PREDICTION OF WORKING-LOAD DISPLACEMENTSUNDER PLATE-LOADING TESTS FROM SEISMIC STIFFNESS MEASUREMENTS
RESEARCH REPORT ICAR - 501-3
Sponsored by the Aggregates Foundation
for Technology, Research and Education
Technical Report Documentation Page
1
1. Report No. ICAR 501-3
2. Government Accession No.
3. Recipient's Catalog No.
5. Report Date October 1998
4. Title and Subtitle PREDICTION OF WORKING LOAD DISPLACEMENTS UNDER
PLATE LOADING TESTS FROM SEISMIC STIFFNESS MEASUREMENTS
6. Performing Organization Code
7. Author(s) Michael L. Myers, Kenneth H. Stokoe, II, and John J. Allen
8. Performing Organization Report No. Research Report ICAR 501-3
10. Work Unit No. (TRAIS)
9. Performing Organization Name and Address International Center for Aggregates Research The University of Texas at Austin ECJ 5.200 Austin, Texas 78712-1076
11. Contract or Grant No. Project No. ICAR-501
13. Type of Report and Period Covered Research Report March 1997-October 1998
12. Sponsoring Agency Name and Address Aggregates Foundation for Technology, Research and Education 1415 Elliott Place NW Washington, D.C. 20007
14. Sponsoring Agency Code
15. Supplementary Notes
16. Abstract
A study was conducted to evaluate the feasibility of compacting unbound aggregate base courses in thicker lifts than currently permitted by state departments of transportation (DOTs). At present, the majority of states allow a maximum lift thickness of 8 inches or less. This project constructed and tested full-scale test section using a variety of material types. Two test pads were constructed in an aggregate quarry in Texas utilizing crushed limestone. Three crushed granite test sections were built as part of a road widening project in Georgia, and two test pads were constructed of uncrushed and partially crushed gravel with loess fines at a gravel production facility near Memphis, Tennessee. Single-lift thicknesses varied from 6 inches to 21 inches. Moisture contents and densities were evaluated using the Nuclear Density Gauge (NDG). Nondestructive seismic testing, using the Spectral-Analysis-of Surface-Waves (SASW) technique, was used to evaluate stiffness profiles within the compacted lifts. Plate load tests were conducted on the surface of the crushed limestone test pads by means of the Rolling Dynamic Deflectometer specially modified for this fixed site application. Low frequency cyclic loads were applied to determine axial stiffness under transient working loads of varying magnitude. The base courses were tested at to moisture contents. The results were evaluated and compared with small strain seismic tests result. Strain amplitudes in the plate load tests led to a 5% to 25% reduction in measured stiffness as compared to the seismic results.
17. Key Words Seismic-Analysis-of-Surface-Waves, Nuclear Density Gauge, Compaction, Granular Base Course, Lift Thickness, Thick Lifts, Plate Load Testing
18. Distribution Statement No restrictions.
19. Security Classif.(of this report) Unclassified
20. Security Classif.(of this page) Unclassified
21. No. of Pages
22. Price
Form DOT F 1700.7 (8-72) Reproduction of completed page authorized
2
PREDICTION OF WORKING LOAD DISPLACEMENTS UNDER PLATE LOADING TESTS FROM SEISMIC STIFFNESS MEASUREMENTS
by
Michael L. Myers Captain, United States Air Force
820th Red Horse Civil Engineering Squardron Nellis Air force Base, Nevada
Kenneth H. Stokoe, II
Cockrell Family Regents Chair No. 9 Civil Engineering Department
The University of Texas at Austin
and
John J. Allen Director, Roadway Research Initiative
Center for Transportation Research The University of Texas at Austin
and Texas Transportation Institute
Texas A&M University
Research Report ICAR 501-3 Research Project Number ICAR 501
Sponsored by the Aggregates Foundation for Technology, Research, and Education
October 1998
International Center for Aggregates Research The University of Texas at Austin
Austin, Texas
and Texas A&M University College Station, Texas
iii
ABSTRACT
A study was conducted to evaluate the feasibility of compacting unbound
aggregate base courses in thicker lifts than currently permitted by state departments of
transportation (DOTs). At present, the majority of states allow a maximum lift thickness
of 8 inches or less. This project constructed and tested full-scale test section using a
variety of material types. Two test pads were constructed in an aggregate quarry in Texas
utilizing crushed limestone. Three crushed granite test sections were built as part of a
road widening project in Georgia, and two test pads were constructed of uncrushed and
partially crushed gravel with loess fines at a gravel production facility near Memphis,
Tennessee. Single-lift thicknesses varied from 6 inches to 21 inches. Moisture contents
and densities were evaluated using the Nuclear Density Gauge (NDG). Nondestructive
seismic testing, using the Spectral-Analysis-of Surface-Waves (SASW) technique, was
used to evaluate stiffness profiles within the compacted lifts. Plate load tests were
conducted on the surface of the crushed limestone test pads by means of the Rolling
Dynamic Deflectometer specially modified for this fixed site application. Low frequency
cyclic loads were applied to determine axial stiffness under transient working loads of
varying magnitude. The base courses were tested at to moisture contents. The results were
evaluated and compared with small strain seismic tests result. Strain amplitudes in the
plate load tests led to a 5% to 25% reduction in measured stiffness as compared to the
seismic results.
TABLE OF CONTENTS
ACKNOWLEDGMENTS ........................................................................................................... vi LIST OF TABLES ..................................................................................................................... xii LIST OF FIGURES .................................................................................................................... xv CHAPTER 1. INTRODUCTION 1.1 Increasing the Single-Lift Thickness of Compacted Aggregate Base Courses ............ 1 1.2 Characterizing Thick Aggregate Lifts .......................................................................... 2 1.3 Scope of Plate-Load and Seismic Testing .................................................................... 3 1.4 Objectives of This Study............................................................................................... 4 1.5 Correlations Between Plate-Load Settlement and Other Field Tests............................ 5 1.6 Organization of This Report ......................................................................................... 5 CHAPTER 2. MATERIAL and TEST SITE 2.1 Construction of Test Pad............................................................................................... 7 2.2 Location of Plate-Load Tests ...................................................................................... 11 2.3 Flexible Base Material ................................................................................................ 12 2.4 In-Situ Density Testing ............................................................................................... 14 CHAPTER 3. PLATE-LOAD TESTING with the ROLLING DYNAMIC
DEFLECTOMETER 3.1 Introduction................................................................................................................. 17 3.2 Plate-Load Testing Equipment ................................................................................... 18 3.2.1 Loading Mechanism........................................................................................... 18 3.2.2 Load-Plate Details.............................................................................................. 21 3.2.3 Load Cell............................................................................................................ 22 3.2.4 Displacement Transducers ................................................................................. 23 3.2.5 Support Frame for DC-LVDTS ......................................................................... 24 3.2.6 Data Acquisition System.................................................................................... 28 3.3 Data Reduction............................................................................................................ 30 3.4 Overview of Plate-Load Testing................................................................................. 30 3.4.1 Modulus of Soil Reaction, Ku’ .......................................................................... 31 3.4.2 Material Equivalent Spring Constant (Stiffness) ............................................... 32 3.4.3 Summary of Plate-Load Tests Performed.......................................................... 32
vi
CHAPTER 4. PRELIMINARY PLATE-LOAD TESTS at LOCATION A on the TEST PAD 4.1 Introduction................................................................................................................. 34 4.2 Test A1 - Incremental Plate-Load Test from 0 to 5 Kips (22.2 kN).......................... 34 4.3 Test A2 - Loading from 0 to 11 Kips (48.9 kN) in 36 Seconds Followed by
Complete Unloading ................................................................................................... 35 4.4 Test A3 - 32 Cycles of 0 to 9 Kips (40.0 kN) in 20 Minutes...................................... 41 4.4.1 Determining Stiffness During Loading.............................................................. 44 4.4.2 Determining Stiffness During Unloading .......................................................... 49 4.4.3 Measurement of Permanent Displacement ........................................................ 52 4.5 Test A4 - Loading from 0 to 40 Kips (178 kN) in 6 Minutes Followed by 56
Complete Unloading ................................................................................................... 56 4.6 Summary of Observations from Preliminary Plate-Load Tests at Location A........... 63 CHAPTER 5. PLATE-LOAD TESTS on DRIER MATERIAL at LOCATION B on the
TEST PAD 5.1 Introduction................................................................................................................. 65 5.2 Test B1 - Incremental Plate-Load Test from 0 to 8.3 Kips (36.9 kN) on
Drier Material (Moisture Content ~ 4.7 %) ................................................................ 65 5.2.1 Adjusted Load-Settlement Curve from Test B1 ................................................ 66 5.2.2 Plotting the Unload-Reload Loops on the Adjusted Load-Settlement
Curve from Test B1 ........................................................................................... 71 5.2.3 Stiffness of the Test Pad Material as Determined from the Overall
Plate-Load Test .................................................................................................. 75 5.2.4 Presentation of Cyclic Stiffness and Overall Stiffness Measurements .............. 77 5.2.5 Calculation of Modulus of Soil Reaction, Ku’, for Drier Material
(Moisture Content ~ 4.7 %) ............................................................................... 79 5.3 Summary of Observations from Incremental Plate-Load Test on
Drier Material (Moisture Content ~ 4.7 %) at Location B.......................................... 79 CHAPTER 6. PLATE-LOAD TESTS on WETTER MATERIAL at LOCATION C on the
TEST PAD 6.1 Introduction................................................................................................................. 81 6.2 Test C1 - Incremental Plate-Load Test from 0 to 8.6 Kips (38.3 kN)
on Wetter Material (Moisture Content ~ 6.1%).......................................................... 82 6.2.1 Adjusted Load-Settlement Curve from Test C1 ................................................ 85 6.2.2 Plotting the Unload-Reload Loops on the Adjusted Load-Settlement
Curve from Test C1 ........................................................................................... 88 6.2.3 Stiffness of the Test Pad Material as Determined from the Overall
Plate-Load Test .................................................................................................. 91 6.2.4 Presentation of Cyclic Stiffness and Overall Stiffness Measurements .............. 93 6.2.5 Calculation of Modulus of Soil Reaction, Ku’, for Wetter Material
(Moisture Content ~ 6.1 %) ............................................................................... 94
vii
6.3. Test C2 - 5 Cycles of 0 to 8 Kips (35.6 kN) in 7 Minutes on Wetter Material (Moisture Content ~ 6.1%) ......................................................................................... 96
6.4 Summary of Observations from Incremental Plate-Load Tests on Wetter Material (Moisture Content ~ 6.1 %) at Location C................................................. 102
CHAPTER7. SEISMIC TESTING and STIFFNESS EVALUATIONS 7.1 Overview................................................................................................................... 104 7.2 SASW Testing .......................................................................................................... 104 7.3 Non-Linear Moduli ................................................................................................... 105 7.4 Determination of Small-Strain Shear Modulus......................................................... 108 7.5 Determination of Small-Strain Equivalent Spring Constant..................................... 108 7.6 Shear Wave Velocity Profiles................................................................................... 110 7.7 Measured Small-Strain Stiffness............................................................................... 113 7.8 Adjustment to the Small-Strain Stiffness for Variations in the
State of Stress............................................................................................................ 114 CHAPTER 8. COMPARISON of STIFFNESS VALUES from PLATE-LOAD and
SEISMIC TEST 8.1 Introduction............................................................................................................... 115 8.1.1 Estimation of Strain Amplitude ....................................................................... 115 8.1.2 Adjustments to Small-Strain Shear Moduli for increase in Strain
Amplitude and increase in State of Stress........................................................ 117 8.2 Small-Strain Stiffness Comparisons ......................................................................... 120 8.2.1 Adjustment to Small-Strain Stiffnesses for increased Strain Amplitude......... 122 8.2.2 Adjustment to Small-Strain Stiffnesses for increased State of Stress
Due to Wetting and Due to increasing the Load on the Plate.......................... 125 8.2.3 Conclusions from Small-Strain Moduli Comparisons..................................... 128 8.3 Large-Strain Stiffness Comparisons ......................................................................... 129 8.3.1 Short Duration Load to Failure ........................................................................ 130 8.3.2 Stiffness Under Large-Amplitude, Short-Duration Cyclic Loading................ 133 8.3.3 Stiffnesses from Incremental Plate-Load Tests ............................................... 141 8.3.4 Sensitivity of the Material to Duration of Loading.......................................... 143 8.4 Summary of Stiffness Comparison ........................................................................... 147 CHAPTER9. SUMMARY, CONCLUSIONS, and RECOMMENDATIONS 9.1 Summary of Testing Program................................................................................... 148 9.2 Summary of Observations......................................................................................... 150 9.3 Conclusions from Plate-Load and Seismic Tests...................................................... 152 9.3 Recommendations for Future Work.......................................................................... 153
viii
APPENDIX A. NUCLEAR DENSITY GAUGE DATA ....................................................... 155 APPENDIX B. INDIVIDUAL LOADING CYCLE PLOTS FOR TEST A3...................... 159 APPENDIX C. INDIVIDUAL UNLOAD-RELOAD LOOPS FOR TEST B1.................... 192 APPENDIX D. INDIVIDUAL UNLOAD-RELOAD LOOPS FOR TEST C1 ................... 198 APPENDIX E. INDIVIDUAL LOADING CYCLE PLOTS FOR TEST C2...................... 205 REFERENCES .......................................................................................................................... 211
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LIST OF TABLES
Table 2.1. Index Properties of Grade 2 Crushed Limestone Base Material from the
Georgetown, Texas Capitol Aggregates Quarry...................................................... 12 Table 2.2. Gradation of Grade 2 Crushed Limestone Base Material from the
Georgetown, Texas Capitol Aggregates Quarry...................................................... 14 Table 2.3. Density and Moisture Content Data at Plate-Load Test Locations A and B
