25 30 35 400

20

40

60

80

100

120

Displacement (mm)

Forc

e (

kN

)

324kg 120kN pull-back 1

324kg Ruaumoko model

609kg 120kN pull-back 1

609kg Ruaumoko model

1275kg 120kN pull-back 1

1275kg Ruaumoko model

Numerical modelling of lateral pile response

166

Figure 6-14: Ruaumoko pushover modelling for the second series of pull-back tests on Pile 4; note manual offset

introduced between each

Table 6-4 summarises geometric non-linear soil behaviour, through pile-soil gap widths and gap

depths, for each pull-back test carried out on Pile 4, and the corresponding pushover model. Refer

to 6.2.3 for discussions regarding gap depth comparisons between test and model. In addition to

the compression gap depth (side one), the width of the compression gap is the other key variable

in Table 6-4 that governs the pushover behaviour. Generally, a larger compression gap was

necessary to capture the test data response in the numerical models for Pile 4. This has been

justified because two sets of hammer tests were carried out on Pile 4, due to a changing pile head

mass, from when gap measurements were taken. Residual pile movement during hammer tests

was previously noted in Figure 5-19, and these were carried out in the opposite direction to the

pull-back force application, resulting in movement that increases the width of the compression

gap. Note that this adjustment was not necessary (although still implemented) for the last two

pull-back tests where the model was desensitised to the width of the compression gap by reducing

the spring yield force defined by the p-y curve at a depth of 0.5 m. Hence this adjustment was

more necessary for earlier tests as the gap was still developing around the pile. For Pile 3 testing,

the residual gap present at the start of testing meant the residual compression gap width showed

little change and was not summarised in the corresponding analysis in Table 6-3.

0 5 10 15 20 25 30 35 40 45 500

20

40

60

80

100

120

Displacement (mm)

Forc

e (

kN

)

1275kg 120kN pull-back 2

1275kg Ruaumoko model

609kg 120kN pull-back 2

609kg Ruaumoko model

324kg 120kN pull-back 2

324kg Ruaumoko model

Numerical modelling of lateral pile response

167

Table 6-4: Gap predictions by Ruaumoko in comparison with gap measurements from field testing of Pile 4 at

Albany site on 06/09/2012, and gaps implemented in Ruaumoko

Stage of testing Measured

gap depth

from end of

previous test

(m)

Gap depths

used in

model (m)

Measured

gap width

from end of

previous test

(mm)

Gap widths

used in

model (mm)

Gap depths

after unload

in Ruaumoko

(m)

Side

1

Side

2

Side

1

Side

2

Side

1

Side

2

Side

1

Side

2

Side

1

Side

2

10 kN pull-

back, 324 kg 1

0 0 0 0 0 0 0 0 0.30 0.10

10 kN pull-

back, 609 kg 1

0 0 0 0 0 0 0 0 0.50 0.30

10 kN pull-

back, 1275 kg 1

0 0 0 0 0 0 0 0 0.50 0.30

120 kN pull-

back, 324 kg 1

0 0 0 0 0 0 0 0 1.55 0.90

120 kN pull-

back, 609 kg 1

0.48 0.53 0.50 0.40 10 2 15 2 1.75 1.00

120 kN pull-

back, 1275 kg 1

0.61 0.76 0.70 0.40 10 10 18 10 1.90 1.00

120 kN pull-

back, 1275 kg 2

0.71 0.71 0.80 0.40 15 10 20 10 1.80 0.60

120 kN pull-

back, 609 kg 2

0.89 0.84 0.85 0.40 15 10 20 10 1.80 0.60

120 kN pull-

back, 324 kg 2

0.76 0.86 0.90 0.40 15 12 20 12 1.80 0.55

As concluded with Pile 3 modelling, gap depths predicted by Ruaumoko after the static unload

overestimated those measured during testing, and used in the subsequent model. Gap depths were

also predicted after the 10 kN pushover models, even though none were noted during testing. It is

possible that a low level of gapping did temporarily develop during 10 kN force tests that was not

noticed during testing. For this case, it is also possible the reduced yield force necessary to

capture the 609 and 1275 kg pull-back responses has resulted in greater gap predictions than those

used in the subsequent model. There is a notable reduction in the gap depth predictions for the

series two 120 kN pushover tests. There was a reduced displacement range used for the p-y curves

Numerical modelling of lateral pile response

168

for these tests because a greater gap depth resulted in a larger proportion of the displacement due

to the pile as opposed to the soil. This has resulted in less soil deformation and hence reduced

gapping during these analyses.

6.4 DYNAMIC RESPONSE

The main extension required to develop a static model, previously defined with mass during the

modal response, for a dynamic analysis is the consideration of damping. Material specific

damping was defined in the model data files so that soil damping could be modelled separately to

the Rayleigh damping used for pile elements. Note that the 2006 Ruaumoko version was utilised

in this section as it offers greater dynamic stability, compared with the 2010 version used

previously.

Damping exists in all structures, and occurs as a result of energy dissipation occurring through

different mechanisms. In most structures damping can be characterised by damping in the elastic

range and damping in the inelastic range. Viscous damping is used to represent energy dissipation

in the elastic range, whilst hysteretic damping is used to represent energy dissipation in the

inelastic range. Equivalent viscous damping can be used to incorporate both forms of damping,

and is often assumed to be 5% by structural engineers. Hysteretic damping is the dissipated

energy represented by the area inside the hysteresis loop (Chopra, 2006).

For soil layers, damping is represented through radiation damping, where energy is radiated away

from the foundation elastically through shear and compression waves, and material damping

where damping is dissipated through the hysteretic action of the soil.

For this study, elastic viscous damping is represented using Rayleigh proportional damping for

pile elements. Elastic radiation damping is represented using linear horizontal dashpots along the

length of the pile, on both sides, in a two dimensional analysis. Hysteretic damping was defined

using hysteresis models in Ruaumoko. Because pile yielding did not occur during testing, no

hysteresis model was defined for pile elements. The bi-linear spring model with slackness, shown

earlier in Figures 6-2 and 6-5, is the hysteresis rule that accounts for material damping.

6.4.1 Rayleigh damping

Rayleigh, or proportional, damping is the most common method of representing damping in a

structure (Carr, 2004). The damping matrix, c, is assumed to be proportional to the mass and

stiffness matrices, m and K, which are already available in the analysis:

(6-5)

Numerical modelling of lateral pile response

169

where α and β are chosen to give the desired fractions of critical damping at two specified natural

frequencies. There is also a choice as to whether the initial or tangent stiffness matrix is used.

Non-linear behaviour of structural elements is not expected for this study so the initial stiffness

matrix is used. The tangent, secant and elastic damping matrices are identical for this case (Carr,

2004). The fraction of critical damping in mode n, ζn, with natural circular frequency ωn is given

by:

(

) (6-6)

Rayleigh damping has specified fractions of critical damping at two frequencies and the variation

at other frequencies is shown in Figure 6-15.

Figure 6-15: Fraction of critical damping relationship with natural frequency for Rayleigh (proportional)

damping (after Carr, 2004)

As a pile with lumped mass is tested/modelled for this study, higher modes of free vibration are

not expected to be significant, thus the selection of α and β are not particularly critical. A fraction

of critical damping (or damping ratio) of 2% was assumed for the first two circular natural

frequency modes. α was then applied to the entire model as a change in mass is not expected, and

then β was applied to the pile elements by specifying material specific damping in the analysis,

Numerical modelling of lateral pile response

170

allowing separate soil damping consideration. Equation (6-6) was re-calculated for each pile-soil

model, including different gap depths, as the modal properties change.

6.4.2 Soil damping

Material specific damping enables zero Rayleigh damping to be specified for soil elements.

Therefore soil damping can be modelled separately as linear elastic radiation damping and

hysteretic material damping. The bi-linear hysteresis rule used to define the load-deformation

behaviour of the springs is used to model material damping. Linear dashpots are coupled with soil

springs along the length of the pile model to account for radiation damping. The two soil element

configurations considered, shown in Figure 6-16, were those utilised by Wotherspoon (2009). The

first configuration is termed parallel radiation damping by Wang et al. (1998); where a single

spring and dashpot element are parallel to each other (Kagawa, 1980). The second configuration

is defined as series radiation damping (Novak and Sheta, 1980; Nogami et al., 1992). Wang et al.

(1998) used this term to describe a non-linear hysteretic element in series with a linear visco-

elastic element. The soil is separated into an inelastic zone close to the pile where non-linear pile-

soil interaction occurs and an elastic zone further away from the pile where soil behaviour is

linear elastic. Unlike the parallel damping model, forces radiating away from the pile must first

travel through the hysteretic zone of the series damping model. By utilising spring and dashpot

elements on Ruaumoko, the near field behaviour is modelled using an inelastic bi-linear spring

and the far field is modelled by an elastic spring and linear dashpot element. The overall stiffness

behaviour is kept the same as the parallel damping model.

Figure 6-16: Two soil element configurations to incorporate soil damping, (a) parallel radiation damping model;

(b) series radiation damping model (after Wotherspoon, 2009)

Numerical modelling of lateral pile response

171

Although overall stiffness behaviour is the same, the different configurations result in different

responses. In the elastic range the responses are identical but as the forces enter the inelastic

range, responses diverge due to the different damper configurations. Parallel radiation damping is

likely to produce the stiffer system because forces can bypass the hysteretic system, consumed as

a function of the damper velocity, resulting in less spring deformation. Because of this significant

drawback, the series radiation damping model was selected to represent the soil elements under

dynamic analyses. The parallel spring-dashpot configuration shown in Figure 6-1 was replaced

with the series configuration in Figure 6-16 (b). The near field behaviour was modelled using an

inelastic bi-linear spring and the far field was modelled using an elastic spring and linear dashpot

element. The inner spring accounts for soil detachment and non-linear behaviour in compression.

The elastic stiffness of the inner spring is much larger than the outer spring so that the outer

spring defines the elastic response of the entire soil element. At low force levels the relative

stiffness of the two springs result in deformation predominately in the outer spring, at higher force

levels the inner spring yields, softening, and hence controlling the non-linear response. When the

force reduces to zero in the inner spring, no force is transferred to the outer spring or damper,

ensuring the soil element only affects the response when in contact with the adjacent pile element.

6.4.2.1 Dashpot coefficient

The linear dashpot coefficient used to represent radiation damping in the dynamic model was

based on elastic theoretical solutions by Gazetas and Dobry (1984) for a horizontally vibrating

pile, shown in Figure 2-4. Compression waves are assumed to develop in two quarter planes in

the direction of pile shaking, and shear waves are assumed to act perpendicular to pile motion.

The damping coefficient is dependent on the characteristic angular frequency, ω, and expressed in

dimensionless form:

(6-7)

Shear wave velocity, Vs, and Lysmer’s wave velocity (instead of compression wave velocity), VLa,

are given by:

√

(6-8)

(6-9)

where ρs is the soil density, νs is the soil Poisson’s ratio, Gs is the soil shear modulus, and D is the

pile diameter.

Numerical modelling of lateral pile response

172

The total horizontal radiation damping coefficient, cH, at each dashpot depth is calculated by:

[ (

)

] (

)

(6-10)

where Lt is the tributary length of pile for each dashpot; this value was halved and applied to

dashpots on each side of the pile. At shallow depths, Gazetas and Dobry indicate that this

expression over-estimates the damping coefficient due to the presence of the ground surface. In

this case surface waves will develop which propagate at velocities close to Vs; consequently this

velocity is used for all quarter planes in this model. For depths less than 2.5D, the radiation

damping coefficient is defined by:

(

)

(6-11)

Equations (6-10) and (6-11) have been altered for pile diameter instead of pile radius, consistent

with notation used by Wotherspoon (2009).

6.4.2.2 Relative stiffness used for series springs

Wotherspoon (2009) found that the use of a series spring layout was the source of two possible

problems in the dynamic model:

If the relative stiffness of the inner spring is too large, convergence problems can develop

in the model, making it more computationally expensive

If the relative stiffness of the inner spring is too small, there will be a significant

difference in velocity at each end of the spring

Because of these factors, trade off was required between the stability and accuracy of the series

damping model. The inner spring stiffness needed to be sufficiently large enough so that the

velocity at the pile node was approximately the same as the velocity in the damper, in parallel

with the outer spring. If the inner spring stiffness was too soft, the inner spring deformations will

result in a reduced velocity in the dashpot and hence lower dashpot forces.

To determine an acceptable inner spring stiffness ratio for modelling, comparisons were made

between purely elastic series and parallel radiation damping models. These were subject to a 0.02

s triangular pulse excitation with a 2 s free vibration response to replicate hammer tests carried

out on the pile. An elastic analysis meant that no gap growth or soil non-linearity was included in

the modelling, with damping provided by the dashpots and pile elements. The Pile 3 model was

utilised for this analysis; with gapping evident throughout testing springs and dashpots were

Numerical modelling of lateral pile response

173

removed from the model to the depth of the gaps used at the start of the second 90 kN pushover

model. This is referred to as a purely elastic model because an elastic analysis with residual gaps

specified in the inner springs above the gapped effective ground level will result in a reset of the

hysteresis rule to linearly elastic. Consequently, any residual gapping will be removed. This type

of modelling approach is desirable as it replicates the expected model layout used in the inelastic

dynamic analysis. Comparisons between purely elastic series and parallel models is done to

measure the level of radiation damping in each model, governed by the velocity of the node

between the inner and outer springs. In order to keep stiffness characteristics identical between

the pushover/parallel and series models, the stiffness of the inner and outer springs were

calculated from the following equation:

(6-12)

where Ktot is the total system stiffness, Kout is the outer spring stiffness, rs is the ratio of inner to

outer spring stiffness. This results in an inner spring stiffness, Kinn, of rsKout. With a constant

overall stiffness between the series and parallel damping models, only the velocity difference at

each end of the inner spring will produce a difference in response. As the stiffness ratio increased,

so did the computational effort, and analysis time, so this was taken into consideration in selecting

an appropriate stiffness ratio.

Free vibration pulse excitation results for inner spring stiffness ratios of 1, 10 and 50 are shown in

Figure 6-17; compared with the corresponding parallel damping model. As the stiffness ratio

increases, the series damping model approaches the benchmark parallel damping model. Using an

initial inner spring stiffness of 50 times the outer spring stiffness was deemed to be sufficiently

accurate. This result suggests that the velocity in the series damper was similar to that of the

parallel model, and thus the stiffness ratio of 50 was developed for material non-linearity. To

ensure the correct solution was found for each analysis, the time step was halved and compared

with the larger time step – if the analyses did not coincide then the time step is halved again in an

iterative procedure. All analyses were carried out at a converged time step of 0.0005 s, so the

computational effort of a stiffness ratio of 50 was satisfactory.

To develop the inner spring elements for an inelastic dynamic analysis, the gapped springs were

restored to the model and the bi-linear factor for the inner spring, rinn, was related to the total bi-

linear factor, r; determined from p-y analysis (Section 6.3). This was done by substituting the post

yield stiffness into equation (6-12):

(6-13)

Numerical modelling of lateral pile response

174

and rearranging for rinn:

(

) (6-14)

Kir is the total post yield stiffness and rsKoutrinn is the inner spring post yield stiffness. The yield

force and preforce of the inner spring are specified as the same as required by the total response

(unchanged from second 90 kN pushover model). The outer spring also has this preforce specified

to ensure there is no force transfer, even though none should occur, between the springs at the

start of the analysis. This can be visualised as the inner spring displacing by less than the original

(total) pushover response in the elastic range. A much higher stiffness results in the inner spring

reaching yield at the same time as the pushover response.

Figure 6-17: Pulse excitation results for parallel and series radiation damping models

At this stage a pushover analysis was carried out on the dynamic model with the modal and static

responses coinciding with earlier analyses for the second 90 kN modal and pushover models to

verify the model is working correctly (dynamic model is based on the gaps at the start of the

second 90 kN pushover model, or at the end of the second 120 kN pushover model).

9.4 9.6 9.8 10 10.2 10.4 10.6 10.8 11 11.2

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time (s)

Dis

pla

cem

ent

at

LV

DT

2 (

mm

)

Parallel model

Series rs=1

Series rs=10

Series rs=50

Numerical modelling of lateral pile response

175

6.4.3 Snap-back impact effects

Significant impact effects were evident during the initial cycles of the snap-back response, as

reported in Chapter Five. Initial results of the series spring model developed in the previous

section showed that when the model was loaded with a shape function to replicate snap-back

tests, it considerably underestimated the level of damping required. This was due to the

significant impact effects causing additional energy dissipation during the early cycles of the

response. This was particularly evident during the first impact of the pile into the soil gap after its

release from the pull-back peak displacement. To account for this contact damping additional

contact members were adopted into the model to account for foundation-soil interaction (Carr,

2004). Contact members are more commonly used to model pounding between adjacent

buildings, and can be defined with damping, stiffness, friction and certain hysteresis rules, which

enable a gap in the positive and negative directions to be specified.

Contact members were set up in the model on both sides of the pile, at the same spacing and

similar to the way existing springs and dashpots have been incorporated into the model (Figures

6-1 and 6-16). The layout that was found to be most suitable to capture these impact effects is

shown in Figure 6-18. The contact members were specified with a damping coefficient and

stiffness, necessary for the analysis to run, but at a factor of 10-3

of the overall stiffness so the

response is kept consistent. If the contact members were incorporated into the inner or outer series

spring arrangement insufficient damping was provided to the system, so end two was connected

to a fixed outer node, keeping it separate from the series spring arrangement. The damping

coefficient for contact members on each side of the pile were specified relative to the damping

coefficient of the corresponding dashpot at that depth, c, which was used to model the elastic

radiation damping of the soil (6.4.2). Due to the asymmetric nature of snap-back testing a

different factor of the radiation damping coefficient was used on each side of the pile, nC and nT

(denoted by compression and tension soil sides during the pull-back), and the combination varied

depending on the snap-back test being modelled. Contact members were utilised from the ground

surface to two metres below ground level (BGL); this region defined where the majority of gap

growth and hence impact effects were assumed to occur.

The bi-linear hysteresis rule is utilised for the contact member arrangement, which enables a

compressive gap to be defined for the contact members within the residual gap depth, consistent

with those defined for the inner spring. The major limitation of the contact member is that it is

unable to be defined with a preforce, so it cannot accurately model gap growth on either side of

the pile. A large tensile gap is defined so that the contact member detaches under tensile loads,

replicating the inability of soil to support tensile stresses. However, with no level of preforce the

Numerical modelling of lateral pile response

176

contact member detaches instantly, earlier than the inner springs with a preforce specified. In the

compressive direction, the contact member can be defined with a factored-down yield force so

that the compressive gap can develop when the contact member is unloaded. The gap is not

accurate as preforce influences the magnitude of the gap in the inner series spring, and this option

requires greater computational effort to achieve a solution. For these reasons no yield force was

defined in the model and only the residual gap and detachment in tension were accounted for. In

terms of computational effort for the selected arrangement in Figure 6-18; the contact model

required the same time step as the series spring model, 0.0005 s; this was deemed to be

satisfactory.

Figure 6-18: (a) Contact member arrangement within existing (b) series spring arrangement

6.4.4 Model comparison with dynamic tests carried out on Pile 3

In this section the dynamic pile model is developed for comparison with two snap-back tests and

corresponding hammer tests carried out on Pile 3. The second series 120 kN and 7.5 kN snap-

back tests were chosen as they cover the range of snap-back force magnitudes employed during

testing. This enables the model to be compared to both low force and high force tests. These tests

Numerical modelling of lateral pile response

177

were also selected because the pull-back peak of the response needs to be considered in the

modelling approach. Hence a clean unfiltered response is desirable, which these two tests provide.

Significant impact effects following the release from the pull-back peak meant that the series

spring model was not capable of capturing the response and the contact model arrangement

needed to be considered. For this reason, the series spring model was released from peaks later in

the response where impact effects were less prominent, to obtain a comparison with field data. All

comparisons are made in the time domain (displacement-time plots) as damping and stiffness

characteristics of the response are more evident than when the hysteretic pile response is

considered.

6.4.4.1 Free-vibration hammer test comparison

The hammer test carried out at the end of the 15 kN snap-back test two was assumed to be

representative of residual gap conditions around Pile 3 at the beginning of the 7.5 kN snap-back

test two. The series spring model was subjected to a 0.02 s triangular pulse shape function that

was applied to the top of the pile that replicated hammer tests carried out on the pile. The dynamic

model was developed based on the corresponding pushover model, so it contained p-y curves and

residual gap conditions specific to that model. There was a slight difference in natural period

between that determined from the modal analysis on the model and the hammer test during testing

(6.2.2). The dynamic response was very sensitive to the natural period (6.5.2) and hence the

tension gap (soil under tension during pull-back) was adjusted. The tension gap was adjusted as it

had good control over the natural period, without being detrimental to the pushover response

modelled previously (6.5.1). It is essential that the dynamic model can capture both the modal

properties and static response investigated in earlier sections. The tension gap was reduced from

0.65 to 0.60 m, and the resulting free vibration hammer response is presented in Figure 6-19 with

the field response. Note that the data is trimmed so that the first peak of the hammer response is

excluded from the response as a much greater displacement was computed for this peak. This

indicated that the hammer is still in contact with the pile during the first half cycle. Therefore the

second cycle of the model is also where the comparison begins.

Both damping and stiffness exhibited from testing appear to be captured well in the model. There

is a slight change in relative frequency mid-way through the response, which is recovered later on

in the response. Analysis of the cyclic behaviour found that the data is responsible for this shift in

frequency, even though there is a definitive extension in the model period due to a tension spring

temporarily detaching. During testing multiple hammer blows are carried out for each hammer

test and a permanent shift in the pile is noted (see Figure 5-19), extending the natural period.

There is a slight recovery in this pile movement later in the response which causes an increase in

Numerical modelling of lateral pile response

178

the cyclic frequency and the response recovers to move in phase with the dynamic model. Noise-

related effects govern the test data response at later stages, whilst the series spring model is still

oscillating.

Figure 6-19: Ruaumoko series spring model comparison with hammer test corresponding to 7.5 kN snap-back

test two

The hammer test carried out after the first 120 kN snap-back test corresponds to the second 120

kN snap-back test analysed for Pile 3. The comparison of this hammer test with the relevant series

spring model subject to a triangular pulse is shown in Figure 6-20. The middle section of the

response for this test is captured with the series spring model by starting the response with a small

phase difference to the test response. Thus the greater non-linearity in the test data has resulted in

the softer response catching up and moving in phase with the model after two to three cycles. This

phase of the test response is where the reported Fast Fourier Transform (FFT) natural frequency

was found to correspond to (Table 5-3).

28.9 29 29.1 29.2 29.3 29.4 29.5 29.6 29.7 29.8 29.9

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time (s)

Dis

pla

cem

ent

(mm

)

Hammer test following 15kN snap-back 2

Ruaumoko series spring model

Numerical modelling of lateral pile response

179

Figure 6-20: Ruaumoko series spring model comparison with hammer test corresponding to 120 kN snap-back

test two

6.4.4.2 Low force 7.5 kN snap-back test two comparison

Significant impact effects during the early peaks of the snap-back tests meant that the series

spring model would more likely be comparable to the test response at subsequent peaks. Analysis

of the test response found that the second 7.5 kN snap-back test contained significant inelasticity

during the first three peaks, including the pull-back peak. The extent of this non-linearity in the

low force test was due to the large gap depth, as this was the last test carried out on Pile 3. The

series spring model was pulled back to the fourth peak, where the elastic response appeared to

commence, and released over a time of 0.01 s and compared to the test response. This process was

repeated for earlier peaks until contact damping required the contact model arrangement to be

adopted to capture the test response. The series spring model comparison from the fourth peak of

the second 7.5 kN snap-back test response is shown in Figure 6-21. There is a varied peak

magnitude evident during the unfiltered test response, which does not properly represent the pile

behaviour and cannot be accounted for in the model. Ignoring these localised changes, the series

spring model appears to capture the level of damping reasonably well. There is however a phase

difference between the two responses that develops throughout. This is assumed to develop

because the series spring model is pulled back to a reduced peak displacement to start at the

9.5 9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4 10.5

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Time (s)

Dis

pla

cem

ent

(mm

)

Hammer test following 120kN snap-back 1

Ruaumoko series spring model

Numerical modelling of lateral pile response

180

fourth peak of the test response, as opposed to pulling back to the first (pull-back) peak. Thus the

model is not entirely representative of test conditions as less gap growth would have developed

than during the test where is was pulled back to a much greater displacement. This has resulted in

a stiffer model response, oscillating with a reduced natural period. This effect is investigated in

the sensitivity analysis on the 7.5 kN series spring model in 6.5.2.

Figure 6-21: Ruaumoko series spring model comparison to 7.5 kN snap-back two when released from fourth

peak

The series spring model is loaded and then released from the third and second peaks of the test

response in Figures 6-22 and 6-23. Impact effects become progressively more noticeable in the

series spring model comparison with each of these responses. The unsymmetrical nature of the

snap-back test response results in the response being centred slightly below zero displacement,

which is not shown in the model. It is still evident that the series spring model produces less

damping than the snap-back response during the initial cycles, where impact effects have a greater

influence. The damping later in the response is still captured well. There is a similarly stiffer

model response due to the greater pull-back peak displacement for the test data. Overall, the series

spring model provides a reasonable approximation to these test responses, and hence a contact

member model has not been deemed necessary.

9.5 9.6 9.7 9.8 9.9 10 10.1 10.2 10.3 10.4 10.5

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Numerical modelling of lateral pile response

181

Figure 6-22: Ruaumoko series spring model comparison to 7.5 kN snap-back two when released from third peak

Figure 6-23: Ruaumoko series spring model comparison to 7.5 kN snap-back two when released from second

peak

9.6 9.8 10 10.2 10.4 10.6

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7.5kN snap-back 2

Ruaumoko series spring model

9.6 9.8 10 10.2 10.4 10.6

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Numerical modelling of lateral pile response

182

Significant contact damping occurs during the initial impact of the pile into the gapped soil

following its release from the 7.5 kN target pull-back force. The series spring model is not

capable of modelling such damping, so the contact model was used to capture the test response.

Several iterations found optimal coefficients of 16 and 4 for nC and nT respectively. This is the

ratio of the contact member damping coefficient and elastic radiation damping coefficient for the

respective compression and tension sides of the pile during the pull-back phase of snap-back tests.

A much greater level of damping was required to capture the contact damping, active during the

elastic and inelastic phases of the response, compared with that required to model the elastic

radiation damping. The other forms of damping evident is structural pile damping and material

damping, captured through the hysteretic response of the inner series springs. Material damping is

more significant after many inelastic cycles of the response. From the series spring model

comparison, this hysteretic damping was not significant enough during the early cycles to

correctly capture the test data damping (6.5.2). Note that during the inelastic response the inner

spring governs the behaviour of the response and a reduced velocity difference passes through the

outer dashpot in the series spring arrangement. Thus some of the hysteretic damping is replacing

the lost elastic damping during post-yield inner spring deformation.

A larger level of damping was required on the compression side of the pile to prevent the pile

entering the tension side during its first cycle with a relatively high velocity. If this did occur, the

damping specified in the contact members on the tension side would cause a ‘rachetting’ of the

response in the negative displacement direction (tension side direction) and the pile would remain

in this zone, resulting in a highly unsymmetrical response (6.5.2).

It can be seen from Figure 6-24 that the contact model manages to capture contact damping

effects during snap-back testing reasonably well. A similar displacement to the field response has

been computed by the model for the first three peaks following release from the pull-back peak.

These were the peaks that the series spring was released from (Figures 6-21 – 6-23). The

responses diverge during later peaks when the elastic response governs. The test data damping

significantly reduces and continues to oscillate with a relatively constant level of damping and

stiffness (shown through the cyclic frequency) during the elastic cycles, which commence at the

fourth peak of the response (including pull-back peak). The limitation of the selected contact

member arrangement (Figure 6-18) is that it is attached to a fixed node away from the pile. This

results in the contact member being active during the entire response (provided deformations are

not within any specified gap in the positive or negative directions). Contact damping effects are

found to occur during the initial, or inelastic, cycles of the test response; they then reduce later on

as the elastic response develops and contact with adjacent soil gaps reduce. Contact damping

effects are unable to reduce later in the model response due to it being active during elastic cycles

Numerical modelling of lateral pile response

183

as well, creating a similarly high level of damping throughout. It makes logical sense to

incorporate the contact member in the inelastic inner spring arrangement to prevent elastic

activity but not enough damping can be provided during the early inelastic cycles. A more

sophisticated damping model would need to be made available/incorporated to enable the contact

model arrangement in Figure 6-18 to capture the entire response.

Figure 6-24: Ruaumoko contact model comparison with 7.5 kN snap-back test two

6.4.4.3 High force 120 kN snap-back test two comparison

Significant impact effects were evident during the first three peaks (peak one is the pull-back

peak) of the second 120 kN snap-back. Thus of the first four peaks modelled, only the fourth peak

(where the elastic response begins) was able to be modelled using the series spring model. The

comparison of this reduced pull-back displacement release with test data is shown in Figure 6-25.

The pile has previously been pulled back by a force of 120 kN before reaching this fourth peak,

compared with the 7.5 kN pull-back in the previous snap-back test considered. This has resulted

in a much greater difference between the level of gap growth that has occurred in the test response

and the model, for this 120 kN test. Thus the relative phase difference developed between the two

responses is much greater than the corresponding comparison in Figure 6-21. This does not affect

the damping, as the peaks between test and model both coincide, illustrated in Figure 6-25.

9.4 9.5 9.6 9.7 9.8 9.9 10 10.1 10.2 10.3

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Numerical modelling of lateral pile response

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Figure 6-25: Ruaumoko series spring model comparison to 120 kN snap-back two when released from fourth

peak

The contact model has been utilised to model the second 120 kN snap-back test, from the pull-

back peak release, and the two subsequent peaks. Starting from the third peak, response

comparisons are shown in Figures 6-26 – 6-28. The test pile behaviour has a very unusual

response in between the third and fourth peaks. The pile appears to be moving down and then

stops and returns back in the positive direction half-way through its cycle. This could be due to

higher order mode effects; however, it is also possibly due to the displacement recording LVDT

losing contact with the pile, even though magnets are used to keep them in contact. Thus, the

contact model is unable to account this change in the response and it can only assume that the pile

should carry out a full cycle in the negative direction before returning. This causes more of an

issue for the responses in Figures 6-26 and 6-27 as the change in response is closer to where the

model is released from, and there are fewer peaks to judge the performance of the model.

Excluding this portion of the response, the models in Figures 6-26 and 6-27 seem to provide an

appropriate model to the level of damping required during subsequent cycles. Note that the less

damping required in the third peak model results in the response continuing through the elastic

cycles for longer than the other two contact models.

7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8 8.1

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Numerical modelling of lateral pile response

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Figure 6-26: Ruaumoko contact model comparison to 120 kN snap-back two when released from third peak

Figure 6-27: Ruaumoko contact model comparison to 120 kN snap-back two when released from second peak

6.8 7 7.2 7.4 7.6 7.8

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Numerical modelling of lateral pile response

186

The contact model in Figure 6-28, releasing from the same pull-back peak as the test, appears to

model the shape of the response the most accurately out of the three contact models. This is

primarily due to the subsequent peak displacements being smaller relative to the scale of the pull-

back peak in Figure 6-28. It is difficult to correctly capture the peaks of the test data, and the

residual pile position at the end of the response. Hence the pile model is offset from the test pile, a

sacrifice necessary to capture the damping of the response.

Figure 6-28: Ruaumoko contact model comparison to 120 kN snap-back two when released from pull-back peak

The values of nC and nT for these responses is summarised in Table 6-5. There is a large variance

in the values of nC and nT used to capture each of the responses in Table 6-5, which also contains

the values used for the 7.5 kN snap-back two test for comparison. Note that the contact model that

is released from the second peak is done so from the negative displacement direction due to the

position of that peak; all other tests are released from the positive direction. The notation of nC

and nT is for a typical pull-back test. This notation is still maintained for the second peak model,

even though it has different sides under compression and tension during its own pull-back phase.