(Drier Material) ........................................................................................................ 16 Table 2.4. Density and Moisture Content Data at Plate-Load Test Location C (Wetter
Material)................................................................................................................... 16 Table 3.1. Direct Current Linear Variable Differential Transformer (DC-LVDTs)
Calibration Factors................................................................................................... 23 Table 5.1. Average Stiffnesses Measured at Various Loading Conditions for Cyclic
Plate-Load Tests on Drier Material (Moisture Content ~ 4.7 %) ............................ 72 Table 5.2. Overall Stiffnesses Measured Over Various Ranges of Loading for Static
Plate-Load Tests on Drier Material (Moisture Content ~ 4.7 %) ............................ 75 Table 6.1. Average Stiffnesses Measured During Small Amplitude Unload-Reload
Loops at Various Loading Conditions for Cyclic Plate-Load Tests on Wetter Material (Moisture Content ~ 6.1 %)....................................................................... 90
Table 6.2. Overall Stiffnesses Measured Over Various Ranges of Loading for Static
Plate-Load Tests on Wetter Material (Moisture Content ~ 6.1 %).......................... 93 Table 7.1. Average Small-Strain Stiffness for an Effective Depth of 12 in. (30.5 Cm)
(One Plate Diameter) ............................................................................................. 113 Table 8.1. Estimated Strain Amplitudes for Small-Strain, Unload-Reload Loops in
Tests B1 and C1 ..................................................................................................... 123 Table 8.2. Young’s Modulus Values Calculated Directly from Unload-Reload Loops in
Plate-Load Tests and from Small-Strain Seismic Tests......................................... 126 Table 8.3. Comparison of Stiffness Values Determined from Large Amplitude Plate-
Load Tests and from Seismic Tests ....................................................................... 136 Table 8.4 AASHTO T-222 Moduli of Soil Reaction for Georgetown Crushed
Limestone Test Pad................................................................................................ 143
x
Table A.1. Nuclear Density Gauge Data for Drier Material (W~ 4.7 %); Collected by
Gene Schlieker, Texas Transportation Institute..................................................... 156 Table A.2. Nuclear Density Gauge Data for Wetter Material (W~ 6.1 %); Collected
by Gene Schlieker, Texas Transportation Institute................................................ 158 Table C.1. Stiffnesses of Individual Small-Amplitude [1 Kip (4.4 kN)] Unload-Reload
Loops; Test B1, Incremental Plate-Load Test from 0 to 8.3 Kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %) ...................................................... 197
Table D.1. Stiffnesses of Individual Small-Amplitude [1 Kip (4.4 kN)] Unload-Reload
Loops; Test C1, Incremental Plate-Load Test from 0 to 8.6 Kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %) ................................... 204
xi
LIST of FIGURES Fig. 2.1. Unbound Base Material Being Delivered to the Test Pad Site.................................. 8 Fig. 2.2. Spreading Unbound Base Material Before Compaction of the Test Pad................... 9 Fig. 2.3. Vibratory Pad-Foot Roller Used to Compact Unbound Base Course Material
Over One-Half of the Test Pad .................................................................................. 9 Fig. 2.4. Vibratory Smooth-Drum Roller Used to Compact Unbound Base Course
Material Over One-Half of the Test Pad.................................................................. 10 Fig. 2.5. Cross Section of Unbound Aggregate Base Course Test Pad Constructed in
Georgetown, Texas .................................................................................................. 10 Fig. 2.6. Plan View of Test Pad and Plate-Load Test Locations............................................ 11 Fig. 2.7. Gradation Curve for Capitol Aggregates Crushed Limestone Base Course............ 13 Fig. 3.1. Rolling Dynamic Deflectometer Configured for Static Plate-Load Testing ........... 18 Fig. 3.2. Plan View of the RDD Showing the Locations of the Truck Tires Relative to
the Location of the Plate-Load Tests ....................................................................... 20 Fig. 3.3. Plate Setup Showing 6 in. (15.2 Cm) Diameter Plate Stacked on Top of the
12 in. (30.5 Cm) Diameter Plate .............................................................................. 22 Fig. 3.4. Measurement Frame Assembled for Plate-Load Testing......................................... 25
Fig. 3.5. Aluminum Adapter Block Attached to the Top of a Tripod.................................... 26 Fig. 3.6. Connection Between Rectangular Tubing and Round Bars [6-In. (15-Cm)
Ruler in Foreground]................................................................................................ 26 Fig. 3.7. Connection of Round Bars [6-In. (15-Cm) Ruler in Foreground] ........................... 27 Fig. 3.8. DC-LVDTs Mounting Block with the Capability of Connecting In-Line with
the Round Bar or at a 90-Degree Angle to the Round Bar ...................................... 27 Fig. 3.9. Schematic of Data Acquisition Hardware................................................................ 29 Fig. 3.10. Data Acquisition System installed in the Cab of the RDD...................................... 29
xii
Fig. 4.1. Estimates of Vertical Stress Delivered to the Top of a Pavement Base Course Beneath the Center of a 12 in. (30.5 cm) Diameter Circular Plate Under a 9000 lb (40.0 kN) Load.............................................................................. 37
Fig. 4.2. Variation of Force with Time; Test A1 - Incremental Pate-Load Test from 0
to 5 Kips (22.2 kN) ................................................................................................. 38 Fig. 4.3. Variation of Displacement with Time; Test A1 - Incremental Plate-Load
Test from 0 to 5 Kips (22.2 kN).............................................................................. 39 Fig. 4.4. Continuous Load-Settlement Curve from Test A1 - Incremental Plate-Load
Test from 0 to 5 Kips (22.2 kN).............................................................................. 40 Fig. 4.5. Variation of Force with Time; Test A2 - Loading from 0 to 11 Kips
(48.9 kN) in 36 Seconds Followed by Complete Unloading ................................... 42 Fig. 4.6. Variation of Displacement with Time; Test A2 - Loading from 0 to 11 Kips
(48.9 kN) in 36 Seconds Followed by Complete Unloading ................................... 43 Fig. 4.7. Continuous Load-Settlement Curve from Test A2 - Loading from 0 to 11
Kips (48.9 kN) in 36 Seconds and Unloading to Zero............................................. 45 Fig. 4.8. Variation of Force with Time; Test A3 - 32 Cycles of 0 to 9 Kips
(40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %) ................ 46 Fig. 4.9. Variation of Displacement with Time; Test A3 - 32 Cycles of 0 to 9 Kips
(40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %) ................ 47 Fig. 4.10. Continuous Cyclic Load-Settlement Curve; Test A3 - 32 Cycles of 0 to 9
Kips (40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %) ........ 48 Fig. 4.11. Illustration of Bi-Linear Stiffness Behavior Upon Loading; Test A3 - 32
Cycles of 0 to 9 Kips (40.0 kN) in 20 Minutes....................................................... 50 Fig. 4.12. Bi-Linear Stiffnesses of Each Cyclic Loop in the Loading Section;
Test A3 - 32 Cycles of 0 to 9 Kips (40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %)....................................................................... 51
Fig. 4.13. Illustration of Stiffness Behavior Upon Unloading; Test A3 - 32 Cycles of 0
to 9 Kips (40.0 kN) in 20 Minutes .......................................................................... 53 Fig. 4.14. Stiffnesses of Individual Loops During Rebound; Test A3 - 32 Loading
Cycles from 0 to 9 Kips on Drier Material (W~ 4.7 %) ......................................... 54 Fig. 4.15. Variation of Force with Time; Test A3 - 32 Cycles of 0 to 9 Kips (40.0 kN)
in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %) ................................. 55
xiii
Fig. 4.16. Variation of Force with Time; Test A4 – Loading to 40 Kips (178 kN) in 6
Minutes Followed by Complete Unloading on Drier Material (Moisture Content ~ 4.7 %) ...................................................................................................... 57
Fig. 4.17. Variation of Displacement with Time; Test A4 – Loading to 40 Kip
(178 kN) in 6 Minutes Followed by Complete Unloading on Dried Material (Moisture Content ~ 4.7 %) ..................................................................................... 58
Fig. 4.18. Continuous Load-Settlement Curve from Test A4 – Loading to 40 Kips (178
kN) in 6 Minutes Followed by Complete Unloading on Drier Material (Moisture Content ~ 4.7 %) ..................................................................................... 59
Fig. 4.19. Load-Settlement Curve Annotated with Values of Relative Stiffness During
Loading; Test A4 – Loading to 40 Kips (178 kN) in 6 Minutes and Unloading to Zero on Drier Material (Moisture Content ~ 4.7 %).......................... 61
Fig. 4.20. Load-Settlement Curve Annotated with Values of Relative Stiffness During
Unloading; Test A4 – Loading to 40 Kips (178 kN) in 6 Minutes and Unloading to Zero on Drier Material (Moisture Content ~ 4.7 %).......................... 62
Fig. 5.1. Variation of Force with Time; Test B1 - Incremental Plate-Load Test from 0
to 8.3 Kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %) .................... 67 Fig. 5.2. Variation of Displacement with Time; Test B1 - Incremental Plate-Load
Test from 0 to 8.3 Kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %) ..................................................................................... 68
Fig. 5.3. Continuous Load-Settlement Curve; Test B1 - Incremental Plate-Load
Test from 0 to 8.3 Kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %) ..................................................................................... 69
Fig. 5.4. Adjusted Load-Settlement Curve; Test B1 - Incremental Plate-Load Test
from 0 to 8.3 Kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %) ..................................................................................... 70
Fig. 5.5. Adjusted Load-Settlement Curve with Unload-Reload Loops Plotted; Test
B1 - Incremental Plate-Load Test from 0 to 8.3 Kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %)....................................................................... 72
Fig. 5.6. Adjusted Load-Settlement Curve with Relative Stiffnesses During Loading
and Unloading Annotated; Test B1 - Incremental Plate-Load Test from 0 to 8.3 Kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %) ......................... 76
xiv
Fig. 5.7. Representation of Stiffness with Varying Degrees of Load on the Loading Plate; Test B1 - Incremental Plate-Load Test from 0 to 8.3 Kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %) ........................................................ 78
Fig. 6.1. Variation of Force with Time; Test C1 - Incremental Plate-Load Test from 0
to 8.6 Kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %).................. 83 Fig. 6.2. Variation of Displacement with Time; Test C1 - Incremental Plate-Load
Test from 0 to 8.6 Kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %) ..................................................................................... 84
Fig. 6.3. Continuous Load-Settlement Curve; Test C1 - Incremental Plate-Load Test
from 0 to 8.6 Kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %) ..................................................................................... 86
Fig. 6.4. Adjusted Load-Settlement Curve; Test C1 - Incremental Plate-Load Test
from 0 to 8.6 Kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %) ..................................................................................... 87
Fig. 6.5. Adjusted Load-Settlement Curve with Unload-Reload Loops Plotted; Test
C1 - Incremental Plate-Load Test from 0 to 8.6 Kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)....................................................................... 89
Fig. 6.6. Adjusted Load-Settlement Curve with Relative Stiffnesses During Loading
and Unloading Annotated; Test C1 - Incremental Plate-Load Test from 0 to 8.6 Kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)....................... 92
Fig. 6.7. Representation of Stiffness with Varying Degrees of Load on the Loading
Plate; Test C1 - Incremental Plate-Load Test from 0 to 8.6 Kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)...................................................... 95
Fig. 6.8. Variation of Force with Time; Test C2 - 5 Cycles of 0 to 8 Kips (35.6 kN)
in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%).................................. 97 Fig. 6.9. Variation of Displacement with Time; Test C2 - 5 Cycles of 0 to 8 Kips
(35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%) ................. 98 Fig. 6.10. Continuous Load-Settlement Curve; Test C2 - 5 Cycles of 0 to 8 Kips (35.6
kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%) .......................... 99 Fig. 6.11. Bi-Linear Stiffnesses of Each Cyclic Loop in the Loading Section;
Test C2 - 5 Cycles of 0 to 8 Kips (35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%) .................................................................................... 100
xv
Fig. 6.12. Illustration of Stabilization Or Closing of Cyclic Loops; Test C2 - 5 Cycles of 0 to 8 Kips (35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%) .................................................................................... 101
Fig. 7.1. Basic Configuration for SASW Testing (from Stokoe Et Al. 1994) ..................... 105 Fig. 7.2. Relationship Between the Monotonic Loading Curve and Material Stiffness
in Shear of a Geotechnical Material....................................................................... 106 Fig. 7.3. Variation in Material Stiffness in Shear with Increasing Strain Amplitude as
Determined from Fig. 7.2....................................................................................... 107 Fig. 7.4. Equivalent Spring Constant, Keff, Determined from Shear Wave Velocity for
Strain Amplitudes in the Small-Strain Range........................................................ 110 Fig. 7.5. Shear Wave Velocity Profile of the Test Pad for the Drier Material
(W~ 4.7 %)............................................................................................................. 111 Fig. 7.6. Shear Wave Velocity Profile of the Test Pad for the Wetter Material
(W~ 6.1 %)............................................................................................................. 111 Fig. 8.1. Variation of Vertical Normal Strain with Depth Beneath A Circular Plate on
Sand After Schmertmann (1970) ........................................................................... 117 Fig. 8.2. Illustration of the Reduction in Shear Modulus with increases in
Strain Amplitude.................................................................................................... 119 Fig. 8. 3. Adjusted Load-Settlement Curve with Unload-Reload Loops for Test B1;
Incremental Plate-Load Test from 0 to 8.3 Kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %) ................................................................................... 121
Fig. 8.4. Adjusted Load-Settlement Curve with Unload-Reload Loops for Test C1;
Incremental Plate-Load Test from 0 to 8.6 Kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)..................................................................... 121
Fig. 8.5. Illustration of Strain Ranges Observed from Multiple Series of Cyclic
Unload-Reload Loops During Plate Load Testing................................................. 124 Fig. 8.6 Relationship Between Pressure Applied to the Plate and Observed increase
in Small-Strain Stiffness ........................................................................................ 128 Fig. 8.7. Illustration of Material Response Under Load to “Failure”; Test A4,
Loading from 0 to 40 Kips (0to 178 kN) in 6 Minutes and Unloading To Zero................................................................................................................... 132
xvi
Fig. 8.8. Continuous Force-Displacement Plot from Test A3; 32 Cycles of 0 to 9 Kips (40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %) ................................................................................... 134
Fig. 8.9. Continuous Force-Displacement Plot from Test C2; 5 Cycles of 0 to 8 Kips
(35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%) ............... 134 Fig. 8.10. Comparison of Stiffness Under Large Amplitude Cyclic Loading; Loop 5
from Tests A3 (Drier Material) and C2 (Wetter Material) .................................... 135 Fig. 8.11. Comparison of Seismically Determined Stiffness with Plate-Load Stiffness
for Large Amplitude Cyclic Plate-Load Tests; Loop 5, Test A3 - 32 Cycles of 0 to 9 Kips (40.0 kN) in 20 Minutes on Drier Material
(Moisture Content ~ 4.7 %) ................................................................................... 137 Fig. 8.12. Comparison of Seismically Determined Stiffness with Plate-Load Stiffness
for Large Amplitude Cyclic Plate-Load Tests; Loop 5, Test C2 - 5 Cycles of 0 to 8 Kips (35.6 kN) in 9 Minutes on Wetter Material
(Moisture Content ~ 6.1%) .................................................................................... 138 Fig. 8.13. Closure of Cyclic Loops from Plate-Load Test A3; 32 Cycles of 0 to 9 Kips
on Drier Material (W~ 4.7 %)................................................................................ 140 Fig. 8.14. Closure of Cyclic Loops from Plate-Load Test C2; 5 Cycles of 0 to 8 Kips
on Wetter Material (W~ 6.1 %) ............................................................................. 140 Fig. 8.15. Closure of Cyclic Loops from Plate-Load Test A3 After Accumulated
Displacement from Application of Previous Loops; 32 Cycles of 0 to 9 Kips on Drier Material (W~ 4.7 %)................................................................................ 141
Fig. 8.16. Long-Term, Adjusted Load-Settlement Curve; Test (B1) on Drier Material
(W~ 4.7 %)............................................................................................................. 144 Fig. 8.17. Long-Term, Adjusted Load-Settlement Curve; Test (C1) on Wetter Material
(W~ 6.1 %)............................................................................................................. 144 Fig. 8.18. Illustration of the Effect of Duration of Loading on Unbound Granular Base
Course Material; Plate-Load Tests at Location C on Drier Material (Moisture Content ~ 4.7%) .................................................................................... 145
Fig. 8.19. Illustration of the Effect of Duration of Loading on Unbound Granular Base
Course Material; Plate-Load Tests at Location C on Wetter Material (Moisture Content ~ 6.1%) .................................................................................... 146
Fig. B.1. Test A3; Loop 1 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 160
xvii
Fig. B.2. Test A3; Loop 2 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 161 Fig. B.3. Test A3; Loop 3 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 162 Fig. B.4. Test A3; Loop 4 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 163 Fig. B.5. Test A3; Loop 5 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 164 Fig. B.6. Test A3; Loop 6 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 165 Fig. B.7. Test A3; Loop 7 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 166 Fig. B.8. Test A3; Loop 8 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 167 Fig. B.9. Test A3; Loop 9 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 168 Fig. B.10. Test A3; Loop 10 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 169 Fig. B.11. Test A3; Loop 11 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 170 Fig. B.12. Test A3; Loop 12 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 171 Fig. B.13. Test A3; Loop 13 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 172 Fig. B.14. Test A3; Loop 14 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 173 Fig. B.15. Test A3; Loop 15 of 32 - 32 Loading Cycles from 0to 9 Kips on Drier Material (W~ 4.7 %) .............................................................. 174 Fig. B.16. Test A3; Loop 16 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 175
xviii
Fig. B.17. Test A3; Loop 17 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier Material (W~ 4.7 %) .............................................................................................. 176
Fig. B.18. Test A3; Loop 18 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 177 Fig. B.19. Test A3; Loop 19 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 178 Fig. B.20. Test A3; Loop 20 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 179 Fig. B.21. Test A3; Loop 21 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 180 Fig. B.22. Test A3; Loop 22 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 181 Fig. B.23. Test A3; Loop 23 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 182 Fig. B.24. Test A3; Loop 24 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 183 Fig. B.25. Test A3; Loop 25 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 184 Fig. B.26. Test A3; Loop 26 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 185 Fig. B.27. Test A3; Loop 27 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 186 Fig. B.28. Test A3; Loop 28 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 187 Fig. B.29. Test A3; Loop 29 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 188 Fig. B.30. Test A3; Loop 30 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 189 Fig. B.31. Test A3; Loop 31 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier
Material (W~ 4.7 %) .............................................................................................. 190
xix
xx
Fig. B.32. Test A3; Loop 32 of 32 - 32 Loading Cycles from 0 to 9 Kips on Drier Material (W~ 4.7 %) .............................................................................................. 191
Fig. C.1. Test B1, Individual Unload-Reload Loops, Group Ab1 ......................................... 193 Fig. C.2. Test B1, Individual Unload-Reload Loops, Group Bb1.......................................... 194 Fig. C.3. Test B1, Individual Unload-Reload Loops, Group Cb1.......................................... 195 Fig. C.4. Test B1, Individual Unload-Reload Loops, Group Db1 ......................................... 196 Fig. D.1. Test C1, Individual Unload-Reload Loops, Group Ac1 ......................................... 199 Fig. D.2. Test C1, Individual Unload-Reload Loops, Group Bc1.......................................... 200 Fig. D.3. Test C1, Individual Unload-Reload Loops, Group Cc1.......................................... 201 Fig. D.4. Test C1, Individual Unload-Reload Loops, Group Dc1 ......................................... 202 Fig. D.5. Test C1, Individual Unload-Reload Loops, Group Ec1 .......................................... 203 Fig. E.1. Test C2; Loop 1 of 5 - 5 Loading Cycles from 0 to 8 Kips on Wetter
Material (W~ 6.1 %) .............................................................................................. 206 Fig. E.2. Test C2; Loop 2 of 5 - 5 Loading Cycles from 0 to 8 Kips on Wetter
Material (W~ 6.1 %) .............................................................................................. 207 Fig. E.3. Test C2; Loop 3 of 5 - 5 Loading Cycles from 0 to 8 Kips on Wetter
Material (W~ 6.1 %) .............................................................................................. 208 Fig. E.4. Test C2; Loop 4 of 5 - 5 Loading Cycles from 0 to 8 Kips on Wetter
Material (W~ 6.1 %) .............................................................................................. 209 Fig. E.5. Test C2; Loop 5 of 5 - 5 Loading Cycles from 0 to 8 Kips on Wetter
Material (W~ 6.1 %) .............................................................................................. 210
CHAPTER ONE
INTRODUCTION
1.1 Increasing the Single-Lift Thickness of Compacted
Aggregate Base Courses
Unbound granular base course material is a common component of
layered pavement structures. According to a survey conducted by the
International Center for Aggregates Research (ICAR), most state departments
of transportation (DoTs) limit the thickness of aggregate base course which
may be compacted in a single lift. Typical limits on the lift thicknesses of
these bases are within the range of 6 to 8 in. (15 to 20 cm), with a few states
allowing somewhat thicker lifts with the design engineer’s approval (Bueno
et.al., 1998). Increasing the allowable lift thickness of granular base course
materials could make the product more cost effective and could improve
construction efficiency. A research project was, therefore, funded by ICAR
(No. ICAR-501) to determine the feasibility of compacting thicker granular
base course layers while achieving the same density as would be obtained by
compacting thinner lifts.
1
1.2 Characterizing Thick Aggregate Lifts
Unbound granular layers with thicknesses greater than 12 in. (30.5 cm)
are difficult to characterize with standard field tests. Field verification
methods typically include sand-cone density, balloon density, or nuclear
density tests. Sand-cone and balloon density tests sample only the near-
surface material, and the nuclear density gauge is restricted to depths of 12 in.
(30.5 cm) or less. Therefore, as part of the ICAR project, seismic testing was
studied to evaluate the feasibility of using seismically determined stiffness
profiles within the lifts to estimate the degree of compaction of the lifts.
Seismic testing was chosen, because it has some advantages over the
density tests mentioned above. Seismic tests are non-invasive and do not alter
the material during testing. Also, there is no depth limitation when using
certain seismic test procedures. Finally, seismic tests show increases or
decreases in stiffness which can not be detected by density testing and which
can affect the performance of the compacted layer under traffic loads.
To study further the characterization of thick lifts by in-situ seismic
and density measurements, plate-load tests were conducted in conjunction
with the seismic tests conducted for the ICAR project. The objective of the
study presented in this report is to determine the relationship between the
seismically determined stiffnesses of a test pad constructed with an unbound
aggregate base and the displacements induced in the material under working
load stresses.
2
1.3 Scope of Plate-Load and Seismic Testing
The ICAR project involved the construction and testing of test pads of
unbound aggregate base. Two test pads were constructed in Texas and three
test strips were constructed in Georgia. The two test pads in Texas were
constructed at the Capitol Aggregates quarry in Georgetown, Texas. Non-
invasive seismic testing using the Spectral Analysis of Surface Waves
(SASW) method (Stokoe et al. 1994) was conducted to determine shear
stiffness profiles of the material with depth. Comparison of the shear stiffness
profiles of thinner and thicker lifts was made to determine whether the same
stiffness properties could be achieved with compaction of thin and thick lifts.
A complete report of the seismic stiffness study is given in Bueno et al.
(1998).
In the study presented herein, static plate-load tests were conducted on
one of the Georgetown test pads to determine how small-strain shear
stiffnesses from seismic testing are related to displacements under working
loads. A unique piece of equipment developed at The University of Texas at
Austin called the Rolling Dynamic Deflectometer (RDD) was used to conduct
the plate-load tests (Bay 1997). The RDD was used in a stationary mode in
this application.
Low-frequency cyclic loading (0.01 Hz) was applied to the plate to
determine axial stiffnesses under transient working loads. Observations were
made of working-load displacements under a variety of load ranges for two
different moisture conditions of the aggregate base. These observations were
3
coupled with small-strain stiffness measurements to evaluate the potential for
predicting working load displacements with seismic testing. This
combination, if successful, would allow seismic measurements to be used to
evaluate the degree of compaction and also to estimate deformations in the
base.
1.4 Objectives of This Study
The primary goal of this study was to evaluate how well working-load
displacements could be predicted using small-strain seismic moduli. Small-
strain moduli were adjusted for the effects of strain amplitude and state of
stress and then used to predict displacements.
A secondary goal of static plate-load testing was to observe material
stiffness under varying states of stress. Cycles of unloading and reloading
were applied to the loading plate, and an equivalent spring constant or
stiffness was observed from the deformational behavior of the material.
These stiffness measurements (equivalent spring constants) were then
compared to those measured with seismic tests in order to quantify the effects
of changing states of stress in granular material.
Lastly, static plate-load tests and seismic tests were used to show how
the material stiffness was affected by increasing the in-situ moisture content
of the material. Nearly identical tests were performed before and after wetting
the test pad. The change in stiffness was observed and quantified in both the
static plate-load tests and seismic tests.
4
1.5 Correlations Between Plate-Load Settlement and Other
Field Tests
Static plate-load tests have been used regularly to evaluate roadbed
material stiffness under pressures in the range of those exerted by working
loads. Previous attempts have been made to predict footing settlement in
granular materials using in-situ test procedures. Terzaghi and Peck (1948)
introduced a procedure for estimating settlement under a footing on granular
material using standard penetration test (SPT) values. Schmertmann (1970)
introduced a method for predicting settlement on granular material using cone
penetration test (CPT) measurements. Recently, seismic testing has started to
receive more attention for use in predicting settlement. For instance, Ahtchi-
Ali and Santamarina (1994) investigated the use of cross-hole and downhole
seismic testing for the prediction of settlement under building foundations on
granular material.
Extension of seismic testing techniques to the loading conditions
applied to pavements has the potential to improve the design, construction,
and performance of pavement systems. Plate-load tests were conducted in an
effort to increase understanding of the relationship between in-situ seismic
stiffness measurements and working-load displacements in pavement layers.
5
1.6 Organization of This Report
This study begins with a description of the construction of the test
pads in Chapter 2 although only one test pad was used for plate-load testing.
An explanation of the equipment used for plate-load testing is presented in
Chapter 3. Seven plate-load tests were performed on one test pad. The
individual test procedures are described in detail in Chapters 4 through 6.
Background information about the seismic tests is summarized in Chapter 7.
The majority of the analysis of the plate-load and seismic test results is
presented in Chapter 8. The relative stiffnesses measured during seismic
testing and plate-load testing are compared and discussed in this chapter.
Detailed discussion of the strain amplitude for both the seismic and plate-load
tests as well as the influence of the state of stress is also included. The
observations and conclusions made from static plate-load tests and seismic
tests are summarized in Chapter 9.
6
CHAPTER TWO
MATERIAL AND TEST SITE
2.1 Construction of Test Pad
A test pad 40 ft (12 m) long by 35 ft (11 m) wide was constructed at the
Capitol Aggregates Quarry in Georgetown, Texas. Crushed limestone base
material with a nominal maximum particle size of 1.5 in. (37.5 mm) was delivered
from the quarry stockpile to the test pad location. The material was dumped from
the belly-dump tractor-trailer shown in Fig. 2.1 and spread with a motor grader as
shown in Fig 2.2. The test pad was divided lengthwise into two equal areas. One
area was compacted with an Ingersoll Rand SD-100F vibratory pad-foot roller
(Fig. 2.3) while the other area was compacted with an Ingersoll Rand SD-100D
vibratory smooth-drum roller (Fig 2.4). Both rollers had a static drum weight of
13,200 lb (58.7 kN) and delivered 52,500 lb (233.5 kN) peak to peak dynamic
force.
The test pad was constructed in two lifts. The first lift was 12 in. (31 cm)
thick. The second lift had an average thickness of 23 in. (58 cm) on the side of
the pad compacted with the pad-foot roller which is the area discussed in this
report. Details of the compaction procedures and material densities throughout
the pad are given by Bueno et al. (1998). A cross section of the test pad is shown
at Fig. 2.5.
7
The pad was constructed prior to the spring of 1998. Unfortunately, part
of the test pad was destroyed before plate-load testing could begin. As a result,
plate-load tests were conducted only on the side of the test pad compacted by the
pad-foot roller.