When this is considered, the larger displacement 120 kN snap-back models have a smaller

damping coefficient on the side that they are pulled back towards (nC for peak one contact model,

nT for peak two contact model). For the small displacement peak three model, a symmetrical ratio

of unity is adopted. This is the only one of the three 120 kN contact models that has a smaller

6.4 6.6 6.8 7 7.2 7.4 7.6 7.8 8 8.2 8.4

-5

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Numerical modelling of lateral pile response

187

peak displacement than the 7.5 kN model. Thus, it contains less impact effects and a more

symmetrical response. A greater level of impact effects on the response does not necessarily mean

a larger ratio of nC and nT is required. The greater peak displacement for the 120 kN snap-back

test results in more ground displacement and hence the contact members having a greater

influence on the response. This is because gap growth is not accounted for in the contact

members. While the inner springs may have detached following the pile release from the

compression side due to post-yield deformation, the contact members will still be active, until the

pile passes the residual compression gap (if any) specified in the member. Thus, as the peak

displacement increases the value of nC decreases to partially offset this extra influence. This has

also resulted in the pull-back peak 120 kN snap-back model requiring a smaller value of nT

compared with lower peak displacement models. This trend is consistent for the 7.5 kN snap-back

contact model but does not hold true for the third peak 120 kN model, with an equal value of nT.

This has been attributed to the reduced level of impact effects at this stage of the test response

(related to gap depth) that need to be captured by the model.

The distribution of nC/nT has also found to generally decrease for larger peak displacements.

Again the lower level of impact effects in the peak three 120 kN contact model does not follow

this trend. The 7.5 kN pull-back peak model has much greater values of nC and nT, as well as a

larger distribution of nC/nT because of the extensive testing carried out between the two tests. A

larger gap depth (Table 6-1) has resulted in more significant impact effects that need to be

captured by the 7.5 kN contact model.

Table 6-5: Summary of contact damping coefficient ratios for Pile 3 contact models

Test data peak

number that

model is released

from

Ratio of contact to

dashpot damping

coefficient on

compression side,

nC

Ratio of contact to

dashpot damping

coefficient on

tension side, nT

Distribution of

contact

damping, nC/nT

Peak

displacement

(mm)

1 0.16 1 0.16 44

2* 4 1 0.25* 5.8

3 1 1 1 2.4

7.5 kN snap-back 16 4 4 3.4

*Note: this distribution is reported as nT/nC because the model is pulled in the opposite direction

Numerical modelling of lateral pile response

188

6.4.5 Model comparison with dynamic tests carried out on Pile 4

This section utilises the full pile-soil contact at the start of Pile 4 testing, and throughout the 10

kN snap-back tests. Full-pile soil contact results in minimum impact effects and enables the series

spring model to be utilised from the pull-back peak for low force 10 kN snap-back tests. A

comparison between the first hammer test for each level of pile head mass (324, 609 and 1275 kg)

and the corresponding series spring model is carried out to access elastic stiffness and damping of

the model. The 609 and 1275 kg series spring models are then subject to a 10 kN snap-back

analysis, and compared with corresponding test data. The first 120 kN snap-back test (324 kg)

was the final test modelled, which excluding the 10 kN tests contained the lowest level of impact

effects from the pull-back peak. Additional damping provided by the contact member

arrangement was required to model this response.

6.4.5.1 Free-vibration hammer test comparison

Three hammer tests, one for each level of pile head mass, are presented in this section and

compared with the relevant series spring model developed for each. Due to pile head mass

variation there was a much more significant change in modal properties between these tests,

compared with Pile 3 where this could only occur through gap growth around the pile.

Comparisons for the hammer test carried out immediately before the commencement of the 10 kN

snap-back tests for each mass level (324, 609 and 1275 kg) are shown in Figures 6-29 – 6-31.

Generally, there is much more deviation between test and model across these three plots, than the

comparisons for Pile 3 in Figures 6-19 and 6-20. This is likely due to the different modal

properties of each test for Pile 4. The stiffness is captured correctly but the peak magnitudes do

not always coincide. This deviation between model and hammer test is due to the elastic damping

models in the numerical analysis not capturing the test data damping. Deviation is more evident

for lower mass levels. As the mass level increases the damping model becomes more accurate,

with respect to the test data it is modelling. The 324 kg mass hammer test in Figure 6-29 exhibits

a much more lightly damped system than the model. The 609 kg test in Figure 6-30 has a slightly

greater level of damping than the model. Both of these occurrences support what was seen during

analysis of test data, where inconsistencies were found for these lower mass levels (Figure 5-23).

In Figure 6-31, the 1275 kg hammer test is captured well by the model. The elastic models used to

account for radiation soil damping and structural damping of the pile are the same for each test,

with only modal results; which have been accurately captured (Table 6-2), influencing the

solutions. This implies that there are issues with the low mass level test data that is unable to be

accounted for in the numerical model.

Numerical modelling of lateral pile response

189

Figure 6-29: Ruaumoko series spring model comparison with hammer test before 324 kg 10 kN snap-back test

Figure 6-30: Ruaumoko series spring model comparison with hammer test before 609 kg 10 kN snap-back test

20.9 21 21.1 21.2 21.3 21.4 21.5 21.6

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Hammer test before 10kN snap-back 324kg

Ruaumoko series spring model

14.2 14.3 14.4 14.5 14.6 14.7 14.8

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Ruaumoko series spring model

Numerical modelling of lateral pile response

190

Figure 6-31: Ruaumoko series spring model comparison with hammer test before 1275 kg 10 kN snap-back test

Inconsistencies in lower mass hammer damping data were based on the SDOF damping ratio

being inversely proportional to mass (equation 5-2). The fact that there was a relative increase in

damping from the 324 kg to 609 kg mass meant that it was difficult to know if both were varied

due to a low pile head mass. The loose lead mass arrangement that moved during testing for the

609 kg pile head (Figure 5-9) had also caused some disruption to previous data, indicating that it

was the more likely test to be responsible for any deviation. Based on these modelling results,

where the model comparison improves with increasing mass, it can be concluded with more

certainty that deviation in hammer data is due to a lower level of pile head mass. Where a greater

proportion of mass is distributed along the length of the pile, it is harder to justify the pile-soil

system as an equivalent Single-Degree-Of-Freedom (SDOF) system. For this reason only the 609

kg and 1275 kg pile head mass models are compared to the 10 kN snap-back test data response.

6.4.5.2 Snap-back test comparison

The larger pile head mass series spring models (609 and 1275 kg) are compared to 10 kN snap-

back tests in Figures 6-32 and 6-33. The 10 kN snap-back tests are the only tests (for both Piles 3

and 4) that the series spring model is able to be released from the pull-back peak and provide

sufficient damping to be comparable to test data. The 1275 kg series spring model in Figure 6-33

7.2 7.4 7.6 7.8 8 8.2

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Hammer test before 10kN snap-back 1275kg

Ruaumoko series spring model

Numerical modelling of lateral pile response

191

contains sufficient damping to correctly capture the peak displacements, however the 609 kg

series spring model does not. This 10 kN snap-back test contained more significant impact effects

that result in greater model displacements during the first half of the response; though the peaks

coincide towards the end of the response. Considering the 609 kg pile head mass is the lighter of

the two tests it is unusual that it should exhibit greater impact effects than the 1275 kg pile head

10 kN snap-back test. A contact model would need to be developed to provide a more accurate

solution to the 609 kg, 10 kN snap-back test. This highlights difficulties in capturing the damping

of these lower mass levels.

Both Figures 6-32 and 6-33 show that the series spring models move significantly out of phase

with the test response. Considering the stiffness was reasonably consistent with hammer tests in

Figures 6-30 and 6-31, there has been a stiffness change developed during the pull-back/snap-

back modelling that has not developed during testing. This stiffness change is noted in Table 6-4,

which was a result of gap growth during the static unloading of Pile 4. A similar case is evident

here where a softer response results in the series spring model moving slower and out of phase

with the corresponding test response. The development of gap growth has been attributed to the

reduced yield force inputted into springs on both sides of each model, necessary to capture the

pushover response. This is confirmed during a sensitivity analysis on these tests in 6.5.2.

Figure 6-32: Ruaumoko series spring model comparison with 609 kg 10 kN snap-back test

13.6 13.7 13.8 13.9 14 14.1 14.2 14.3 14.4

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Ruaumoko series spring model

Numerical modelling of lateral pile response

192

Figure 6-33: Ruaumoko series spring model comparison with 1275 kg 10 kN snap-back test

The first 120 kN snap-back test with a 324 kg pile head mass resulted in significant impact effects

developed during the initial release of the pile into the soil detached in tension during the pull-

back. This is the lowest level of impact effects for a high force level test (60 kN and greater) of all

the tests carried out on Piles 3 and 4. This is due to a lighter pile head mass in conjunction with a

relatively shallow gap depth, all of which was developed during the pull-back of this test only.

Thus much lower values of the contact damping coefficient ratios were necessary to capture the

response. Values of 0.05 and 0.1 for nC and nT respectively, were used for this test comparison.

Both of these values are much lower than those used previously for Pile 3, see Table 6-5. This is

due to the relatively low level of contact damping developed during this 324 kg, 120 kN Pile 4

snap-back test.

The first three peak magnitudes are reasonably coherent between test and model response, which

is a good result considering there are no impact effects following the initial impact of the pile on

the tension side. This has occurred because of the lower contact damping coefficients specified in

the model, which have also resulted in the response continuing to cycle later on in the response,

when the elastic outer springs govern the response. There is a clear shift in the cyclic frequency of

the response, with the model frequency reducing relative to the test data response. This could be

due to greater gap growth, however, there is additional contact damping provided by the model

18.4 18.6 18.8 19 19.2 19.4 19.6 19.8

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Numerical modelling of lateral pile response

193

later on in the response. Note from the following relationship the damping ratio decreases the

(damped) frequency of the pile-soil system:

√ (5-6)

By idealising all forms of damping into the damping ratio, the additional contact damping during

the elastic cycles of the contact model response, not evident during the test response, results in a

difference in the cyclic frequency between the two responses.

The hammer test carried out before this 120 kN 324 kg snap-back test produced similar results in

comparison with the series spring model (not shown), to those found in Figure 6-29 for the

hammer test before the 10 kN snap-back test. The elastic damping predicted by the model was

much greater than that shown from the data. This may have contributed to a lower ratio of contact

damping required to capture the 120 kN test response. It has also meant that the series spring

model competency was not investigated at subsequent peaks, as per Pile 3 snap-back analysis, to

capture a predominately elastic pile response.

Figure 6-34: Ruaumoko contact model comparison with 324 kg 120 kN snap-back test one

17.4 17.6 17.8 18 18.2 18.4 18.6

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5

10

15

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25

30

35

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120kN snap-back test - 324kg series one

Ruaumoko contact model

Numerical modelling of lateral pile response

194

6.5 SENSITIVITY ANALYSIS ON KEY PARAMETERS

OF NUMERICAL MODELS

Sensitivity analyses presented in this section are carried out by varying key parameters of specific

numerical pile models presented earlier in this chapter. Note that similar Winkler Spring models

are used throughout, and Piles 3 and 4 were tested at the same site, so sensitivity results are

comparable between each.

This section is split up into the following sensitivity analyses:

Pushover model response, including modal analysis, and gap predictions of pushover

model

Dynamic response, of both hammer and snap-back tests (series spring and contact

arrangements)

6.5.1 Pushover model (including modal analysis) sensitivity analysis

This section comprises of two different types of sensitivity analyses carried out on the Pile 3

pushover model (with mass included for modal analysis):

Effect on pushover response and natural period by varying key parameters of residual

compression gap depth, residual tension gap depth, compression gap width at ground

surface, gap cross-section shape, modulus of subgrade reaction and coefficient of earth

pressure at rest.

Gap depth predictions following unload based on the variation of key parameters

coefficient of earth pressure at rest, modulus of subgrade reaction, soil unit weight and

residual tension gap depth.

Table 6-6 summarises the different models run in the sensitivity analysis. It highlights the key

parameter that has been changed, and the resulting natural period. All changes aimed to stiffen the

pile-soil system so analyses were more comparable. The sensitivity analysis is carried out on the

second 90 kN pushover Pile 3 model, with the base model below the headed row of Table 6-6.

The gap shape was originally assumed to taper linearly from the gap width at the ground surface

to the specified gap depth. The fifth analysis uses a taper raised to the power of three. This has the

effect of rapidly narrowing the gap width as a function of the depth below the ground surface. The

reason a cubic function was chosen was because the deflected shape of a cantilever is proportional

to its length cubed.

Numerical modelling of lateral pile response

195

Of these analyses the gap depth and modulus of subgrade reaction variations have the only effect

on the natural period. The tension gap depth has the most significant effect on the natural period,

where as the compression gap depth produces the smallest change in natural period of the three

analyses. This is due to the difference in depth of these gaps either side of the pile.

Table 6-6: Key parameters varied in the sensitivity analysis on the Pile 3 pushover model

Analysis

number

Compression

gap depth

(m)

Tension

gap depth

(m)

Compression

gap width

(mm)

Gap

shape

Mod. of

subgrade

reaction

Coeff. of

earth

pressure

Period

(s)

1 (base) 0.9 0.65 23 linear 1 1 0.0914

2 0.7 0.65 23 linear 1 1 0.0873

3 0.9 0.45 23 linear 1 1 0.0819

4 0.9 0.65 18 linear 1 1 0.0914

5 0.9 0.65 23 cubic 1 1 0.0914

6 0.9 0.65 23 linear 2 1 0.0828

7 0.9 0.65 23 linear 1 2 0.0914

Figure 6-35: Sensitivity analysis on second 90 kN Ruaumoko pushover model part one

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100

Displacement (mm)

Forc

e (

kN

)

90kN Ruaumoko base model

Compression gap depth

Tension gap depth

Compression gap width

Numerical modelling of lateral pile response

196

Figure 6-36: Sensitivity analysis on second 90 kN Ruaumoko pushover model part two

Figures 6-35 and 6-36 demonstrate the effect each of these key parameters has on the pushover

response. It is evident from Figures 6-35 and 6-36 that the width, depth and shape of the gap on

the compression side of the pile during the pull-back, has the most significant effect on the model.

The pushover response is relatively insensitive to the variation in the tension gap, and modulus of

subgrade reaction. In this case a stiffer response on the compression side of the pile is offset with

a quicker detachment on the tension side of the pile.

The gap depths predicted by Ruaumoko following the unload of the pushover force found to

overestimate what occurred during field testing. Key parameters are varied in Table 6-7 in an

attempt to produce more reasonable gap depth predictions. Note each of the analyses carried out

stiffen the pushover response, hence are no longer applicable at providing a model to the field

data presented earlier.

Key parameters were selected where uncertainty or variability is present. All of the analyses in

Table 6-7 failed to produce significantly reduced gap predictions. An increase in the coefficient of

earth pressure at rest and a decrease in the modulus of subgrade reaction were the most effective

means of reducing the gap depth predictions. However, unrealistic values would have to be used

to achieve better gap depth predictions, so this has not been investigated.

0 5 10 15 20 25 300

10

20

30

40

50

60

70

80

90

100

Displacement (mm)

Forc

e (

kN

)

90kN Ruaumoko base model

Cubic gap shape

Modulus of subgrade reaction

Coefficient of earth pressure at rest

Numerical modelling of lateral pile response

197

Table 6-7: Key parameters varied in the sensitivity analysis on the Pile 3 pushover model gap depth predictions

Analysis

number

Tension

gap depth

(m)

Clay unit

weight

(kN/m3)

Mod. Of

subgrade

reaction

Coeff. of

earth

pressure

Compression

gap

predicted

(m)

Tension

gap

predicted

(m)

1 (base) 0.65 17 1 1 2.20 1.05

2 0.65 17 1 2 2.05 1.00

3 0.65 17 1 5 1.85 0.90

4 0.65 17 2 1 2.50 0.65

5 0.65 22 1 1 2.25 0.90

6 0.65 17 0.5 2 1.75 0.80

7 0.90 17 1 5 1.85 1.20

6.5.2 Dynamic sensitivity analysis

In this section sensitivity analyses are carried out on the three types of dynamic models presented

in this chapter:

Series spring model used to capture hammer tests (for Pile 3 model only)

Series spring model used to capture snap-back tests (Pile 3 and Pile 4 models)

Contact model used to capture significant impact effects during snap-back tests (Pile 3

model only)

Each sensitivity analysis involves varying key parameters for that model type, with no overlap in

parameters between the three models. All sensitivity analyses for Pile 3 are based on the 7.5 kN

snap-back series two model and corresponding hammer. The sensitivity analysis carried out on

Pile 4 is different in that the effect of using different hysteresis rules on two 10 kN snap-back

models (609 and 1275 kg pile head masses) is investigated.

6.5.2.1 Hammer series spring model

The modal properties and elastic damping govern the response of the series spring pile model

when it is subjected to a triangular pulse excitation, to replicate the response from instrumented

hammer tests carried out during field testing. Key parameters varied and the basis of their

selection is provided on the following page.

Numerical modelling of lateral pile response

198

Gap depth on both compression and tension sides (sides named based on soil stress

conditions during pull-back) – governs the modal response (6.5.1)

Modulus of subgrade reaction – defines the elastic stiffness of the soil

Radiation damping coefficient of dashpot – defines the elastic soil damping

Specified damping ratio for Rayleigh damping – defines pile structural damping

The variations carried out for each sensitivity analysis is provided in Table 6-8. All variations aim

to stiffen the pile response or reduce the damping, and parameters are varied by realistic amounts.

The results of the sensitivity analysis are presented in Figures 6-37 and 6-38. Figure 6-37 presents

the variables that influence the modal response characteristics. The variation in the tension gap

depth and the modulus of subgrade reaction result in the greatest change in the cyclic frequency of

response, which is expected given the results from the sensitivity analysis in 6.5.1. The modulus

of subgrade reaction was increased by 100%; when compared to the 33% reduction in tension gap

depth, it is clear the model is more sensitive to the tension gap depth. The model is insensitive to

the change in the compression gap depth. This is presumably due to the fact it always extends

deeper than the tension gap depth. The increase in the modulus of subgrade reaction results in an

increase in the peak amplitude of each free-vibration cycle. Increasing the stiffness, whilst

maintaining the same level of preforce, promotes detachment of the inner spring during the

response, thus allowing the pile to reach greater displacements. On the contrary, a reduced gap

depth on the tension side results in a reduction in the peak displacement.

The peak displacement amplitude is more sensitive to the change in the radiation damping

coefficient than the pile Rayleigh damping variation. Also note that the radiation damping is

decreased by 50%, where as the Rayleigh damping is reduced by 75%, given the uncertainty in

the assumed damping ratio. Therefore, the radiation damping parameter contains the greatest

influence over the elastic damping of the pile-soil system.

Table 6-8: Key parameters varied in the sensitivity analysis on the Pile 3 hammer series spring model

Analysis

number

Compression

gap depth (m)

Tension gap

depth (m)

Mod. Of

subgrade

reaction

Radiation

damping

coefficient

Damping

ratio for

Rayleigh (%)

1 (base) 1.05 0.6 1 1 2

2 0.85 0.6 1 1 2

3 1.05 0.4 1 1 2

4 1.05 0.6 2 1 2

5 1.05 0.6 1 0.5 2

6 1.05 0.6 1 1 0.5

Numerical modelling of lateral pile response

199

Figure 6-37: Sensitivity analysis on hammer series spring Ruaumoko model corresponding to second 7.5 kN

snap-back test part one

Figure 6-38: Sensitivity analysis on hammer series spring Ruaumoko model corresponding to second 7.5 kN

snap-back test part two

29 29.1 29.2 29.3 29.4 29.5 29.6 29.7

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time (s)

Dis

pla

cem

ent

(mm

)

Ruaumoko base model

Compression gap depth

Tension gap depth

Modulus of subgrade reaction

29 29.1 29.2 29.3 29.4 29.5 29.6 29.7

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time (s)

Dis

pla

cem

ent

(mm

)

Ruaumoko base model

Radiation damping coefficient

Pile Rayleigh damping

Numerical modelling of lateral pile response

200

6.5.2.2 Snap-back series spring model

The main extension between the hammer response and snap-back response is the inelasticity

evident in the response when a snap-back test is replicated using dynamic loading shape functions

on Ruaumoko. Key parameters varied and the basis of their selection is provided below:

Compression and tension gap widths – possible residual gap contact with pile

Coefficient of earth pressure at rest – controls level of preforce and hence gap growth of

response

Pull-back peak displacement history – carried out to replicate subsequent peak modelling

where a greater pull-back displacement was carried out for testing in comparison to the

series spring model

Bi-linear inelastic and linear elastic inner spring hysteresis rules – bi-linear inelastic with

slackness hysteresis rule was changed for Pile 4 to accomplish more comparable models

to field data for 609 and 1275 kg 10 kN snap-back tests

Analyses were carried out on the 7.5 kN snap-back model two, except for those detailed in the last

bullet point above. Table 6-9 summarises the variations of each of the key parameters used in the

Pile 3 series spring model sensitivity analysis. Changes are made to stiffen the response,

consistent with previous sensitivity analyses. However, for the pull-back displacement sensitivity

the analysis aims to soften the response. This is done by pulling the pile back to a greater

displacement, then statically reducing the displacement to the original pull-back peak

displacement before releasing. This sensitivity analysis was carried out to replicate the situation

for subsequent series spring peak modelling where it was assumed that a softer response would be

achieved by pulling the pile back to a greater displacement before releasing from the reduced

peak. This would be more representative of test conditions where the test pile had already

undergone the large pull-back peak displacement before the lower displacement cycles that the

subsequent peak modelling looks to capture.

Table 6-9: Key parameters varied in the sensitivity analysis on the Pile 3 snap-back series spring model

Analysis number Compression gap

width (mm)

Tension gap

width (mm)

Coefficient of

earth pressure

Maximum pull-

back peak (mm)

1 (base) 20 20 1 3.5

2 15 20 1 3.5

3 20 15 1 3.5

4 20 20 2 3.5

5 20 20 1 7

Numerical modelling of lateral pile response

201

Results from the sensitivity analysis are presented in Figure 6-39. Both gap width reductions

collapse onto the original base model response. In other words, no residual gap interaction occurs

with the pile at these magnitudes of gap widths. This may be more prominent for the 7.5 kN snap-

back model two, where the greatest residual gap depth during testing of either Pile 3 or 4 is

present. The coefficient of earth pressure at rest restricts the pile displacement due to increased

resistance behind the pile; by delaying detachment of springs which occurs when subject to

tensile force. This also stiffens the response, evident through an increase in cyclic frequency. As

expected, pulling the pile back to two times the pull-back displacement beforehand softens the

response. The frequency of the model changes more than when the coefficient of earth pressure at

rest is varied. However the peak displacement during each cycle does not change for the increased

pull-back displacement model. This is a good result as the subsequent peak models captured the

individual peak displacements and only required a shift in frequency to provide a better model to

test data, which occurs in Figure 6-39.

Figure 6-39: Sensitivity analysis on second 7.5 kN snap-back series spring Pile 3 model

The effect of using different inner spring hysteresis rules for Pile 4, when subject to 10 kN snap-

back tests, is shown in Figures 6-40 and 6-41; for the 609 and 1275 kg pile head masses

respectively. Both hysteresis rules are compared to the original model (bi-linear with slackness)

and relevant test data. These analyses were carried out to determine if the gap growth within the

9.4 9.6 9.8 10 10.2 10.4 10.6

-2

-1

0

1

2

3

Time (s)

Dis

pla

cem

ent

(mm

)

Ruaumoko base model

Compression gap width

Tension gap width

Coefficient of earth pressure at rest

Pull-back peak displacement

Numerical modelling of lateral pile response

202

model (none noted during testing) was responsible for the softer model not capturing the field

response. The bi-linear inelastic hysteresis model is the same as the original hysteresis rule used,

except that no gap can be defined in either direction. Thus accounting for non-linear soil

deformation that may be causing non-linear test response, whilst preventing gapping that was not

observed during these tests. An elastic analysis (resetting hysteresis rule to linear elastic) was also

carried out, which prevents non-linear soil deformation and geometrical effects (gapping). The bi-

linear inelastic hysteresis rule is shown to change the frequency of the response in both Figures 6-

40 and 6-41. However, this does not correctly capture the test data frequency and exhibits a

‘rachetting’ effect, where the response moves permanently in the positive displacement direction.

This is possibly due to a reduction in stiffness in the positive compression direction that cannot be

offset by soil detachment on the tension side. This reduction in stiffness on the tension side has

occurred in the original analysis, evident through a symmetric response.

Figure 6-40: Sensitivity analysis on 609 kg 10 kN snap-back series spring Pile 4 model

The elastic analysis produces better results with the same frequency as the response for the 609 kg

pile head mass in Figure 6-40, and a slightly stiffer frequency than the 1275 kg pile head mass in

Figure 6-41. The pushover curves for these tests started with the same stiffness, but the 1275 kg

test softened earlier than 609 kg test. In conjunction with field observations, it seems more likely

that the difference in stiffness between the 1275 kg test response and the elastic analysis is a result

13.6 13.7 13.8 13.9 14 14.1

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time (s)

Dis

pla

cem

ent

(mm

)

10kN snap-back test - 609kg

Ruaumoko series spring model

Bi-linear inelastic

Elastic analysis

Numerical modelling of lateral pile response

203

of soil softening due to yielding. Given the agreement with the elastic analysis, the majority of

deviation observed between the original series spring model and 10 kN snap-back tests, was due

to confirmed gapping that developed within the model. Some softening due to yielding would be

necessary to capture the 1275 kg 10kN snap-back test.

Figure 6-41: Sensitivity analysis on 1275 kg 10 kN snap-back series spring Pile 4 model

6.5.2.3 Contact member model

A range of contact damping coefficient ratios, nC and nT, and depths to which contact members

are utilised has been investigated for the sensitivity analysis on the contact model. The variations

that are carried out for each analysis are summarised in Table 6-10. Predominantly symmetric

contact member depths are investigated, excluding analysis 6 where contact members terminate at

the residual gap depth, whilst variations in the contact damping coefficient ratios (to the radiation

damping coefficient) are done so separately for each side of the pile. For the latter, a 50% increase

and decrease is carried out for ratios on each side of the pile. The base series spring model (no

contact members) is also included in the sensitivity analysis for comparative purposes. Results are

presented in Figures 6-42 and 6-43.

18.3 18.4 18.5 18.6 18.7 18.8 18.9 19 19.1 19.2 19.3

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time (s)

Dis

pla

cem

ent

(mm

)

10kN snap-back test - 1275kg

Ruaumoko series spring model

Bi-linear inelastic

Elastic analysis

Numerical modelling of lateral pile response

204

Table 6-10: Key parameters varied in the sensitivity analysis on the Pile 3 snap-back contact member model

Analysis number Compression side

contact damping

coefficient ratio, nC

Tension side contact

damping coefficient

ratio, nT

Depth of contact

members

1 (base) 16 4 2.0 m

2 8 4 2.0 m

3 24 4 2.0 m

4 16 2 2.0 m

5 16 6 2.0 m

6 16 4 Gap depth (1.05,0.6m)

7 16 4 1.5 m

8 16 4 Full depth (6.75 m)

9 (series spring

model)

- - -

The model is more sensitive to the compression side ratio than the corresponding tension side

ratio, from the results in Figure 6-42. All variations are made using the same percentage change.

Gap growth for the contact members is not accounted for when loaded in compression, however

instant tension detachment occurs. Due to preforce in the inner springs, the tension side contact

members are behind the inner springs, whereas on the compression side they are significantly in

front of the inner springs. This increases the relative influence of the compression springs. In

conjunction with the larger pull-back displacement occurring in the compressive direction, this

results in the contact model being more sensitive to the change in the compression side contact

damping coefficient ratio. From Figure 6-42, decreasing the compression ratio allows the pile to

reach greater displacements in the tension direction, where contact damping in that direction

causes the pile to have a residual displacement below the horizontal axis. The series spring model

shows why contact members were necessary to capture these responses. Contact members

solutions produce a much a higher level of damping, necessary to capture the impact effects

developed from the pull-back peak release. It is interesting to note that the series spring model

oscillates with a lower frequency than the contact model. This is not expected due to increased

damping provided by the contact model. The increased damping provided by the contact model

must have resulted in a significant reduction in the gap depths produced during the dynamic

response, and hence provided a stiffer system, relative to the series spring response.

Numerical modelling of lateral pile response

205

Figure 6-42: Sensitivity analysis on second 7.5 kN snap-back contact member Pile 3 model part one

Figure 6-43: Sensitivity analysis on second 7.5 kN snap-back contact member Pile 3 model part two

9.5 9.6 9.7 9.8 9.9 10 10.1

-2

-1

0

1

2

3

Time (s)

Dis

pla

cem

ent

(mm

)

Ruaumoko base model c=16,4

Ruaumoko series spring model

c=8,4

c=24,4

c=16,2

c=16,6

9.5 9.6 9.7 9.8 9.9 10 10.1

-2

-1

0

1

2

3

Time (s)

Dis

pla

cem

ent

(mm

)

Ruaumoko base model 2.0m

Ruaumoko series spring model

Gap depth (1.05,0.6m)

1.5m

Full pile depth

Numerical modelling of lateral pile response

206

It is evident from Figure 6-43, that the contact members between the bottom of the gap depth and

1.5 m have the most significant effect on the response. This is because the greatest change in the

contact model response occurs between analyses 6 and 7, where the depth of contact members

extends to the gap depth and 1.5 m below ground level (BGL). The gap depth contact member

analysis 6 response is identical to that of the series spring model. This supports what was seen

during the series spring model sensitivity analysis, in that no interaction was evident between the

pile and residual gap widths during the dynamic response. There is only a small change in

response when the gap depth is increased from 2.0 m (base contact model) to the full pile

embedment depth (6.75 m). This is expected as the majority of pile response occurs near the

bottom of the gap, or effective ground surface (2.2.2).

6.6 SUMMARY

The full-scale response of single Piles 3 and 4 has been captured in Ruaumoko, under a range of

test arrangements, by adopting a Winkler Spring model. Existing elements and hysteresis rules

available in the structural analysis program were utilised to adequately represent the

characteristics of each pile:

Soil stiffness has been represented by spring elements, based on the modulus of subgrade

reaction. Springs were utilised on both sides of the pile due to different behaviour in

compression and tension.

The bi-linear hysteresis rule with slackness was utilised for spring elements. This reduced

spring stiffness to zero in the tension range, and also accounted for residual soil gaps

present around the pile during field testing by specifying a compressive gap that had to be

overcome for actions to be transferred to the spring element. Where no residual gapping

was evident, springs were preloaded to account for in-situ earth pressures in the soil under

zero lateral strain.

The non-linear force displacement relationship of the springs was defined by fitting a bi-

linear approximation to p-y curves in stiff clay with no free water at five representative

depths.

Material specific damping was specified in the model so that soil damping could be

considered separately to the Rayleigh (proportional) damping of the pile. This also

enabled zero damping to be specified in spring elements, so that dashpots incorporated

into the model could define the elastic radiation soil damping. Material damping was

provided by the hysteretic action of the springs.

The dashpots were incorporated into the model using a series spring arrangement. Near-

field behaviour (inelastic response and gapping behaviour) was controlled by a stiff inner

Numerical modelling of lateral pile response

207

spring, and far-field behaviour was controlled by an elastic spring and linear dashpot

element. A stiff inner spring was necessary to ensure a small velocity difference across

the element so that adequate damping is provided by the outer dashpot element. A softer

outer spring maintained the overall stiffness of the response.

Additional contact damping developed following the release of the pile from the pull-

back peak during snap-back tests was accounted for by introducing contact members into

the model. These were kept separate to the existing series spring arrangement, and

utilised three to four pile diameters beneath the effective ground level. A different

damping coefficient on each side of the pile, specified relative to the linear dashpot

coefficient at that depth, was necessary to capture the response. The coefficients also

changed between tests. These could not accurately model gap growth.

Reasonable comparisons with test data were obtained for the modal, pushover and dynamic

models under different test conditions. These conditions include the pile modelled, season during

testing, residual pile-soil gap conditions and pile head details. The following key points are drawn

from model comparison with corresponding field tests:

The shallow gap depth (tension side during pull-back tests) had significant control over

the natural period of the pile. The pushover response was insensitive to the change in this

parameter enabling accurate modal analysis comparisons to the natural periods computed

from full-scale hammer tests. There was significant uncertainty in gap depth

measurements taken during testing so gap depths employed were justified when the

response was captured. Reduced tension gap depths were employed to account for side

contact influencing the natural period computed during field testing.

The full pile-soil contact to ground surface during 10 kN pull-back tests on Pile 4 meant

that only one unknown variable was present in the determination of the initial stiffness. A

scaling factor of 0.5 was applied to the modulus of subgrade reaction, defining the spring

stiffness. A scaling factor of 1.0 was used for Pile 3; this difference was attributed to the

unknown existing gap depth present at the start of Pile 3 testing, and because Pile 4

testing was carried out following the wet season, Pile 3 the dry season .

The gap depth employed in front of the pile (compression side during pull-back tests) had

the greatest control over the pushover response. Similar values were employed to

extensive measurements taken during Pile 4 testing.

Larger gap depths were predicted by Ruaumoko following the static pile unload, than

those used in the subsequent pushover model. These gap growths were possible during

testing, where some recovery of the gap depth may have occurred before the next test was

Numerical modelling of lateral pile response

208

carried out. The only way this effect could be represented was by using a different

pushover model for each test, resetting the gap depths to the desired level.

Elastic soil stiffness and damping were well represented by the dynamic series spring

model due to favourable comparisons with hammer tests. Discrepancies occurred for low

mass (324 and 609 kg) Pile 4 responses, where inconsistent levels of damping were

evident in these test responses. It was important that the modal properties and non-linear

static stiffness were well represented before considering the dynamic response.

In general, the series spring model was only capable of modelling snap-back responses at

later cycles where only low impact effects were evident or the elastic response governed.

Significant impact effects developed near the pull-back release for low (7.5 kN) and high

(120 kN) force snap-back tests were captured using contact members. Contact members

were fixed at end two, away from the pile; hence they were active during the inelastic and

elastic phases of the response. This meant they could only capture the first few cycles of

the response, preventing the model from oscillating at later stages in the response with a

similarly low level of damping to the test response. The contact member model needs to

be further developed so that both portions of the response can be accounted for.

Conclusions

209

Chapter 7

Conclusions

The objective of this research program was to experimentally investigate the full-scale response

of single free-headed piles, and look to characterise the response numerically. Non-linear pile-soil

interaction was the focal point of work undertaken as it distinguishes Soil-Foundation-Structure

Interaction (SFSI) from existing linear elastic Soil-Structure Interaction (SSI) methods.

Previous full-scale single pile testing presented in the Literature Review has highlighted the

influence of non-linear pile-soil behaviour at relatively low levels of strain. Most notably, gaps

forming between the pile shaft and surrounding soil (non-linear geometric effects), and softening

of the soil near the pile (non-linear soil deformation). The majority of existing dynamic full-scale

experimental work was performed using forced vibration tests. It was noted by some researchers

that snap-back testing is a more time and cost effective alternative, providing similar results to

forced vibration tests. Thus, snap-back testing was carried out at an existing site to obtain non-

linear static and dynamic lateral pile response data. The current study differentiated from previous

work by focusing on snap-back testing, and hence implementing a more detailed dynamic

Conclusions

210

analysis. There was also an added emphasis on the response in the time domain and associated

non-linear damping, and capturing this in a rigorous numerical modelling approach.

The testing program involved two full days of testing on two 273 mm diameter steel tube piles

(Piles 3 and 4) at a stiff Auckland residual clay site in Albany. Previous site investigation data

was combined with spectral analysis of surface waves (SASW) tests carried out during the first

phase of the testing program. This aimed to determine the shear modulus of the soil at small

strain. A representative soil profile for the site was developed that was utilised during numerical

modelling. Snap-back tests were carried out by pulling the test pile towards a reaction pile with a

hydraulic jack, to a target force, and then releasing the pile. The pull-back phase provides a

measure of the static pile response. Snap-back tests were carried out at a range of release forces to

measure the dynamic response, in conjunction with free-vibration instrumented hammer tests

which were also used to determine the natural period of the pile-soil system. Hammer tests were

combined with extensive gap measurement to determine softening that had occurred to the pile-

soil system due to gapping. The second phase of the testing program involved varying the level of

mass added to the pile head, with the dynamic response compared between each.

Non-linear pile response was investigated in the frequency and time domains, as well as the

hysteretic load-deformation response. The Fast Fourier Transform (FFT) is used to convert the

response to the frequency domain and enables peak frequencies of hammer and snap-back tests to

be determined. For the high force snap-back tests two separate inelastic and elastic peak

frequencies are evident. The time domain is used to determine the damping of the system. This

can be attributed between inelastic and elastic damping by filtering the response based on the

FFT, or by inspection in the time domain. Load-deformation plots are used to assess both the

static and dynamic stiffness of the pile, during the respective pull-back and snap-back tests.

The different test responses were modelled in the structural analysis program Ruaumoko 3D,

which is capable of inelastic response history analysis in two and three dimensions. Discrete

springs were used to represent non-linear pile-soil interaction. Mass and elastic stiffness were

defined for the modal response, and compared with the natural period from hammer tests. A non-

linear hysteresis rule was used for the springs in order to capture pull-back tests with the pushover

response. Damping was then incorporated into the model to extend it for a dynamic analysis, to

model hammer and snap-back tests.

Obtaining full-scale snap-back testing data that has been shown to provide a good representation

of pile response to earthquake forces, enabling a worthwhile numerical characterisation of the

response, was the critical step in this study.

Conclusions

211

A summary of the main conclusions from relevant chapters is provided below, followed by

recommendations for a future research program.

Static pile response from full-scale field tests (including gap observations)

Non-linear geometrical effects were evident through soil behind the pile detaching from

the pile during the pull-back of the pile as soil was unable to support tensile stresses to

resist lateral pile movement. Also, after the snap-back release residual gaps were present

between the pile and the soil, more notably on the side loaded in compression during the

pull-back test. This was due to irrecoverable soil deformation that removed the initial

horizontal pre-stresses acting on the pile from the soil. This had the effect of lowering the

effective ground surface around the pile (Figure 4-3).

Pile 3 was found to accumulate residual displacement in the direction of the pile pull-back

after each pull-back and release (Figure 4-5). Horizontal stresses that were reduced in the

soil as it detached from behind the pile during the pull-back, has caused the soil to move

into the tension gap, thus displacing the pile following its release (Figure 4-6).

Detailed gap measurements taken during Pile 4 testing found that the maximum residual

gap depth during testing extended to four pile diameters (1.085 m) below the ground

surface, on the side of the pile loaded in compression during pull-back tests.

A thin metal tape was used to take gap measurements, although significant uncertainty

was associated with depth measurements due to a lack of visibility beneath the ground

surface, the cohesive nature of clay as well as any clay saturation effects.

These large gap depths contributed to significant elastic cantilever action of the test pile

during subsequent pull-back tests. This was exhibited through an approximately linear

force-displacement relationship (Figures 4-2 and 4-8). Later stages of loading had to be

reached before significant displacements occurred at the bottom of the gap depth, which

resulted in a non-linear response of the pile-soil system.

A decrease in the initial stiffness between tests confirmed an increase in residual gap

depth has occurred.

Non-linear response more evident during the initial stages of loading was attributed to

soil detachment at the back of the pile, or soil yielding in front of the pile, lowering the

stiffness of the pile-soil system.

Conclusions

212

Dynamic pile response from full-scale field tests

From the response in the frequency domain:

A decreasing natural frequency of the pile was computed from free-vibration hammer

tests throughout testing, due to a reduction in pile-soil contact from gap growth. For Pile

4, a much greater range in natural frequency was computed because three different mass

levels were tested. This varied from 19.1 Hz at the start of testing, for the 324 kg pile

head where no residual gapping between the pile shaft and soil was present, to 6.99 Hz,

following the second 120 kN snap-back test for the 1275 kg pile head with significant

gapping developed around Pile 4. There was residual gapping around Pile 3 at the start of

testing which reduced the change in frequency during testing to 2.4 Hz.

Snap-back tests were categorised as high force (60, 90, 120 kN) and low force (7.5, 10,

15, 30 kN) tests in the frequency domain, by taking the Fast Fourier Transform (FFT) of

the response. This was based on high force level tests containing elastic and inelastic peak

frequencies (Figure 5-5 – 5-8). From this analysis, elastic and inelastic responses were

able to be separated on MATLAB for high force tests. This was one method that enabled

damping data in the time domain to be attributed as elastic or inelastic.

The frequency between cycles for all dynamic tests (hammer, low force and high force

snap-back tests) was also assessed, and it was found that even a small amount inelasticity

is evident in all tests (Tables 5-2 and 5-3), shown through an increase in frequency as the

pile-soil system stiffens during subsequent cycles. Results verified the FFT analysis

carried out in MATLAB.

From the response of Pile 4 in the time domain:

The high force 120 kN snap-back tests’ inelastic and elastic components were separated

by considering the cyclic behaviour of the response in the time domain (Table 5-4), as

opposed to separation in MATLAB. Carrying this out over the time domain is suggested

as filtering based on the response in the frequency domain significantly alters the

response in both domains (Figure 5-22).

Damping was calculated using the logarithmic decrement method and by fitting SDOF

exponential envelopes to the response to determine the ‘system damping’ of different

tests. The exponential envelopes were important as they were not affected by

unsymmetrical pile response evident in all dynamic tests. This was not the case for cycle

to cycle damping calculated using the logarithmic decrement method. This was evident

through the reduced conclusions that could be drawn from the Pile 3 response, where

damping was only computed using the logarithmic decrement method.

Conclusions

213

Significant inelasticity was generally evident in the pull-back peak of the 10 kN snap-

back tests and low mass (324 kg) 120 kN snap-back tests, and the first three cycles of the

two higher mass level (609 and 1275 kg) 120 kN snap-back tests (separation in the time

domain) (Table 5-4). This required that two different sets of envelopes were fitted for the

elastic and inelastic responses, to give the elastic and inelastic ‘system damping’.

Including the pull-back peak is beneficial as it contains inelastic impact effects which are

an important nature of snap-back testing. For the inclusion of the pull-back peak a clean,

unfiltered response is desirable. These impact effects are possible during an earthquake,

and are not easily captured during eccentric mass shaker testing (Figure 5-49). Thus,

excluding its cost and time benefits snap-back testing is still preferred.

Elastic system damping, of around 5%, was often found to increase for decreasing mass

levels, and as testing progressed due to increased gap depths and a resulting reduction in

pile-soil stiffness (Figure 5-23). This is consistent with the mathematical definition of the

damping ratio (5.3.1). There were deviations for the two lower mass levels (324 and 609

kg), which was attributed to the significant contribution of the distributed pile mass to the

overall mass at the pile head. Thus it is suggested that larger mass levels are

predominately tested in future, with natural frequencies no greater than 10 Hz.

The inelastic system damping for the high force 120 kN snap-back tests was found to

increase with increasing mass levels (Figures 5-30 – 5-32), due to highly inelastic impact

effects that become more prominent. A maximum system damping ratio of 50% was

computed for the high mass level (1275 kg); a result of large displacements and

significant impact effects. Note this damping is computed during the early cycles only

and is not representative of an elastic level of damping that should be associated with

these pile-soil systems.

From the hysteretic pile response:

The snap-back responses were found to have a ‘ratcheting’ movement in the direction of

the snap-back release (Figures 5-48, 5-50, 5-55). This was attributed to the pile vibrating

against the soil that was imparted with large impact damage following the initial cycle of

the snap-back release. It is also likely that the clay on this side of the pile had moved

(Figure 4-5), and hence become less dense, due to reducing lateral earth pressures in the

soil as the pile moves away during the pull-back test (Figure 4-6). This response occurs

because of the unsymmetrical nature of snap-back testing; these types of responses were

not experienced for eccentric mass shaker testing carried out during previous research at

the same site (Figure 5-49).

Conclusions

214

The hysteretic response for low force level snap-back tests (Figures 5-52 and 5-53) was

much cleaner than high force snap-back tests (Figures 5-54 and 5-55) due to significant

impact effects disrupting the response for high force tests. The relative displacement of

the hysteresis loops to pull-back displacement was also much greater for low force level

tests (Figure 5-52), similarly due to reduced impact effects for these tests.

Hysteresis loops evident at low displacement cycles for low and high force tests mean

that there is some inelasticity occurring during the assumed elastic response.

The dynamic stiffness of the pile was the most difficult to measure during testing. The

operational stiffness was used to define an ‘average’ stiffness of the hysteresis loop, and

compared between subsequent tests to assess degradation in stiffness (Figures 5-50, 5-53,

5-55). Little data is generated in addition to the force-displacement relationships. This is

consistent with the qualitative approach used to measure the static stiffness of the pile as

well. This is where a numerical analysis, or other, is important. If a model is able to

characterise a complex response with simple geotechnical parameters then a qualitative

approach like this one is sufficient.

Numerical modelling of lateral pile response

The numerical Ruaumoko pile models were able to capture the following responses of Piles 3 and

4 during field tests:

Hammer tests (natural period) – modal response

Pull-back phase of snap-back tests – pushover response

Snap-back and hammer tests – dynamic response

Existing elements and hysteresis rules available in the structural analysis program were utilised to

adequately represent the characteristics of each pile:

Soil stiffness has been represented by spring elements, based on the modulus of subgrade

reaction. Springs were utilised on both sides of the pile due to different behaviour in

compression and tension.

The bi-linear hysteresis rule with slackness was utilised for spring elements (Figure 6-2).

This reduced spring stiffness to zero in the tension range, and also accounted for residual

soil gaps present around the pile during field testing by specifying a compressive gap that

had to be overcome for actions to be transferred to the spring element. Where no residual

gapping was evident, springs were preloaded to account for in-situ earth pressures in the

soil under zero lateral strain.

Conclusions

215

Material specific damping was specified in the model so that soil damping could be

considered separately to the Rayleigh (proportional) damping of the pile. This also

enabled zero damping to be specified in spring elements, so that dashpots incorporated

into the model could define the elastic radiation soil damping. Material damping was

provided by the hysteretic action of the springs.

The dashpots were incorporated into the model using a series spring arrangement (Figure

6-16). Near-field behaviour (inelastic response and gapping behaviour) was controlled by

a stiff inner spring, and far-field behaviour was controlled by an elastic spring and linear

dashpot element. A stiff inner spring was necessary to ensure a small velocity difference

across the element so that adequate damping is provided by the outer dashpot element. A

softer outer spring maintained the overall stiffness of the response.

Additional contact damping developed following the release of the pile from the pull-

back peak during snap-back tests was accounted for by introducing contact members into

the model (Figure 6-18). These were kept separate to the existing series spring

arrangement, and utilised three to four pile diameters beneath the effective ground level

(Figure 4-3). A different damping coefficient on each side of the pile, specified relative to

the linear dashpot coefficient at that depth, was necessary to capture the response. The

coefficients also changed between tests. These contact members could not accurately

model gap growth.

The following key points are summarised from model comparison with corresponding field tests:

The shallow gap depth (tension side during pull-back tests) had significant control over

the natural period of the pile (6.5.1). The pushover response was insensitive to the change

in this parameter (6.5.1) enabling accurate modal analysis comparisons to the natural

periods computed from full-scale hammer tests. Reduced tension gap depths were

employed to account for side contact influencing the natural period computed during field

testing.

The gap depth employed in front of the pile (compression side during pull-back tests) had

the greatest control over the pushover response (6.5.1). Similar values were employed to

the extensive measurements taken during Pile 4 testing (Table 6-2).

Larger gap depths were predicted by Ruaumoko following the static pile unload, than

those used in the subsequent pushover model (Tables 6-3 and 6-4). These gap growths

were possible during testing, where some recovery of the gap depth may have occurred

before the next test was carried out.

Conclusions

216

Performing testing on a pile with no residual gapping at the start of testing is favourable.

Pile 3 had residual gapping at the start of testing; the additional unknown meant that it

was difficult to determine if a scaling factor should be applied to the spring stiffness.

Elastic soil stiffness and damping were well represented by the dynamic series spring

model due to favourable comparisons with hammer tests (Figures 6-19, 6-20, 6-31).

Discrepancies occurred for low mass (324 and 609 kg) Pile 4 responses, where

inconsistent levels of damping were evident in these test responses (Figures 6-29 and 6-

30). This supports the earlier conclusion that higher mass levels should be tested in future.

It was important that the modal properties and non-linear static stiffness were well

represented (Figures 6-6 – 6-9, 6-11 – 6-14) before considering the dynamic response.

In general, the series spring model was only capable of modelling snap-back responses at

later cycles where only low impact effects were evident or the elastic response governed

(Figures 6-21, 6-22, 6-23, 6-25).

Significant impact effects developed near the pull-back release for low (7.5 kN) and high

(120 kN) force snap-back tests were captured using contact members (Figures 6-24, 6-26,

6-27, 6-28, 6-34). Contact members were fixed at end two away from the pile; hence they

were active during the inelastic and elastic phases of the response. This meant they could

only capture the first few cycles of the response, preventing the model from oscillating at

later stages in the response with a similarly low level of damping to the test response. The

contact member model needs to be further developed so that both portions of the response

can be accounted for.

7.1 RECOMMENDATIONS FOR FUTURE RESEARCH

This thesis has numerically captured the full-scale response of two 273 mm diameter steel tube

piles in stiff clay. A limitation identified in the modelling approach is that the large contact

damping evident near the pull-back release of snap-back tests required contact members to be

incorporated into the dynamic model. This meant that the elastic portion of the response

developed after several cycles, was no longer captured by the model. An alternative method needs

to be incorporated to account for the entire response with a single model.

This research amalgamates as part of Soil-Foundation-Structure Interaction (SFSI). Non-linear

foundation-soil interaction has been well documented by extensive research in this area (Pender,

2007; Pender et al., 2009; Wotherspoon, 2009; M.Sa’don, 2010; Orense et al., 2010; Pender et al.,

2011; M.Sa’don, 2012; Pender et al., 2012a). Analytical work by Wotherspoon (2009) has shown

that foundation-structure interaction is significant. The connecting step that is required in this

field is to link experimental foundation non-linearity into an analytical integrated foundation-

Conclusions

217

structure modelling approach carried out by Wotherspoon. The current study has undertaken the

testing and modelling approach that is required. However, a greater range of test conditions need

to be captured in a similar modelling approach for such a model to be incorporated in an

integrated structure-foundation model. These test conditions include:

Re-driving the piles to a different embedment depth (such that the piles extend to a

different height above ground level)

Varying the installation procedure (e.g. driven open-ended, bored)

Varying the pile type (e.g. solid timber piles, cast-in-place reinforced concrete piles)

Testing in different soil profiles (e.g. soft clays, loose sands, dense sands)

Investigating different soil behaviour (e.g. liquefaction of loose sands)

Fixing the pile head, and investigating different levels of pile-head fixity

Investigating group interaction effects, utilising different pile cap arrangements and/or

driving piles closer together

Simple scale models that incorporate a combined foundation-structure system

From the list provided, it is evident that there is a range of different conditions possible for

foundations. Any number of factors should be changed for each new testing program as the

objective is to capture the greatest possible range of test conditions in a comparable modelling

approach. A similar approach also needs to be incorporated for shallow and raft foundations.

Conclusions

218

References

219

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Pile 3 dynamic data file input into Ruaumoko

A-1

APPENDIX A PILE 3 DYNAMIC DATA FILE

INPUT INTO RUAUMOKO

Albany Pile 3 model

*Principal analysis options

2 1 0 5 -1 0 0 0 0 0

*Frame control parameters

696 967 681 6 0 0 9.81 2.59477 0 0.0005 6 1

*Output intervals and plotting control parameters

0 10 10 10 1 1 1 1 0 0 1 0

*Plot axes transformation

default

*Iteration control and wave velocities

10 3 0 0 0 0 0 0 0 0 0 0

*Nodal data

* X direction perpendicular to load application; Y direction vertical; Z direction parallel to load application