Fig. 2.1. Unbound Base Material Being Delivered to the Test Pad Site
8
Fig. 2.2. Spreading Unbound Base Material Before Compaction of the Test Pad
Fig. 2.3. Vibratory Pad-Foot Roller Used to Compact Unbound Base Course Material Over One-Half of the Ttest Pad
9
Fig. 2.4. Vibratory Smooth-Drum Roller Used to Compact Unbound Base Course Material Over One-Half of the Test Pad
23 in. (58 cm)
12 in. (30 cm)
~ 40o
Fig. 2.5. Cross Section of Unbound Aggregate Base Course Test Pad Constructed in Georgetown, Texas
10
2.2 Location of Plate-Load Tests
Three locations were selected for plate-load testing. These locations are
labeled A, B, and C in Fig. 2.6. The geometry of the test equipment dictated that
tests be conducted in the center of the pad-foot lane. This was a convenient
location in that it allowed avoidance of the edge of the pad. Details of the test pad
and the plate-load test locations are shown in Fig. 2.6.
.
C B A
40 ft. (12 m)
NCompactedWith Pad-FootRoller
Effective Plate-LoadTesting Area
5 ft. 5 ft.(1.5 m) (1.5 m)
35 ft
. (11
m)
~ 3 ft(0.9 m)
~ 20 ft (6.1 m)
Fig. 2.6. Plan View of Test Pad and Plate-Load Test Locations
11
2.3 Flexible Base Material
The material used to construct the test pad was produced by Capitol
Aggregates for sale as road base material. This product meets TxDOT
specifications for Grade 2 Flexible Base material. The stockpile material had
moisture content near optimum (6.5 %) and required no added moisture before
compaction. Gradation of the stockpile material showed 12 % passing the #40
(0.475 mm) sieve and 7.1 % passing the # 200 sieve. The fines were non-plastic.
A summary of the index properties is presented in Table 2.1. The gradation curve
is shown in Fig. 2.7. The gradation data are also presented in Table 2.2.
Table 2.1. Index properties of Grade 2 crushed limestone base material from the Georgetown, Texas Capitol Aggregates Quarry Liquid Limit Non-Plastic Plastic Limit Non-Plastic Optimum Moisture Content 6.5 % AASHTO T180 (modified Proctor) Max. Density 141 pcf (2263 kg/m3)
12
100
80
60
40
20
0 890.1
234567891
2345678910
2345
Grain Size, mm
#200#60#20#10#4
U.S. Standard Sieve Number
#40 #1400.317in.
0.75 in.2.0in.
1.5in.1.0in.
Fig. 2.7. Gradation Curve for Capitol Aggregates Crushed Limestone Base Course
13
Table 2.2. Gradation of Grade 2 crushed limestone base material from the
Georgetown, Texas Capitol Aggregates Quarry
Sieve Size % Passing mm
2.0 in. 50.000 100 1.5 in. 37.500 98.8 1.0 in. 25.000 85.1 0.75 in. 19.000 73.0 0.317 in. 9.275 51.5
#4 4.750 35.0 #10 2.000 23.2 #20 0.850 15.3 #40 0.425 12.0 #60 0.250 10.1 #140 0.106 7.9 #200 0.075 7.1
2.4 In-Situ Density Testing
A Troxler nuclear density gauge (NDG) was used to estimate total in-
situ density and moisture content before plate-load tests were performed at
locations A and C (Fig. 2.6). No moisture was added to the flexible base test
pad before tests A and B, and no significant weather changes took place
during the 25 days between the two sets of tests. The NDG data for location
A can, therefore, be considered representative of the material at location B.
Moisture was added, however, to the material before plate-load and seismic
tests were performed at location C as described in Chapter 3. Density
14
measurements were made every 2 in. (5 cm) to a depth of 12 in. (31 cm).
Moisture content specimens were collected at the conclusion of the plate-load
tests and used to correct the NDG data. Relatively large moisture content
specimens were collected to provide an accurate representation of the
moisture of the base course. The moisture content specimens weighed
between 6.2 and 7.3 lb (2.8 kg and 3.3 kg). The difference between the
laboratory moisture content and that measured at a depth of 2 in. (5 cm) in the
field was subtracted from NDG readings at every depth. Average density and
moisture content data for tests at locations A and B are presented in Table 2.3.
The same information for location C after wetting is given in Table 2.4.
Complete records of the nuclear density data are given in Appendix A.
15
16
Table 2.3. Density and moisture content data at plate-load test locations A and B (drier material)
Depth Wet Density Corrected Moisture Content 1
Dry Density
(in.) (lb./ft3) (%) (lb./ft3) Back Scatter 126 4.7 120
2 124 4.9 119 4 133 4.5 128 6 138 4.5 132 8 141 4.5 135 10 143 4.3 137 12 142 4.3 136
1 NDG moisture content data were corrected by subtracting a correction factor from every NDG reading. The correction factor was determined by taking the difference between the surface moisture content determined by the NDG and the surface moisture content determined in the laboratory. (Correction for drier material: w NDG - wLAB = 0.8)
Table 2.4. Density and moisture content data at plate-load test location C (wetter material)
Depth Wet Density Corrected Moisture Content
2
Dry Density
(in.) (lb./ft3) (%) (lb./ft3) Back Scatter 134 6.3 126
2 134 6.3 126 4 140 6.1 132 6 144 5.7 136 8 147 5.9 139 10 147 5.7 139 12 147 5.5 139
2 NDG moisture content data were corrected by subtracting a correction factor from every NDG reading. The correction factor was determined by taking the difference between the surface moisture content determined by the NDG and the surface moisture content determined in the laboratory. (Correction for wetter material: w NDG - wLAB = 1.7.
CHAPTER THREE
PLATE-LOAD TESTING WITH THE ROLLING DYNAMIC
DEFLECTOMETER
3.1 Introduction
Plate-load testing was conducted by adapting the Rolling Dynamic
Deflectometer (RDD) to this static application. The RDD is a vibroseis truck
modified to apply continuous rolling dynamic loads to a pavement surface while
deflections are measured via rolling sensors. The equipment was developed by
Bay (1997) at The University of Texas at Austin and is shown in static
configuration in Fig. 3.1. Static plate load tests were facilitated by the addition of
a 100-kip (445 kN) static load cell in the center of the truck’s hydraulic loading
frame. With these modifications, static load and displacement data could be
continually monitored using the computerized data acquisition system of the
RDD. Electronic data collection provided precise measurement of displacement
over short periods of time which would not have been possible with dial gauges.
This unique arrangement allowed incremental static loading as well as short-
duration cyclic loading and unloading tests to be performed during plate loading.
All of this equipment is discussed below.
17
Fig. 3.1. Rolling Dynamic Deflectometer Configured for Static Plate-Load Testing
3.2 Plate-Load Testing Equipment
3.2.1 Loading Mechanism
The load was applied to the plate through the hydraulic loading
mechanism on the RDD. The pressure in the hydraulic cylinders which control
the load can be increased or decreased from controls inside the cab of the truck.
Complete details of the loading system are given in Bay (1997).
To mount the static load cell under the truck, additional structural supports
had to be designed, machined, and installed on the truck’s loading frame.
Structural sections were machined from 6-in. (15.2 cm) wide by 2-in. (5.1 cm)
18
thick solid steel bar stock to minimize compliance of the loading system. The
structural members were welded and bolted to the loading frame.
Due to the geometry of the truck’s loading mechanism and chassis
configuration, the rear wheels of the truck were within 5-ft (1.5 m) of the edge of
the plate. The locations of the truck tires and loading plate are diagrammed in
plan view in Fig 3.2 to show their relative positions. Standard test methods for
repetitive and non-repetitive plate-load tests published by the American
Association of State Highway and Transportation Officials (AASHTO, 1986)
specify a minimum clearance of 8-ft (2.4 m) between the reaction points for the
load mechanism and the edge of the plate. This was not possible without
significant modifications to the truck. To limit the effects of the truck’s rear
wheels on the material being sampled in the plate-load test, the plate size was
limited to 1-ft (30.5 cm.). Because the sampling depth is related to the diameter
of the plate, a larger plate would sample to a greater depth with greater potential
for influence from the truck’s wheels. Future modifications to the truck may
include the addition of hydraulic jacks mounted on the front and rear bumpers
which would lift the truck and move the reaction points well outside the
deflection basin produced during plate-load testing. This would allow the use of
larger plates and facilitate sampling deeper material.
19
76 in. (193 cm)
Tire Contact Area[Approx 12 in. by 14 in.(30.5 cm by 35.6 cm)]
187
in. (
475
cm)
72 in. (183 cm)
Load Plate12 in. (30.5 cm)
54 in
. (13
7 cm
)
53 in
. (13
5 cm
)
56 in
. (14
2 cm
)
Truck Tires
Fig. 3.2. Plan View of the RDD Showing the Locations of the Truck Tires Relative to the Location of the Plate-Load Tests
20
The advantage of the hydraulic loading system on the RDD is that cycles
of loading and unloading can be easily applied at pre-selected rates to the load
plate. Such cyclic loading more closely simulates the loads induced by repeated
traffic. In addition, small cycles of unloading and reloading can be superimposed
over a static force on the plate. It was sometimes difficult, however, to carefully
apply a small increment of load. The loading mechanism occasionally exhibited a
“stick-slip” behavior which produced a jump of 1000 to 2000 lb (4.45 to 8.90 kN)
when a small adjustment was applied to the hydraulic pressure.
3.2.2 Load-Plate Details
A circular aluminum plate 1-ft (30.5 cm) in diameter and 1.5-in. (3.8 cm)
thick was used for the plate-load tests. For each test, the plate was seated in a thin
layer of hydrostone, which is a mixture of plaster of Paris, Portland cement, and
lime. The hydrostone was allowed to cure for about one hour before application
of the load. For tests at locations A and B, a 6-in. (15.2 cm) diameter plate was
stacked on top of the 12-in. (30.5 cm) diameter plate as shown in Fig 3.3. Tests at
location C were conducted with the 12-in. (30.5 cm) diameter plate alone due to
clearance limitations beneath the load cell. Because the test pad was ramped at
each end, the clearance below the load cell decreased as the front wheels of the
RDD truck began to descend the ramp. This did not happen when the back
wheels were near the ramp during testing at location A. It is shown in Fig. 3.2
that the load plate is closer to the back wheels of the RDD. The truck, therefore,
took less space on the pad behind the loading plate than in front of the loading
plate.
21
Fig. 3.3. Plate Setup Showing 6 in. (15.2 cm) Diameter Plate Stacked on Top of the 12 in. (30.5 cm) Diameter Plate
3.2.3 Load Cell
A Beowulf model 330 load cell was bolted to the structural cross brace on
the truck’s loading mechanism. An excitation voltage of 5.00 volts DC was
applied to the load cell with a Lambda LL-902-OV regulated power supply. The
output signal was amplified with a Neff model 128 DC signal amplifier with a
gain setting of 1000. The load cell was calibrated in the laboratory and verified to
have a calibration factor of 2-mV/volt excitation/100 kips.
22
3.2.4 Displacement Transducers
Displacement of the plate was measured using three Direct Current Linear
Variable Differential Transformers (DC-LVDTs) placed at third points around the
circumference of the plate. Trans-Tek 0243-0000 DC-LVDTs were used for
these tests. The sensors had a maximum range of +/- 0.750 in. (+/- 19.1 mm)
from the center or neutral position with a working range of +/- 0.5 in. (+/- 12.7
mm) from the center or neutral position.
DC-LVDTs are excited with a DC voltage and output a DC voltage which
varies with the position of an iron core traveling freely inside the sensor’s
magnetic field. A 5.00-volt excitation signal was applied to the sensors with a
Lambda LL-902-OV regulated power supply. Calibration factors for each sensor
were determined in the laboratory using a 5.00-volt excitation signal. The sensors
were operated in the linear range, and the calibration factors are given in Table
3.1. A complete discussion of the application of calibration factors and other
details of the data reduction is given in Section 3.3.
Table 3.1. Direct Current Linear Variable Differential Transformer (DC-LVDT) Calibration Factors
Sensor Calibration Factor (volts/in.) # 1 5.081 # 2 5.136 # 3 5.089
23
3.2.5 Support Frame for DC-LVDTs
For small plate deflections to be measured precisely, the supports for the
DC-LVDT sensors had to be placed outside the deflection basin. In addition, the
instrumentation system had to provide clearance for the truck’s loading deck to
move freely throughout the test. This combination of constraints posed some
unique challenges in designing the support frame for the DC-LVDTs.
A framework of rectangular aluminum tubing and round aluminum bars
was used to hold the sensors in place during the test. A photograph of the test
frame erected under the truck is shown in Fig. 3.4. The frame consisted of two,
21-ft (6.4 m) lengths of 1-in. by 2-in. (25 mm by 51 mm) aluminum tubing
supported by photographic tripods. The tripods were chosen to support the
framework because the terrain was uneven, and the elevation around the test site
varied as much as 3 ft (0.9 m). The supports on one side of the test site were
required to be over 5 ft (1.5 m) tall, while the supports on the other side of the test
site needed only be 2 ft (0.6 m) tall. The tripods also offered flexibility for future
configurations of the measurement system.
24
Fig. 3.4. Measurement Frame Assembled for Plate-Load Testing
The camera attachment head was removed from the top of the tripods, and
replaced with an aluminum block machined to hold the aluminum tubing
(Fig. 3.5). Round aluminum bars, 5/8 in. (16 mm) in diameter were attached to
the tubing with machined blocks designed to provide flexibility in adjusting the
framework in the field (Fig 3.6). Laboratory apparatus clamps were used to
connect two aluminum bars at a 90-degree angle (Fig. 3.7). The DC-LVDTs were
attached to the round bars with mounting blocks as shown in Fig. 3.8. Hex-head
set screws were used to hold the components in place. All of the components of
the measurement frame were designed to be flexible and adjustable so that
changes to the configuration could be made easily in the field. This feature was
exploited numerous times during testing.
25
Fig. 3.5. Aluminum Adapter Block Attached to the Top of a Tripod
Fig. 3.6. Connection Between Rectangular Tubing and Round Bars [6-in. (15-cm) Ruler in Foreground]
26
Fig. 3.7. Connection of Round Bars [6-in. (15-cm) Ruler in Foreground]
Fig. 3.8. DC-LVDT Mounting Block with the Capability of Connecting In-Line With the Round Bar or at a 90-Degree Angle to the Round Bar
27
Unfortunately, it was uncovered during testing that the instrument frame
should have been stiffer in order to prevent vibrations from strong winds
experienced at the quarry. Noticeable vibration noise in the deflection data was
observed during periods of high wind. Plywood and corrugated metal wind
breaks were installed to reduce the effects of wind on the measurement system.
This proved very effective in reducing noise in the displacement data; however
stiffer cross braces would have decreased vibration noise even further.
3.2.6 Data Acquisition System
A computerized data acquisition system was employed to sample output
voltages from the load cell and DC-LVDTs. The computer and other data
acquisition hardware were mounted in the cab of the RDD. A Power Macintosh
7500/100 personal computer with a National Instruments data acquisition card
was coupled with a National Instruments Signal Conditioning extensions for
Instrumentation (SCXI) chassis to collect the data. National Instruments
LabVIEW software was used to sample the four data channels continuously at a
frequency of 32 Hz. Plots of the output voltages from the load cell and
displacement sensors were displayed in real time on the computer screen as the
test was running. This was particularly useful for selecting load and time
increments based on material response under the initial loading. The hardware
configuration is detailed in Fig. 3.9, and a photograph of the equipment installed
in the RDD is shown at Fig. 3.10.
28
LabVIEW DataAcquisition Software
SCXI Chassis
Iomega zip
Power Macintosh 7500/100
3 Channelsto DC-LVDTSensors
Neff Model 128InstrumentationAmplifier
1 Channelto Load Cell
Fig. 3.9. Schematic of Data Acquisition Hardware
Fig. 3.10. Data Acquisition System Installed in the Cab of the RDD
29
3.3 Data Reduction
Output voltages from the load cell and DC-LVDTs were recorded in
multiplex format during testing. Each channel was sampled at 32 Hz, and the
four voltages were recorded in a group of four binary numbers for each time
increment. To reduce the data, the binary stream was de-multiplexed into its four
channel components for each plate-load test.
Calibration factors were applied to the load cell data and to each
displacement transducer separately. The data were then zeroed based on the
initial offset load in the load cell and starting average displacement in the
displacement transducers.
For each test, the data were averaged over 31 points (1 second) to reduce
the effects of noise due to vibration in the measurement system. The force in the
load cell and the average displacement in the three sensors were plotted with
respect to time on separate plots. A continuous plot of displacement vs. load was
then plotted for each test.
3.4 Overview of Plate-Load Testing
Six tests were performed at three test locations on the base-course test
pad. The locations are labeled A, B, and C for reference (Fig. 2.6). Tests at a
given location were run consecutively, meaning for example, Test A2 was begun
after the completion of Test A1 without moving the plate or the truck. The suite
of tests included: (1) loading in the range of expected wheel loads in a pavement
structure; (2) loading well above the expected wheel loads in a pavement
structure; (3) traditional incremental loading over a long period of time (duration
30
of load ~ 2 hr); (4) cyclic loading over short periods of time (duration of load ~ 1
min.)
3.4.1 Modulus of Soil Reaction, ku’
The modulus of soil reaction, ku’ is used in rigid pavement design and is
defined by AASHTO T222 (1986) according to the following expression:
ku’ = 10 psi / (average deflection at 10 psi) ......................... (3.1)
The units of ku’ are lb/in.2/in. The value as obtained by plate load tests is
normally corrected for seasonal variation, composite effect due to layering, depth
to bedrock, and loss of sub-base support due to pumping. Typical values for the
composite k range from 50 lb/in.2/in. to 2000 lb/in.2/in. (13.6 kPa/mm to 543
kPa/mm) according to the AASHTO Guide for Design of Pavement Structures
(AASHTO, 1993).
The modulus of soil reaction has been linearly correlated to resilient
modulus, MR according to AASHTO (1993) as shown below for reference.
k = MR / 19.4 ........................................................ (3.2)
Equation 3.2 is not dimensionally correct, so care must be taken in using it. The
units of MR in equation 3.2 are lb/in.2.
31
3.4.2 Material Equivalent Spring Constant (Stiffness)
Material stiffness in the following discussion is defined in terms of an
equivalent spring constant keff. The spring constant is expressed as the amount of
displacement experienced under any given load. The equivalent stiffness was
determined at various points of interest in the plate load tests and is expressed in
units of lb/in. The stiffness was typically determined using one of two methods:
(1) taking the slope of a linear curve fit to a section of the loading or unloading
curve; or (2) taking the slope of the tangent of a polynomial curve fit to a section
of the curve.
3.4.3 Summary of Plate-Load Tests Performed
Tests at location A were performed to determine the capabilities of the
loading mechanism and measurement system as well as to determine the general
characteristics of the material. No moisture was added to the material before
testing, and these tests are referred to as “drier” tests (w ~ 4.7 %). The following
four tests were conducted at this location: (1) loading to a maximum force of 5
kips (22.2 kN) using traditional incremental loading procedures and performing
one cycle of unloading-reloading midway through the loading cycle; (2) quick
loading to 11 kips (48.9 kN) and quick unloading; (3) 32 cycles of loading-
unloading of 0 to 9 kips (40.0 kN); (4) quick loading to 40 kips (178 kN)
followed by quick unloading back to zero load.
One test was performed at location B. No moisture was added to the test
pad before testing, and these tests are also referred to as the “drier” tests (moisture
content ~ 4.7 %). Traditional incremental loading to 8.3 kips (36.9 kN) was
32
applied to the plate, and four unloading-reloading loops were applied at various
points during the test.
Two plate-load tests were performed at location C. Moisture was
periodically added to the surface of the test pad for two days prior to the plate-
load tests. The tests at location C are referred to the “wetter” tests (moisture
content ~ 6.1 %). The first test at location C was similar to the test at location B
except for the fact that the material was wetted before the test, and the maximum
load was approximately 8.6 kips (38.3 kN) as opposed to 8.3 kips (36.9 kN). The
second test at location C was similar to third test at location A where 32 cycles of
a 9-kip (40.0 kN) load were applied, except that the material was wetted and only
5 cycles of an 8-kip (35.6 kN) load were applied. The tests are described in detail
in Chapters 4-6.
33
CHAPTER FOUR
PRELIMINARY PLATE-LOAD TESTS AT
LOCATION A ON THE TEST PAD
4.1 Introduction
To initiate the field study and to learn about plate-load testing with the
Rolling Dynamic Deflectometer (RDD), four preliminary tests were performed at
location A on the Georgetown test pad (Figure 2.6). The plate-load tests were
performed on the top of the second lift for a total thickness of aggregate base
under the plate of 35 in. (89 cm). These were the first tests performed with the
RDD on the test pad, so they were used to evaluate the loading capabilities of the
RDD as well as the load-displacement behavior of the test pad under a variety of
loading conditions. No moisture was added to the surface of the test pad before
the plate-load tests were conducted. The surface moisture content was determined
to be 4.7%. These initial plate-load tests are discussed in detail below.
It should be noted that the effective plate area for tests at location A was
107 in.2 (690 cm2), as opposed to 113 in.2 (729 cm2) as would be calculated for a
12 in. (30.5 cm) diameter plate. The reason for this reduction in effective area is
that the hydrostone used to seat the loading plate did not flow completely to the
edge of the plate during seating. Because the loading plate was placed after the
truck was in position, the clearance did not allow placement in such a way that the
hydrostone would flow out around the entire circumference of the plate. This
35
problem was corrected in subsequent tests by seating the plate in hydrostone
before positioning the truck over the test location.
4.2 Test A1 - Incremental Plate-Load Test from 0 to 5 kips (22.2
kN)
The first plate-load test performed on the test pad was used to evaluate the
approximate magnitude of displacement under a typical working load and to
determine the capabilities of the loading system and data acquisition system. An
estimate of the typical range of working loads was made using a chart showing
the interface stresses in a two-layer pavement system presented by Huang (1969).
The estimates are presented in Figure 4.1. The typical working load was taken as
that stress level which would be applied by an 18 kip (80 kN) equivalent single
axle load (ESAL) on a 3 to 4 in. (7.6 to 10.2 cm) asphalt concrete pavement over
compacted aggregate base. This level was estimated to be in the range of 5 kips
(22.2 kN) and represented an average vertical stress under the loading plate of 47
psi (324 kPa).
36
This test is not discussed in detail because of its preliminary nature.
However, it was observed that the load plate displaced approximately 48 mils
(1.22 mm) vertically under the 5 kip (22.2 kN) load. A permanent (un-recovered)
displacement of 32 mils (0.81 mm) was also recorded. The variations in force and
displacement with time are shown in Figs. 4.2 and 4.3, respectively. The
continuous load-settlement curve is shown in Figure 4.4.
37
2.5 in. (6.4 cm) ACC 4 in. (10.2 cm) ACC6 in. (15.2 cm) ACC
8 in. (20.3 cm) Aggregate Base
10 in. (25.4 cm) Aggregate Base
12 in. 30.5 cm) Aggregate Base
Material Properties
Asphalt Cement Concrete (ACC), E1 = 500 ksi (3.4 X 106 kN/m2)
Aggregate Base, E2 = 33 ksi (2.3 x 105 kN/m2)
σc
σcσc
σc = 56 psi (386 kPa)
σc = 21 psi (145 kPa)
σc = 36 psi (248 kPa)
9000 lb (40.0 kN) 9000 lb (40.0 kN)9000 lb (40.0 kN)6 in.(15.3 cm)
6 in.(15.3 cm)
6 in.(15.3 cm)
Fig. 4.1. Estimates of Vertical Stress Delivered to the Top of a Pavement Base Course Beneath the Center of a 12 in. (30.5 cm) Diameter Circular Plate Under a 9000 lb (40.0 kN) Load
7
6
5
4
3
2
1
0
30
25
20
15
10
5
0140120100806040200
Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Fig. 4.2. Variation of Force with Time; Test A1 - Incremental Pate-Load Test from 0 to 5 kips (22.2 kN)
70
60
50
40
30
20
10
0
1.5
1.0
0.5
0.0
140120100806040200Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Fig. 4.3. Variation of Displacement with Time; Test A1 - Incremental Plate-Load Test from 0 to 5 kips (22.2 kN)
70
60
50
40
30
20
10
06420
Force (kips)
1.5
1.0
0.5
0.0
302520151050Force (kN)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Fig. 4.4. Continuous Load-Settlement Curve from Test A1 - Incremental Plate-Load Test from 0 to 5 kips (22.2 kN)
4.3 Test A2 - Loading from 0 to 11 kips (48.9 kN) in 36 Seconds
Followed by Complete Unloading
The second test at location A on the Georgetown test pad was performed
to determine the effect of the duration of loading on the response of the unbound
aggregate base. A load of 11 kips (48.9 kN) was applied to the loading plate in 36
seconds. This load was maintained on the loading plate for 10 minutes. The load
was then removed in 4 seconds and the material was allowed to rebound for 11
minutes. The displacement under the 11 kip (48.9 kN) load was 42 mils (1.07
mm) after the 36-second load application. The maximum displacement under the
11 kip (48.9 kN) load increased to 60 mils (1.52 mm) after maintaining the load
for 10 minutes, showing significant creep in the unbound base material.
The variations of force and displacement with time for Test A2 are shown
in Figure 4.5 and 4.6, respectively. A decreasing rate of displacement with time
can be observed from the displacement-time record shown in Figure 4.5. The
average rate of displacement during the final 30 seconds of the loading was
observed to be nearly zero. In fact, the material was rebounding slightly due to the
fact that the load was gradually decreasing. The results of Test A2 allowed the
selection of appropriate load duration for future tests. Load duration of 15
minutes was selected in many of the subsequent tests to ensure that the rate of
displacement at the end point was nearly zero.
38
12
10
8
6
4
2
0
2520151050
50
40
30
20
10
02520151050
Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Fig. 4.5. Variation of Force with Time; Test A2 - Loading from 0 to 11 kips (48.9 kN) in 36 Seconds Followed by Complete Unloading
60
50
40
30
20
10
0
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
2520151050Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Fig. 4.6. Variation of Displacement with Time; Test A2 - Loading from 0 to 11 kips (48.9 kN) in 36 Seconds Followed by Complete Unloading
The permanent (un-recovered) displacement was measured 11 minutes
after the load was removed and found to be 38 mils (0.97 mm). The continuous
load-settlement curve for Test A2 is given in Figure 4.7.
4.4 Test A3 - 32 Cycles of 0 to 9 kips (40.0 kN) in 20 Minutes
Cyclic loading was applied to the test pad in Test A3 to better simulate the
loading conditions induced by traffic. Thirty-two cycles of loading and unloading
with a maximum load of approximately 9 kips (40.0 kN) were applied to the
plate. The average duration of each cycle was 1.5 minutes. Time plots of force
and displacement are shown in Figs. 4.8 and 4.9, respectively. The continuous
load-settlement curve showing all 32 cycles is given in Figure 4.10. It can be seen
that there is a general increase in permanent deformation with increasing number
of cycles. The deformation became approximately constant, and the cyclic
unload-reload loops were observed to “close” or plot on top of one another after 7
or 8 cycles. The displacement then increased for a few cycles, and the loops
began to close again after about 15 cycles. The displacement started increasing
again when the load was accidentally increased from 9 kips (40 kN) to 11 kips (49
kN) for cycle number 25.