NODES

1 0 0.85 0 1 0 0 0 1 1 !Lead weight node

2 0 0.75 0 1 0 0 0 1 1 !Cantilever nodes

3 0 0.7 0 1 0 0 0 1 1

4 0 0.65 0 1 0 0 0 1 1

5 0 0.6 0 1 0 0 0 1 1

6 0 0.55 0 1 0 0 0 1 1

7 0 0.5 0 1 0 0 0 1 1 !LVDT 1

8 0 0.45 0 1 0 0 0 1 1

9 0 0.4 0 1 0 0 0 1 1

10 0 0.35 0 1 0 0 0 1 1

11 0 0.3 0 1 0 0 0 1 1 !Load cell

12 0 0.25 0 1 0 0 0 1 1 !LVDT 2

13 0 0.2 0 1 0 0 0 1 1

14 0 0.15 0 1 0 0 0 1 1

15 0 0.1 0 1 0 0 0 1 1

16 0 0.05 0 1 0 0 0 1 1

17 0 0 0 1 0 0 0 1 1 !Pile nodes

18 0 -0.05 0 1 0 0 0 1 1

19 0 -0.1 0 1 0 0 0 1 1

20 0 -0.15 0 1 0 0 0 1 1

21 0 -0.2 0 1 0 0 0 1 1

22 0 -0.25 0 1 0 0 0 1 1

23 0 -0.3 0 1 0 0 0 1 1

24 0 -0.35 0 1 0 0 0 1 1

25 0 -0.4 0 1 0 0 0 1 1

26 0 -0.45 0 1 0 0 0 1 1

27 0 -0.5 0 1 0 0 0 1 1

28 0 -0.55 0 1 0 0 0 1 1

29 0 -0.6 0 1 0 0 0 1 1

30 0 -0.65 0 1 0 0 0 1 1

Pile 3 dynamic data file input into Ruaumoko

A-2

31 0 -0.7 0 1 0 0 0 1 1

32 0 -0.75 0 1 0 0 0 1 1

33 0 -0.8 0 1 0 0 0 1 1

34 0 -0.85 0 1 0 0 0 1 1

35 0 -0.9 0 1 0 0 0 1 1

36 0 -0.95 0 1 0 0 0 1 1

37 0 -1 0 1 0 0 0 1 1

38 0 -1.05 0 1 0 0 0 1 1

39 0 -1.1 0 1 0 0 0 1 1

40 0 -1.15 0 1 0 0 0 1 1

41 0 -1.2 0 1 0 0 0 1 1

42 0 -1.25 0 1 0 0 0 1 1

43 0 -1.3 0 1 0 0 0 1 1

44 0 -1.35 0 1 0 0 0 1 1

45 0 -1.4 0 1 0 0 0 1 1

46 0 -1.45 0 1 0 0 0 1 1

47 0 -1.5 0 1 0 0 0 1 1

48 0 -1.55 0 1 0 0 0 1 1

49 0 -1.6 0 1 0 0 0 1 1

50 0 -1.65 0 1 0 0 0 1 1

51 0 -1.7 0 1 0 0 0 1 1

52 0 -1.75 0 1 0 0 0 1 1

53 0 -1.8 0 1 0 0 0 1 1

54 0 -1.85 0 1 0 0 0 1 1

55 0 -1.9 0 1 0 0 0 1 1

56 0 -1.95 0 1 0 0 0 1 1

57 0 -2 0 1 0 0 0 1 1

58 0 -2.05 0 1 0 0 0 1 1

59 0 -2.1 0 1 0 0 0 1 1

60 0 -2.15 0 1 0 0 0 1 1

61 0 -2.2 0 1 0 0 0 1 1

62 0 -2.25 0 1 0 0 0 1 1

63 0 -2.3 0 1 0 0 0 1 1

64 0 -2.35 0 1 0 0 0 1 1

65 0 -2.4 0 1 0 0 0 1 1

66 0 -2.45 0 1 0 0 0 1 1

67 0 -2.5 0 1 0 0 0 1 1

68 0 -2.55 0 1 0 0 0 1 1

69 0 -2.6 0 1 0 0 0 1 1

70 0 -2.65 0 1 0 0 0 1 1

71 0 -2.7 0 1 0 0 0 1 1

72 0 -2.75 0 1 0 0 0 1 1

73 0 -2.8 0 1 0 0 0 1 1

74 0 -2.85 0 1 0 0 0 1 1

75 0 -2.9 0 1 0 0 0 1 1

76 0 -2.95 0 1 0 0 0 1 1

77 0 -3 0 1 0 0 0 1 1

78 0 -3.05 0 1 0 0 0 1 1

79 0 -3.1 0 1 0 0 0 1 1

80 0 -3.15 0 1 0 0 0 1 1

Pile 3 dynamic data file input into Ruaumoko

A-3

81 0 -3.2 0 1 0 0 0 1 1

82 0 -3.25 0 1 0 0 0 1 1

83 0 -3.3 0 1 0 0 0 1 1

84 0 -3.35 0 1 0 0 0 1 1

85 0 -3.4 0 1 0 0 0 1 1

86 0 -3.45 0 1 0 0 0 1 1

87 0 -3.5 0 1 0 0 0 1 1

88 0 -3.55 0 1 0 0 0 1 1

89 0 -3.6 0 1 0 0 0 1 1

90 0 -3.65 0 1 0 0 0 1 1

91 0 -3.7 0 1 0 0 0 1 1

92 0 -3.75 0 1 0 0 0 1 1

93 0 -3.8 0 1 0 0 0 1 1

94 0 -3.85 0 1 0 0 0 1 1

95 0 -3.9 0 1 0 0 0 1 1

96 0 -3.95 0 1 0 0 0 1 1

97 0 -4 0 1 0 0 0 1 1

98 0 -4.05 0 1 0 0 0 1 1

99 0 -4.1 0 1 0 0 0 1 1

100 0 -4.15 0 1 0 0 0 1 1

101 0 -4.2 0 1 0 0 0 1 1

102 0 -4.25 0 1 0 0 0 1 1

103 0 -4.3 0 1 0 0 0 1 1

104 0 -4.35 0 1 0 0 0 1 1

105 0 -4.4 0 1 0 0 0 1 1

106 0 -4.45 0 1 0 0 0 1 1

107 0 -4.5 0 1 0 0 0 1 1

108 0 -4.55 0 1 0 0 0 1 1

109 0 -4.6 0 1 0 0 0 1 1

110 0 -4.65 0 1 0 0 0 1 1

111 0 -4.7 0 1 0 0 0 1 1

112 0 -4.75 0 1 0 0 0 1 1

113 0 -4.8 0 1 0 0 0 1 1

114 0 -4.85 0 1 0 0 0 1 1

115 0 -4.9 0 1 0 0 0 1 1

116 0 -4.95 0 1 0 0 0 1 1

117 0 -5 0 1 0 0 0 1 1

118 0 -5.05 0 1 0 0 0 1 1

119 0 -5.1 0 1 0 0 0 1 1

120 0 -5.15 0 1 0 0 0 1 1

121 0 -5.2 0 1 0 0 0 1 1

122 0 -5.25 0 1 0 0 0 1 1

123 0 -5.3 0 1 0 0 0 1 1

124 0 -5.35 0 1 0 0 0 1 1

125 0 -5.4 0 1 0 0 0 1 1

126 0 -5.45 0 1 0 0 0 1 1

127 0 -5.5 0 1 0 0 0 1 1

128 0 -5.55 0 1 0 0 0 1 1

129 0 -5.6 0 1 0 0 0 1 1

130 0 -5.65 0 1 0 0 0 1 1

Pile 3 dynamic data file input into Ruaumoko

A-4

131 0 -5.7 0 1 0 0 0 1 1

132 0 -5.75 0 1 0 0 0 1 1

133 0 -5.8 0 1 0 0 0 1 1

134 0 -5.85 0 1 0 0 0 1 1

135 0 -5.9 0 1 0 0 0 1 1

136 0 -5.95 0 1 0 0 0 1 1

137 0 -6 0 1 0 0 0 1 1

138 0 -6.05 0 1 0 0 0 1 1

139 0 -6.1 0 1 0 0 0 1 1

140 0 -6.15 0 1 0 0 0 1 1

141 0 -6.2 0 1 0 0 0 1 1

142 0 -6.25 0 1 0 0 0 1 1

143 0 -6.3 0 1 0 0 0 1 1

144 0 -6.35 0 1 0 0 0 1 1

145 0 -6.4 0 1 0 0 0 1 1

146 0 -6.45 0 1 0 0 0 1 1

147 0 -6.5 0 1 0 0 0 1 1

148 0 -6.55 0 1 0 0 0 1 1

149 0 -6.6 0 1 0 0 0 1 1

150 0 -6.65 0 1 0 0 0 1 1

151 0 -6.7 0 1 0 0 0 1 1

152 0 -6.75 0 1 1 0 0 1 1

153 0 0 5 1 1 0 1 1 1 !Internal spring nodes

side one

154 0 -0.05 5 1 1 0 1 1 1

155 0 -0.1 5 1 1 0 1 1 1

156 0 -0.15 5 1 1 0 1 1 1

157 0 -0.2 5 1 1 0 1 1 1

158 0 -0.25 5 1 1 0 1 1 1

159 0 -0.3 5 1 1 0 1 1 1

160 0 -0.35 5 1 1 0 1 1 1

161 0 -0.4 5 1 1 0 1 1 1

162 0 -0.45 5 1 1 0 1 1 1

163 0 -0.5 5 1 1 0 1 1 1

164 0 -0.55 5 1 1 0 1 1 1

165 0 -0.6 5 1 1 0 1 1 1

166 0 -0.65 5 1 1 0 1 1 1

167 0 -0.7 5 1 1 0 1 1 1

168 0 -0.75 5 1 1 0 1 1 1

169 0 -0.8 5 1 1 0 1 1 1

170 0 -0.85 5 1 1 0 1 1 1

171 0 -0.9 5 1 1 0 1 1 1

172 0 -0.95 5 1 1 0 1 1 1

173 0 -1 5 1 1 0 1 1 1

174 0 -1.05 5 1 1 0 1 1 1

175 0 -1.1 5 1 1 0 1 1 1

176 0 -1.15 5 1 1 0 1 1 1

177 0 -1.2 5 1 1 0 1 1 1

178 0 -1.25 5 1 1 0 1 1 1

179 0 -1.3 5 1 1 0 1 1 1

Pile 3 dynamic data file input into Ruaumoko

A-5

180 0 -1.35 5 1 1 0 1 1 1

181 0 -1.4 5 1 1 0 1 1 1

182 0 -1.45 5 1 1 0 1 1 1

183 0 -1.5 5 1 1 0 1 1 1

184 0 -1.55 5 1 1 0 1 1 1

185 0 -1.6 5 1 1 0 1 1 1

186 0 -1.65 5 1 1 0 1 1 1

187 0 -1.7 5 1 1 0 1 1 1

188 0 -1.75 5 1 1 0 1 1 1

189 0 -1.8 5 1 1 0 1 1 1

190 0 -1.85 5 1 1 0 1 1 1

191 0 -1.9 5 1 1 0 1 1 1

192 0 -1.95 5 1 1 0 1 1 1

193 0 -2 5 1 1 0 1 1 1

194 0 -2.05 5 1 1 0 1 1 1

195 0 -2.1 5 1 1 0 1 1 1

196 0 -2.15 5 1 1 0 1 1 1

197 0 -2.2 5 1 1 0 1 1 1

198 0 -2.25 5 1 1 0 1 1 1

199 0 -2.3 5 1 1 0 1 1 1

200 0 -2.35 5 1 1 0 1 1 1

201 0 -2.4 5 1 1 0 1 1 1

202 0 -2.45 5 1 1 0 1 1 1

203 0 -2.5 5 1 1 0 1 1 1

204 0 -2.55 5 1 1 0 1 1 1

205 0 -2.6 5 1 1 0 1 1 1

206 0 -2.65 5 1 1 0 1 1 1

207 0 -2.7 5 1 1 0 1 1 1

208 0 -2.75 5 1 1 0 1 1 1

209 0 -2.8 5 1 1 0 1 1 1

210 0 -2.85 5 1 1 0 1 1 1

211 0 -2.9 5 1 1 0 1 1 1

212 0 -2.95 5 1 1 0 1 1 1

213 0 -3 5 1 1 0 1 1 1

214 0 -3.05 5 1 1 0 1 1 1

215 0 -3.1 5 1 1 0 1 1 1

216 0 -3.15 5 1 1 0 1 1 1

217 0 -3.2 5 1 1 0 1 1 1

218 0 -3.25 5 1 1 0 1 1 1

219 0 -3.3 5 1 1 0 1 1 1

220 0 -3.35 5 1 1 0 1 1 1

221 0 -3.4 5 1 1 0 1 1 1

222 0 -3.45 5 1 1 0 1 1 1

223 0 -3.5 5 1 1 0 1 1 1

224 0 -3.55 5 1 1 0 1 1 1

225 0 -3.6 5 1 1 0 1 1 1

226 0 -3.65 5 1 1 0 1 1 1

227 0 -3.7 5 1 1 0 1 1 1

228 0 -3.75 5 1 1 0 1 1 1

229 0 -3.8 5 1 1 0 1 1 1

Pile 3 dynamic data file input into Ruaumoko

A-6

230 0 -3.85 5 1 1 0 1 1 1

231 0 -3.9 5 1 1 0 1 1 1

232 0 -3.95 5 1 1 0 1 1 1

233 0 -4 5 1 1 0 1 1 1

234 0 -4.05 5 1 1 0 1 1 1

235 0 -4.1 5 1 1 0 1 1 1

236 0 -4.15 5 1 1 0 1 1 1

237 0 -4.2 5 1 1 0 1 1 1

238 0 -4.25 5 1 1 0 1 1 1

239 0 -4.3 5 1 1 0 1 1 1

240 0 -4.35 5 1 1 0 1 1 1

241 0 -4.4 5 1 1 0 1 1 1

242 0 -4.45 5 1 1 0 1 1 1

243 0 -4.5 5 1 1 0 1 1 1

244 0 -4.55 5 1 1 0 1 1 1

245 0 -4.6 5 1 1 0 1 1 1

246 0 -4.65 5 1 1 0 1 1 1

247 0 -4.7 5 1 1 0 1 1 1

248 0 -4.75 5 1 1 0 1 1 1

249 0 -4.8 5 1 1 0 1 1 1

250 0 -4.85 5 1 1 0 1 1 1

251 0 -4.9 5 1 1 0 1 1 1

252 0 -4.95 5 1 1 0 1 1 1

253 0 -5 5 1 1 0 1 1 1

254 0 -5.05 5 1 1 0 1 1 1

255 0 -5.1 5 1 1 0 1 1 1

256 0 -5.15 5 1 1 0 1 1 1

257 0 -5.2 5 1 1 0 1 1 1

258 0 -5.25 5 1 1 0 1 1 1

259 0 -5.3 5 1 1 0 1 1 1

260 0 -5.35 5 1 1 0 1 1 1

261 0 -5.4 5 1 1 0 1 1 1

262 0 -5.45 5 1 1 0 1 1 1

263 0 -5.5 5 1 1 0 1 1 1

264 0 -5.55 5 1 1 0 1 1 1

265 0 -5.6 5 1 1 0 1 1 1

266 0 -5.65 5 1 1 0 1 1 1

267 0 -5.7 5 1 1 0 1 1 1

268 0 -5.75 5 1 1 0 1 1 1

269 0 -5.8 5 1 1 0 1 1 1

270 0 -5.85 5 1 1 0 1 1 1

271 0 -5.9 5 1 1 0 1 1 1

272 0 -5.95 5 1 1 0 1 1 1

273 0 -6 5 1 1 0 1 1 1

274 0 -6.05 5 1 1 0 1 1 1

275 0 -6.1 5 1 1 0 1 1 1

276 0 -6.15 5 1 1 0 1 1 1

277 0 -6.2 5 1 1 0 1 1 1

278 0 -6.25 5 1 1 0 1 1 1

279 0 -6.3 5 1 1 0 1 1 1

Pile 3 dynamic data file input into Ruaumoko

A-7

280 0 -6.35 5 1 1 0 1 1 1

281 0 -6.4 5 1 1 0 1 1 1

282 0 -6.45 5 1 1 0 1 1 1

283 0 -6.5 5 1 1 0 1 1 1

284 0 -6.55 5 1 1 0 1 1 1

285 0 -6.6 5 1 1 0 1 1 1

286 0 -6.65 5 1 1 0 1 1 1

287 0 -6.7 5 1 1 0 1 1 1

288 0 -6.75 5 1 1 0 1 1 1

289 0 0 -5 1 1 0 1 1 1 !Internal spring nodes

side two

290 0 -0.05 -5 1 1 0 1 1 1

291 0 -0.1 -5 1 1 0 1 1 1

292 0 -0.15 -5 1 1 0 1 1 1

293 0 -0.2 -5 1 1 0 1 1 1

294 0 -0.25 -5 1 1 0 1 1 1

295 0 -0.3 -5 1 1 0 1 1 1

296 0 -0.35 -5 1 1 0 1 1 1

297 0 -0.4 -5 1 1 0 1 1 1

298 0 -0.45 -5 1 1 0 1 1 1

299 0 -0.5 -5 1 1 0 1 1 1

300 0 -0.55 -5 1 1 0 1 1 1

301 0 -0.6 -5 1 1 0 1 1 1

302 0 -0.65 -5 1 1 0 1 1 1

303 0 -0.7 -5 1 1 0 1 1 1

304 0 -0.75 -5 1 1 0 1 1 1

305 0 -0.8 -5 1 1 0 1 1 1

306 0 -0.85 -5 1 1 0 1 1 1

307 0 -0.9 -5 1 1 0 1 1 1

308 0 -0.95 -5 1 1 0 1 1 1

309 0 -1 -5 1 1 0 1 1 1

310 0 -1.05 -5 1 1 0 1 1 1

311 0 -1.1 -5 1 1 0 1 1 1

312 0 -1.15 -5 1 1 0 1 1 1

313 0 -1.2 -5 1 1 0 1 1 1

314 0 -1.25 -5 1 1 0 1 1 1

315 0 -1.3 -5 1 1 0 1 1 1

316 0 -1.35 -5 1 1 0 1 1 1

317 0 -1.4 -5 1 1 0 1 1 1

318 0 -1.45 -5 1 1 0 1 1 1

319 0 -1.5 -5 1 1 0 1 1 1

320 0 -1.55 -5 1 1 0 1 1 1

321 0 -1.6 -5 1 1 0 1 1 1

322 0 -1.65 -5 1 1 0 1 1 1

323 0 -1.7 -5 1 1 0 1 1 1

324 0 -1.75 -5 1 1 0 1 1 1

325 0 -1.8 -5 1 1 0 1 1 1

326 0 -1.85 -5 1 1 0 1 1 1

327 0 -1.9 -5 1 1 0 1 1 1

328 0 -1.95 -5 1 1 0 1 1 1

Pile 3 dynamic data file input into Ruaumoko

A-8

329 0 -2 -5 1 1 0 1 1 1

330 0 -2.05 -5 1 1 0 1 1 1

331 0 -2.1 -5 1 1 0 1 1 1

332 0 -2.15 -5 1 1 0 1 1 1

333 0 -2.2 -5 1 1 0 1 1 1

334 0 -2.25 -5 1 1 0 1 1 1

335 0 -2.3 -5 1 1 0 1 1 1

336 0 -2.35 -5 1 1 0 1 1 1

337 0 -2.4 -5 1 1 0 1 1 1

338 0 -2.45 -5 1 1 0 1 1 1

339 0 -2.5 -5 1 1 0 1 1 1

340 0 -2.55 -5 1 1 0 1 1 1

341 0 -2.6 -5 1 1 0 1 1 1

342 0 -2.65 -5 1 1 0 1 1 1

343 0 -2.7 -5 1 1 0 1 1 1

344 0 -2.75 -5 1 1 0 1 1 1

345 0 -2.8 -5 1 1 0 1 1 1

346 0 -2.85 -5 1 1 0 1 1 1

347 0 -2.9 -5 1 1 0 1 1 1

348 0 -2.95 -5 1 1 0 1 1 1

349 0 -3 -5 1 1 0 1 1 1

350 0 -3.05 -5 1 1 0 1 1 1

351 0 -3.1 -5 1 1 0 1 1 1

352 0 -3.15 -5 1 1 0 1 1 1

353 0 -3.2 -5 1 1 0 1 1 1

354 0 -3.25 -5 1 1 0 1 1 1

355 0 -3.3 -5 1 1 0 1 1 1

356 0 -3.35 -5 1 1 0 1 1 1

357 0 -3.4 -5 1 1 0 1 1 1

358 0 -3.45 -5 1 1 0 1 1 1

359 0 -3.5 -5 1 1 0 1 1 1

360 0 -3.55 -5 1 1 0 1 1 1

361 0 -3.6 -5 1 1 0 1 1 1

362 0 -3.65 -5 1 1 0 1 1 1

363 0 -3.7 -5 1 1 0 1 1 1

364 0 -3.75 -5 1 1 0 1 1 1

365 0 -3.8 -5 1 1 0 1 1 1

366 0 -3.85 -5 1 1 0 1 1 1

367 0 -3.9 -5 1 1 0 1 1 1

368 0 -3.95 -5 1 1 0 1 1 1

369 0 -4 -5 1 1 0 1 1 1

370 0 -4.05 -5 1 1 0 1 1 1

371 0 -4.1 -5 1 1 0 1 1 1

372 0 -4.15 -5 1 1 0 1 1 1

373 0 -4.2 -5 1 1 0 1 1 1

374 0 -4.25 -5 1 1 0 1 1 1

375 0 -4.3 -5 1 1 0 1 1 1

376 0 -4.35 -5 1 1 0 1 1 1

377 0 -4.4 -5 1 1 0 1 1 1

378 0 -4.45 -5 1 1 0 1 1 1

Pile 3 dynamic data file input into Ruaumoko

A-9

379 0 -4.5 -5 1 1 0 1 1 1

380 0 -4.55 -5 1 1 0 1 1 1

381 0 -4.6 -5 1 1 0 1 1 1

382 0 -4.65 -5 1 1 0 1 1 1

383 0 -4.7 -5 1 1 0 1 1 1

384 0 -4.75 -5 1 1 0 1 1 1

385 0 -4.8 -5 1 1 0 1 1 1

386 0 -4.85 -5 1 1 0 1 1 1

387 0 -4.9 -5 1 1 0 1 1 1

388 0 -4.95 -5 1 1 0 1 1 1

389 0 -5 -5 1 1 0 1 1 1

390 0 -5.05 -5 1 1 0 1 1 1

391 0 -5.1 -5 1 1 0 1 1 1

392 0 -5.15 -5 1 1 0 1 1 1

393 0 -5.2 -5 1 1 0 1 1 1

394 0 -5.25 -5 1 1 0 1 1 1

395 0 -5.3 -5 1 1 0 1 1 1

396 0 -5.35 -5 1 1 0 1 1 1

397 0 -5.4 -5 1 1 0 1 1 1

398 0 -5.45 -5 1 1 0 1 1 1

399 0 -5.5 -5 1 1 0 1 1 1

400 0 -5.55 -5 1 1 0 1 1 1

401 0 -5.6 -5 1 1 0 1 1 1

402 0 -5.65 -5 1 1 0 1 1 1

403 0 -5.7 -5 1 1 0 1 1 1

404 0 -5.75 -5 1 1 0 1 1 1

405 0 -5.8 -5 1 1 0 1 1 1

406 0 -5.85 -5 1 1 0 1 1 1

407 0 -5.9 -5 1 1 0 1 1 1

408 0 -5.95 -5 1 1 0 1 1 1

409 0 -6 -5 1 1 0 1 1 1

410 0 -6.05 -5 1 1 0 1 1 1

411 0 -6.1 -5 1 1 0 1 1 1

412 0 -6.15 -5 1 1 0 1 1 1

413 0 -6.2 -5 1 1 0 1 1 1

414 0 -6.25 -5 1 1 0 1 1 1

415 0 -6.3 -5 1 1 0 1 1 1

416 0 -6.35 -5 1 1 0 1 1 1

417 0 -6.4 -5 1 1 0 1 1 1

418 0 -6.45 -5 1 1 0 1 1 1

419 0 -6.5 -5 1 1 0 1 1 1

420 0 -6.55 -5 1 1 0 1 1 1

421 0 -6.6 -5 1 1 0 1 1 1

422 0 -6.65 -5 1 1 0 1 1 1

423 0 -6.7 -5 1 1 0 1 1 1

424 0 -6.75 -5 1 1 0 1 1 1

425 0 0 10 1 1 1 1 1 1 !External spring nodes

side one

426 0 -0.05 10 1 1 1 1 1 1

427 0 -0.1 10 1 1 1 1 1 1

Pile 3 dynamic data file input into Ruaumoko

A-10

428 0 -0.15 10 1 1 1 1 1 1

429 0 -0.2 10 1 1 1 1 1 1

430 0 -0.25 10 1 1 1 1 1 1

431 0 -0.3 10 1 1 1 1 1 1

432 0 -0.35 10 1 1 1 1 1 1

433 0 -0.4 10 1 1 1 1 1 1

434 0 -0.45 10 1 1 1 1 1 1

435 0 -0.5 10 1 1 1 1 1 1

436 0 -0.55 10 1 1 1 1 1 1

437 0 -0.6 10 1 1 1 1 1 1

438 0 -0.65 10 1 1 1 1 1 1

439 0 -0.7 10 1 1 1 1 1 1

440 0 -0.75 10 1 1 1 1 1 1

441 0 -0.8 10 1 1 1 1 1 1

442 0 -0.85 10 1 1 1 1 1 1

443 0 -0.9 10 1 1 1 1 1 1

444 0 -0.95 10 1 1 1 1 1 1

445 0 -1 10 1 1 1 1 1 1

446 0 -1.05 10 1 1 1 1 1 1

447 0 -1.1 10 1 1 1 1 1 1

448 0 -1.15 10 1 1 1 1 1 1

449 0 -1.2 10 1 1 1 1 1 1

450 0 -1.25 10 1 1 1 1 1 1

451 0 -1.3 10 1 1 1 1 1 1

452 0 -1.35 10 1 1 1 1 1 1

453 0 -1.4 10 1 1 1 1 1 1

454 0 -1.45 10 1 1 1 1 1 1

455 0 -1.5 10 1 1 1 1 1 1

456 0 -1.55 10 1 1 1 1 1 1

457 0 -1.6 10 1 1 1 1 1 1

458 0 -1.65 10 1 1 1 1 1 1

459 0 -1.7 10 1 1 1 1 1 1

460 0 -1.75 10 1 1 1 1 1 1

461 0 -1.8 10 1 1 1 1 1 1

462 0 -1.85 10 1 1 1 1 1 1

463 0 -1.9 10 1 1 1 1 1 1

464 0 -1.95 10 1 1 1 1 1 1

465 0 -2 10 1 1 1 1 1 1

466 0 -2.05 10 1 1 1 1 1 1

467 0 -2.1 10 1 1 1 1 1 1

468 0 -2.15 10 1 1 1 1 1 1

469 0 -2.2 10 1 1 1 1 1 1

470 0 -2.25 10 1 1 1 1 1 1

471 0 -2.3 10 1 1 1 1 1 1

472 0 -2.35 10 1 1 1 1 1 1

473 0 -2.4 10 1 1 1 1 1 1

474 0 -2.45 10 1 1 1 1 1 1

475 0 -2.5 10 1 1 1 1 1 1

476 0 -2.55 10 1 1 1 1 1 1

477 0 -2.6 10 1 1 1 1 1 1

Pile 3 dynamic data file input into Ruaumoko

A-11

478 0 -2.65 10 1 1 1 1 1 1

479 0 -2.7 10 1 1 1 1 1 1

480 0 -2.75 10 1 1 1 1 1 1

481 0 -2.8 10 1 1 1 1 1 1

482 0 -2.85 10 1 1 1 1 1 1

483 0 -2.9 10 1 1 1 1 1 1

484 0 -2.95 10 1 1 1 1 1 1

485 0 -3 10 1 1 1 1 1 1

486 0 -3.05 10 1 1 1 1 1 1

487 0 -3.1 10 1 1 1 1 1 1

488 0 -3.15 10 1 1 1 1 1 1

489 0 -3.2 10 1 1 1 1 1 1

490 0 -3.25 10 1 1 1 1 1 1

491 0 -3.3 10 1 1 1 1 1 1

492 0 -3.35 10 1 1 1 1 1 1

493 0 -3.4 10 1 1 1 1 1 1

494 0 -3.45 10 1 1 1 1 1 1

495 0 -3.5 10 1 1 1 1 1 1

496 0 -3.55 10 1 1 1 1 1 1

497 0 -3.6 10 1 1 1 1 1 1

498 0 -3.65 10 1 1 1 1 1 1

499 0 -3.7 10 1 1 1 1 1 1

500 0 -3.75 10 1 1 1 1 1 1

501 0 -3.8 10 1 1 1 1 1 1

502 0 -3.85 10 1 1 1 1 1 1

503 0 -3.9 10 1 1 1 1 1 1

504 0 -3.95 10 1 1 1 1 1 1

505 0 -4 10 1 1 1 1 1 1

506 0 -4.05 10 1 1 1 1 1 1

507 0 -4.1 10 1 1 1 1 1 1

508 0 -4.15 10 1 1 1 1 1 1

509 0 -4.2 10 1 1 1 1 1 1

510 0 -4.25 10 1 1 1 1 1 1

511 0 -4.3 10 1 1 1 1 1 1

512 0 -4.35 10 1 1 1 1 1 1

513 0 -4.4 10 1 1 1 1 1 1

514 0 -4.45 10 1 1 1 1 1 1

515 0 -4.5 10 1 1 1 1 1 1

516 0 -4.55 10 1 1 1 1 1 1

517 0 -4.6 10 1 1 1 1 1 1

518 0 -4.65 10 1 1 1 1 1 1

519 0 -4.7 10 1 1 1 1 1 1

520 0 -4.75 10 1 1 1 1 1 1

521 0 -4.8 10 1 1 1 1 1 1

522 0 -4.85 10 1 1 1 1 1 1

523 0 -4.9 10 1 1 1 1 1 1

524 0 -4.95 10 1 1 1 1 1 1

525 0 -5 10 1 1 1 1 1 1

526 0 -5.05 10 1 1 1 1 1 1

527 0 -5.1 10 1 1 1 1 1 1

Pile 3 dynamic data file input into Ruaumoko

A-12

528 0 -5.15 10 1 1 1 1 1 1

529 0 -5.2 10 1 1 1 1 1 1

530 0 -5.25 10 1 1 1 1 1 1

531 0 -5.3 10 1 1 1 1 1 1

532 0 -5.35 10 1 1 1 1 1 1

533 0 -5.4 10 1 1 1 1 1 1

534 0 -5.45 10 1 1 1 1 1 1

535 0 -5.5 10 1 1 1 1 1 1

536 0 -5.55 10 1 1 1 1 1 1

537 0 -5.6 10 1 1 1 1 1 1

538 0 -5.65 10 1 1 1 1 1 1

539 0 -5.7 10 1 1 1 1 1 1

540 0 -5.75 10 1 1 1 1 1 1

541 0 -5.8 10 1 1 1 1 1 1

542 0 -5.85 10 1 1 1 1 1 1

543 0 -5.9 10 1 1 1 1 1 1

544 0 -5.95 10 1 1 1 1 1 1

545 0 -6 10 1 1 1 1 1 1

546 0 -6.05 10 1 1 1 1 1 1

547 0 -6.1 10 1 1 1 1 1 1

548 0 -6.15 10 1 1 1 1 1 1

549 0 -6.2 10 1 1 1 1 1 1

550 0 -6.25 10 1 1 1 1 1 1

551 0 -6.3 10 1 1 1 1 1 1

552 0 -6.35 10 1 1 1 1 1 1

553 0 -6.4 10 1 1 1 1 1 1

554 0 -6.45 10 1 1 1 1 1 1

555 0 -6.5 10 1 1 1 1 1 1

556 0 -6.55 10 1 1 1 1 1 1

557 0 -6.6 10 1 1 1 1 1 1

558 0 -6.65 10 1 1 1 1 1 1

559 0 -6.7 10 1 1 1 1 1 1

560 0 -6.75 10 1 1 1 1 1 1

561 0 0 -10 1 1 1 1 1 1 !External spring nodes

side two

562 0 -0.05 -10 1 1 1 1 1 1

563 0 -0.1 -10 1 1 1 1 1 1

564 0 -0.15 -10 1 1 1 1 1 1

565 0 -0.2 -10 1 1 1 1 1 1

566 0 -0.25 -10 1 1 1 1 1 1

567 0 -0.3 -10 1 1 1 1 1 1

568 0 -0.35 -10 1 1 1 1 1 1

569 0 -0.4 -10 1 1 1 1 1 1

570 0 -0.45 -10 1 1 1 1 1 1

571 0 -0.5 -10 1 1 1 1 1 1

572 0 -0.55 -10 1 1 1 1 1 1

573 0 -0.6 -10 1 1 1 1 1 1

574 0 -0.65 -10 1 1 1 1 1 1

575 0 -0.7 -10 1 1 1 1 1 1

576 0 -0.75 -10 1 1 1 1 1 1

Pile 3 dynamic data file input into Ruaumoko

A-13

577 0 -0.8 -10 1 1 1 1 1 1

578 0 -0.85 -10 1 1 1 1 1 1

579 0 -0.9 -10 1 1 1 1 1 1

580 0 -0.95 -10 1 1 1 1 1 1

581 0 -1 -10 1 1 1 1 1 1

582 0 -1.05 -10 1 1 1 1 1 1

583 0 -1.1 -10 1 1 1 1 1 1

584 0 -1.15 -10 1 1 1 1 1 1

585 0 -1.2 -10 1 1 1 1 1 1

586 0 -1.25 -10 1 1 1 1 1 1

587 0 -1.3 -10 1 1 1 1 1 1

588 0 -1.35 -10 1 1 1 1 1 1

589 0 -1.4 -10 1 1 1 1 1 1

590 0 -1.45 -10 1 1 1 1 1 1

591 0 -1.5 -10 1 1 1 1 1 1

592 0 -1.55 -10 1 1 1 1 1 1

593 0 -1.6 -10 1 1 1 1 1 1

594 0 -1.65 -10 1 1 1 1 1 1

595 0 -1.7 -10 1 1 1 1 1 1

596 0 -1.75 -10 1 1 1 1 1 1

597 0 -1.8 -10 1 1 1 1 1 1

598 0 -1.85 -10 1 1 1 1 1 1

599 0 -1.9 -10 1 1 1 1 1 1

600 0 -1.95 -10 1 1 1 1 1 1

601 0 -2 -10 1 1 1 1 1 1

602 0 -2.05 -10 1 1 1 1 1 1

603 0 -2.1 -10 1 1 1 1 1 1

604 0 -2.15 -10 1 1 1 1 1 1

605 0 -2.2 -10 1 1 1 1 1 1

606 0 -2.25 -10 1 1 1 1 1 1

607 0 -2.3 -10 1 1 1 1 1 1

608 0 -2.35 -10 1 1 1 1 1 1

609 0 -2.4 -10 1 1 1 1 1 1

610 0 -2.45 -10 1 1 1 1 1 1

611 0 -2.5 -10 1 1 1 1 1 1

612 0 -2.55 -10 1 1 1 1 1 1

613 0 -2.6 -10 1 1 1 1 1 1

614 0 -2.65 -10 1 1 1 1 1 1

615 0 -2.7 -10 1 1 1 1 1 1

616 0 -2.75 -10 1 1 1 1 1 1

617 0 -2.8 -10 1 1 1 1 1 1

618 0 -2.85 -10 1 1 1 1 1 1

619 0 -2.9 -10 1 1 1 1 1 1

620 0 -2.95 -10 1 1 1 1 1 1

621 0 -3 -10 1 1 1 1 1 1

622 0 -3.05 -10 1 1 1 1 1 1

623 0 -3.1 -10 1 1 1 1 1 1

624 0 -3.15 -10 1 1 1 1 1 1

625 0 -3.2 -10 1 1 1 1 1 1

626 0 -3.25 -10 1 1 1 1 1 1

Pile 3 dynamic data file input into Ruaumoko

A-14

627 0 -3.3 -10 1 1 1 1 1 1

628 0 -3.35 -10 1 1 1 1 1 1

629 0 -3.4 -10 1 1 1 1 1 1

630 0 -3.45 -10 1 1 1 1 1 1

631 0 -3.5 -10 1 1 1 1 1 1

632 0 -3.55 -10 1 1 1 1 1 1

633 0 -3.6 -10 1 1 1 1 1 1

634 0 -3.65 -10 1 1 1 1 1 1

635 0 -3.7 -10 1 1 1 1 1 1

636 0 -3.75 -10 1 1 1 1 1 1

637 0 -3.8 -10 1 1 1 1 1 1

638 0 -3.85 -10 1 1 1 1 1 1

639 0 -3.9 -10 1 1 1 1 1 1

640 0 -3.95 -10 1 1 1 1 1 1

641 0 -4 -10 1 1 1 1 1 1

642 0 -4.05 -10 1 1 1 1 1 1

643 0 -4.1 -10 1 1 1 1 1 1

644 0 -4.15 -10 1 1 1 1 1 1

645 0 -4.2 -10 1 1 1 1 1 1

646 0 -4.25 -10 1 1 1 1 1 1

647 0 -4.3 -10 1 1 1 1 1 1

648 0 -4.35 -10 1 1 1 1 1 1

649 0 -4.4 -10 1 1 1 1 1 1

650 0 -4.45 -10 1 1 1 1 1 1

651 0 -4.5 -10 1 1 1 1 1 1

652 0 -4.55 -10 1 1 1 1 1 1

653 0 -4.6 -10 1 1 1 1 1 1

654 0 -4.65 -10 1 1 1 1 1 1

655 0 -4.7 -10 1 1 1 1 1 1

656 0 -4.75 -10 1 1 1 1 1 1

657 0 -4.8 -10 1 1 1 1 1 1

658 0 -4.85 -10 1 1 1 1 1 1

659 0 -4.9 -10 1 1 1 1 1 1

660 0 -4.95 -10 1 1 1 1 1 1

661 0 -5 -10 1 1 1 1 1 1

662 0 -5.05 -10 1 1 1 1 1 1

663 0 -5.1 -10 1 1 1 1 1 1

664 0 -5.15 -10 1 1 1 1 1 1

665 0 -5.2 -10 1 1 1 1 1 1

666 0 -5.25 -10 1 1 1 1 1 1

667 0 -5.3 -10 1 1 1 1 1 1

668 0 -5.35 -10 1 1 1 1 1 1

669 0 -5.4 -10 1 1 1 1 1 1

670 0 -5.45 -10 1 1 1 1 1 1

671 0 -5.5 -10 1 1 1 1 1 1

672 0 -5.55 -10 1 1 1 1 1 1

673 0 -5.6 -10 1 1 1 1 1 1

674 0 -5.65 -10 1 1 1 1 1 1

675 0 -5.7 -10 1 1 1 1 1 1

676 0 -5.75 -10 1 1 1 1 1 1

Pile 3 dynamic data file input into Ruaumoko

A-15

677 0 -5.8 -10 1 1 1 1 1 1

678 0 -5.85 -10 1 1 1 1 1 1

679 0 -5.9 -10 1 1 1 1 1 1

680 0 -5.95 -10 1 1 1 1 1 1

681 0 -6 -10 1 1 1 1 1 1

682 0 -6.05 -10 1 1 1 1 1 1

683 0 -6.1 -10 1 1 1 1 1 1

684 0 -6.15 -10 1 1 1 1 1 1

685 0 -6.2 -10 1 1 1 1 1 1

686 0 -6.25 -10 1 1 1 1 1 1

687 0 -6.3 -10 1 1 1 1 1 1

688 0 -6.35 -10 1 1 1 1 1 1

689 0 -6.4 -10 1 1 1 1 1 1

690 0 -6.45 -10 1 1 1 1 1 1

691 0 -6.5 -10 1 1 1 1 1 1

692 0 -6.55 -10 1 1 1 1 1 1

693 0 -6.6 -10 1 1 1 1 1 1

694 0 -6.65 -10 1 1 1 1 1 1

695 0 -6.7 -10 1 1 1 1 1 1

696 0 -6.75 -10 1 1 1 1 1 1

*Element data

ELEMENTS

1 1 1 2 0 0 =-x 0 !Cantilever elements

2 1 2 3 0 0 =-x 0

3 1 3 4 0 0 =-x 0

4 1 4 5 0 0 =-x 0

5 1 5 6 0 0 =-x 0

6 1 6 7 0 0 =-x 0

7 1 7 8 0 0 =-x 0

8 1 8 9 0 0 =-x 0

9 1 9 10 0 0 =-x 0

10 1 10 11 0 0 =-x 0

11 1 11 12 0 0 =-x 0

12 1 12 13 0 0 =-x 0

13 1 13 14 0 0 =-x 0

14 1 14 15 0 0 =-x 0

15 1 15 16 0 0 =-x 0

16 1 16 17 0 0 =-x 0

17 1 17 18 0 0 =-x 0 !Pile elements

18 1 18 19 0 0 =-x 0

19 1 19 20 0 0 =-x 0

20 1 20 21 0 0 =-x 0

21 1 21 22 0 0 =-x 0

22 1 22 23 0 0 =-x 0

23 1 23 24 0 0 =-x 0

24 1 24 25 0 0 =-x 0

25 1 25 26 0 0 =-x 0

26 1 26 27 0 0 =-x 0

27 1 27 28 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-16

28 1 28 29 0 0 =-x 0

29 1 29 30 0 0 =-x 0

30 1 30 31 0 0 =-x 0

31 1 31 32 0 0 =-x 0

32 1 32 33 0 0 =-x 0

33 1 33 34 0 0 =-x 0

34 1 34 35 0 0 =-x 0

35 1 35 36 0 0 =-x 0

36 1 36 37 0 0 =-x 0

37 1 37 38 0 0 =-x 0

38 1 38 39 0 0 =-x 0

39 1 39 40 0 0 =-x 0

40 1 40 41 0 0 =-x 0

41 1 41 42 0 0 =-x 0

42 1 42 43 0 0 =-x 0

43 1 43 44 0 0 =-x 0

44 1 44 45 0 0 =-x 0

45 1 45 46 0 0 =-x 0

46 1 46 47 0 0 =-x 0

47 1 47 48 0 0 =-x 0

48 1 48 49 0 0 =-x 0

49 1 49 50 0 0 =-x 0

50 1 50 51 0 0 =-x 0

51 1 51 52 0 0 =-x 0

52 1 52 53 0 0 =-x 0

53 1 53 54 0 0 =-x 0

54 1 54 55 0 0 =-x 0

55 1 55 56 0 0 =-x 0

56 1 56 57 0 0 =-x 0

57 1 57 58 0 0 =-x 0

58 1 58 59 0 0 =-x 0

59 1 59 60 0 0 =-x 0

60 1 60 61 0 0 =-x 0

61 1 61 62 0 0 =-x 0

62 1 62 63 0 0 =-x 0

63 1 63 64 0 0 =-x 0

64 1 64 65 0 0 =-x 0

65 1 65 66 0 0 =-x 0

66 1 66 67 0 0 =-x 0

67 1 67 68 0 0 =-x 0

68 1 68 69 0 0 =-x 0

69 1 69 70 0 0 =-x 0

70 1 70 71 0 0 =-x 0

71 1 71 72 0 0 =-x 0

72 1 72 73 0 0 =-x 0

73 1 73 74 0 0 =-x 0

74 1 74 75 0 0 =-x 0

75 1 75 76 0 0 =-x 0

76 1 76 77 0 0 =-x 0

77 1 77 78 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-17

78 1 78 79 0 0 =-x 0

79 1 79 80 0 0 =-x 0

80 1 80 81 0 0 =-x 0

81 1 81 82 0 0 =-x 0

82 1 82 83 0 0 =-x 0

83 1 83 84 0 0 =-x 0

84 1 84 85 0 0 =-x 0

85 1 85 86 0 0 =-x 0

86 1 86 87 0 0 =-x 0

87 1 87 88 0 0 =-x 0

88 1 88 89 0 0 =-x 0

89 1 89 90 0 0 =-x 0

90 1 90 91 0 0 =-x 0

91 1 91 92 0 0 =-x 0

92 1 92 93 0 0 =-x 0

93 1 93 94 0 0 =-x 0

94 1 94 95 0 0 =-x 0

95 1 95 96 0 0 =-x 0

96 1 96 97 0 0 =-x 0

97 1 97 98 0 0 =-x 0

98 1 98 99 0 0 =-x 0

99 1 99 100 0 0 =-x 0

100 1 100 101 0 0 =-x 0

101 1 101 102 0 0 =-x 0

102 1 102 103 0 0 =-x 0

103 1 103 104 0 0 =-x 0

104 1 104 105 0 0 =-x 0

105 1 105 106 0 0 =-x 0

106 1 106 107 0 0 =-x 0

107 1 107 108 0 0 =-x 0

108 1 108 109 0 0 =-x 0

109 1 109 110 0 0 =-x 0

110 1 110 111 0 0 =-x 0

111 1 111 112 0 0 =-x 0

112 1 112 113 0 0 =-x 0

113 1 113 114 0 0 =-x 0

114 1 114 115 0 0 =-x 0

115 1 115 116 0 0 =-x 0

116 1 116 117 0 0 =-x 0

117 1 117 118 0 0 =-x 0

118 1 118 119 0 0 =-x 0

119 1 119 120 0 0 =-x 0

120 1 120 121 0 0 =-x 0

121 1 121 122 0 0 =-x 0

122 1 122 123 0 0 =-x 0

123 1 123 124 0 0 =-x 0

124 1 124 125 0 0 =-x 0

125 1 125 126 0 0 =-x 0

126 1 126 127 0 0 =-x 0

127 1 127 128 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-18

128 1 128 129 0 0 =-x 0

129 1 129 130 0 0 =-x 0

130 1 130 131 0 0 =-x 0

131 1 131 132 0 0 =-x 0

132 1 132 133 0 0 =-x 0

133 1 133 134 0 0 =-x 0

134 1 134 135 0 0 =-x 0

135 1 135 136 0 0 =-x 0

136 1 136 137 0 0 =-x 0

137 1 137 138 0 0 =-x 0

138 1 138 139 0 0 =-x 0

139 1 139 140 0 0 =-x 0

140 1 140 141 0 0 =-x 0

141 1 141 142 0 0 =-x 0

142 1 142 143 0 0 =-x 0

143 1 143 144 0 0 =-x 0

144 1 144 145 0 0 =-x 0

145 1 145 146 0 0 =-x 0

146 1 146 147 0 0 =-x 0

147 1 147 148 0 0 =-x 0

148 1 148 149 0 0 =-x 0

149 1 149 150 0 0 =-x 0

150 1 150 151 0 0 =-x 0

151 1 151 152 0 0 =-x 0

152 2 17 153 0 0 =-x 0 !Inner springs side one

153 3 18 154 0 0 =-x 0

154 4 19 155 0 0 =-x 0

155 5 20 156 0 0 =-x 0

156 6 21 157 0 0 =-x 0

157 7 22 158 0 0 =-x 0

158 8 23 159 0 0 =-x 0

159 9 24 160 0 0 =-x 0

160 10 25 161 0 0 =-x 0

161 11 26 162 0 0 =-x 0

162 12 27 163 0 0 =-x 0

163 13 28 164 0 0 =-x 0

164 14 29 165 0 0 =-x 0

165 15 30 166 0 0 =-x 0

166 16 31 167 0 0 =-x 0

167 17 32 168 0 0 =-x 0

168 18 33 169 0 0 =-x 0

169 19 34 170 0 0 =-x 0

170 20 35 171 0 0 =-x 0

171 21 36 172 0 0 =-x 0

172 22 37 173 0 0 =-x 0

173 23 38 174 0 0 =-x 0

174 24 39 175 0 0 =-x 0

175 25 40 176 0 0 =-x 0

176 26 41 177 0 0 =-x 0

177 27 42 178 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-19

178 28 43 179 0 0 =-x 0

179 29 44 180 0 0 =-x 0

180 30 45 181 0 0 =-x 0

181 31 46 182 0 0 =-x 0

182 32 47 183 0 0 =-x 0

183 33 48 184 0 0 =-x 0

184 34 49 185 0 0 =-x 0

185 35 50 186 0 0 =-x 0

186 36 51 187 0 0 =-x 0

187 37 52 188 0 0 =-x 0

188 38 53 189 0 0 =-x 0

189 39 54 190 0 0 =-x 0

190 40 55 191 0 0 =-x 0

191 41 56 192 0 0 =-x 0

192 42 57 193 0 0 =-x 0

193 43 58 194 0 0 =-x 0

194 44 59 195 0 0 =-x 0

195 45 60 196 0 0 =-x 0

196 46 61 197 0 0 =-x 0

197 47 62 198 0 0 =-x 0

198 48 63 199 0 0 =-x 0

199 49 64 200 0 0 =-x 0

200 50 65 201 0 0 =-x 0

201 51 66 202 0 0 =-x 0

202 52 67 203 0 0 =-x 0

203 53 68 204 0 0 =-x 0

204 54 69 205 0 0 =-x 0

205 55 70 206 0 0 =-x 0

206 56 71 207 0 0 =-x 0

207 57 72 208 0 0 =-x 0

208 58 73 209 0 0 =-x 0

209 59 74 210 0 0 =-x 0

210 60 75 211 0 0 =-x 0

211 61 76 212 0 0 =-x 0

212 62 77 213 0 0 =-x 0

213 63 78 214 0 0 =-x 0

214 64 79 215 0 0 =-x 0

215 65 80 216 0 0 =-x 0

216 66 81 217 0 0 =-x 0

217 67 82 218 0 0 =-x 0

218 68 83 219 0 0 =-x 0

219 69 84 220 0 0 =-x 0

220 70 85 221 0 0 =-x 0

221 71 86 222 0 0 =-x 0

222 72 87 223 0 0 =-x 0

223 73 88 224 0 0 =-x 0

224 74 89 225 0 0 =-x 0

225 75 90 226 0 0 =-x 0

226 76 91 227 0 0 =-x 0

227 77 92 228 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-20

228 78 93 229 0 0 =-x 0

229 79 94 230 0 0 =-x 0

230 80 95 231 0 0 =-x 0

231 81 96 232 0 0 =-x 0

232 82 97 233 0 0 =-x 0

233 83 98 234 0 0 =-x 0

234 84 99 235 0 0 =-x 0

235 85 100 236 0 0 =-x 0

236 86 101 237 0 0 =-x 0

237 87 102 238 0 0 =-x 0

238 88 103 239 0 0 =-x 0

239 89 104 240 0 0 =-x 0

240 90 105 241 0 0 =-x 0

241 91 106 242 0 0 =-x 0

242 92 107 243 0 0 =-x 0

243 93 108 244 0 0 =-x 0

244 94 109 245 0 0 =-x 0

245 95 110 246 0 0 =-x 0

246 96 111 247 0 0 =-x 0

247 97 112 248 0 0 =-x 0

248 98 113 249 0 0 =-x 0

249 99 114 250 0 0 =-x 0

250 100 115 251 0 0 =-x 0

251 101 116 252 0 0 =-x 0

252 102 117 253 0 0 =-x 0

253 103 118 254 0 0 =-x 0

254 104 119 255 0 0 =-x 0

255 105 120 256 0 0 =-x 0

256 106 121 257 0 0 =-x 0

257 107 122 258 0 0 =-x 0

258 108 123 259 0 0 =-x 0

259 109 124 260 0 0 =-x 0

260 110 125 261 0 0 =-x 0

261 111 126 262 0 0 =-x 0

262 112 127 263 0 0 =-x 0

263 113 128 264 0 0 =-x 0

264 114 129 265 0 0 =-x 0

265 115 130 266 0 0 =-x 0

266 116 131 267 0 0 =-x 0

267 117 132 268 0 0 =-x 0

268 118 133 269 0 0 =-x 0

269 119 134 270 0 0 =-x 0

270 120 135 271 0 0 =-x 0

271 121 136 272 0 0 =-x 0

272 122 137 273 0 0 =-x 0

273 123 138 274 0 0 =-x 0

274 124 139 275 0 0 =-x 0

275 125 140 276 0 0 =-x 0

276 126 141 277 0 0 =-x 0

277 127 142 278 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-21

278 128 143 279 0 0 =-x 0

279 129 144 280 0 0 =-x 0

280 130 145 281 0 0 =-x 0

281 131 146 282 0 0 =-x 0

282 132 147 283 0 0 =-x 0

283 133 148 284 0 0 =-x 0

284 134 149 285 0 0 =-x 0

285 135 150 286 0 0 =-x 0

286 136 151 287 0 0 =-x 0

287 137 152 288 0 0 =-x 0

288 138 17 289 0 0 =-x 0 !Inner springs side two

289 139 18 290 0 0 =-x 0

290 140 19 291 0 0 =-x 0

291 141 20 292 0 0 =-x 0

292 142 21 293 0 0 =-x 0

293 143 22 294 0 0 =-x 0

294 144 23 295 0 0 =-x 0

295 145 24 296 0 0 =-x 0

296 146 25 297 0 0 =-x 0

297 147 26 298 0 0 =-x 0

298 148 27 299 0 0 =-x 0

299 149 28 300 0 0 =-x 0

300 150 29 301 0 0 =-x 0

301 151 30 302 0 0 =-x 0

302 152 31 303 0 0 =-x 0

303 153 32 304 0 0 =-x 0

304 154 33 305 0 0 =-x 0

305 155 34 306 0 0 =-x 0

306 156 35 307 0 0 =-x 0

307 157 36 308 0 0 =-x 0

308 158 37 309 0 0 =-x 0

309 159 38 310 0 0 =-x 0

310 160 39 311 0 0 =-x 0

311 161 40 312 0 0 =-x 0

312 162 41 313 0 0 =-x 0

313 163 42 314 0 0 =-x 0

314 164 43 315 0 0 =-x 0

315 165 44 316 0 0 =-x 0

316 166 45 317 0 0 =-x 0

317 167 46 318 0 0 =-x 0

318 168 47 319 0 0 =-x 0

319 169 48 320 0 0 =-x 0

320 170 49 321 0 0 =-x 0

321 171 50 322 0 0 =-x 0

322 172 51 323 0 0 =-x 0

323 173 52 324 0 0 =-x 0

324 174 53 325 0 0 =-x 0

325 175 54 326 0 0 =-x 0

326 176 55 327 0 0 =-x 0

327 177 56 328 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-22

328 178 57 329 0 0 =-x 0

329 179 58 330 0 0 =-x 0

330 180 59 331 0 0 =-x 0

331 181 60 332 0 0 =-x 0

332 182 61 333 0 0 =-x 0

333 183 62 334 0 0 =-x 0

334 184 63 335 0 0 =-x 0

335 185 64 336 0 0 =-x 0

336 186 65 337 0 0 =-x 0

337 187 66 338 0 0 =-x 0

338 188 67 339 0 0 =-x 0

339 189 68 340 0 0 =-x 0

340 190 69 341 0 0 =-x 0

341 191 70 342 0 0 =-x 0

342 192 71 343 0 0 =-x 0

343 193 72 344 0 0 =-x 0

344 194 73 345 0 0 =-x 0

345 195 74 346 0 0 =-x 0

346 196 75 347 0 0 =-x 0

347 197 76 348 0 0 =-x 0

348 198 77 349 0 0 =-x 0

349 199 78 350 0 0 =-x 0

350 200 79 351 0 0 =-x 0

351 201 80 352 0 0 =-x 0

352 202 81 353 0 0 =-x 0

353 203 82 354 0 0 =-x 0

354 204 83 355 0 0 =-x 0

355 205 84 356 0 0 =-x 0

356 206 85 357 0 0 =-x 0

357 207 86 358 0 0 =-x 0

358 208 87 359 0 0 =-x 0

359 209 88 360 0 0 =-x 0

360 210 89 361 0 0 =-x 0

361 211 90 362 0 0 =-x 0

362 212 91 363 0 0 =-x 0

363 213 92 364 0 0 =-x 0

364 214 93 365 0 0 =-x 0

365 215 94 366 0 0 =-x 0

366 216 95 367 0 0 =-x 0

367 217 96 368 0 0 =-x 0

368 218 97 369 0 0 =-x 0

369 219 98 370 0 0 =-x 0

370 220 99 371 0 0 =-x 0

371 221 100 372 0 0 =-x 0

372 222 101 373 0 0 =-x 0

373 223 102 374 0 0 =-x 0

374 224 103 375 0 0 =-x 0

375 225 104 376 0 0 =-x 0

376 226 105 377 0 0 =-x 0

377 227 106 378 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-23

378 228 107 379 0 0 =-x 0

379 229 108 380 0 0 =-x 0

380 230 109 381 0 0 =-x 0

381 231 110 382 0 0 =-x 0

382 232 111 383 0 0 =-x 0

383 233 112 384 0 0 =-x 0

384 234 113 385 0 0 =-x 0

385 235 114 386 0 0 =-x 0

386 236 115 387 0 0 =-x 0

387 237 116 388 0 0 =-x 0

388 238 117 389 0 0 =-x 0

389 239 118 390 0 0 =-x 0

390 240 119 391 0 0 =-x 0

391 241 120 392 0 0 =-x 0

392 242 121 393 0 0 =-x 0

393 243 122 394 0 0 =-x 0

394 244 123 395 0 0 =-x 0

395 245 124 396 0 0 =-x 0

396 246 125 397 0 0 =-x 0

397 247 126 398 0 0 =-x 0

398 248 127 399 0 0 =-x 0

399 249 128 400 0 0 =-x 0

400 250 129 401 0 0 =-x 0

401 251 130 402 0 0 =-x 0

402 252 131 403 0 0 =-x 0

403 253 132 404 0 0 =-x 0

404 254 133 405 0 0 =-x 0

405 255 134 406 0 0 =-x 0

406 256 135 407 0 0 =-x 0

407 257 136 408 0 0 =-x 0

408 258 137 409 0 0 =-x 0

409 259 138 410 0 0 =-x 0

410 260 139 411 0 0 =-x 0

411 261 140 412 0 0 =-x 0

412 262 141 413 0 0 =-x 0

413 263 142 414 0 0 =-x 0

414 264 143 415 0 0 =-x 0

415 265 144 416 0 0 =-x 0

416 266 145 417 0 0 =-x 0

417 267 146 418 0 0 =-x 0

418 268 147 419 0 0 =-x 0

419 269 148 420 0 0 =-x 0

420 270 149 421 0 0 =-x 0

421 271 150 422 0 0 =-x 0

422 272 151 423 0 0 =-x 0

423 273 152 424 0 0 =-x 0

424 274 153 425 0 0 =-x 0 !Outer springs side one

425 275 154 426 0 0 =-x 0

426 276 155 427 0 0 =-x 0

427 277 156 428 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-24

428 278 157 429 0 0 =-x 0

429 279 158 430 0 0 =-x 0

430 280 159 431 0 0 =-x 0

431 281 160 432 0 0 =-x 0

432 282 161 433 0 0 =-x 0

433 283 162 434 0 0 =-x 0

434 284 163 435 0 0 =-x 0

435 285 164 436 0 0 =-x 0

436 286 165 437 0 0 =-x 0

437 287 166 438 0 0 =-x 0

438 288 167 439 0 0 =-x 0

439 289 168 440 0 0 =-x 0

440 290 169 441 0 0 =-x 0

441 291 170 442 0 0 =-x 0

442 292 171 443 0 0 =-x 0

443 293 172 444 0 0 =-x 0

444 294 173 445 0 0 =-x 0

445 295 174 446 0 0 =-x 0

446 296 175 447 0 0 =-x 0

447 297 176 448 0 0 =-x 0

448 298 177 449 0 0 =-x 0

449 299 178 450 0 0 =-x 0

450 300 179 451 0 0 =-x 0

451 301 180 452 0 0 =-x 0

452 302 181 453 0 0 =-x 0

453 303 182 454 0 0 =-x 0

454 304 183 455 0 0 =-x 0

455 305 184 456 0 0 =-x 0

456 306 185 457 0 0 =-x 0

457 307 186 458 0 0 =-x 0

458 308 187 459 0 0 =-x 0

459 309 188 460 0 0 =-x 0

460 310 189 461 0 0 =-x 0

461 311 190 462 0 0 =-x 0

462 312 191 463 0 0 =-x 0

463 313 192 464 0 0 =-x 0

464 314 193 465 0 0 =-x 0

465 315 194 466 0 0 =-x 0

466 316 195 467 0 0 =-x 0

467 317 196 468 0 0 =-x 0

468 318 197 469 0 0 =-x 0

469 319 198 470 0 0 =-x 0

470 320 199 471 0 0 =-x 0

471 321 200 472 0 0 =-x 0

472 322 201 473 0 0 =-x 0

473 323 202 474 0 0 =-x 0

474 324 203 475 0 0 =-x 0

475 325 204 476 0 0 =-x 0

476 326 205 477 0 0 =-x 0

477 327 206 478 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-25

478 328 207 479 0 0 =-x 0

479 329 208 480 0 0 =-x 0

480 330 209 481 0 0 =-x 0

481 331 210 482 0 0 =-x 0

482 332 211 483 0 0 =-x 0

483 333 212 484 0 0 =-x 0

484 334 213 485 0 0 =-x 0

485 335 214 486 0 0 =-x 0

486 336 215 487 0 0 =-x 0

487 337 216 488 0 0 =-x 0

488 338 217 489 0 0 =-x 0

489 339 218 490 0 0 =-x 0

490 340 219 491 0 0 =-x 0

491 341 220 492 0 0 =-x 0

492 342 221 493 0 0 =-x 0

493 343 222 494 0 0 =-x 0

494 344 223 495 0 0 =-x 0

495 345 224 496 0 0 =-x 0

496 346 225 497 0 0 =-x 0

497 347 226 498 0 0 =-x 0

498 348 227 499 0 0 =-x 0

499 349 228 500 0 0 =-x 0

500 350 229 501 0 0 =-x 0

501 351 230 502 0 0 =-x 0

502 352 231 503 0 0 =-x 0

503 353 232 504 0 0 =-x 0

504 354 233 505 0 0 =-x 0

505 355 234 506 0 0 =-x 0

506 356 235 507 0 0 =-x 0

507 357 236 508 0 0 =-x 0

508 358 237 509 0 0 =-x 0

509 359 238 510 0 0 =-x 0

510 360 239 511 0 0 =-x 0

511 361 240 512 0 0 =-x 0

512 362 241 513 0 0 =-x 0

513 363 242 514 0 0 =-x 0

514 364 243 515 0 0 =-x 0

515 365 244 516 0 0 =-x 0

516 366 245 517 0 0 =-x 0

517 367 246 518 0 0 =-x 0

518 368 247 519 0 0 =-x 0

519 369 248 520 0 0 =-x 0

520 370 249 521 0 0 =-x 0

521 371 250 522 0 0 =-x 0

522 372 251 523 0 0 =-x 0

523 373 252 524 0 0 =-x 0

524 374 253 525 0 0 =-x 0

525 375 254 526 0 0 =-x 0

526 376 255 527 0 0 =-x 0

527 377 256 528 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-26

528 378 257 529 0 0 =-x 0

529 379 258 530 0 0 =-x 0

530 380 259 531 0 0 =-x 0

531 381 260 532 0 0 =-x 0

532 382 261 533 0 0 =-x 0

533 383 262 534 0 0 =-x 0

534 384 263 535 0 0 =-x 0

535 385 264 536 0 0 =-x 0

536 386 265 537 0 0 =-x 0

537 387 266 538 0 0 =-x 0

538 388 267 539 0 0 =-x 0

539 389 268 540 0 0 =-x 0

540 390 269 541 0 0 =-x 0

541 391 270 542 0 0 =-x 0

542 392 271 543 0 0 =-x 0

543 393 272 544 0 0 =-x 0

544 394 273 545 0 0 =-x 0

545 395 274 546 0 0 =-x 0

546 396 275 547 0 0 =-x 0

547 397 276 548 0 0 =-x 0

548 398 277 549 0 0 =-x 0

549 399 278 550 0 0 =-x 0

550 400 279 551 0 0 =-x 0

551 401 280 552 0 0 =-x 0

552 402 281 553 0 0 =-x 0

553 403 282 554 0 0 =-x 0

554 404 283 555 0 0 =-x 0

555 405 284 556 0 0 =-x 0

556 406 285 557 0 0 =-x 0

557 407 286 558 0 0 =-x 0

558 408 287 559 0 0 =-x 0

559 409 288 560 0 0 =-x 0

560 410 289 561 0 0 =-x 0 !Outer springs side two

561 411 290 562 0 0 =-x 0

562 412 291 563 0 0 =-x 0

563 413 292 564 0 0 =-x 0

564 414 293 565 0 0 =-x 0

565 415 294 566 0 0 =-x 0

566 416 295 567 0 0 =-x 0

567 417 296 568 0 0 =-x 0

568 418 297 569 0 0 =-x 0

569 419 298 570 0 0 =-x 0

570 420 299 571 0 0 =-x 0

571 421 300 572 0 0 =-x 0

572 422 301 573 0 0 =-x 0

573 423 302 574 0 0 =-x 0

574 424 303 575 0 0 =-x 0

575 425 304 576 0 0 =-x 0

576 426 305 577 0 0 =-x 0

577 427 306 578 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-27

578 428 307 579 0 0 =-x 0

579 429 308 580 0 0 =-x 0

580 430 309 581 0 0 =-x 0

581 431 310 582 0 0 =-x 0

582 432 311 583 0 0 =-x 0

583 433 312 584 0 0 =-x 0

584 434 313 585 0 0 =-x 0

585 435 314 586 0 0 =-x 0

586 436 315 587 0 0 =-x 0

587 437 316 588 0 0 =-x 0

588 438 317 589 0 0 =-x 0

589 439 318 590 0 0 =-x 0

590 440 319 591 0 0 =-x 0

591 441 320 592 0 0 =-x 0

592 442 321 593 0 0 =-x 0

593 443 322 594 0 0 =-x 0

594 444 323 595 0 0 =-x 0

595 445 324 596 0 0 =-x 0

596 446 325 597 0 0 =-x 0

597 447 326 598 0 0 =-x 0

598 448 327 599 0 0 =-x 0

599 449 328 600 0 0 =-x 0

600 450 329 601 0 0 =-x 0

601 451 330 602 0 0 =-x 0

602 452 331 603 0 0 =-x 0

603 453 332 604 0 0 =-x 0

604 454 333 605 0 0 =-x 0

605 455 334 606 0 0 =-x 0

606 456 335 607 0 0 =-x 0

607 457 336 608 0 0 =-x 0

608 458 337 609 0 0 =-x 0

609 459 338 610 0 0 =-x 0

610 460 339 611 0 0 =-x 0

611 461 340 612 0 0 =-x 0

612 462 341 613 0 0 =-x 0

613 463 342 614 0 0 =-x 0

614 464 343 615 0 0 =-x 0

615 465 344 616 0 0 =-x 0

616 466 345 617 0 0 =-x 0

617 467 346 618 0 0 =-x 0

618 468 347 619 0 0 =-x 0

619 469 348 620 0 0 =-x 0

620 470 349 621 0 0 =-x 0

621 471 350 622 0 0 =-x 0

622 472 351 623 0 0 =-x 0

623 473 352 624 0 0 =-x 0

624 474 353 625 0 0 =-x 0

625 475 354 626 0 0 =-x 0

626 476 355 627 0 0 =-x 0

627 477 356 628 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-28

628 478 357 629 0 0 =-x 0

629 479 358 630 0 0 =-x 0

630 480 359 631 0 0 =-x 0

631 481 360 632 0 0 =-x 0

632 482 361 633 0 0 =-x 0

633 483 362 634 0 0 =-x 0

634 484 363 635 0 0 =-x 0

635 485 364 636 0 0 =-x 0

636 486 365 637 0 0 =-x 0

637 487 366 638 0 0 =-x 0

638 488 367 639 0 0 =-x 0

639 489 368 640 0 0 =-x 0

640 490 369 641 0 0 =-x 0

641 491 370 642 0 0 =-x 0

642 492 371 643 0 0 =-x 0

643 493 372 644 0 0 =-x 0

644 494 373 645 0 0 =-x 0

645 495 374 646 0 0 =-x 0

646 496 375 647 0 0 =-x 0

647 497 376 648 0 0 =-x 0

648 498 377 649 0 0 =-x 0

649 499 378 650 0 0 =-x 0

650 500 379 651 0 0 =-x 0

651 501 380 652 0 0 =-x 0

652 502 381 653 0 0 =-x 0

653 503 382 654 0 0 =-x 0

654 504 383 655 0 0 =-x 0

655 505 384 656 0 0 =-x 0

656 506 385 657 0 0 =-x 0

657 507 386 658 0 0 =-x 0

658 508 387 659 0 0 =-x 0

659 509 388 660 0 0 =-x 0

660 510 389 661 0 0 =-x 0

661 511 390 662 0 0 =-x 0

662 512 391 663 0 0 =-x 0

663 513 392 664 0 0 =-x 0

664 514 393 665 0 0 =-x 0

665 515 394 666 0 0 =-x 0

666 516 395 667 0 0 =-x 0

667 517 396 668 0 0 =-x 0

668 518 397 669 0 0 =-x 0

669 519 398 670 0 0 =-x 0

670 520 399 671 0 0 =-x 0

671 521 400 672 0 0 =-x 0

672 522 401 673 0 0 =-x 0

673 523 402 674 0 0 =-x 0

674 524 403 675 0 0 =-x 0

675 525 404 676 0 0 =-x 0

676 526 405 677 0 0 =-x 0

677 527 406 678 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-29

678 528 407 679 0 0 =-x 0

679 529 408 680 0 0 =-x 0

680 530 409 681 0 0 =-x 0

681 531 410 682 0 0 =-x 0

682 532 411 683 0 0 =-x 0

683 533 412 684 0 0 =-x 0

684 534 413 685 0 0 =-x 0

685 535 414 686 0 0 =-x 0

686 536 415 687 0 0 =-x 0

687 537 416 688 0 0 =-x 0

688 538 417 689 0 0 =-x 0

689 539 418 690 0 0 =-x 0

690 540 419 691 0 0 =-x 0

691 541 420 692 0 0 =-x 0

692 542 421 693 0 0 =-x 0

693 543 422 694 0 0 =-x 0

694 544 423 695 0 0 =-x 0

695 545 424 696 0 0 =-x 0

696 546 153 425 0 0 =-x 0 !Outer dampers side one

697 547 154 426 0 0 =-x 0

698 548 155 427 0 0 =-x 0

699 549 156 428 0 0 =-x 0

700 550 157 429 0 0 =-x 0

701 551 158 430 0 0 =-x 0

702 552 159 431 0 0 =-x 0

703 553 160 432 0 0 =-x 0

704 554 161 433 0 0 =-x 0

705 555 162 434 0 0 =-x 0

706 556 163 435 0 0 =-x 0

707 557 164 436 0 0 =-x 0

708 558 165 437 0 0 =-x 0

709 559 166 438 0 0 =-x 0

710 560 167 439 0 0 =-x 0

711 561 168 440 0 0 =-x 0

712 562 169 441 0 0 =-x 0

713 563 170 442 0 0 =-x 0

714 564 171 443 0 0 =-x 0

715 565 172 444 0 0 =-x 0

716 566 173 445 0 0 =-x 0

717 567 174 446 0 0 =-x 0

718 568 175 447 0 0 =-x 0

719 569 176 448 0 0 =-x 0

720 570 177 449 0 0 =-x 0

721 571 178 450 0 0 =-x 0

722 572 179 451 0 0 =-x 0

723 573 180 452 0 0 =-x 0

724 574 181 453 0 0 =-x 0

725 575 182 454 0 0 =-x 0

726 576 183 455 0 0 =-x 0

727 577 184 456 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-30

728 578 185 457 0 0 =-x 0

729 579 186 458 0 0 =-x 0

730 580 187 459 0 0 =-x 0

731 581 188 460 0 0 =-x 0

732 582 189 461 0 0 =-x 0

733 583 190 462 0 0 =-x 0

734 584 191 463 0 0 =-x 0

735 585 192 464 0 0 =-x 0

736 586 193 465 0 0 =-x 0

737 587 194 466 0 0 =-x 0

738 588 195 467 0 0 =-x 0

739 589 196 468 0 0 =-x 0

740 590 197 469 0 0 =-x 0

741 591 198 470 0 0 =-x 0

742 592 199 471 0 0 =-x 0

743 593 200 472 0 0 =-x 0

744 594 201 473 0 0 =-x 0

745 595 202 474 0 0 =-x 0

746 596 203 475 0 0 =-x 0

747 597 204 476 0 0 =-x 0

748 598 205 477 0 0 =-x 0

749 599 206 478 0 0 =-x 0

750 600 207 479 0 0 =-x 0

751 601 208 480 0 0 =-x 0

752 602 209 481 0 0 =-x 0

753 603 210 482 0 0 =-x 0

754 604 211 483 0 0 =-x 0

755 605 212 484 0 0 =-x 0

756 606 213 485 0 0 =-x 0

757 607 214 486 0 0 =-x 0

758 608 215 487 0 0 =-x 0

759 609 216 488 0 0 =-x 0

760 610 217 489 0 0 =-x 0

761 611 218 490 0 0 =-x 0

762 612 219 491 0 0 =-x 0

763 613 220 492 0 0 =-x 0

764 614 221 493 0 0 =-x 0

765 615 222 494 0 0 =-x 0

766 616 223 495 0 0 =-x 0

767 617 224 496 0 0 =-x 0

768 618 225 497 0 0 =-x 0

769 619 226 498 0 0 =-x 0

770 620 227 499 0 0 =-x 0

771 621 228 500 0 0 =-x 0

772 622 229 501 0 0 =-x 0

773 623 230 502 0 0 =-x 0

774 624 231 503 0 0 =-x 0

775 625 232 504 0 0 =-x 0

776 626 233 505 0 0 =-x 0

777 627 234 506 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-31

778 628 235 507 0 0 =-x 0

779 629 236 508 0 0 =-x 0

780 630 237 509 0 0 =-x 0

781 631 238 510 0 0 =-x 0

782 632 239 511 0 0 =-x 0

783 633 240 512 0 0 =-x 0

784 634 241 513 0 0 =-x 0

785 635 242 514 0 0 =-x 0

786 636 243 515 0 0 =-x 0

787 637 244 516 0 0 =-x 0

788 638 245 517 0 0 =-x 0

789 639 246 518 0 0 =-x 0

790 640 247 519 0 0 =-x 0

791 641 248 520 0 0 =-x 0

792 642 249 521 0 0 =-x 0

793 643 250 522 0 0 =-x 0

794 644 251 523 0 0 =-x 0

795 645 252 524 0 0 =-x 0

796 646 253 525 0 0 =-x 0

797 647 254 526 0 0 =-x 0

798 648 255 527 0 0 =-x 0

799 649 256 528 0 0 =-x 0

800 650 257 529 0 0 =-x 0

801 651 258 530 0 0 =-x 0

802 652 259 531 0 0 =-x 0

803 653 260 532 0 0 =-x 0

804 654 261 533 0 0 =-x 0

805 655 262 534 0 0 =-x 0

806 656 263 535 0 0 =-x 0

807 657 264 536 0 0 =-x 0

808 658 265 537 0 0 =-x 0

809 659 266 538 0 0 =-x 0

810 660 267 539 0 0 =-x 0

811 661 268 540 0 0 =-x 0

812 662 269 541 0 0 =-x 0

813 663 270 542 0 0 =-x 0

814 664 271 543 0 0 =-x 0

815 665 272 544 0 0 =-x 0

816 666 273 545 0 0 =-x 0

817 667 274 546 0 0 =-x 0

818 668 275 547 0 0 =-x 0

819 669 276 548 0 0 =-x 0

820 670 277 549 0 0 =-x 0

821 671 278 550 0 0 =-x 0

822 672 279 551 0 0 =-x 0

823 673 280 552 0 0 =-x 0

824 674 281 553 0 0 =-x 0

825 675 282 554 0 0 =-x 0

826 676 283 555 0 0 =-x 0

827 677 284 556 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-32

828 678 285 557 0 0 =-x 0

829 679 286 558 0 0 =-x 0

830 680 287 559 0 0 =-x 0

831 681 288 560 0 0 =-x 0

832 546 289 561 0 0 =-x 0 !Outer dampers side two

833 547 290 562 0 0 =-x 0

834 548 291 563 0 0 =-x 0

835 549 292 564 0 0 =-x 0

836 550 293 565 0 0 =-x 0

837 551 294 566 0 0 =-x 0

838 552 295 567 0 0 =-x 0

839 553 296 568 0 0 =-x 0

840 554 297 569 0 0 =-x 0

841 555 298 570 0 0 =-x 0

842 556 299 571 0 0 =-x 0

843 557 300 572 0 0 =-x 0

844 558 301 573 0 0 =-x 0

845 559 302 574 0 0 =-x 0

846 560 303 575 0 0 =-x 0

847 561 304 576 0 0 =-x 0

848 562 305 577 0 0 =-x 0

849 563 306 578 0 0 =-x 0

850 564 307 579 0 0 =-x 0

851 565 308 580 0 0 =-x 0

852 566 309 581 0 0 =-x 0

853 567 310 582 0 0 =-x 0

854 568 311 583 0 0 =-x 0

855 569 312 584 0 0 =-x 0

856 570 313 585 0 0 =-x 0

857 571 314 586 0 0 =-x 0

858 572 315 587 0 0 =-x 0

859 573 316 588 0 0 =-x 0

860 574 317 589 0 0 =-x 0

861 575 318 590 0 0 =-x 0

862 576 319 591 0 0 =-x 0

863 577 320 592 0 0 =-x 0

864 578 321 593 0 0 =-x 0

865 579 322 594 0 0 =-x 0

866 580 323 595 0 0 =-x 0

867 581 324 596 0 0 =-x 0

868 582 325 597 0 0 =-x 0

869 583 326 598 0 0 =-x 0

870 584 327 599 0 0 =-x 0

871 585 328 600 0 0 =-x 0

872 586 329 601 0 0 =-x 0

873 587 330 602 0 0 =-x 0

874 588 331 603 0 0 =-x 0

875 589 332 604 0 0 =-x 0

876 590 333 605 0 0 =-x 0

877 591 334 606 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-33

878 592 335 607 0 0 =-x 0

879 593 336 608 0 0 =-x 0

880 594 337 609 0 0 =-x 0

881 595 338 610 0 0 =-x 0

882 596 339 611 0 0 =-x 0

883 597 340 612 0 0 =-x 0

884 598 341 613 0 0 =-x 0

885 599 342 614 0 0 =-x 0

886 600 343 615 0 0 =-x 0

887 601 344 616 0 0 =-x 0

888 602 345 617 0 0 =-x 0

889 603 346 618 0 0 =-x 0

890 604 347 619 0 0 =-x 0

891 605 348 620 0 0 =-x 0

892 606 349 621 0 0 =-x 0

893 607 350 622 0 0 =-x 0

894 608 351 623 0 0 =-x 0

895 609 352 624 0 0 =-x 0

896 610 353 625 0 0 =-x 0

897 611 354 626 0 0 =-x 0

898 612 355 627 0 0 =-x 0

899 613 356 628 0 0 =-x 0

900 614 357 629 0 0 =-x 0

901 615 358 630 0 0 =-x 0

902 616 359 631 0 0 =-x 0

903 617 360 632 0 0 =-x 0

904 618 361 633 0 0 =-x 0

905 619 362 634 0 0 =-x 0

906 620 363 635 0 0 =-x 0

907 621 364 636 0 0 =-x 0

908 622 365 637 0 0 =-x 0

909 623 366 638 0 0 =-x 0

910 624 367 639 0 0 =-x 0

911 625 368 640 0 0 =-x 0

912 626 369 641 0 0 =-x 0

913 627 370 642 0 0 =-x 0

914 628 371 643 0 0 =-x 0

915 629 372 644 0 0 =-x 0

916 630 373 645 0 0 =-x 0

917 631 374 646 0 0 =-x 0

918 632 375 647 0 0 =-x 0

919 633 376 648 0 0 =-x 0

920 634 377 649 0 0 =-x 0

921 635 378 650 0 0 =-x 0

922 636 379 651 0 0 =-x 0

923 637 380 652 0 0 =-x 0

924 638 381 653 0 0 =-x 0

925 639 382 654 0 0 =-x 0

926 640 383 655 0 0 =-x 0

927 641 384 656 0 0 =-x 0

Pile 3 dynamic data file input into Ruaumoko

A-34

928 642 385 657 0 0 =-x 0

929 643 386 658 0 0 =-x 0

930 644 387 659 0 0 =-x 0

931 645 388 660 0 0 =-x 0

932 646 389 661 0 0 =-x 0

933 647 390 662 0 0 =-x 0

934 648 391 663 0 0 =-x 0

935 649 392 664 0 0 =-x 0

936 650 393 665 0 0 =-x 0

937 651 394 666 0 0 =-x 0

938 652 395 667 0 0 =-x 0

939 653 396 668 0 0 =-x 0

940 654 397 669 0 0 =-x 0

941 655 398 670 0 0 =-x 0

942 656 399 671 0 0 =-x 0

943 657 400 672 0 0 =-x 0

944 658 401 673 0 0 =-x 0

945 659 402 674 0 0 =-x 0

946 660 403 675 0 0 =-x 0

947 661 404 676 0 0 =-x 0

948 662 405 677 0 0 =-x 0

949 663 406 678 0 0 =-x 0

950 664 407 679 0 0 =-x 0

951 665 408 680 0 0 =-x 0

952 666 409 681 0 0 =-x 0

953 667 410 682 0 0 =-x 0

954 668 411 683 0 0 =-x 0

955 669 412 684 0 0 =-x 0

956 670 413 685 0 0 =-x 0

957 671 414 686 0 0 =-x 0

958 672 415 687 0 0 =-x 0

959 673 416 688 0 0 =-x 0

960 674 417 689 0 0 =-x 0

961 675 418 690 0 0 =-x 0

962 676 419 691 0 0 =-x 0

963 677 420 692 0 0 =-x 0

964 678 421 693 0 0 =-x 0

965 679 422 694 0 0 =-x 0

966 680 423 695 0 0 =-x 0

967 681 424 696 0 0 =-x 0

*Element properties

PROPS

1 Beam !Cantilever/Pile properties

1 1 0 0 0 0 0 0 0 0

200000000 0 0.007683406 0 6.69342E-05 6.69342E-05 0 0

0 0 0

0 0 0 0 0 0 0

3.78377E-05 0 0

Pile 3 dynamic data file input into Ruaumoko

A-35

2 Spring !Inner spring properties side one (loaded in compression during pull-back)

1 5 0 0 1 0

92263.05772 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 0.669359438 0 0 0 0