39
60
50
40
30
20
10
0121086420
Force (kips)
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
50403020100Force (kN)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Time-DependentDisplacementUnder a SustainedConstant Load
Fig. 4.7. Continuous Load-Settlement Curve from Test A2 - Loading from 0 to 11 kips (48.9 kN) in 36 Seconds and Unloading to Zero
12
10
8
6
4
2
0
50
40
30
20
10
03020100
Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Fig. 4.8. Variation of Force with Time; Test A3 - 32 Cycles of 0 to 9 kips (40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %)
30
25
20
15
10
5
0
0.8
0.6
0.4
0.2
0.0
3020100Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Fig. 4.9. Variation of Displacement with Time; Test A3 - 32 Cycles of 0 to 9 kips (40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.8
0.6
0.4
0.2
0.0
50403020100Force (kN)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Loop 25
Loop 30
Fig. 4.10. Continuous Cyclic Load-Settlement Curve; Test A3 - 32 Cycles of 0 to 9 kips (40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %)
4.4.1 Determining Stiffness During Loading
The material equivalent spring constant, keff, is defined as the force
divided by the displacement at a given point in the loading cycle as discussed in
Section 3.4.2. The keff, is the inverse of the slope of the load-settlement curve at a
given point during loading or unloading. This equivalent spring constant is
referred to as the “stiffness” of the material.
Each of the 32 load cycles was plotted separately, and the stiffnesses of
the material at various points along the load-displacement plots were determined.
The slope of the loading curves was observed to be approximately bi-linear for
most loops as illustrated conceptually in Figure 4.11. The two stiffnesses were
determined by performing a linear curve fit to the data above and below the
observed break as shown by the dashed lines in Figure 4.11. Because loop 25 far
exceeded the average value of the maximum load in the preceding cycles, the
stiffness values for only the first 24 loops were recorded. The stiffness values for
the two sections of loading for curves 1-24 are shown in Figure 4.12.
40
Force
k eff-initial loading
k eff-final loading
Figure 4.11. Illustration of Bi-Linear Stiffness Behavior Upon Loading; Test A3 - 32 Cycles of 0 to 9 kips (40.0 kN) in 20 Minutes
41
It can be observed in Figure 4.12 that the initial stiffness increased
approximately 25 % over 24 loading cycles. The stiffness during the second
portion of the loading cycle increased by 50% suddenly, after 12 cycles, and
remained relatively constant for the remaining 12 cycles. It is not clear why the
material became suddenly stiffer. No significant load spike was experienced
before cycle 25, and no unusual disturbance was observed during testing. The
individual loading loops annotated with the bi-linear curve fits are included in
Appendix B.
4.4.2 Determining Stiffness During Unloading
The stiffness of the test pad material during unloading was also evaluated
and recorded at three points on the unloading curve for each large-amplitude
unload-reload loop as illustrated conceptually in Figure 4.13. The rebound curves
were divided into thirds, and a polynomial curve-fit was performed on each third
of each loop. The derivative of each polynomial was evaluated at the center of
each segment to determine the slope of the tangent to the curve at the center. The
stiffness values for the three load ranges on the unloading loops are shown in
individual plots in Figure 4.14 and together in Figure 4.15.
It should be noted that the slope of the rebound curve is very slightly
negative at the beginning of rebound. This would suggest that the displacement
continued to increase after the load was released. This is counter-intuitive;
however, no investigation was made in this study to attempt to explain this
behavior.
42
1.6x106
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.024222018161412108642
Cycle Number
0.250x106
0.200
0.150
0.100
0.050
0.000
Stiffness During Initial Loading Stiffness During Final Loading
Fig. 4.12. Bi-Linear Stiffnesses of Each Cyclic Loop in the Loading Section; Test A3 - 32 Cycles of 0 to 9 kips (40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %)
Force
k eff-beginning of rebound
k eff-middle of rebound
k eff-end of rebound
Figure 4.13. Illustration of Stiffness Behavior Upon Unloading; Test A3 - 32 Cycles of 0 to 9 kips (40.0 kN) in 20 Minutes
The stiffnesses measured at the beginning of rebound were greater than
the stiffnesses measured during loading or at any other point on the rebound
curve. It was observed that the stiffnesses measured during unloading showed
significantly more scatter than the stiffnesses measured during loading.
43
-12x106
-8
-4
0
2015105Cycle Number
-60x106
-40
-20
0
stiffness at beginning of rebound
0.10x106 0.080.060.040.020.00
2015105Cycle Number
0.60x106 0.500.400.300.200.100.00
stiffness at end of rebound
2.5x106 2.01.51.00.50.0
2015105Cycle Number
16x106
12
8
4
0
stiffness at middle of rebound
Figure 4.14. Stiffnesses of Individual Loops During Rebound; Test A3 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
44
-60x106
-40
-20
0
242220181614121086420Cycle Number
-12x106
-10
-8
-6
-4
-2
0
2
stiffness at beginning of rebound stiffness at middle of rebound stiffnes at end of rebound
Fig. 4.15. Variation of Force with Time; Test A3 - 32 Cycles of 0 to 9 kips (40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %)
4.4.3 Measurement of Permanent Displacement
After having undergone 70 mils (1.78 mm) of permanent displacement
from Tests A1 and A2, the plate displaced a maximum of 30 mils (0.76 mm) as a
result of the 32 cycles of approximately 9 kips (40.0 kN) each. Of those 30 mils
(0.76 mm), the additional permanent displacement after test A3 was
approximately 15 mils (0.38 mm). This resulted in a total permanent displacement
of 85 mils (2.16 mm) for the three plate-load tests (A1, A2, and A3).
4.5 Test A4 - Loading from 0 to 40 kips (178 kN) in 6 Minutes
Followed by Complete Unloading
The last test at location A involved loading to 40 kips (178 kN) followed
by complete unloading. The 40-kip (178 kN) load was applied in approximately 6
minutes and held for 2 minutes. The force versus time and displacement versus
time plots are shown in Figs. 4.16 and 4.17, respectively. It should be noted that
this test began after the material had already sustained 85 mils (2.16 mm) of
permanent displacement from the previous tests. Only 58 mils (1.47 mm) of
displacement were observed before the load was released as can been seen in the
load-settlement curve shown in Figure 4.18. The load was released in 2 minutes,
and the material was allowed to recover for 2 minutes. A permanent displacement
of approximately 38 mils (0.97 mm) was recorded at the conclusion of the test. A
cumulative permanent displacement of 123 mils (3.12 mm) was recorded from all
four tests at location A.
45
40
30
20
10
0
200
150
100
50
014121086420
Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Fig. 4.16. Variation of Force with Time; Test A4 - Loading to 40 kips (178 kN) in 6 Minutes Followed by Complete Unloading on Drier Material (Moisture Content ~ 4.7 %)
160
140
120
100
80
60
40
20
0
4
3
2
1
0
14121086420Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Fig. 4.17. Variation of Displacement with Time; Test A4 - Loading to 40 kips (178 kN) in 6 Minutes Followed by Complete Unloading on Drier Material (Moisture Content ~ 4.7 %)
160
140
120
100
80
60
40
20
0403020100
Force (kips)
4
3
2
1
0
200150100500Force (kN)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Fig. 4.18. Continuous Load-Settlement Curve from Test A4 - Loading to 40 kips (178 kN) in 6 Minutes Followed by Complete Unloading on Drier Material (Moisture Content ~ 4.7 %)
The effective stiffness, keff, was determined over three load ranges on the
loading portion of the load-settlement curve (AA4-CA4) and over two load ranges
on the unloading portion of the load-settlement curve (zones DA4-EA4) as shown
in Figure 4.19 and 4.20, respectively. It is postulated that the initial stiffness of
the material (AA4) was dominated by soil stiffening due to compression.
Secondary stiffness in the load range over which BA4 was determined, which was
between 5 and 18 kips (22.2 kN and 66.7 kN), was greater than that determined
during the load range for AA4. The material stiffness decreased with increased
loading [above 18 kips (66.7 kN)] and increased again upon initial unloading
(DA4) due to the presence of locked in horizontal stresses. Once the load was
completely released from the plate, the material stiffness again decreased (EA4). It
is thought that the material began to fail in shear as the vertical stress was
decreased, and the passive pressure exerted on the material by the locked-in
horizontal stresses exceeded the material shear strength.
46
160
140
120
100
80
60
40
20
0403020100
Force (kips)
4
3
2
1
0
200150100500Force (kN)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2
k =0.218 X 106lb/in.(0.038 X 106 kN/m)
AA4
BA4
CA4
Fig. 4.19. Load-Settlement Curve Annotated with Values of Relative Stiffness During Loading; Test A4 - Loading to 40 kips (178 kN) in 6 Minutes and Unloading to Zero on Drier Material (Moisture Content ~ 4.7 %)
160
140
120
100
80
60
40
20
0403020100
Force (kips)
4
3
2
1
0
200150100500Force (kN)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
keff = 0.428 X 106lb/in.(0.075 X 106 kN/m)
keff = 5.05 X 106lb/in.(0.88 X 106 kN/m)EA4
DA4
Fig. 4.20. Load-Settlement Curve Annotated with Values of Relative Stiffness During Unloading; Test A4 - Loading to 40 kips (178 kN) in 6 Minutes and Unloading to Zero on Drier Material (Moisture Content ~ 4.7 %)
4.6 Summary of Observations From Preliminary Plate-Load Tests
at Location A
Five observations were made from plate-load tests at location A which
were useful in establishing the test conditions for plate-load tests at locations B
and C. First, it was observed that although the crushed limestone material used to
construct the test pad is a granular material with non-plastic fines, it exhibited a
significant time-dependent deformation behavior under sustained load. This
observation aided in selecting the time increment for subsequent incremental
plate-load tests. Secondly, the material was observed to increase in stiffness after
a load of 1 to 3 kips (4.4 to 13.3 kN) was applied. This corresponds to a pressure
of 9.3 to 28 psi (64 to 193 kPa) under a 107 in.2 (690 cm2) plate. This is believed
to be the result of initial compression in the near-surface material. Thirdly,
softening of the material was observed at pressures exceeding 159 psi (1096 kPa).
Such pressures are above those normally experienced in pavement base courses. It
is expected that the material began to experience shear deformation at pressures
greater than 159 psi (1096 kPa). For this reason, the pressures selected for plate-
load tests at locations B and C were well below 159 psi (1096 kPa). The fourth
observation was that the slope of the unloading curve was nearly flat at the
beginning of unloading, but increased sharply once the load was almost
completely released. It is postulated that the material began to fail in shear under
passive pressures from locked in horizontal stresses. Finally it was observed that
the material began to stabilize with respect to displacement under cyclic load after
only 7 or 8 cycles of loading. It was observed, however, that the displacement
47
increased significantly with small increases in the applied load. The loading plate
continued to displace at a higher rate after only one cycle of increased load
magnitude was applied, followed by subsequent cycles of the previous smaller
load.
48
CHAPTER FIVE
PLATE-LOAD TESTS ON DRIER MATERIAL AT
LOCATION B ON THE TEST PAD
5.1 Introduction
One plate-load test was performed at location B on top of the second
lift on the Georgetown test pad (Fig. 2.6). The thickness of the aggregate base
under the test plate was 35 in. (89 cm). This test was a traditional,
incremental plate-load test with one cycle of loading to a maximum load
followed by unloading to zero. However, four subsets of unload-reload cycles
at various points within the overall cycle were also applied. No moisture was
added to the surface of the test pad before plate-load testing at location B, so
the moisture content was approximately 4.7 % as in the tests at location A.
5.2 Test B1 - Incremental Plate-Load Test from 0 to 8.3 kips
(36.9 kN) on Drier Material (Moisture Content ~ 4.7 %)
Five increments of loading and six increments of unloading were
applied to the plate over approximately 180 minutes at test location B. The
maximum load during the test was approximately 8.3 kips (36.9 kN). The
load versus time plot and the displacement versus time plot are shown in Figs.
5.1 and 5.2, respectively. A total displacement of approximately 50 mils (1.27
65
mm) was observed at the end of the loading sequence. A permanent
displacement of 35 mils (0.89 mm) was observed at the end of the test.
It can be seen in Fig. 5.1 that, at four different times during the test,
five cycles of unloading and reloading were delivered to the plate. The load
was decreased approximately 1 kip (4.4 kN) for each unloading cycle, and
increased 1 kip (4.4 kN) for each reloading cycle. The resulting continuous
load-settlement curve is shown in Fig. 5.3.
5.2.1 Adjusted Load-Settlement Curve from Test B1
The adjusted load-settlement curve shown in Fig. 5.4 was constructed
by determining the end-point displacement under each increment of loading
and unloading, and plotting this displacement against the average load for that
increment.
A seating load of approximately 1 kip (4.4 kN) was applied to the
loading plate and released to zero before the overall load sequence was started
as called for in AASHTO T222-81 (AASHTO, 1986). When, the seating load
was released, no additional seating load was applied before the first load
increment. This is a slight variation from the AASHTO procedure in that the
AASHTO procedure calls for application of one half of the original seating
load before zeroing the displacement sensors. For this test, the displacement
sensors were not zeroed. The complete load-settlement behavior, including
the seating load and resulting deformation, are included on the figures plotted
for this test.
66
10
8
6
4
2
0
40
30
20
10
0200150100500
Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)
Fig. 5.1. Variation of Force with Time; Test B1 - Incremental Plate-Load Test from 0 to 8.3 kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %)
60
50
40
30
20
10
0
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
200150100500Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)
Fig. 5.2. Variation of Displacement with Time; Test B1 - Incremental Plate-Load Test from 0 to 8.3 kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %)
60
50
40
30
20
10
01086420
Force (kips)
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
403020100Force (kN)
Plate Diameter: 12 in. (305 mm)
Fig. 5.3. Continuous Load-Settlement Curve; Test B1 - Incremental Plate-Load Test from 0 to 8.3 kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %)
50
40
30
20
10
01086420
Force (kips)
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
403020100
Force (kN)
Plate Diameter: 12 in. (305 mm)
After Seating Sequence Plotted at Ave. Load
Using the Displ. After 15 Min. for Each Load Increment
Fig. 5.4. Adjusted Load-Settlement Curve; Test B1 - Incremental Plate-Load Test from 0 to 8.3 kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %)
It can be seen in Fig. 5.4 that the seating sequence is denoted by a different
marker than the rest of the overall plate-load test.
It was observed that the load decreased slightly during the application
of each load increment as shown in Fig. 5.1. This was also previously
observed for tests at Location A. The loading mechanism of the RDD is
controlled by the pressure in the loading cylinders, and is capable of
compensating for creep in the test material. However, the feedback system
was not sensitive enough to compensate for the slight decreases in load
observed during plate-load testing. The loading mechanism also periodically
delivered a spike at the beginning of the load increment which affected the
instantaneous displacement of the plate. It is known that the duration of
load and the magnitude of the maximum load are both important in
determining the final displacement. However, by loading in nearly equal time
increments and taking the average load during each increment, it was hoped
that the effects of time and changing load magnitude could be minimized.