0 0 0 0 0 0

1 0.02 0 0.002666667 0 0 0

3 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.019047619 0 0.002666667 0 0 0

4 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.018095238 0 0.002666667 0 0 0

5 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.017142857 0 0.002666667 0 0 0

6 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.016190476 0 0.002666667 0 0 0

7 Spring

Pile 3 dynamic data file input into Ruaumoko

A-36

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.015238095 0 0.002666667 0 0 0

8 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.014285714 0 0.002666667 0 0 0

9 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.013333333 0 0.002666667 0 0 0

10 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.012380952 0 0.002666667 0 0 0

11 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.011428571 0 0.002666667 0 0 0

12 Spring

Pile 3 dynamic data file input into Ruaumoko

A-37

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.01047619 0 0.002666667 0 0 0

13 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.385754945 0 0 0 0

0 0 0 0 0 0

1 0.00952381 0 0.002705747 0 0 0

14 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.432791014 0 0 0 0

0 0 0 0 0 0

1 0.008571429 0 0.002744828 0 0 0

15 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.479827083 0 0 0 0

0 0 0 0 0 0

1 0.007619048 0 0.002783908 0 0 0

16 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.526863151 0 0 0 0

0 0 0 0 0 0

1 0.006666667 0 0.002822989 0 0 0

17 Spring

Pile 3 dynamic data file input into Ruaumoko

A-38

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.57389922 0 0 0 0

0 0 0 0 0 0

1 0.005714286 0 0.002862069 0 0 0

18 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.620935289 0 0 0 0

0 0 0 0 0 0

1 0.004761905 0 0.002901149 0 0 0

19 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.667971357 0 0 0 0

0 0 0 0 0 0

1 0.003809524 0 0.00294023 0 0 0

20 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.715007426 0 0 0 0

0 0 0 0 0 0

1 0.002857143 0 0.00297931 0 0 0

21 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.762043495 0 0 0 0

0 0 0 0 0 0

1 0.001904762 0 0.003018391 0 0 0

22 Spring

Pile 3 dynamic data file input into Ruaumoko

A-39

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.809079563 0 0 0 0

0 0 0 0 0 0

1 0.000952381 0 0.003057471 0 0 0

23 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.24374175 0 0 0 0 0 0

0 2.099857382 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003096552 0 0 0

24 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.2553485 0 0 0 0 0 0

0 2.158500201 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003135632 0 0 0

25 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.26695525 0 0 0 0 0 0

0 2.217143019 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003174713 0 0 0

26 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.278562 0 0 0 0 0 0

0 2.275785838 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003213793 0 0 0

27 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.29016875 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-40

0 2.334428656 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003252874 0 0 0

28 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.3017755 0 0 0 0 0 0

0 2.393071475 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003291954 0 0 0

29 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.31338225 0 0 0 0 0 0

0 2.451714294 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003331034 0 0 0

30 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.324989 0 0 0 0 0 0

0 2.510357112 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003370115 0 0 0

31 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.33659575 0 0 0 0 0 0

0 2.568999931 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003409195 0 0 0

32 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.3482025 0 0 0 0 0 0

0 2.62764275 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003448276 0 0 0

33 Spring

Pile 3 dynamic data file input into Ruaumoko

A-41

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.35980925 0 0 0 0 0 0

0 2.686051008 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003495935 0 0 0

34 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.371416 0 0 0 0 0 0

0 2.744459267 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003543594 0 0 0

35 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.38302275 0 0 0 0 0 0

0 2.802867526 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003591253 0 0 0

36 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.3946295 0 0 0 0 0 0

0 2.861275785 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003638912 0 0 0

37 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.40623625 0 0 0 0 0 0

0 2.919684043 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003686571 0 0 0

38 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.417843 0 0 0 0 0 0

0 2.978092302 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-42

0 0 0 0 0 0

1 0 0 0.00373423 0 0 0

39 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.42944975 0 0 0 0 0 0

0 3.036500561 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00378189 0 0 0

40 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.4410565 0 0 0 0 0 0

0 3.094908819 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003829549 0 0 0

41 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.45266325 0 0 0 0 0 0

0 3.153317078 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003877208 0 0 0

42 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.46427 0 0 0 0 0 0

0 3.211725337 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003924867 0 0 0

43 Spring

1 5 0 0 1 0

185199.6057 0 0 0 0 0 0

0 0 0

-0.47587675 0 0 0 0 0 0

0 3.270133595 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003972526 0 0 0

44 Spring

1 5 0 0 1 0

Pile 3 dynamic data file input into Ruaumoko

A-43

185859.8902 0 0 0 0 0 0

0 0 0

-0.4874835 0 0 0 0 0 0

0 3.328541854 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004020185 0 0 0

45 Spring

1 5 0 0 1 0

186520.1747 0 0 0 0 0 0

0 0 0

-0.49909025 0 0 0 0 0 0

0 3.386950113 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004067844 0 0 0

46 Spring

1 5 0 0 1 0

187180.4592 0 0 0 0 0 0

0 0 0

-0.510697 0 0 0 0 0 0

0 3.445358372 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004115503 0 0 0

47 Spring

1 5 0 0 1 0

187840.7438 0 0 0 0 0 0

0 0 0

-0.52230375 0 0 0 0 0 0

0 3.50376663 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004163162 0 0 0

48 Spring

1 5 0 0 1 0

188501.0283 0 0 0 0 0 0

0 0 0

-0.5339105 0 0 0 0 0 0

0 3.562174889 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004210821 0 0 0

49 Spring

1 5 0 0 1 0

189161.3128 0 0 0 0 0 0

0 0 0

-0.54551725 0 0 0 0 0 0

0 3.620583148 0 0 0 0

0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-44

1 0 0 0.004258481 0 0 0

50 Spring

1 5 0 0 1 0

189821.5973 0 0 0 0 0 0

0 0 0

-0.557124 0 0 0 0 0 0

0 3.678991406 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00430614 0 0 0

51 Spring

1 5 0 0 1 0

190481.8819 0 0 0 0 0 0

0 0 0

-0.56873075 0 0 0 0 0 0

0 3.737399665 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004353799 0 0 0

52 Spring

1 5 0 0 1 0

191142.1664 0 0 0 0 0 0

0 0 0

-0.5803375 0 0 0 0 0 0

0 3.795807924 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004401458 0 0 0

53 Spring

1 5 0 0 1 0

191802.4509 0 0 0 0 0 0

0 0 0

-0.59194425 0 0 0 0 0 0

0 3.854216183 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004449117 0 0 0

54 Spring

1 5 0 0 1 0

192462.7354 0 0 0 0 0 0

0 0 0

-0.603551 0 0 0 0 0 0

0 3.912624441 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004496776 0 0 0

55 Spring

1 5 0 0 1 0

193123.02 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-45

0 0 0

-0.61515775 0 0 0 0 0 0

0 3.9710327 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004544435 0 0 0

56 Spring

1 5 0 0 1 0

193783.3045 0 0 0 0 0 0

0 0 0

-0.6267645 0 0 0 0 0 0

0 4.029440959 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004592094 0 0 0

57 Spring

1 5 0 0 1 0

194443.589 0 0 0 0 0 0

0 0 0

-0.63837125 0 0 0 0 0 0

0 4.087849217 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004639753 0 0 0

58 Spring

1 5 0 0 1 0

195103.8735 0 0 0 0 0 0

0 0 0

-0.649978 0 0 0 0 0 0

0 4.146257476 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004687412 0 0 0

59 Spring

1 5 0 0 1 0

195764.1581 0 0 0 0 0 0

0 0 0

-0.66158475 0 0 0 0 0 0

0 4.204665735 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004735071 0 0 0

60 Spring

1 5 0 0 1 0

196424.4426 0 0 0 0 0 0

0 0 0

-0.6731915 0 0 0 0 0 0

0 4.263073994 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004782731 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-46

61 Spring

1 5 0 0 1 0

197084.7271 0 0 0 0 0 0

0 0 0

-0.68479825 0 0 0 0 0 0

0 4.321482252 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00483039 0 0 0

62 Spring

1 5 0 0 1 0

197745.0116 0 0 0 0 0 0

0 0 0

-0.696405 0 0 0 0 0 0

0 4.379890511 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004878049 0 0 0

63 Spring

1 5 0 0 1 0

198405.2962 0 0 0 0 0 0

0 0 0

-0.70801175 0 0 0 0 0 0

0 4.424724032 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004863415 0 0 0

64 Spring

1 5 0 0 1 0

199065.5807 0 0 0 0 0 0

0 0 0

-0.7196185 0 0 0 0 0 0

0 4.469557553 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00484878 0 0 0

65 Spring

1 5 0 0 1 0

199725.8652 0 0 0 0 0 0

0 0 0

-0.73122525 0 0 0 0 0 0

0 4.514391074 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004834146 0 0 0

66 Spring

1 5 0 0 1 0

200386.1497 0 0 0 0 0 0

0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-47

-0.742832 0 0 0 0 0 0

0 4.559224594 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004819512 0 0 0

67 Spring

1 5 0 0 1 0

201046.4343 0 0 0 0 0 0

0 0 0

-0.75443875 0 0 0 0 0 0

0 4.604058115 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004804878 0 0 0

68 Spring

1 5 0 0 1 0

201706.7188 0 0 0 0 0 0

0 0 0

-0.7660455 0 0 0 0 0 0

0 4.648891636 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004790244 0 0 0

69 Spring

1 5 0 0 1 0

202367.0033 0 0 0 0 0 0

0 0 0

-0.77765225 0 0 0 0 0 0

0 4.693725157 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00477561 0 0 0

70 Spring

1 5 0 0 1 0

203027.2878 0 0 0 0 0 0

0 0 0

-0.789259 0 0 0 0 0 0

0 4.738558678 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004760976 0 0 0

71 Spring

1 5 0 0 1 0

203687.5724 0 0 0 0 0 0

0 0 0

-0.80086575 0 0 0 0 0 0

0 4.783392199 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004746341 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-48

72 Spring

1 5 0 0 1 0

204347.8569 0 0 0 0 0 0

0 0 0

-0.8124725 0 0 0 0 0 0

0 4.82822572 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004731707 0 0 0

73 Spring

1 5 0 0 1 0

205008.1414 0 0 0 0 0 0

0 0 0

-0.82407925 0 0 0 0 0 0

0 4.873059241 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004717073 0 0 0

74 Spring

1 5 0 0 1 0

205668.4259 0 0 0 0 0 0

0 0 0

-0.835686 0 0 0 0 0 0

0 4.917892761 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004702439 0 0 0

75 Spring

1 5 0 0 1 0

206328.7105 0 0 0 0 0 0

0 0 0

-0.84729275 0 0 0 0 0 0

0 4.962726282 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004687805 0 0 0

76 Spring

1 5 0 0 1 0

206988.995 0 0 0 0 0 0

0 0 0

-0.8588995 0 0 0 0 0 0

0 5.007559803 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004673171 0 0 0

77 Spring

1 5 0 0 1 0

207649.2795 0 0 0 0 0 0

0 0 0

-0.87050625 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-49

0 5.052393324 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004658537 0 0 0

78 Spring

1 5 0 0 1 0

208309.564 0 0 0 0 0 0

0 0 0

-0.882113 0 0 0 0 0 0

0 5.097226845 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004643902 0 0 0

79 Spring

1 5 0 0 1 0

208969.8486 0 0 0 0 0 0

0 0 0

-0.89371975 0 0 0 0 0 0

0 5.142060366 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004629268 0 0 0

80 Spring

1 5 0 0 1 0

209630.1331 0 0 0 0 0 0

0 0 0

-0.9053265 0 0 0 0 0 0

0 5.186893887 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004614634 0 0 0

81 Spring

1 5 0 0 1 0

210290.4176 0 0 0 0 0 0

0 0 0

-0.91693325 0 0 0 0 0 0

0 5.231727408 0 0 0 0

0 0 0 0 0 0

1 0 0 0.0046 0 0 0

82 Spring

1 5 0 0 1 0

211095.9647 0 0 0 0 0 0

0 0 0

-0.92854 0 0 0 0 0 0

0 5.276560928 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004585366 0 0 0

83 Spring

Pile 3 dynamic data file input into Ruaumoko

A-50

1 5 0 0 1 0

213796.6978 0 0 0 0 0 0

0 0 0

-0.94014675 0 0 0 0 0 0

0 5.321394449 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004570732 0 0 0

84 Spring

1 5 0 0 1 0

217259.176 0 0 0 0 0 0

0 0 0

-0.9517535 0 0 0 0 0 0

0 5.36622797 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004556098 0 0 0

85 Spring

1 5 0 0 1 0

220721.6543 0 0 0 0 0 0

0 0 0

-0.96336025 0 0 0 0 0 0

0 5.411061491 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004541463 0 0 0

86 Spring

1 5 0 0 1 0

224184.1325 0 0 0 0 0 0

0 0 0

-0.974967 0 0 0 0 0 0

0 5.455895012 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004526829 0 0 0

87 Spring

1 5 0 0 1 0

227646.6108 0 0 0 0 0 0

0 0 0

-0.98657375 0 0 0 0 0 0

0 5.500728533 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004512195 0 0 0

88 Spring

1 5 0 0 1 0

231109.089 0 0 0 0 0 0

0 0 0

-0.9981805 0 0 0 0 0 0

0 5.545562054 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-51

0 0 0 0 0 0

1 0 0 0.004497561 0 0 0

89 Spring

1 5 0 0 1 0

234571.5672 0 0 0 0 0 0

0 0 0

-1.00978725 0 0 0 0 0 0

0 5.590395575 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004482927 0 0 0

90 Spring

1 5 0 0 1 0

238034.0455 0 0 0 0 0 0

0 0 0

-1.021394 0 0 0 0 0 0

0 5.635229095 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004468293 0 0 0

91 Spring

1 5 0 0 1 0

241496.5237 0 0 0 0 0 0

0 0 0

-1.03300075 0 0 0 0 0 0

0 5.680062616 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004453659 0 0 0

92 Spring

1 5 0 0 1 0

244959.002 0 0 0 0 0 0

0 0 0

-1.0446075 0 0 0 0 0 0

0 5.724896137 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004439024 0 0 0

93 Spring

1 5 0 0 1 0

248421.4802 0 0 0 0 0 0

0 0 0

-1.05621425 0 0 0 0 0 0

0 5.769729658 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00442439 0 0 0

94 Spring

1 5 0 0 1 0

Pile 3 dynamic data file input into Ruaumoko

A-52

251883.9585 0 0 0 0 0 0

0 0 0

-1.067821 0 0 0 0 0 0

0 5.814563179 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004409756 0 0 0

95 Spring

1 5 0 0 1 0

255346.4367 0 0 0 0 0 0

0 0 0

-1.07942775 0 0 0 0 0 0

0 5.8593967 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004395122 0 0 0

96 Spring

1 5 0 0 1 0

258808.915 0 0 0 0 0 0

0 0 0

-1.0910345 0 0 0 0 0 0

0 5.904230221 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004380488 0 0 0

97 Spring

1 5 0 0 1 0

262271.3932 0 0 0 0 0 0

0 0 0

-1.10264125 0 0 0 0 0 0

0 5.949063742 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004365854 0 0 0

98 Spring

1 5 0 0 1 0

265733.8714 0 0 0 0 0 0

0 0 0

-1.114248 0 0 0 0 0 0

0 5.993897262 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00435122 0 0 0

99 Spring

1 5 0 0 1 0

269196.3497 0 0 0 0 0 0

0 0 0

-1.12585475 0 0 0 0 0 0

0 6.038730783 0 0 0 0

0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-53

1 0 0 0.004336585 0 0 0

100 Spring

1 5 0 0 1 0

272658.8279 0 0 0 0 0 0

0 0 0

-1.1374615 0 0 0 0 0 0

0 6.083564304 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004321951 0 0 0

101 Spring

1 5 0 0 1 0

276121.3062 0 0 0 0 0 0

0 0 0

-1.14906825 0 0 0 0 0 0

0 6.128397825 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004307317 0 0 0

102 Spring

1 5 0 0 1 0

279583.7844 0 0 0 0 0 0

0 0 0

-1.160675 0 0 0 0 0 0

0 6.173231346 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004292683 0 0 0

103 Spring

1 5 0 0 1 0

283046.2627 0 0 0 0 0 0

0 0 0

-1.17228175 0 0 0 0 0 0

0 6.218064867 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004278049 0 0 0

104 Spring

1 5 0 0 1 0

286508.7409 0 0 0 0 0 0

0 0 0

-1.1838885 0 0 0 0 0 0

0 6.262898388 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004263415 0 0 0

105 Spring

1 5 0 0 1 0

289971.2192 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-54

0 0 0

-1.19549525 0 0 0 0 0 0

0 6.307731909 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00424878 0 0 0

106 Spring

1 5 0 0 1 0

293433.6974 0 0 0 0 0 0

0 0 0

-1.207102 0 0 0 0 0 0

0 6.352565429 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004234146 0 0 0

107 Spring

1 5 0 0 1 0

296896.1756 0 0 0 0 0 0

0 0 0

-1.21870875 0 0 0 0 0 0

0 6.39739895 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004219512 0 0 0

108 Spring

1 5 0 0 1 0

300358.6539 0 0 0 0 0 0

0 0 0

-1.2303155 0 0 0 0 0 0

0 6.442232471 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004204878 0 0 0

109 Spring

1 5 0 0 1 0

303821.1321 0 0 0 0 0 0

0 0 0

-1.24192225 0 0 0 0 0 0

0 6.487065992 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004190244 0 0 0

110 Spring

1 5 0 0 1 0

307283.6104 0 0 0 0 0 0

0 0 0

-1.253529 0 0 0 0 0 0

0 6.531899513 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00417561 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-55

111 Spring

1 5 0 0 1 0

310746.0886 0 0 0 0 0 0

0 0 0

-1.26513575 0 0 0 0 0 0

0 6.576733034 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004160976 0 0 0

112 Spring

1 5 0 0 1 0

314208.5669 0 0 0 0 0 0

0 0 0

-1.2767425 0 0 0 0 0 0

0 6.621566555 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004146341 0 0 0

113 Spring

1 5 0 0 1 0

317671.0451 0 0 0 0 0 0

0 0 0

-1.28834925 0 0 0 0 0 0

0 6.666400076 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004131707 0 0 0

114 Spring

1 5 0 0 1 0

321133.5234 0 0 0 0 0 0

0 0 0

-1.299956 0 0 0 0 0 0

0 6.711233596 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004117073 0 0 0

115 Spring

1 5 0 0 1 0

324596.0016 0 0 0 0 0 0

0 0 0

-1.31156275 0 0 0 0 0 0

0 6.756067117 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004102439 0 0 0

116 Spring

1 5 0 0 1 0

328058.4799 0 0 0 0 0 0

0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-56

-1.3231695 0 0 0 0 0 0

0 6.800900638 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004087805 0 0 0

117 Spring

1 5 0 0 1 0

331520.9581 0 0 0 0 0 0

0 0 0

-1.33477625 0 0 0 0 0 0

0 6.845734159 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004073171 0 0 0

118 Spring

1 5 0 0 1 0

334983.4363 0 0 0 0 0 0

0 0 0

-1.346383 0 0 0 0 0 0

0 6.89056768 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004058537 0 0 0

119 Spring

1 5 0 0 1 0

338445.9146 0 0 0 0 0 0

0 0 0

-1.35798975 0 0 0 0 0 0

0 6.935401201 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004043902 0 0 0

120 Spring

1 5 0 0 1 0

341908.3928 0 0 0 0 0 0

0 0 0

-1.3695965 0 0 0 0 0 0

0 6.980234722 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004029268 0 0 0

121 Spring

1 5 0 0 1 0

345370.8711 0 0 0 0 0 0

0 0 0

-1.38120325 0 0 0 0 0 0

0 7.025068243 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004014634 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-57

122 Spring

1 5 0 0 1 0

348833.3493 0 0 0 0 0 0

0 0 0

-1.39281 0 0 0 0 0 0

0 7.069901763 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004 0 0 0

123 Spring

1 5 0 0 1 0

352295.8276 0 0 0 0 0 0

0 0 0

-1.40441675 0 0 0 0 0 0

0 7.170649466 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004043902 0 0 0

124 Spring

1 5 0 0 1 0

355758.3058 0 0 0 0 0 0

0 0 0

-1.4160235 0 0 0 0 0 0

0 7.271397169 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004087805 0 0 0

125 Spring

1 5 0 0 1 0

359220.7841 0 0 0 0 0 0

0 0 0

-1.42763025 0 0 0 0 0 0

0 7.372144872 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004131707 0 0 0

126 Spring

1 5 0 0 1 0

362683.2623 0 0 0 0 0 0

0 0 0

-1.439237 0 0 0 0 0 0

0 7.472892575 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00417561 0 0 0

127 Spring

1 5 0 0 1 0

366145.7405 0 0 0 0 0 0

0 0 0

-1.45084375 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-58

0 7.573640278 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004219512 0 0 0

128 Spring

1 5 0 0 1 0

369608.2188 0 0 0 0 0 0

0 0 0

-1.4624505 0 0 0 0 0 0

0 7.674387981 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004263415 0 0 0

129 Spring

1 5 0 0 1 0

373070.697 0 0 0 0 0 0

0 0 0

-1.47405725 0 0 0 0 0 0

0 7.775135684 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004307317 0 0 0

130 Spring

1 5 0 0 1 0

376533.1753 0 0 0 0 0 0

0 0 0

-1.485664 0 0 0 0 0 0

0 7.875883387 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00435122 0 0 0

131 Spring

1 5 0 0 1 0

379995.6535 0 0 0 0 0 0

0 0 0

-1.49727075 0 0 0 0 0 0

0 7.97663109 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004395122 0 0 0

132 Spring

1 5 0 0 1 0

383458.1318 0 0 0 0 0 0

0 0 0

-1.5088775 0 0 0 0 0 0

0 8.077378793 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004439024 0 0 0

133 Spring

Pile 3 dynamic data file input into Ruaumoko

A-59

1 5 0 0 1 0

386920.61 0 0 0 0 0 0

0 0 0

-1.52048425 0 0 0 0 0 0

0 8.178126496 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004482927 0 0 0

134 Spring

1 5 0 0 1 0

390383.0883 0 0 0 0 0 0

0 0 0

-1.532091 0 0 0 0 0 0

0 8.278874199 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004526829 0 0 0

135 Spring

1 5 0 0 1 0

393845.5665 0 0 0 0 0 0

0 0 0

-1.54369775 0 0 0 0 0 0

0 8.379621902 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004570732 0 0 0

136 Spring

1 5 0 0 1 0

397308.0447 0 0 0 0 0 0

0 0 0

-1.5553045 0 0 0 0 0 0

0 8.480369605 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004614634 0 0 0

137 Spring

1 5 0 0 1 0

200385.2615 0 0 0 0 0 0

0 0 0

-0.782004781 0 0 0 0 0 0

0 4.28910781 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004658537 0 0 0

138 Spring ! Inner spring properties side two (loaded in tension during pull-back)

1 5 0 0 1 0

92263.05772 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 0.669359438 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-60

0 0 0 0 0 0

1 0.02 0 0.002666667 0 0 0

139 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.018333333 0 0.002666667 0 0 0

140 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.016666667 0 0.002666667 0 0 0

141 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.015 0 0.002666667 0 0 0

142 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.013333333 0 0.002666667 0 0 0

143 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-61

1 0.011666667 0 0.002666667 0 0 0

144 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.01 0 0.002666667 0 0 0

145 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.008333333 0 0.002666667 0 0 0

146 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.006666667 0 0.002666667 0 0 0

147 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.005 0 0.002666667 0 0 0

148 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.338718877 0 0 0 0

0 0 0 0 0 0

1 0.003333333 0 0.002666667 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-62

149 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

0 1.385754945 0 0 0 0

0 0 0 0 0 0

1 0.001666667 0 0.002705747 0 0 0

150 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.139281 0 0 0 0 0 0

0 1.572072014 0 0 0 0

0 0 0 0 0 0

1 0 0 0.002744828 0 0 0

151 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.15088775 0 0 0 0 0 0

0 1.630714833 0 0 0 0

0 0 0 0 0 0

1 0 0 0.002783908 0 0 0

152 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.1624945 0 0 0 0 0 0

0 1.689357651 0 0 0 0

0 0 0 0 0 0

1 0 0 0.002822989 0 0 0

153 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.17410125 0 0 0 0 0 0

0 1.74800047 0 0 0 0

0 0 0 0 0 0

1 0 0 0.002862069 0 0 0

154 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-63

0 0 0

-0.185708 0 0 0 0 0 0

0 1.806643289 0 0 0 0

0 0 0 0 0 0

1 0 0 0.002901149 0 0 0

155 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.19731475 0 0 0 0 0 0

0 1.865286107 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00294023 0 0 0

156 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.2089215 0 0 0 0 0 0

0 1.923928926 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00297931 0 0 0

157 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.22052825 0 0 0 0 0 0

0 1.982571745 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003018391 0 0 0

158 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.232135 0 0 0 0 0 0

0 2.041214563 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003057471 0 0 0

159 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.24374175 0 0 0 0 0 0

0 2.099857382 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003096552 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-64

160 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.2553485 0 0 0 0 0 0

0 2.158500201 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003135632 0 0 0

161 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.26695525 0 0 0 0 0 0

0 2.217143019 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003174713 0 0 0

162 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.278562 0 0 0 0 0 0

0 2.275785838 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003213793 0 0 0

163 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.29016875 0 0 0 0 0 0

0 2.334428656 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003252874 0 0 0

164 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.3017755 0 0 0 0 0 0

0 2.393071475 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003291954 0 0 0

165 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-65

-0.31338225 0 0 0 0 0 0

0 2.451714294 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003331034 0 0 0

166 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.324989 0 0 0 0 0 0

0 2.510357112 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003370115 0 0 0

167 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.33659575 0 0 0 0 0 0

0 2.568999931 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003409195 0 0 0

168 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.3482025 0 0 0 0 0 0

0 2.62764275 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003448276 0 0 0

169 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.35980925 0 0 0 0 0 0

0 2.686051008 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003495935 0 0 0

170 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.371416 0 0 0 0 0 0

0 2.744459267 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003543594 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-66

171 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.38302275 0 0 0 0 0 0

0 2.802867526 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003591253 0 0 0

172 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.3946295 0 0 0 0 0 0

0 2.861275785 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003638912 0 0 0

173 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.40623625 0 0 0 0 0 0

0 2.919684043 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003686571 0 0 0

174 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.417843 0 0 0 0 0 0

0 2.978092302 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00373423 0 0 0

175 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.42944975 0 0 0 0 0 0

0 3.036500561 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00378189 0 0 0

176 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.4410565 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-67

0 3.094908819 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003829549 0 0 0

177 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.45266325 0 0 0 0 0 0

0 3.153317078 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003877208 0 0 0

178 Spring

1 5 0 0 1 0

184526.1154 0 0 0 0 0 0

0 0 0

-0.46427 0 0 0 0 0 0

0 3.211725337 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003924867 0 0 0

179 Spring

1 5 0 0 1 0

185199.6057 0 0 0 0 0 0

0 0 0

-0.47587675 0 0 0 0 0 0

0 3.270133595 0 0 0 0

0 0 0 0 0 0

1 0 0 0.003972526 0 0 0

180 Spring

1 5 0 0 1 0

185859.8902 0 0 0 0 0 0

0 0 0

-0.4874835 0 0 0 0 0 0

0 3.328541854 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004020185 0 0 0

181 Spring

1 5 0 0 1 0

186520.1747 0 0 0 0 0 0

0 0 0

-0.49909025 0 0 0 0 0 0

0 3.386950113 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004067844 0 0 0

182 Spring

Pile 3 dynamic data file input into Ruaumoko

A-68

1 5 0 0 1 0

187180.4592 0 0 0 0 0 0

0 0 0

-0.510697 0 0 0 0 0 0

0 3.445358372 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004115503 0 0 0

183 Spring

1 5 0 0 1 0

187840.7438 0 0 0 0 0 0

0 0 0

-0.52230375 0 0 0 0 0 0

0 3.50376663 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004163162 0 0 0

184 Spring

1 5 0 0 1 0

188501.0283 0 0 0 0 0 0

0 0 0

-0.5339105 0 0 0 0 0 0

0 3.562174889 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004210821 0 0 0

185 Spring

1 5 0 0 1 0

189161.3128 0 0 0 0 0 0

0 0 0

-0.54551725 0 0 0 0 0 0

0 3.620583148 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004258481 0 0 0

186 Spring

1 5 0 0 1 0

189821.5973 0 0 0 0 0 0

0 0 0

-0.557124 0 0 0 0 0 0

0 3.678991406 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00430614 0 0 0

187 Spring

1 5 0 0 1 0

190481.8819 0 0 0 0 0 0

0 0 0

-0.56873075 0 0 0 0 0 0

0 3.737399665 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-69

0 0 0 0 0 0

1 0 0 0.004353799 0 0 0

188 Spring

1 5 0 0 1 0

191142.1664 0 0 0 0 0 0

0 0 0

-0.5803375 0 0 0 0 0 0

0 3.795807924 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004401458 0 0 0

189 Spring

1 5 0 0 1 0

191802.4509 0 0 0 0 0 0

0 0 0

-0.59194425 0 0 0 0 0 0

0 3.854216183 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004449117 0 0 0

190 Spring

1 5 0 0 1 0

192462.7354 0 0 0 0 0 0

0 0 0

-0.603551 0 0 0 0 0 0

0 3.912624441 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004496776 0 0 0

191 Spring

1 5 0 0 1 0

193123.02 0 0 0 0 0 0

0 0 0

-0.61515775 0 0 0 0 0 0

0 3.9710327 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004544435 0 0 0

192 Spring

1 5 0 0 1 0

193783.3045 0 0 0 0 0 0

0 0 0

-0.6267645 0 0 0 0 0 0

0 4.029440959 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004592094 0 0 0

193 Spring

1 5 0 0 1 0

Pile 3 dynamic data file input into Ruaumoko

A-70

194443.589 0 0 0 0 0 0

0 0 0

-0.63837125 0 0 0 0 0 0

0 4.087849217 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004639753 0 0 0

194 Spring

1 5 0 0 1 0

195103.8735 0 0 0 0 0 0

0 0 0

-0.649978 0 0 0 0 0 0

0 4.146257476 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004687412 0 0 0

195 Spring

1 5 0 0 1 0

195764.1581 0 0 0 0 0 0

0 0 0

-0.66158475 0 0 0 0 0 0

0 4.204665735 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004735071 0 0 0

196 Spring

1 5 0 0 1 0

196424.4426 0 0 0 0 0 0

0 0 0

-0.6731915 0 0 0 0 0 0

0 4.263073994 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004782731 0 0 0

197 Spring

1 5 0 0 1 0

197084.7271 0 0 0 0 0 0

0 0 0

-0.68479825 0 0 0 0 0 0

0 4.321482252 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00483039 0 0 0

198 Spring

1 5 0 0 1 0

197745.0116 0 0 0 0 0 0

0 0 0

-0.696405 0 0 0 0 0 0

0 4.379890511 0 0 0 0

0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-71

1 0 0 0.004878049 0 0 0

199 Spring

1 5 0 0 1 0

198405.2962 0 0 0 0 0 0

0 0 0

-0.70801175 0 0 0 0 0 0

0 4.424724032 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004863415 0 0 0

200 Spring

1 5 0 0 1 0

199065.5807 0 0 0 0 0 0

0 0 0

-0.7196185 0 0 0 0 0 0

0 4.469557553 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00484878 0 0 0

201 Spring

1 5 0 0 1 0

199725.8652 0 0 0 0 0 0

0 0 0

-0.73122525 0 0 0 0 0 0

0 4.514391074 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004834146 0 0 0

202 Spring

1 5 0 0 1 0

200386.1497 0 0 0 0 0 0

0 0 0

-0.742832 0 0 0 0 0 0

0 4.559224594 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004819512 0 0 0

203 Spring

1 5 0 0 1 0

201046.4343 0 0 0 0 0 0

0 0 0

-0.75443875 0 0 0 0 0 0

0 4.604058115 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004804878 0 0 0

204 Spring

1 5 0 0 1 0

201706.7188 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-72

0 0 0

-0.7660455 0 0 0 0 0 0

0 4.648891636 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004790244 0 0 0

205 Spring

1 5 0 0 1 0

202367.0033 0 0 0 0 0 0

0 0 0

-0.77765225 0 0 0 0 0 0

0 4.693725157 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00477561 0 0 0

206 Spring

1 5 0 0 1 0

203027.2878 0 0 0 0 0 0

0 0 0

-0.789259 0 0 0 0 0 0

0 4.738558678 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004760976 0 0 0

207 Spring

1 5 0 0 1 0

203687.5724 0 0 0 0 0 0

0 0 0

-0.80086575 0 0 0 0 0 0

0 4.783392199 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004746341 0 0 0

208 Spring

1 5 0 0 1 0

204347.8569 0 0 0 0 0 0

0 0 0

-0.8124725 0 0 0 0 0 0

0 4.82822572 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004731707 0 0 0

209 Spring

1 5 0 0 1 0

205008.1414 0 0 0 0 0 0

0 0 0

-0.82407925 0 0 0 0 0 0

0 4.873059241 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004717073 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-73

210 Spring

1 5 0 0 1 0

205668.4259 0 0 0 0 0 0

0 0 0

-0.835686 0 0 0 0 0 0

0 4.917892761 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004702439 0 0 0

211 Spring

1 5 0 0 1 0

206328.7105 0 0 0 0 0 0

0 0 0

-0.84729275 0 0 0 0 0 0

0 4.962726282 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004687805 0 0 0

212 Spring

1 5 0 0 1 0

206988.995 0 0 0 0 0 0

0 0 0

-0.8588995 0 0 0 0 0 0

0 5.007559803 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004673171 0 0 0

213 Spring

1 5 0 0 1 0

207649.2795 0 0 0 0 0 0

0 0 0

-0.87050625 0 0 0 0 0 0

0 5.052393324 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004658537 0 0 0

214 Spring

1 5 0 0 1 0

208309.564 0 0 0 0 0 0

0 0 0

-0.882113 0 0 0 0 0 0

0 5.097226845 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004643902 0 0 0

215 Spring

1 5 0 0 1 0

208969.8486 0 0 0 0 0 0

0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-74

-0.89371975 0 0 0 0 0 0

0 5.142060366 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004629268 0 0 0

216 Spring

1 5 0 0 1 0

209630.1331 0 0 0 0 0 0

0 0 0

-0.9053265 0 0 0 0 0 0

0 5.186893887 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004614634 0 0 0

217 Spring

1 5 0 0 1 0

210290.4176 0 0 0 0 0 0

0 0 0

-0.91693325 0 0 0 0 0 0

0 5.231727408 0 0 0 0

0 0 0 0 0 0

1 0 0 0.0046 0 0 0

218 Spring

1 5 0 0 1 0

211095.9647 0 0 0 0 0 0

0 0 0

-0.92854 0 0 0 0 0 0

0 5.276560928 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004585366 0 0 0

219 Spring

1 5 0 0 1 0

213796.6978 0 0 0 0 0 0

0 0 0

-0.94014675 0 0 0 0 0 0

0 5.321394449 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004570732 0 0 0

220 Spring

1 5 0 0 1 0

217259.176 0 0 0 0 0 0

0 0 0

-0.9517535 0 0 0 0 0 0

0 5.36622797 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004556098 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-75

221 Spring

1 5 0 0 1 0

220721.6543 0 0 0 0 0 0

0 0 0

-0.96336025 0 0 0 0 0 0

0 5.411061491 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004541463 0 0 0

222 Spring

1 5 0 0 1 0

224184.1325 0 0 0 0 0 0

0 0 0

-0.974967 0 0 0 0 0 0

0 5.455895012 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004526829 0 0 0

223 Spring

1 5 0 0 1 0

227646.6108 0 0 0 0 0 0

0 0 0

-0.98657375 0 0 0 0 0 0

0 5.500728533 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004512195 0 0 0

224 Spring

1 5 0 0 1 0

231109.089 0 0 0 0 0 0

0 0 0

-0.9981805 0 0 0 0 0 0

0 5.545562054 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004497561 0 0 0

225 Spring

1 5 0 0 1 0

234571.5672 0 0 0 0 0 0

0 0 0

-1.00978725 0 0 0 0 0 0

0 5.590395575 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004482927 0 0 0

226 Spring

1 5 0 0 1 0

238034.0455 0 0 0 0 0 0

0 0 0

-1.021394 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-76

0 5.635229095 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004468293 0 0 0

227 Spring

1 5 0 0 1 0

241496.5237 0 0 0 0 0 0

0 0 0

-1.03300075 0 0 0 0 0 0

0 5.680062616 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004453659 0 0 0

228 Spring

1 5 0 0 1 0

244959.002 0 0 0 0 0 0

0 0 0

-1.0446075 0 0 0 0 0 0

0 5.724896137 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004439024 0 0 0

229 Spring

1 5 0 0 1 0

248421.4802 0 0 0 0 0 0

0 0 0

-1.05621425 0 0 0 0 0 0

0 5.769729658 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00442439 0 0 0

230 Spring

1 5 0 0 1 0

251883.9585 0 0 0 0 0 0

0 0 0

-1.067821 0 0 0 0 0 0

0 5.814563179 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004409756 0 0 0

231 Spring

1 5 0 0 1 0

255346.4367 0 0 0 0 0 0

0 0 0

-1.07942775 0 0 0 0 0 0

0 5.8593967 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004395122 0 0 0

232 Spring

Pile 3 dynamic data file input into Ruaumoko

A-77

1 5 0 0 1 0

258808.915 0 0 0 0 0 0

0 0 0

-1.0910345 0 0 0 0 0 0

0 5.904230221 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004380488 0 0 0

233 Spring

1 5 0 0 1 0

262271.3932 0 0 0 0 0 0

0 0 0

-1.10264125 0 0 0 0 0 0

0 5.949063742 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004365854 0 0 0

234 Spring

1 5 0 0 1 0

265733.8714 0 0 0 0 0 0

0 0 0

-1.114248 0 0 0 0 0 0

0 5.993897262 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00435122 0 0 0

235 Spring

1 5 0 0 1 0

269196.3497 0 0 0 0 0 0

0 0 0

-1.12585475 0 0 0 0 0 0

0 6.038730783 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004336585 0 0 0

236 Spring

1 5 0 0 1 0

272658.8279 0 0 0 0 0 0

0 0 0

-1.1374615 0 0 0 0 0 0

0 6.083564304 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004321951 0 0 0

237 Spring

1 5 0 0 1 0

276121.3062 0 0 0 0 0 0

0 0 0

-1.14906825 0 0 0 0 0 0

0 6.128397825 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-78

0 0 0 0 0 0

1 0 0 0.004307317 0 0 0

238 Spring

1 5 0 0 1 0

279583.7844 0 0 0 0 0 0

0 0 0

-1.160675 0 0 0 0 0 0

0 6.173231346 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004292683 0 0 0

239 Spring

1 5 0 0 1 0

283046.2627 0 0 0 0 0 0

0 0 0

-1.17228175 0 0 0 0 0 0

0 6.218064867 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004278049 0 0 0

240 Spring

1 5 0 0 1 0

286508.7409 0 0 0 0 0 0

0 0 0

-1.1838885 0 0 0 0 0 0

0 6.262898388 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004263415 0 0 0

241 Spring

1 5 0 0 1 0

289971.2192 0 0 0 0 0 0

0 0 0

-1.19549525 0 0 0 0 0 0

0 6.307731909 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00424878 0 0 0

242 Spring

1 5 0 0 1 0

293433.6974 0 0 0 0 0 0

0 0 0

-1.207102 0 0 0 0 0 0

0 6.352565429 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004234146 0 0 0

243 Spring

1 5 0 0 1 0

Pile 3 dynamic data file input into Ruaumoko

A-79

296896.1756 0 0 0 0 0 0

0 0 0

-1.21870875 0 0 0 0 0 0

0 6.39739895 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004219512 0 0 0

244 Spring

1 5 0 0 1 0

300358.6539 0 0 0 0 0 0

0 0 0

-1.2303155 0 0 0 0 0 0

0 6.442232471 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004204878 0 0 0

245 Spring

1 5 0 0 1 0

303821.1321 0 0 0 0 0 0

0 0 0

-1.24192225 0 0 0 0 0 0

0 6.487065992 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004190244 0 0 0

246 Spring

1 5 0 0 1 0

307283.6104 0 0 0 0 0 0

0 0 0

-1.253529 0 0 0 0 0 0

0 6.531899513 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00417561 0 0 0

247 Spring

1 5 0 0 1 0

310746.0886 0 0 0 0 0 0

0 0 0

-1.26513575 0 0 0 0 0 0

0 6.576733034 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004160976 0 0 0

248 Spring

1 5 0 0 1 0

314208.5669 0 0 0 0 0 0

0 0 0

-1.2767425 0 0 0 0 0 0

0 6.621566555 0 0 0 0

0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-80

1 0 0 0.004146341 0 0 0

249 Spring

1 5 0 0 1 0

317671.0451 0 0 0 0 0 0

0 0 0

-1.28834925 0 0 0 0 0 0

0 6.666400076 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004131707 0 0 0

250 Spring

1 5 0 0 1 0

321133.5234 0 0 0 0 0 0

0 0 0

-1.299956 0 0 0 0 0 0

0 6.711233596 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004117073 0 0 0

251 Spring

1 5 0 0 1 0

324596.0016 0 0 0 0 0 0

0 0 0

-1.31156275 0 0 0 0 0 0

0 6.756067117 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004102439 0 0 0

252 Spring

1 5 0 0 1 0

328058.4799 0 0 0 0 0 0

0 0 0

-1.3231695 0 0 0 0 0 0

0 6.800900638 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004087805 0 0 0

253 Spring

1 5 0 0 1 0

331520.9581 0 0 0 0 0 0

0 0 0

-1.33477625 0 0 0 0 0 0

0 6.845734159 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004073171 0 0 0

254 Spring

1 5 0 0 1 0

334983.4363 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-81

0 0 0

-1.346383 0 0 0 0 0 0

0 6.89056768 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004058537 0 0 0

255 Spring

1 5 0 0 1 0

338445.9146 0 0 0 0 0 0

0 0 0

-1.35798975 0 0 0 0 0 0

0 6.935401201 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004043902 0 0 0

256 Spring

1 5 0 0 1 0

341908.3928 0 0 0 0 0 0

0 0 0

-1.3695965 0 0 0 0 0 0

0 6.980234722 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004029268 0 0 0

257 Spring

1 5 0 0 1 0

345370.8711 0 0 0 0 0 0

0 0 0

-1.38120325 0 0 0 0 0 0

0 7.025068243 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004014634 0 0 0

258 Spring

1 5 0 0 1 0

348833.3493 0 0 0 0 0 0

0 0 0

-1.39281 0 0 0 0 0 0

0 7.069901763 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004 0 0 0

259 Spring

1 5 0 0 1 0

352295.8276 0 0 0 0 0 0

0 0 0

-1.40441675 0 0 0 0 0 0

0 7.170649466 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004043902 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-82

260 Spring

1 5 0 0 1 0

355758.3058 0 0 0 0 0 0

0 0 0

-1.4160235 0 0 0 0 0 0

0 7.271397169 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004087805 0 0 0

261 Spring

1 5 0 0 1 0

359220.7841 0 0 0 0 0 0

0 0 0

-1.42763025 0 0 0 0 0 0

0 7.372144872 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004131707 0 0 0

262 Spring

1 5 0 0 1 0

362683.2623 0 0 0 0 0 0

0 0 0

-1.439237 0 0 0 0 0 0

0 7.472892575 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00417561 0 0 0

263 Spring

1 5 0 0 1 0

366145.7405 0 0 0 0 0 0

0 0 0

-1.45084375 0 0 0 0 0 0

0 7.573640278 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004219512 0 0 0

264 Spring

1 5 0 0 1 0

369608.2188 0 0 0 0 0 0

0 0 0

-1.4624505 0 0 0 0 0 0

0 7.674387981 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004263415 0 0 0

265 Spring

1 5 0 0 1 0

373070.697 0 0 0 0 0 0

0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-83

-1.47405725 0 0 0 0 0 0

0 7.775135684 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004307317 0 0 0

266 Spring

1 5 0 0 1 0

376533.1753 0 0 0 0 0 0

0 0 0

-1.485664 0 0 0 0 0 0

0 7.875883387 0 0 0 0

0 0 0 0 0 0

1 0 0 0.00435122 0 0 0

267 Spring

1 5 0 0 1 0

379995.6535 0 0 0 0 0 0

0 0 0

-1.49727075 0 0 0 0 0 0

0 7.97663109 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004395122 0 0 0

268 Spring

1 5 0 0 1 0

383458.1318 0 0 0 0 0 0

0 0 0

-1.5088775 0 0 0 0 0 0

0 8.077378793 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004439024 0 0 0

269 Spring

1 5 0 0 1 0

386920.61 0 0 0 0 0 0

0 0 0

-1.52048425 0 0 0 0 0 0

0 8.178126496 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004482927 0 0 0

270 Spring

1 5 0 0 1 0

390383.0883 0 0 0 0 0 0

0 0 0

-1.532091 0 0 0 0 0 0

0 8.278874199 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004526829 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-84

271 Spring

1 5 0 0 1 0

393845.5665 0 0 0 0 0 0

0 0 0

-1.54369775 0 0 0 0 0 0

0 8.379621902 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004570732 0 0 0

272 Spring

1 5 0 0 1 0

397308.0447 0 0 0 0 0 0

0 0 0

-1.5553045 0 0 0 0 0 0

0 8.480369605 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004614634 0 0 0

273 Spring

1 5 0 0 1 0

200385.2615 0 0 0 0 0 0

0 0 0

-0.782004781 0 0 0 0 0 0

0 4.28910781 0 0 0 0

0 0 0 0 0 0

1 0 0 0.004658537 0 0 0

274 Spring !Outer spring properties side one

1 0 0 0 1 0

1845.261154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

275 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

276 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

277 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-85

278 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

279 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

280 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

281 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

282 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

283 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

284 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

285 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

286 Spring

Pile 3 dynamic data file input into Ruaumoko

A-86

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

287 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

288 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

289 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

290 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

291 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

292 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

293 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

294 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-87

0 0 0

0 0 0 0 0 0 0

295 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.24374175 0 0 0 0 0 0

296 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.2553485 0 0 0 0 0 0

297 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.26695525 0 0 0 0 0 0

298 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.278562 0 0 0 0 0 0

299 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.29016875 0 0 0 0 0 0

300 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.3017755 0 0 0 0 0 0

301 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.31338225 0 0 0 0 0 0

302 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.324989 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-88

303 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.33659575 0 0 0 0 0 0

304 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.3482025 0 0 0 0 0 0

305 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.35980925 0 0 0 0 0 0

306 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.371416 0 0 0 0 0 0

307 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.38302275 0 0 0 0 0 0

308 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.3946295 0 0 0 0 0 0

309 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.40623625 0 0 0 0 0 0

310 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.417843 0 0 0 0 0 0

311 Spring

Pile 3 dynamic data file input into Ruaumoko

A-89

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.42944975 0 0 0 0 0 0

312 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.4410565 0 0 0 0 0 0

313 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.45266325 0 0 0 0 0 0

314 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.46427 0 0 0 0 0 0

315 Spring

1 0 0 0 1 0

3703.992113 0 0 0 0 0 0

0 0 0

-0.47587675 0 0 0 0 0 0

316 Spring

1 0 0 0 1 0

3717.197804 0 0 0 0 0 0

0 0 0

-0.4874835 0 0 0 0 0 0

317 Spring

1 0 0 0 1 0

3730.403494 0 0 0 0 0 0

0 0 0

-0.49909025 0 0 0 0 0 0

318 Spring

1 0 0 0 1 0

3743.609185 0 0 0 0 0 0

0 0 0

-0.510697 0 0 0 0 0 0

319 Spring

1 0 0 0 1 0

3756.814875 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-90

0 0 0

-0.52230375 0 0 0 0 0 0

320 Spring

1 0 0 0 1 0

3770.020566 0 0 0 0 0 0

0 0 0

-0.5339105 0 0 0 0 0 0

321 Spring

1 0 0 0 1 0

3783.226256 0 0 0 0 0 0

0 0 0

-0.54551725 0 0 0 0 0 0

322 Spring

1 0 0 0 1 0

3796.431947 0 0 0 0 0 0

0 0 0

-0.557124 0 0 0 0 0 0

323 Spring

1 0 0 0 1 0

3809.637637 0 0 0 0 0 0

0 0 0

-0.56873075 0 0 0 0 0 0

324 Spring

1 0 0 0 1 0

3822.843328 0 0 0 0 0 0

0 0 0

-0.5803375 0 0 0 0 0 0

325 Spring

1 0 0 0 1 0

3836.049018 0 0 0 0 0 0

0 0 0

-0.59194425 0 0 0 0 0 0

326 Spring

1 0 0 0 1 0

3849.254709 0 0 0 0 0 0

0 0 0

-0.603551 0 0 0 0 0 0

327 Spring

1 0 0 0 1 0

3862.460399 0 0 0 0 0 0

0 0 0

-0.61515775 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-91

328 Spring

1 0 0 0 1 0

3875.66609 0 0 0 0 0 0

0 0 0

-0.6267645 0 0 0 0 0 0

329 Spring

1 0 0 0 1 0

3888.87178 0 0 0 0 0 0

0 0 0

-0.63837125 0 0 0 0 0 0

330 Spring

1 0 0 0 1 0

3902.077471 0 0 0 0 0 0

0 0 0

-0.649978 0 0 0 0 0 0

331 Spring

1 0 0 0 1 0

3915.283161 0 0 0 0 0 0

0 0 0

-0.66158475 0 0 0 0 0 0

332 Spring

1 0 0 0 1 0

3928.488852 0 0 0 0 0 0

0 0 0

-0.6731915 0 0 0 0 0 0

333 Spring

1 0 0 0 1 0

3941.694542 0 0 0 0 0 0

0 0 0

-0.68479825 0 0 0 0 0 0

334 Spring

1 0 0 0 1 0

3954.900233 0 0 0 0 0 0

0 0 0

-0.696405 0 0 0 0 0 0

335 Spring

1 0 0 0 1 0

3968.105923 0 0 0 0 0 0

0 0 0

-0.70801175 0 0 0 0 0 0

336 Spring

Pile 3 dynamic data file input into Ruaumoko

A-92

1 0 0 0 1 0

3981.311614 0 0 0 0 0 0

0 0 0

-0.7196185 0 0 0 0 0 0

337 Spring

1 0 0 0 1 0

3994.517304 0 0 0 0 0 0

0 0 0

-0.73122525 0 0 0 0 0 0

338 Spring

1 0 0 0 1 0

4007.722995 0 0 0 0 0 0

0 0 0

-0.742832 0 0 0 0 0 0

339 Spring

1 0 0 0 1 0

4020.928685 0 0 0 0 0 0

0 0 0

-0.75443875 0 0 0 0 0 0

340 Spring

1 0 0 0 1 0

4034.134376 0 0 0 0 0 0

0 0 0

-0.7660455 0 0 0 0 0 0

341 Spring

1 0 0 0 1 0

4047.340066 0 0 0 0 0 0

0 0 0

-0.77765225 0 0 0 0 0 0

342 Spring

1 0 0 0 1 0

4060.545757 0 0 0 0 0 0

0 0 0

-0.789259 0 0 0 0 0 0

343 Spring

1 0 0 0 1 0

4073.751447 0 0 0 0 0 0

0 0 0

-0.80086575 0 0 0 0 0 0

344 Spring

1 0 0 0 1 0

4086.957138 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-93

0 0 0

-0.8124725 0 0 0 0 0 0

345 Spring

1 0 0 0 1 0

4100.162828 0 0 0 0 0 0

0 0 0

-0.82407925 0 0 0 0 0 0

346 Spring

1 0 0 0 1 0

4113.368519 0 0 0 0 0 0

0 0 0

-0.835686 0 0 0 0 0 0

347 Spring

1 0 0 0 1 0

4126.574209 0 0 0 0 0 0

0 0 0

-0.84729275 0 0 0 0 0 0

348 Spring

1 0 0 0 1 0

4139.7799 0 0 0 0 0 0

0 0 0

-0.8588995 0 0 0 0 0 0

349 Spring

1 0 0 0 1 0

4152.98559 0 0 0 0 0 0

0 0 0

-0.87050625 0 0 0 0 0 0

350 Spring

1 0 0 0 1 0

4166.191281 0 0 0 0 0 0

0 0 0

-0.882113 0 0 0 0 0 0

351 Spring

1 0 0 0 1 0

4179.396971 0 0 0 0 0 0

0 0 0

-0.89371975 0 0 0 0 0 0

352 Spring

1 0 0 0 1 0

4192.602662 0 0 0 0 0 0

0 0 0

-0.9053265 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-94

353 Spring

1 0 0 0 1 0

4205.808352 0 0 0 0 0 0

0 0 0

-0.91693325 0 0 0 0 0 0

354 Spring

1 0 0 0 1 0

4221.919295 0 0 0 0 0 0

0 0 0

-0.92854 0 0 0 0 0 0

355 Spring

1 0 0 0 1 0

4275.933955 0 0 0 0 0 0

0 0 0

-0.94014675 0 0 0 0 0 0

356 Spring

1 0 0 0 1 0

4345.18352 0 0 0 0 0 0

0 0 0

-0.9517535 0 0 0 0 0 0

357 Spring

1 0 0 0 1 0

4414.433085 0 0 0 0 0 0

0 0 0

-0.96336025 0 0 0 0 0 0

358 Spring

1 0 0 0 1 0

4483.68265 0 0 0 0 0 0

0 0 0

-0.974967 0 0 0 0 0 0

359 Spring

1 0 0 0 1 0

4552.932215 0 0 0 0 0 0

0 0 0

-0.98657375 0 0 0 0 0 0

360 Spring

1 0 0 0 1 0

4622.18178 0 0 0 0 0 0

0 0 0

-0.9981805 0 0 0 0 0 0

361 Spring

Pile 3 dynamic data file input into Ruaumoko

A-95

1 0 0 0 1 0

4691.431345 0 0 0 0 0 0

0 0 0

-1.00978725 0 0 0 0 0 0

362 Spring

1 0 0 0 1 0

4760.68091 0 0 0 0 0 0

0 0 0

-1.021394 0 0 0 0 0 0

363 Spring

1 0 0 0 1 0

4829.930475 0 0 0 0 0 0

0 0 0

-1.03300075 0 0 0 0 0 0

364 Spring

1 0 0 0 1 0

4899.18004 0 0 0 0 0 0

0 0 0

-1.0446075 0 0 0 0 0 0

365 Spring

1 0 0 0 1 0

4968.429604 0 0 0 0 0 0

0 0 0

-1.05621425 0 0 0 0 0 0

366 Spring

1 0 0 0 1 0

5037.679169 0 0 0 0 0 0

0 0 0

-1.067821 0 0 0 0 0 0

367 Spring

1 0 0 0 1 0

5106.928734 0 0 0 0 0 0

0 0 0

-1.07942775 0 0 0 0 0 0

368 Spring

1 0 0 0 1 0

5176.178299 0 0 0 0 0 0

0 0 0

-1.0910345 0 0 0 0 0 0

369 Spring

1 0 0 0 1 0

5245.427864 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-96

0 0 0

-1.10264125 0 0 0 0 0 0

370 Spring

1 0 0 0 1 0

5314.677429 0 0 0 0 0 0

0 0 0

-1.114248 0 0 0 0 0 0

371 Spring

1 0 0 0 1 0

5383.926994 0 0 0 0 0 0

0 0 0

-1.12585475 0 0 0 0 0 0

372 Spring

1 0 0 0 1 0

5453.176559 0 0 0 0 0 0

0 0 0

-1.1374615 0 0 0 0 0 0

373 Spring

1 0 0 0 1 0

5522.426124 0 0 0 0 0 0

0 0 0

-1.14906825 0 0 0 0 0 0

374 Spring

1 0 0 0 1 0

5591.675688 0 0 0 0 0 0

0 0 0

-1.160675 0 0 0 0 0 0

375 Spring

1 0 0 0 1 0

5660.925253 0 0 0 0 0 0

0 0 0

-1.17228175 0 0 0 0 0 0

376 Spring

1 0 0 0 1 0

5730.174818 0 0 0 0 0 0

0 0 0

-1.1838885 0 0 0 0 0 0

377 Spring

1 0 0 0 1 0

5799.424383 0 0 0 0 0 0

0 0 0

-1.19549525 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-97

378 Spring

1 0 0 0 1 0

5868.673948 0 0 0 0 0 0

0 0 0

-1.207102 0 0 0 0 0 0

379 Spring

1 0 0 0 1 0

5937.923513 0 0 0 0 0 0

0 0 0

-1.21870875 0 0 0 0 0 0

380 Spring

1 0 0 0 1 0

6007.173078 0 0 0 0 0 0

0 0 0

-1.2303155 0 0 0 0 0 0

381 Spring

1 0 0 0 1 0

6076.422643 0 0 0 0 0 0

0 0 0

-1.24192225 0 0 0 0 0 0

382 Spring

1 0 0 0 1 0

6145.672208 0 0 0 0 0 0

0 0 0

-1.253529 0 0 0 0 0 0

383 Spring

1 0 0 0 1 0

6214.921773 0 0 0 0 0 0

0 0 0

-1.26513575 0 0 0 0 0 0

384 Spring

1 0 0 0 1 0

6284.171337 0 0 0 0 0 0

0 0 0

-1.2767425 0 0 0 0 0 0

385 Spring

1 0 0 0 1 0

6353.420902 0 0 0 0 0 0

0 0 0

-1.28834925 0 0 0 0 0 0

386 Spring

Pile 3 dynamic data file input into Ruaumoko

A-98

1 0 0 0 1 0

6422.670467 0 0 0 0 0 0

0 0 0

-1.299956 0 0 0 0 0 0

387 Spring

1 0 0 0 1 0

6491.920032 0 0 0 0 0 0

0 0 0

-1.31156275 0 0 0 0 0 0

388 Spring

1 0 0 0 1 0

6561.169597 0 0 0 0 0 0

0 0 0

-1.3231695 0 0 0 0 0 0

389 Spring

1 0 0 0 1 0

6630.419162 0 0 0 0 0 0

0 0 0

-1.33477625 0 0 0 0 0 0

390 Spring

1 0 0 0 1 0

6699.668727 0 0 0 0 0 0

0 0 0

-1.346383 0 0 0 0 0 0

391 Spring

1 0 0 0 1 0

6768.918292 0 0 0 0 0 0

0 0 0

-1.35798975 0 0 0 0 0 0

392 Spring

1 0 0 0 1 0

6838.167857 0 0 0 0 0 0

0 0 0

-1.3695965 0 0 0 0 0 0

393 Spring

1 0 0 0 1 0

6907.417421 0 0 0 0 0 0

0 0 0

-1.38120325 0 0 0 0 0 0

394 Spring

1 0 0 0 1 0

6976.666986 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-99

0 0 0

-1.39281 0 0 0 0 0 0

395 Spring

1 0 0 0 1 0

7045.916551 0 0 0 0 0 0

0 0 0

-1.40441675 0 0 0 0 0 0

396 Spring

1 0 0 0 1 0

7115.166116 0 0 0 0 0 0

0 0 0

-1.4160235 0 0 0 0 0 0

397 Spring

1 0 0 0 1 0

7184.415681 0 0 0 0 0 0

0 0 0

-1.42763025 0 0 0 0 0 0

398 Spring

1 0 0 0 1 0

7253.665246 0 0 0 0 0 0

0 0 0

-1.439237 0 0 0 0 0 0

399 Spring

1 0 0 0 1 0

7322.914811 0 0 0 0 0 0

0 0 0

-1.45084375 0 0 0 0 0 0

400 Spring

1 0 0 0 1 0

7392.164376 0 0 0 0 0 0

0 0 0

-1.4624505 0 0 0 0 0 0

401 Spring

1 0 0 0 1 0

7461.413941 0 0 0 0 0 0

0 0 0

-1.47405725 0 0 0 0 0 0

402 Spring

1 0 0 0 1 0

7530.663506 0 0 0 0 0 0

0 0 0

-1.485664 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-100

403 Spring

1 0 0 0 1 0

7599.91307 0 0 0 0 0 0

0 0 0

-1.49727075 0 0 0 0 0 0

404 Spring

1 0 0 0 1 0

7669.162635 0 0 0 0 0 0

0 0 0

-1.5088775 0 0 0 0 0 0

405 Spring

1 0 0 0 1 0

7738.4122 0 0 0 0 0 0

0 0 0

-1.52048425 0 0 0 0 0 0

406 Spring

1 0 0 0 1 0

7807.661765 0 0 0 0 0 0

0 0 0

-1.532091 0 0 0 0 0 0

407 Spring

1 0 0 0 1 0

7876.91133 0 0 0 0 0 0

0 0 0

-1.54369775 0 0 0 0 0 0

408 Spring

1 0 0 0 1 0

7946.160895 0 0 0 0 0 0

0 0 0

-1.5553045 0 0 0 0 0 0

409 Spring

1 0 0 0 1 0

4007.70523 0 0 0 0 0 0

0 0 0

-0.782004781 0 0 0 0 0 0

410 Spring !Outer spring properties side two

1 0 0 0 1 0

1845.261154 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

411 Spring

Pile 3 dynamic data file input into Ruaumoko

A-101

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

412 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

413 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

414 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

415 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

416 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

417 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

418 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

419 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-102

0 0 0

0 0 0 0 0 0 0

420 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

421 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

0 0 0 0 0 0 0

422 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.139281 0 0 0 0 0 0

423 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.15088775 0 0 0 0 0 0

424 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.1624945 0 0 0 0 0 0

425 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.17410125 0 0 0 0 0 0

426 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.185708 0 0 0 0 0 0

427 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.19731475 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-103