5.2.2 Plotting the Unload-Reload Loops on the Adjusted Load-
Settlement Curve from Test B1
Four groups of unload-reload loops were delivered to the loading plate
at different times during the overall plate-load test. Each loop was plotted
separately, and a linear curve-fit was performed on each loop. The average of
the slopes of the fitted lines was used to plot the unload-reload behavior for
each group on the adjusted load-settlement curve in Fig. 5.5. A straight-line
67
50
40
30
20
10
01086420
Force (kips)
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
403020100
Force (kN)
Plate Diameter: 12 in. (305 mm)
A B1
B B1
C B1
D B1
After Seating Sequence Plotted at Ave. Load
Using the Displ. After 15 Min. for Each Load Increment
Fig. 5.5. Adjusted Load-Settlement Curve With Unload-Reload Loops Plotted; Test B1 - Incremental Plate-Load Test from 0 to 8.3 kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %)
idealization of the unload-reload behavior was used to illustrate the load-
settlement behavior in the test pad material during application of the unload-
reload loops. The average stiffnesses are presented in Table 5.1. The
individual unload-reload loops with the linear curve-fits are plotted in
Appendix C along with the values used to calculate the average stiffness for
each group of unload-reload loops.
Table 5.1. Average Stiffnesses Measured at Various Loading Conditions for Cyclic Plate-Load Tests on Drier Material (Moisture Content ~ 4.7 %)
Unload-Reload Group 1
Mean Pressure Directly Under the Plate
Equivalent Spring Constant (Stiffness), keff , Under Cyclic
Unloading-Reloading (psi) (kPa) lb/in. kN/m
AB1 13.3 92 1.8 X 106 0.32 X 106 BB1 32.7 225 2.2 X 106 0.39 X 106 CB1 28.3 195 2.5 X 106 0.44 X 106 DB1 14.1 97 1.2 X106 0.21 X 106
1 From Fig. 5.5.
The linear idealizations of each of the four unload-reload groups as
described above are labeled AB1, BB1, CB1, and DB1 in Fig. 5.5. It can be
observed that two of the unload-reload groups were applied during the loading
phase of the plate-load test, and the other two unload-reload groups were
applied during the unloading phase of the test. Group CB1 was intentionally
applied near the load range in which BB1 was applied. Similarly, group DB1
was applied in the load range in which AB1 was applied. The load range on
68
the plate was approximately the same for the coupled groupings (AB1 and DB1
for one coupled grouping; and BB1 and CB1 for the other coupled grouping).
However, the state of stress in the material was higher upon unloading than
during loading for a given pressure on the loading plate. This increase in the
state of stress is due to horizontal stresses which remained locked-in the
material upon unloading. Careful selection of the load ranges for the
application of the unload-reload loops allowed observation of the change in
stiffness due to locked-in stresses.
The stiffnesses determined during the cyclic unload-reload groups can
be seen to increase slightly as the static load level increases. The average
stiffness of the test pad material under group CB1 is the largest stiffness
observed among the unload-reload groups. This is presumably because the
highest locked-in horizontal stresses were present in the material at this
loading condition.
It can be seen that cyclic stiffnesses determined during unloading are
greater than those determined during loading for coupled groups BB1 and CB1
which were applied at similar load ranges. This is the expected result of
locking in horizontal stresses during loading. The same behavior was not
observed for coupled groups AB1 and DB1 as would be expected. The
observation is offered without explanation because there seems to be no
evidence as to why this behavior is observed. It will be shown that in
subsequent tests at location C the material showed the expected behavior.
69
5.2.3 Stiffness of the Test Pad Material as Determined from the
Overall Plate-Load Test
The adjusted load-settlement curve from Fig. 5.4 is re-plotted in Fig.
5.6 with annotations of three relative stiffness measurements which are
labeled EB1, FB1, and GB1. These stiffness measurements may be considered
the “long-term” stiffness of the material, while the stiffnesses determined with
unloading-reloading loops AB1 through DB1 may be considered the “short-
term” stiffness of the material. The measured overall stiffness values are
presented in Table 5.2.
Table 5.2. Overall Stiffnesses Measured Over Various Ranges of Loading for Static Plate-Load Tests on Drier Material (Moisture Content ~ 4.7 %)
Range for Determining Overall Stiffness 2
Overall Equivalent Spring Constant (Stiffness), keff, Under Static Loading and Unloading
lb/in. kN/m EB1 0.184 X 106 0.032 X 106 FB1 2.15 X 106 0.38 X 106 GB1 0.188 X 106 0.033 X 106
2 As shown in Fig. 5.6.
It was observed that the overall stiffness upon initial unloading (FB1)
was greater than for any other part of the overall loading or unloading curves
(EB1 or GB1). The stiffness upon initial unloading is similar to the stiffnesses
70
50
40
30
20
10
01086420
Force (kips)
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
403020100
Force (kN)
Plate Diameter: 12 in. (305 mm)
E B1
F B1
G B1
After Seating Sequence Plotted at Ave. Load
Using the Displ. After 15 Min. for Each Load Increment
Fig. 5.6. Adjusted Load-Settlement Curve With Relative Stiffnesses During Loading and Unloading Annotated; Test B1 - Incremental Plate-Load Test from 0 to 8.3 kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7
measured under the cyclic unloading-reloading groups. This is the expected
behavior resulting from locked-in horizontal stresses.
The stiffness upon final unloading (GB1) was the lowest overall
stiffnesses recorded. It is surprising that the material became softer during
unloading (GB1) than it had been during initial loading (EB1) after having been
compressed under a load of 8.3 kips (36.9 kN). It is hypothesized that
horizontal stresses are locked into the material during loading, and that when
the vertical stress due to load on the plate is decreased sufficiently, the
material begins to fail under the passive pressure from the locked-in
horizontal stresses. As the material particles begin to rearrange, shear
deformation occurs, and the apparent stiffness of the material decreases.
5.2.4 Presentation of Cyclic Stiffness and Overall Stiffness
Measurements
The average stiffnesses at each load condition at which unload-reload
cycles were applied in the incremental plate-load test are shown on a bar chart
in Fig. 5.7. The overall (“long-term”) stiffnesses during loading and
unloading are also shown with the cyclic stiffness values on the bar chart in
Fig. 5.7.
It can be seen that the small-strain cyclic stiffnesses measured from the
plate-load tests are greater than the overall stiffnesses. This is partially the
result of having greater strain amplitude in the overall test than in the small-
amplitude cyclic unload-reload loops. However, the time-dependent
71
2.5x106
2.0
1.5
1.0
0.5
0.01.5 3.7 3.2 1.6
Force on Plate, kips (kN)
400x103
300
200
100
0
AB1
BB1
CB1
DB1
Loading
LoadingUnloading
Unloading
(6.7) (16.5) (14.2) (7.1)
EB1
FB1
GB1Loading
Unloading
Unloading
Fig. 5.7. Representation of Stiffness with Varying Degrees of Load on the Loading Plate; Test B1 - Incremental Plate-Load Test from 0 to 8.3 kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %)
deflection behavior of the unbound base course was a more significant factor
in determining the stiffness during plate-load testing than the strain amplitude
was.
5.2.5 Calculation of Modulus of Soil Reaction, ku’, for Drier
Material (Moisture Content ~ 4.7 %)
The modulus of soil reaction, ku’ is determined from plate-load tests
according to AASHTO (1986) by measuring the displacement of the loading
plate under a loading pressure of 10 psi (69.0 kPa) and dividing the loading
pressure by the deflection. This procedure is described in Section 3.4.1. It
should be noted that the AASHTO procedure requires that the instruments for
measuring displacement be zeroed after application of the seating load.
Therefore, in this test, the seating load displacement was subtracted from the
displacement measured at 10 psi (69.0 kPa) in Fig. 6.4. The modulus of soil
reaction, ku’, for the drier material (w ~ 4.7 %) in Test B1 was determined to
be 2141 psi/in. (581 kPa/mm).
5.3 Summary of Observations from Incremental Plate-Load
Test on Drier Material (Moisture Content ~ 4.7 %) at
Location B
It can be observed from the results of cyclic plate-load tests at location
B that the cyclic stiffness of the material increases significantly with
increasing pressure on the loading plate. However, the overall static stiffness
72
73
of the material remained relatively constant throughout the loading cycle. It is
believed that increasing the loading pressure increases the degree to which
horizontal stresses are locked into the material. The effect of locking in
horizontal stresses on the overall stiffness of the test pad material was also
observed upon static unloading. It can be seen that the overall stiffness at the
beginning of rebound (FB1) is much greater than the stiffness during loading
(EB1) at the same pressure. The same result was observed to be true for both
the cyclic unload-reload stiffnesses (AB1 through DB1) and for the overall
static stiffness upon unloading (FB1).
These results restate the importance of maintaining confining pressure
on unbound granular materials during loading. In a pavement system, this is
accomplished through the use of shoulders on the edge of the pavement which
help maintain a higher horizontal stress state. The significance of locking in
horizontal stresses during loading or during compaction is illustrated in these
observations.
CHAPTER SIX
PLATE-LOAD TESTS ON WETTER MATERIAL AT
LOCATION C ON THE TEST PAD
6.1 Introduction
As with plate-load tests described in Chapters 4 and 5, plate-load tests
were conducted at location C on top of lift two of the Georgetown test pad. The
thickness of aggregate base under the test plate was 35 in. (89 cm). The base
course material was wetted from the surface before seismic or plate-load tests
were conducted at location C by first placing a 48 in. (122 cm) diameter by 24 in.
(61 cm) high steel ring on the pad over the test site and sealing around the bottom
with hydrostone. The ring was filled with water and the surrounding area was
soaked three to four times over the two-day period preceding the plate-load and
seismic tests. Surface moisture content measurements made on specimens
collected before and after wetting indicated a 1.5 % increase in moisture content
in the top 3-4 in. (8-10 cm) of the material due to wetting from the surface. The
near-surface moisture content was 6.1 % after wetting. This value was confirmed
by corrected nuclear density gauge (NDG) readings. A 1.2 % increase in moisture
content at a depth of 12 in. (31 cm) was observed (yielding w ~ 5.5 %) as
calculated from the corrected NDG readings previously reported in Tables 2.3 and
2.4.
81
Two tests were performed at location C to compare the deformation of a
wetter base course material to that of the same material in a drier state. The
loading cycles in the tests at location C were closely matched with the loading
cycles from two previous tests in order to observe the effects of wetting the
unbound base course. The loading cycle for Test C1 which was performed on the
wetter material (w ~ 6.1 %) was similar to the loading cycle for Test B1 which
was performed on the drier material (w ~ 4.7 %). The loading cycle for Test C2
(wetter material) was similar to the loading cycle for Test A3 (drier material).
6.2 Test C1 - Incremental Plate-Load Test from 0 to 8.6 kips (38.3
kN) on Wetter Material (Moisture Content ~ 6.1%)
Five increments of loading and four increments of unloading were applied
to the loading plate over a period of 200 minutes in the incremental plate-load test
at location C. The maximum force applied to the plate during the test was
approximately 8.6 kips (38.3 kN). This loading sequence is shown in the force
versus time and displacement versus time plots in Figs. 6.1 and 6.2, respectively.
A displacement of 90 mils (2.29 mm) was observed at the conclusion of the
loading cycle. A permanent displacement of 68 mils (1.73 mm) was recorded 15
minutes after the load was decreased to zero.
It can be seen in Fig. 6.1 that groups of unload-reload cycles were applied
to the loading plate at five different times during the overall plate-load test. Five
unload-reload cycles were applied for each group. The load was decreased
approximately 1 kip (4.4 kN) for each unloading cycle and increased 1 kip (4.4
82
10
8
6
4
2
0
40
30
20
10
0200150100500
Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)
Fig. 6.1. Variation of Force with Time; Test C1 - Incremental Plate-Load Test from 0 to 8.6 kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)
100
80
60
40
20
0
2.5
2.0
1.5
1.0
0.5
0.0
200150100500Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)
Fig. 6.2. Variation of Displacement with Time; Test C1 - Incremental Plate-Load Test from 0 to 8.6 kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)
kN) for each reloading cycle. The resulting continuous load-settlement curve is
shown in Fig. 6.3.
6.2.1 Adjusted Load-Settlement Curve from Test C1
The end-point displacement for each load increment was plotted against
the average load for the increment as described in Section 5.2.1 for Test B1. This
approach simply “adjusts for” or minimizes the effect of creep on the load-
settlement curve. It can be seen from both the force versus time plot in Fig. 6.1
and the continuous load-settlement plot in Fig. 6.3 that the load decreased slightly
during each increment of loading. This behavior is the same behavior observed in
the previous tests. The adjusted load-settlement curve plotted with the average
load values is shown in Fig. 6.4.
As in Test B1, a seating load of approximately 1000 lb (4.4 kN) was
applied to the loading plate and released before the overall load sequence was
started as called for in AASHTO T222-81 (1986). The seating load was
completely released, and no additional seating load was applied before the first
load increment. This is a slight variation from the AASHTO procedure in that the
AASHTO procedure calls for application of one half of the original seating load
before zeroing the displacement sensors. For this test, the displacement sensors
were not zeroed. The complete load-settlement behavior, including the seating
load and resulting deformation, are included on the figures plotted for this test. It
can be seen in Fig. 6.4 that the seating sequence is denoted by a different marker
than the rest of the overall plate-load test.