428 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.2089215 0 0 0 0 0 0

429 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.22052825 0 0 0 0 0 0

430 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.232135 0 0 0 0 0 0

431 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.24374175 0 0 0 0 0 0

432 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.2553485 0 0 0 0 0 0

433 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.26695525 0 0 0 0 0 0

434 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.278562 0 0 0 0 0 0

435 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.29016875 0 0 0 0 0 0

436 Spring

Pile 3 dynamic data file input into Ruaumoko

A-104

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.3017755 0 0 0 0 0 0

437 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.31338225 0 0 0 0 0 0

438 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.324989 0 0 0 0 0 0

439 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.33659575 0 0 0 0 0 0

440 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.3482025 0 0 0 0 0 0

441 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.35980925 0 0 0 0 0 0

442 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.371416 0 0 0 0 0 0

443 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.38302275 0 0 0 0 0 0

444 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-105

0 0 0

-0.3946295 0 0 0 0 0 0

445 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.40623625 0 0 0 0 0 0

446 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.417843 0 0 0 0 0 0

447 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.42944975 0 0 0 0 0 0

448 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.4410565 0 0 0 0 0 0

449 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.45266325 0 0 0 0 0 0

450 Spring

1 0 0 0 1 0

3690.522309 0 0 0 0 0 0

0 0 0

-0.46427 0 0 0 0 0 0

451 Spring

1 0 0 0 1 0

3703.992113 0 0 0 0 0 0

0 0 0

-0.47587675 0 0 0 0 0 0

452 Spring

1 0 0 0 1 0

3717.197804 0 0 0 0 0 0

0 0 0

-0.4874835 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-106

453 Spring

1 0 0 0 1 0

3730.403494 0 0 0 0 0 0

0 0 0

-0.49909025 0 0 0 0 0 0

454 Spring

1 0 0 0 1 0

3743.609185 0 0 0 0 0 0

0 0 0

-0.510697 0 0 0 0 0 0

455 Spring

1 0 0 0 1 0

3756.814875 0 0 0 0 0 0

0 0 0

-0.52230375 0 0 0 0 0 0

456 Spring

1 0 0 0 1 0

3770.020566 0 0 0 0 0 0

0 0 0

-0.5339105 0 0 0 0 0 0

457 Spring

1 0 0 0 1 0

3783.226256 0 0 0 0 0 0

0 0 0

-0.54551725 0 0 0 0 0 0

458 Spring

1 0 0 0 1 0

3796.431947 0 0 0 0 0 0

0 0 0

-0.557124 0 0 0 0 0 0

459 Spring

1 0 0 0 1 0

3809.637637 0 0 0 0 0 0

0 0 0

-0.56873075 0 0 0 0 0 0

460 Spring

1 0 0 0 1 0

3822.843328 0 0 0 0 0 0

0 0 0

-0.5803375 0 0 0 0 0 0

461 Spring

Pile 3 dynamic data file input into Ruaumoko

A-107

1 0 0 0 1 0

3836.049018 0 0 0 0 0 0

0 0 0

-0.59194425 0 0 0 0 0 0

462 Spring

1 0 0 0 1 0

3849.254709 0 0 0 0 0 0

0 0 0

-0.603551 0 0 0 0 0 0

463 Spring

1 0 0 0 1 0

3862.460399 0 0 0 0 0 0

0 0 0

-0.61515775 0 0 0 0 0 0

464 Spring

1 0 0 0 1 0

3875.66609 0 0 0 0 0 0

0 0 0

-0.6267645 0 0 0 0 0 0

465 Spring

1 0 0 0 1 0

3888.87178 0 0 0 0 0 0

0 0 0

-0.63837125 0 0 0 0 0 0

466 Spring

1 0 0 0 1 0

3902.077471 0 0 0 0 0 0

0 0 0

-0.649978 0 0 0 0 0 0

467 Spring

1 0 0 0 1 0

3915.283161 0 0 0 0 0 0

0 0 0

-0.66158475 0 0 0 0 0 0

468 Spring

1 0 0 0 1 0

3928.488852 0 0 0 0 0 0

0 0 0

-0.6731915 0 0 0 0 0 0

469 Spring

1 0 0 0 1 0

3941.694542 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-108

0 0 0

-0.68479825 0 0 0 0 0 0

470 Spring

1 0 0 0 1 0

3954.900233 0 0 0 0 0 0

0 0 0

-0.696405 0 0 0 0 0 0

471 Spring

1 0 0 0 1 0

3968.105923 0 0 0 0 0 0

0 0 0

-0.70801175 0 0 0 0 0 0

472 Spring

1 0 0 0 1 0

3981.311614 0 0 0 0 0 0

0 0 0

-0.7196185 0 0 0 0 0 0

473 Spring

1 0 0 0 1 0

3994.517304 0 0 0 0 0 0

0 0 0

-0.73122525 0 0 0 0 0 0

474 Spring

1 0 0 0 1 0

4007.722995 0 0 0 0 0 0

0 0 0

-0.742832 0 0 0 0 0 0

475 Spring

1 0 0 0 1 0

4020.928685 0 0 0 0 0 0

0 0 0

-0.75443875 0 0 0 0 0 0

476 Spring

1 0 0 0 1 0

4034.134376 0 0 0 0 0 0

0 0 0

-0.7660455 0 0 0 0 0 0

477 Spring

1 0 0 0 1 0

4047.340066 0 0 0 0 0 0

0 0 0

-0.77765225 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-109

478 Spring

1 0 0 0 1 0

4060.545757 0 0 0 0 0 0

0 0 0

-0.789259 0 0 0 0 0 0

479 Spring

1 0 0 0 1 0

4073.751447 0 0 0 0 0 0

0 0 0

-0.80086575 0 0 0 0 0 0

480 Spring

1 0 0 0 1 0

4086.957138 0 0 0 0 0 0

0 0 0

-0.8124725 0 0 0 0 0 0

481 Spring

1 0 0 0 1 0

4100.162828 0 0 0 0 0 0

0 0 0

-0.82407925 0 0 0 0 0 0

482 Spring

1 0 0 0 1 0

4113.368519 0 0 0 0 0 0

0 0 0

-0.835686 0 0 0 0 0 0

483 Spring

1 0 0 0 1 0

4126.574209 0 0 0 0 0 0

0 0 0

-0.84729275 0 0 0 0 0 0

484 Spring

1 0 0 0 1 0

4139.7799 0 0 0 0 0 0

0 0 0

-0.8588995 0 0 0 0 0 0

485 Spring

1 0 0 0 1 0

4152.98559 0 0 0 0 0 0

0 0 0

-0.87050625 0 0 0 0 0 0

486 Spring

Pile 3 dynamic data file input into Ruaumoko

A-110

1 0 0 0 1 0

4166.191281 0 0 0 0 0 0

0 0 0

-0.882113 0 0 0 0 0 0

487 Spring

1 0 0 0 1 0

4179.396971 0 0 0 0 0 0

0 0 0

-0.89371975 0 0 0 0 0 0

488 Spring

1 0 0 0 1 0

4192.602662 0 0 0 0 0 0

0 0 0

-0.9053265 0 0 0 0 0 0

489 Spring

1 0 0 0 1 0

4205.808352 0 0 0 0 0 0

0 0 0

-0.91693325 0 0 0 0 0 0

490 Spring

1 0 0 0 1 0

4221.919295 0 0 0 0 0 0

0 0 0

-0.92854 0 0 0 0 0 0

491 Spring

1 0 0 0 1 0

4275.933955 0 0 0 0 0 0

0 0 0

-0.94014675 0 0 0 0 0 0

492 Spring

1 0 0 0 1 0

4345.18352 0 0 0 0 0 0

0 0 0

-0.9517535 0 0 0 0 0 0

493 Spring

1 0 0 0 1 0

4414.433085 0 0 0 0 0 0

0 0 0

-0.96336025 0 0 0 0 0 0

494 Spring

1 0 0 0 1 0

4483.68265 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-111

0 0 0

-0.974967 0 0 0 0 0 0

495 Spring

1 0 0 0 1 0

4552.932215 0 0 0 0 0 0

0 0 0

-0.98657375 0 0 0 0 0 0

496 Spring

1 0 0 0 1 0

4622.18178 0 0 0 0 0 0

0 0 0

-0.9981805 0 0 0 0 0 0

497 Spring

1 0 0 0 1 0

4691.431345 0 0 0 0 0 0

0 0 0

-1.00978725 0 0 0 0 0 0

498 Spring

1 0 0 0 1 0

4760.68091 0 0 0 0 0 0

0 0 0

-1.021394 0 0 0 0 0 0

499 Spring

1 0 0 0 1 0

4829.930475 0 0 0 0 0 0

0 0 0

-1.03300075 0 0 0 0 0 0

500 Spring

1 0 0 0 1 0

4899.18004 0 0 0 0 0 0

0 0 0

-1.0446075 0 0 0 0 0 0

501 Spring

1 0 0 0 1 0

4968.429604 0 0 0 0 0 0

0 0 0

-1.05621425 0 0 0 0 0 0

502 Spring

1 0 0 0 1 0

5037.679169 0 0 0 0 0 0

0 0 0

-1.067821 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-112

503 Spring

1 0 0 0 1 0

5106.928734 0 0 0 0 0 0

0 0 0

-1.07942775 0 0 0 0 0 0

504 Spring

1 0 0 0 1 0

5176.178299 0 0 0 0 0 0

0 0 0

-1.0910345 0 0 0 0 0 0

505 Spring

1 0 0 0 1 0

5245.427864 0 0 0 0 0 0

0 0 0

-1.10264125 0 0 0 0 0 0

506 Spring

1 0 0 0 1 0

5314.677429 0 0 0 0 0 0

0 0 0

-1.114248 0 0 0 0 0 0

507 Spring

1 0 0 0 1 0

5383.926994 0 0 0 0 0 0

0 0 0

-1.12585475 0 0 0 0 0 0

508 Spring

1 0 0 0 1 0

5453.176559 0 0 0 0 0 0

0 0 0

-1.1374615 0 0 0 0 0 0

509 Spring

1 0 0 0 1 0

5522.426124 0 0 0 0 0 0

0 0 0

-1.14906825 0 0 0 0 0 0

510 Spring

1 0 0 0 1 0

5591.675688 0 0 0 0 0 0

0 0 0

-1.160675 0 0 0 0 0 0

511 Spring

Pile 3 dynamic data file input into Ruaumoko

A-113

1 0 0 0 1 0

5660.925253 0 0 0 0 0 0

0 0 0

-1.17228175 0 0 0 0 0 0

512 Spring

1 0 0 0 1 0

5730.174818 0 0 0 0 0 0

0 0 0

-1.1838885 0 0 0 0 0 0

513 Spring

1 0 0 0 1 0

5799.424383 0 0 0 0 0 0

0 0 0

-1.19549525 0 0 0 0 0 0

514 Spring

1 0 0 0 1 0

5868.673948 0 0 0 0 0 0

0 0 0

-1.207102 0 0 0 0 0 0

515 Spring

1 0 0 0 1 0

5937.923513 0 0 0 0 0 0

0 0 0

-1.21870875 0 0 0 0 0 0

516 Spring

1 0 0 0 1 0

6007.173078 0 0 0 0 0 0

0 0 0

-1.2303155 0 0 0 0 0 0

517 Spring

1 0 0 0 1 0

6076.422643 0 0 0 0 0 0

0 0 0

-1.24192225 0 0 0 0 0 0

518 Spring

1 0 0 0 1 0

6145.672208 0 0 0 0 0 0

0 0 0

-1.253529 0 0 0 0 0 0

519 Spring

1 0 0 0 1 0

6214.921773 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-114

0 0 0

-1.26513575 0 0 0 0 0 0

520 Spring

1 0 0 0 1 0

6284.171337 0 0 0 0 0 0

0 0 0

-1.2767425 0 0 0 0 0 0

521 Spring

1 0 0 0 1 0

6353.420902 0 0 0 0 0 0

0 0 0

-1.28834925 0 0 0 0 0 0

522 Spring

1 0 0 0 1 0

6422.670467 0 0 0 0 0 0

0 0 0

-1.299956 0 0 0 0 0 0

523 Spring

1 0 0 0 1 0

6491.920032 0 0 0 0 0 0

0 0 0

-1.31156275 0 0 0 0 0 0

524 Spring

1 0 0 0 1 0

6561.169597 0 0 0 0 0 0

0 0 0

-1.3231695 0 0 0 0 0 0

525 Spring

1 0 0 0 1 0

6630.419162 0 0 0 0 0 0

0 0 0

-1.33477625 0 0 0 0 0 0

526 Spring

1 0 0 0 1 0

6699.668727 0 0 0 0 0 0

0 0 0

-1.346383 0 0 0 0 0 0

527 Spring

1 0 0 0 1 0

6768.918292 0 0 0 0 0 0

0 0 0

-1.35798975 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-115

528 Spring

1 0 0 0 1 0

6838.167857 0 0 0 0 0 0

0 0 0

-1.3695965 0 0 0 0 0 0

529 Spring

1 0 0 0 1 0

6907.417421 0 0 0 0 0 0

0 0 0

-1.38120325 0 0 0 0 0 0

530 Spring

1 0 0 0 1 0

6976.666986 0 0 0 0 0 0

0 0 0

-1.39281 0 0 0 0 0 0

531 Spring

1 0 0 0 1 0

7045.916551 0 0 0 0 0 0

0 0 0

-1.40441675 0 0 0 0 0 0

532 Spring

1 0 0 0 1 0

7115.166116 0 0 0 0 0 0

0 0 0

-1.4160235 0 0 0 0 0 0

533 Spring

1 0 0 0 1 0

7184.415681 0 0 0 0 0 0

0 0 0

-1.42763025 0 0 0 0 0 0

534 Spring

1 0 0 0 1 0

7253.665246 0 0 0 0 0 0

0 0 0

-1.439237 0 0 0 0 0 0

535 Spring

1 0 0 0 1 0

7322.914811 0 0 0 0 0 0

0 0 0

-1.45084375 0 0 0 0 0 0

536 Spring

Pile 3 dynamic data file input into Ruaumoko

A-116

1 0 0 0 1 0

7392.164376 0 0 0 0 0 0

0 0 0

-1.4624505 0 0 0 0 0 0

537 Spring

1 0 0 0 1 0

7461.413941 0 0 0 0 0 0

0 0 0

-1.47405725 0 0 0 0 0 0

538 Spring

1 0 0 0 1 0

7530.663506 0 0 0 0 0 0

0 0 0

-1.485664 0 0 0 0 0 0

539 Spring

1 0 0 0 1 0

7599.91307 0 0 0 0 0 0

0 0 0

-1.49727075 0 0 0 0 0 0

540 Spring

1 0 0 0 1 0

7669.162635 0 0 0 0 0 0

0 0 0

-1.5088775 0 0 0 0 0 0

541 Spring

1 0 0 0 1 0

7738.4122 0 0 0 0 0 0

0 0 0

-1.52048425 0 0 0 0 0 0

542 Spring

1 0 0 0 1 0

7807.661765 0 0 0 0 0 0

0 0 0

-1.532091 0 0 0 0 0 0

543 Spring

1 0 0 0 1 0

7876.91133 0 0 0 0 0 0

0 0 0

-1.54369775 0 0 0 0 0 0

544 Spring

1 0 0 0 1 0

7946.160895 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-117

0 0 0

-1.5553045 0 0 0 0 0 0

545 Spring

1 0 0 0 1 0

4007.70523 0 0 0 0 0 0

0 0 0

-0.782004781 0 0 0 0 0 0

546 Damper !Outer damper properties both sides

0 4.728328552 0 0 0 0 0 0 0 0 0

547 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

548 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

549 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

550 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

551 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

552 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

553 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

554 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

555 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

556 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

557 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

558 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

559 Damper

0 9.456657103 0 0 0 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-118

560 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

561 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

562 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

563 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

564 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

565 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

566 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

567 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

568 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

569 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

570 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

571 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

572 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

573 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

574 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

575 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

576 Damper

Pile 3 dynamic data file input into Ruaumoko

A-119

0 17.1421772 0 0 0 0 0 0 0 0 0

577 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

578 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

579 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

580 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

581 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

582 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

583 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

584 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

585 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

586 Damper

0 17.1421772 0 0 0 0 0 0 0 0 0

587 Damper

0 17.1765665 0 0 0 0 0 0 0 0 0

588 Damper

0 17.21031431 0 0 0 0 0 0 0 0 0

589 Damper

0 17.24409473 0 0 0 0 0 0 0 0 0

590 Damper

0 17.27790784 0 0 0 0 0 0 0 0 0

591 Damper

0 17.31175374 0 0 0 0 0 0 0 0 0

592 Damper

0 17.34563255 0 0 0 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-120

593 Damper

0 17.37954434 0 0 0 0 0 0 0 0 0

594 Damper

0 17.41348924 0 0 0 0 0 0 0 0 0

595 Damper

0 17.44746733 0 0 0 0 0 0 0 0 0

596 Damper

0 17.48147872 0 0 0 0 0 0 0 0 0

597 Damper

0 17.51552351 0 0 0 0 0 0 0 0 0

598 Damper

0 17.5496018 0 0 0 0 0 0 0 0 0

599 Damper

0 17.5837137 0 0 0 0 0 0 0 0 0

600 Damper

0 17.61785932 0 0 0 0 0 0 0 0 0

601 Damper

0 17.65203874 0 0 0 0 0 0 0 0 0

602 Damper

0 17.68625208 0 0 0 0 0 0 0 0 0

603 Damper

0 17.72049945 0 0 0 0 0 0 0 0 0

604 Damper

0 17.75478095 0 0 0 0 0 0 0 0 0

605 Damper

0 17.78909668 0 0 0 0 0 0 0 0 0

606 Damper

0 17.82344675 0 0 0 0 0 0 0 0 0

607 Damper

0 17.85783127 0 0 0 0 0 0 0 0 0

608 Damper

0 17.89225035 0 0 0 0 0 0 0 0 0

609 Damper

0 17.92670409 0 0 0 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-121

610 Damper

0 17.96119261 0 0 0 0 0 0 0 0 0

611 Damper

0 17.995716 0 0 0 0 0 0 0 0 0

612 Damper

0 18.03027439 0 0 0 0 0 0 0 0 0

613 Damper

0 18.06486788 0 0 0 0 0 0 0 0 0

614 Damper

0 18.09949658 0 0 0 0 0 0 0 0 0

615 Damper

0 18.1341606 0 0 0 0 0 0 0 0 0

616 Damper

0 18.16886006 0 0 0 0 0 0 0 0 0

617 Damper

0 18.20359507 0 0 0 0 0 0 0 0 0

618 Damper

0 18.23836574 0 0 0 0 0 0 0 0 0

619 Damper

0 18.27317218 0 0 0 0 0 0 0 0 0

620 Damper

0 18.30801451 0 0 0 0 0 0 0 0 0

621 Damper

0 18.34289284 0 0 0 0 0 0 0 0 0

622 Damper

0 18.37780729 0 0 0 0 0 0 0 0 0

623 Damper

0 18.41275797 0 0 0 0 0 0 0 0 0

624 Damper

0 18.447745 0 0 0 0 0 0 0 0 0

625 Damper

0 18.48276849 0 0 0 0 0 0 0 0 0

626 Damper

Pile 3 dynamic data file input into Ruaumoko

A-122

0 18.52554671 0 0 0 0 0 0 0 0 0

627 Damper

0 18.62653602 0 0 0 0 0 0 0 0 0

628 Damper

0 18.75629933 0 0 0 0 0 0 0 0 0

629 Damper

0 18.8863908 0 0 0 0 0 0 0 0 0

630 Damper

0 19.01681313 0 0 0 0 0 0 0 0 0

631 Damper

0 19.14756907 0 0 0 0 0 0 0 0 0

632 Damper

0 19.2786614 0 0 0 0 0 0 0 0 0

633 Damper

0 19.41009294 0 0 0 0 0 0 0 0 0

634 Damper

0 19.54186656 0 0 0 0 0 0 0 0 0

635 Damper

0 19.67398513 0 0 0 0 0 0 0 0 0

636 Damper

0 19.80645159 0 0 0 0 0 0 0 0 0

637 Damper

0 19.93926892 0 0 0 0 0 0 0 0 0

638 Damper

0 20.07244011 0 0 0 0 0 0 0 0 0

639 Damper

0 20.20596823 0 0 0 0 0 0 0 0 0

640 Damper

0 20.33985636 0 0 0 0 0 0 0 0 0

641 Damper

0 20.47410762 0 0 0 0 0 0 0 0 0

642 Damper

0 20.60872521 0 0 0 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-123

643 Damper

0 20.74371233 0 0 0 0 0 0 0 0 0

644 Damper

0 20.87907225 0 0 0 0 0 0 0 0 0

645 Damper

0 21.01480827 0 0 0 0 0 0 0 0 0

646 Damper

0 21.15092374 0 0 0 0 0 0 0 0 0

647 Damper

0 21.28742206 0 0 0 0 0 0 0 0 0

648 Damper

0 21.42430668 0 0 0 0 0 0 0 0 0

649 Damper

0 21.56158109 0 0 0 0 0 0 0 0 0

650 Damper

0 21.69924883 0 0 0 0 0 0 0 0 0

651 Damper

0 21.8373135 0 0 0 0 0 0 0 0 0

652 Damper

0 21.97577873 0 0 0 0 0 0 0 0 0

653 Damper

0 22.11464823 0 0 0 0 0 0 0 0 0

654 Damper

0 22.25392574 0 0 0 0 0 0 0 0 0

655 Damper

0 22.39361507 0 0 0 0 0 0 0 0 0

656 Damper

0 22.53372006 0 0 0 0 0 0 0 0 0

657 Damper

0 22.67424464 0 0 0 0 0 0 0 0 0

658 Damper

0 22.81519277 0 0 0 0 0 0 0 0 0

659 Damper

0 22.95656849 0 0 0 0 0 0 0 0 0

Pile 3 dynamic data file input into Ruaumoko

A-124

660 Damper

0 23.09837587 0 0 0 0 0 0 0 0 0

661 Damper

0 23.24061907 0 0 0 0 0 0 0 0 0

662 Damper

0 23.3833023 0 0 0 0 0 0 0 0 0

663 Damper

0 23.52642982 0 0 0 0 0 0 0 0 0

664 Damper

0 23.67000598 0 0 0 0 0 0 0 0 0

665 Damper

0 23.81403518 0 0 0 0 0 0 0 0 0

666 Damper

0 23.95852189 0 0 0 0 0 0 0 0 0

667 Damper

0 24.10347065 0 0 0 0 0 0 0 0 0

668 Damper

0 24.24888605 0 0 0 0 0 0 0 0 0

669 Damper

0 24.39477279 0 0 0 0 0 0 0 0 0

670 Damper

0 24.54113561 0 0 0 0 0 0 0 0 0

671 Damper

0 24.68797933 0 0 0 0 0 0 0 0 0

672 Damper

0 24.83530886 0 0 0 0 0 0 0 0 0

673 Damper

0 24.98312917 0 0 0 0 0 0 0 0 0

674 Damper

0 25.13144532 0 0 0 0 0 0 0 0 0

675 Damper

0 25.28026244 0 0 0 0 0 0 0 0 0

676 Damper

Pile 3 dynamic data file input into Ruaumoko

A-125

0 25.42958576 0 0 0 0 0 0 0 0 0

677 Damper

0 25.57942057 0 0 0 0 0 0 0 0 0

678 Damper

0 25.72977227 0 0 0 0 0 0 0 0 0

679 Damper

0 25.88064632 0 0 0 0 0 0 0 0 0

680 Damper

0 26.03204831 0 0 0 0 0 0 0 0 0

681 Damper

0 13.09199193 0 0 0 0 0 0 0 0 0

*Nodal weight data

WEIGHTS1

1 0 0 4.477284 0 0 0

2 0 0 1.65854026 0 0 0

3 0 0 0.030338121 0 0 0

4 0 0 0.030338121 0 0 0

11 0 0 0.275588121 0 0 0

12 0 0 0.030338121 0 0 0

13 0 0 0.030338121 0 0 0

152 0 0 0.01516906 0 0 0

153 0 0 0 0 0 0

696 0 0 0 0 0 0

*Nodal static load data

LOADS

1 0 0 0 0 0 0

696 0 0 0 0 0 0

*Nodal dynamic load patterns

SHAPE

11 0 0 120 0 0 0

696 0 0 0 0 0 0

*Dynamic load response history

EQUAKE

3 1 0.01 1 0 0 0 1

*Dynamic loading pattern to represent 7.5 kN snap-back

START

1 0 0

2 0.99 0.0993333 !Increase load at rate of 0.1*120=12kN per second

3 2.99 0.0993333 !Hold maximum load for 2 seconds

4 3.00 0 !Release over a time of 0.01s

Pile 3 dynamic data file input into Ruaumoko

A-126

5 6.00 0 !Allow for 3 seconds of free vibration

Example data analysis file on MATLAB

B-1

APPENDIX B EXAMPLE DATA ANALYSIS FILE

ON MATLAB

%Pile 4 data analysis in the time and frequency domain

clear

clc

cd('[data file directory]') %import data from text file

A=importdata('50Mass_Snapback-120Kn_SR2000_1.txt', '\t', 11);

t=A.data(:,1); %time vector

d=A.data(:,4); %displacement vector

n=length(t);

x=15.62; %range for trim

x2=t(n);

tx=abs(t-x);

tx2=abs(t-x2);

z=find(tx==min(tx),1);

z2=find(tx2==min(tx2),1);

t2=t(z:z2);

dtrim=d(z:z2); %trim

dzero=detrend(dtrim); %zero response about time axis

[b,a]=butter(4,0.04,'low'); %filter noise

dfil=filter(b,a,dzero);

[b,a]=butter(4,0.0005,'high'); %filter to remove low frequency effect

% [b,a]=butter(4,0.006214,'high'); %filter to extract elastic response

dfil2=filter(b,a,dfil);

d2=dzero; %specify level of filtering required

%d2=dfil-dfil2 for inelastic

figure(1) %subplot for time domain response

subplot(2,1,1)

hold on

plot(t2,d2,P,'LineWidth',2);

xlabel('Time (s)')

ylabel('Displacement (mm)')

set(gcf, 'PaperPositionMode', 'manual');

set(gcf, 'PaperUnits', 'inches');

set(gcf, 'PaperPosition', [0.25 2.5 5 3.75]);

box on

figure(2) %figure for damping plot

X=[t(z);t(z2)]; %horizontal line

Y=[0;0];

plot(t2,d2,'b',X,Y);

Example data analysis file on MATLAB

B-2

xlabel('Time (s)')

ylabel('Displacement (mm)')

hold on

figure(3) %open time domain plot if required

plot(t,d);

xlabel('Time (sec)')

ylabel('Displacement (mm)')

%Damping calculation - logarithmic decrement method (Thompson, 1988)

npeaks=15; %number of peaks+1

m=length(t2);

Ft=gradient(d2); %consider gradient of trimmed response

peak=zeros(2,1);

time=zeros(2,1);

c4=0; %peak count

for i=1:m

if abs(Ft(i))<=0.03 %make sure slope is close to zero

if c4==0; %pick up first peak

c4=c4+1;

peak(c4)=d2(i);

time(c4)=t2(i);

c6=abs(Ft(i));

else

if sign(d2(i))~=sign(peak(c4)) && abs(d2(i))>0.02

c4=c4+1; %check if different peak

peak(c4)=d2(i);

time(c4)=t2(i);

c6=abs(Ft(i));

elseif abs(d2(i))>abs(peak(c4))

peak(c4)=d2(i); %ensure maximum displacement taken

time(c4)=t2(i);

c6=abs(Ft(i));

else

end

end

else

end

if c4==npeaks %limit on damping values calculated

peak=peak(1:(npeaks-1),1);

time=time(1:(npeaks-1),1);

break

else

end

end

l=length(peak)-2;

x1=zeros(l,1);

x2=zeros(l,1);

xi=zeros(l,1);

Example data analysis file on MATLAB

B-3

dtfull=zeros(l,1);

freqfull=zeros(l,1);

for i=1:l

x1(i)=peak(i);

x2(i)=peak(i+2);

dtfull(i)=time(i+2)-time(i); %time between peaks

freqfull(i)=1/(time(i+2)-time(i));

if sign(x1(i))~=sign(x2(i))

xi(i)=0;

else %damping ratio calculation

xi(i)=log(abs(x1(i)/x2(i)))/(2*pi);

end

end

dt=zeros((l+1),1);

for i=1:(l+1)

dt(i)=time(i+1)-time(i); %time between half cycles

end

figure(4) %response differential if required

plot(t2,Ft)

xlabel('Time (sec)')

ylabel('Velocity (mm/s)')

figure(5) %plot damping

plot(abs(x1),xi,'o')

xlabel('Displacement x1 (mm)')

ylabel('Damping fraction')

figure(2) %check correct peaks are taken

plot(time,peak,'bo')

hold off

display(dt) %outputs

display(peak)

display(time)

display(xi)

display(x1)

display(x2)

t1=t(z);

tn=t(z2);

display(t1)

display(tn)

display(dtfull)

display(freqfull)

%FFT of response

NFFT=m;

Fs=2000;

Y=fft(d2,NFFT)/m;

Example data analysis file on MATLAB

B-4

f=Fs/2*linspace(0,1,NFFT/2+1);

y=2*abs(Y(1:NFFT/2+1));

y2=y(10:length(y));

f2=f(10:length(f));

k=length(f2); %find natural frequency

for i=1:k

if y2(i)==max(y2)

break

else

end

end

freq=f2(i);

display(freq)

period=1/freq;

display(period); %outputs

figure(1) %subplot for frequency domain response

subplot(2,1,2)

hold on

plot(f,y,'b','LineWidth',2)

xlabel('Frequency (Hz)')

ylabel('FFT - displacement amplitude')

box on

%Exponential envelope fitting (Chopra, 2006)

freq=freq; %inelastic frequency (if maximum peak)

freq2=14.92; %elastic frequency (usually manual)

freq3=14.92; %elastic frequency (usually manual)

zeta=0.13; %guess damping for inelastic envelope

e=peak(1)*factor*exp(-zeta*freq*2*pi*t);

c=find(t2==time(1),1);

zeta2=0.09; %guess damping for elastic envelope 1

e2=peak(2)*factor2*exp(-zeta2*freq2*2*pi*t);

c2=find(t2==time(2),1);

zeta3=0.09; %guess damping for elastic envelope 2

e3=peak(3)*factor*exp(-zeta3*freq3*2*pi*t);

c3=find(t2==time(3),1);

figure(2) %plot envelopes on response

hold on

plot(t2(c:m),e(1:m-c+1),'r',t2(c:m),-e(1:m-c+1),'r')

plot(t2(c2:m),e2(1:m-c2+1),'g',t2(c2:m),-e2(1:m-c2+1),'g')

plot(t2(c3:m),e3(1:m-c3+1),'c',t2(c3:m),-e3(1:m-c3+1),'c')

hold off

Example data analysis file on MATLAB

B-5

%SDOF displacement solution (Chopra, 2006)

freqn=freq/sqrt(1-zeta^2); %using inelastic frequency

om=freq*(2*pi);

omn=freqn*(2*pi);

ze=zeta;

u=exp(-ze*omn*t).*(peak(1)*cos(om*t)+(ze*omn*peak(1))/om.*sin(om*t));

c4=find(t2==time(1),1);

figure(2) %add solution to same plot

hold on

plot(t2(c4:m),u(1:m-c4+1),'k')

hold off

display(zeta) %outputs

display(zeta2)

display(zeta3)

display(xi(1))

display(x1(1))

display(t1)

display(freqfull(1))

inelastic_damping=zeta;

elastic_damping=(zeta2+zeta3)/2;

display(inelastic_damping)

display(elastic_damping)

display(npeaks)

%store each test detail below