83
100
80
60
40
20
01086420
Force (kips)
2.5
2.0
1.5
1.0
0.5
0.0
403020100Force (kN)
Plate Diameter: 12 in. (305 mm)
Fig. 6.3. Continuous Load-Settlement Curve; Test C1 - Incremental Plate-Load Test from 0 to 8.6 kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)
100
80
60
40
20
01086420
Force (kips)
2.5
2.0
1.5
1.0
0.5
0.0
403020100
Force (kN)
Plate Diameter 12 in. (305 mm)
After Seating Sequence Plotted at Ave. Load
Using the Displ. After 15 Min. for Each Load Increment
Fig. 6.4. Adjusted Load-Settlement Curve; Test C1 - Incremental Plate-Load Test from 0 to 8.6 kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)
6.2.2 Plotting the Unload-Reload Loops on the Adjusted Load-
Settlement Curve from Test C1
Five groups of unload-reload cycles were delivered to the plate at different
load conditions during the overall plate-load test. Three of the five groups were
applied during the loading phase of the overall plate-load test, and the other two
groups were applied during the unloading phase of the overall plate-load test. For
each unload-reload cycle, the load was decreased or increased approximately
1000 lb (4.4 kN).
The loops were plotted individually, and a linear curve-fit was performed
on each loop. The average of the slopes of the fitted lines was used to plot the
unload-reload behavior for each group on the adjusted load-settlement curve in
Fig. 6.5. A straight-line idealization of the unload-reload behavior was used to
illustrate the load-settlement behavior in the test pad material during application
of the unload-reload loops. The unload-reload groups are labeled AC1, BC1, CC1,
DC1, and EC1 on the adjusted load-settlement curve in Fig. 6.5. The stiffnesses for
each group of unload-reload loops are presented in Table 6.1. The individual
loops are shown in Appendix D. The stiffness values for each individual loop are
also presented in tabular form in Appendix D.
84
100
80
60
40
20
01086420
Force (kips)
2.5
2.0
1.5
1.0
0.5
0.0
403020100
Force (kN)
BC1
AC1
CC1DC1EC1
Plate Diameter 12 in. (30.5 cm)
After Seating Sequence Plotted at Ave. Load
Using the Displ. After 15 Min. for Each Load Increment
Fig. 6.5. Adjusted Load-Settlement Curve With Unload-Reload Loops Plotted; Test C1 - Incremental Plate-Load Test from 0 to 8.6 kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)
Table 6.1. Average Stiffnesses Measured During Small Amplitude Unload-Reload Loops at Various Loading Conditions for Cyclic Plate-Load Tests on Wetter Material (Moisture Content ~ 6.1 %)
Unload-Reload Group 1
Mean Pressure Directly Under the Plate
Equivalent Spring Constant (Stiffness), keff, Under Cyclic
Unloading-Reloading (psi) (kPa) lb/in. kN/m
AC1 19.5 134 0.90 X 106 0.16 X 106 BC1 32.7 225 2.3 X106 0.40 X 106 CC1 71.6 494 14 X 106 2.5 X 106 DC1 31.8 219 3.0 X 106 0.53 X 106 EC1 20.3 140 2.7 X 106 0.47 X 106
1 From Fig. 6.5.
The unload-reload groups in this test were coupled as described in Section
5.2.2 for Test B1. Group EC1 was applied near the load range used for group AC1.
Group DC1 was applied near the load range used for group BC1. The load range on
the plate was approximately the same for the coupled groups (AC1 and EC1 for one
coupled group; and BC1 and DC1 for the other coupled group). However, the state
of stress in the material was higher upon unloading than during loading for a
given pressure on the loading plate due to the stiffening effect of locked-in
horizontal stresses. It can be seen that cyclic stiffnesses determined during
unloading are greater than those determined during loading despite the fact that
the load on the plate is approximately the same for a coupled group. This has been
observed for coupled groups AC1 and EC1 and for coupled groups BC1 and DC1 and
is the expected result of stiffening due to locked-in horizontal stresses.
85
The stiffnesses determined during the application of cyclic unload-reload
groups increased slightly as the static load level increased which was the same
behavior observed during Test B1. The average stiffness of the test pad material
under cyclic unload-reload group CB1 is significantly larger than for any other
group. It is presumed that the highest locked-in horizontal stresses were present in
the material at this loading condition. However, it is not apparent why the
stiffness at this loading condition is almost 5 times greater than the next largest
stiffness which was measured from group DC1.
6.2.3 Stiffness of the Test Pad Material as Determined from the
Overall Plate-Load Test
The adjusted overall load-settlement curve from Fig. 6.4 is re-plotted with
annotations of four relative stiffness measurements which are labeled FC1, GC1,
HC1, and IC1 in Fig. 6.6. These stiffness measurements may be considered the
“long-term” stiffness of the material, while the stiffnesses determined from
unload-reload loops AC1 through EC1 may be considered the “short-term” stiffness
of the material. The overall stiffness values are presented in Table 6.2.
86
100
80
60
40
20
01086420
Force (kips)
2.5
2.0
1.5
1.0
0.5
0.0
403020100
Force (kN)
FC1
GC1
HC1
IC1
Plate Diameter 12 in. (305 mm)
After Seating Sequence Plotted at Ave. Load
Using the Displ. After 15 Min. for Each Load Increment
Fig. 6.6. Adjusted Load-Settlement Curve with Relative Stiffnesses During Loading and Unloading Annotated; Test C1 - Incremental Plate-Load Test from 0 to 8.6 kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)
Table 6.2. Overall Stiffnesses Measured Over Various Ranges of Loading for Static Plate-Load Tests on Wetter Material (Moisture Content ~ 6.1 %)
Range for Determining Overall Stiffness 2
Overall Equivalent Spring Constant (Stiffness), keff, Under Static Loading and Unloading
lb/in. kN/m FC1 0.092 X 106 0.016 X 106 GC1 0.14 X 106 0.025 X 106 HC1 1.2 X 106 0.21 X 106 IC1 0.10 X 106 0.018 X 106
2 As shown in Fig. 6.6.
It was also observed that the overall stiffness upon initial unloading (HC1)
was greater than for any other part of the overall loading or unloading curves
(FC1, GC1, or IC1). The stiffness upon initial unloading is similar to the stiffnesses
measured under the cyclic unload-reload groups. This is, again, the expected
behavior resulting from locked-in horizontal stresses.
The stiffness upon initial loading (FC1) and the stiffness upon final
unloading (IC1) were the lowest overall stiffnesses recorded. The initial loading
(FC1) and final unloading (IC1) curves can be seen to be approximately parallel in
Fig. 6.6 indicating equal stiffness under these two loading conditions.
6.2.4 Presentation of Cyclic Stiffness and Overall Stiffness
Measurements
The average stiffnesses at each load condition at which unload-reload
cycles were applied in the incremental plate-load test are shown on a bar chart in
87
Fig. 6.7. The overall (“long-term”) stiffnesses during loading and unloading are
shown with the cyclic stiffness values on the bar chart in Fig. 6.7.
It was observed in Test B1 and again here in Test C1 that the small-strain
cyclic stiffnesses measured from the plate-load tests are greater than the overall
stiffnesses. This result can be partially accounted for because the strain amplitude
in the overall test is greater than that in the small-amplitude cyclic unload-reload
loops. However, the time-dependent deflection behavior of the unbound base
course appears to have a more significant effect on the stiffness of the material
than the strain amplitude does.
6.2.5 Calculation of Modulus of Soil Reaction, ku’, for Wetter
Material (Moisture Content ~ 6.1 %)
The modulus of soil reaction, ku’, is determined from plate-load tests
according to AASHTO (1986) by measuring the displacement of the loading plate
under a loading pressure of 10 psi (69.0 kPa) and dividing the loading pressure by
the deflection. This procedure is described in Section 3.4.1. It should be noted
that the AASHTO procedure requires that instruments for measuring
displacement are zeroed after application of the seating load. Therefore, in this
test, the seating load displacement was subtracted from the displacement
measured at 10 psi (69.0 kPa) in Fig. 6.4. The modulus of soil reaction, ku’, for
the wetter material (w ~ 6.1 %) in Test C1 was determined to be 635 psi/in. (172
kPa/mm).
88
16x106
14
12
10
8
6
4
2
02.2 3.9 8.1 3.6 2.3
Force on Plate, kips (kN)
2.5x106
2.0
1.5
1.0
0.5
0.0
AC1
BC1
CC1
DC1
EC1
Loading
Loading
Loading
UnloadingUnloading
FC1 GC1
HC1IC1
Loading Loading UnloadingUnloading
(9.8) (17.3) (36.0) (16.0) (10.2)
Fig. 6.7. Representation of Stiffness with Varying Degrees of Load on the Loading Plate; Test C1 - Incremental Plate-Load Test from 0 to 8.6 kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)
6.3. Test C2 - 5 Cycles of 0 to 8 kips (35.6 kN) in 7 Minutes on
Wetter Material (Moisture Content ~ 6.1%)
Five cycles of approximately 8 kips (35.6 kN) each were applied to the
plate during the second test at location C. Each complete cycle was applied and
released over a period of 1.5 to 2 minutes as shown on the force versus time and
displacement versus time plots in Fig 6.8 and 6.9, respectively. This loading
sequence was similar to that of plate-load Test A3 in which 32 cycles of load
were applied to the plate in 20 minutes. As with the previous tests, load-
settlement data were collected continuously and are plotted in Fig. 6.10. A bi-
linear stiffness relationship was observed on four of the five loops similar to that
seen in Test A3. Each loop was plotted separately, and the stiffness was recorded
for the initial part of the loading curve and for the final part of the loading curve.
The stiffness values are plotted for comparison in Fig. 6.11, and the individual
loops are shown in Appendix E.
It was observed that the deformational behavior under cyclic loading
stabilized after a relatively few number of cycles. The cyclic loops began to plot
on top of one another when the load range and rate of loading were nearly
constant. Loops 4 and 5 from Test C2 are plotted in Fig. 6.12 to illustrate this
observation. This is an important finding, because it indicates that far less
permanent deformation due to volume change is occurring once the material is
conditioned (from previous loading during Test C1). No stiffnesses during
unloading are presented for Test C2. However, general behavior similar to that
observed in Test A3 was observed for Test C2.
89
10
8
6
4
2
0
40
30
20
10
0121086420
Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)
Fig. 6.8. Variation of Force with Time; Test C2 - 5 Cycles of 0 to 8 kips (35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%)
30
25
20
15
10
5
0
0.8
0.6
0.4
0.2
0.0
121086420Elapsed Time (minutes)
Plate Diameter: 12 in. (305 mm)
Fig. 6.9. Variation of Displacement with Time; Test C2 - 5 Cycles of 0 to 8 kips (35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%)
30
25
20
15
10
5
01086420
Force (kips)
0.8
0.6
0.4
0.2
0.0
403020100Force (kN)
Plate Diameter: 12 in. (305 mm)
Fig. 6.10. Continuous Load-Settlement Curve; Test C2 - 5 Cycles of 0 to 8 kips (35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%)
700x103
600
500
400
300
200
10054321
Cycle Number
120x103
100
80
60
40
20
Stiffness During Initial Loading Stiffness During Final Loading
Fig. 6.11. Bi-Linear Stiffnesses of Each Cyclic Loop in the Loading Section; Test C2 - 5 Cycles of 0 to 8 kips (35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%)
30
25
20
15
10
5
086420
Force (kips)
0.6
0.4
0.2
0.0
403020100Force (kN)
Loop 4
Loop 5
Fig. 6.12. Illustration of Stabilization or Closing of Cyclic Loops; Test C2 - 5 Cycles of 0 to 8 kips (35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%)
6.4 Summary of Observations from Incremental Plate-Load Tests
on Wetter Material (Moisture Content ~ 6.1 %) at Location C
It was observed that increasing the moisture content in situ had significant
softening effects on the granular base course material used to construct the test
pad. The average near-surface moisture content increased from 4.7% (drier
material) to 6.1% (wetter material) as a result of wetting the test pad material
prior to performing these tests.
A 70% increase in the total displacement was observed between the
incremental plate-load test on the drier material (Test B1) and the incremental
plate-load test on the wetter material (Test C1) after wetting the test pad from the
surface. This increase was determined by taking the difference between the
observed displacement in Test B1 on the drier material (w ~ 4.7 %) and Test C1
on the wetter material (w ~ 6.1 %). The load on the plate was approximately equal
for the two tests [8.3 kips (36.9 kN) for Test B1 on the drier material and 8.6 kips
(38.3 kN) for Test C1 on the wetter material].
The most significant decrease in overall stiffness due to wetting the
material was observed during the incremental plate-load test with low load on the
plate. The stiffness of the drier material was approximately two times the stiffness
of the wetter material at loads below 2.7 kips (12.0 kN) as can be observed from
the slope of the initial loading curves for incremental plate-load Tests B1 and C1
(Figs. 5.4 and 6.4 respectively). The initial overall stiffness for Test B1 (EB1, drier
material, w ~ 4.7%) was observed to be 0.184 X 106 lb/in. (0.032 X 106 kN/m).
The initial overall stiffness for Test C1 (FC1, wetter material, w = 6.1%) was
90
observed to be 0.092 X 106 lb/in. (0.016 X 106 kN/m) which is half of the
stiffness observed for the drier material. Once the load increased above 2.7 kips
(12.0 kN), the difference in stiffness between the wetter material and the drier
material was less significant. The overall stiffness upon initial unloading also
differed by a factor of two between the wetter test and the drier test.
It was observed that the stiffness during initial loading (FC1) and the
stiffness during final unloading (IC1) were similar. However, at higher loads on
the plate, the stiffness during unloading (GC1) was greater than the stiffness
during loading (HC1).
Decreases in stiffness were also observed under cyclic loading between
Test A3 (drier material, w ~ 4.7 %) and Test C2 (wetter material, w ~ 6.1 %).
Detailed comparison of the stiffness measurements among the tests is included in
Chapter 8.
91
CHAPTER SEVEN
SEISMIC TESTING AND STIFFNESS EVALUATIONS
7.1 Overview
Seismic testing was conducted to determine the small-strain stiffness
of the test pad material in-situ. The Spectral-Analysis-of-Surface-Waves
(SASW) technique was chosen because it is non-invasive and allows
characterization of the material at varying depths. SASW testing produces a
profile of shear wave velocity with depth which can then be related to the
shear modulus and Young’s modulus (which equals resilient modulus at small
strains), and equivalent stiffness of the material as discussed below.
7.2 SASW Testing
SASW testing was performed by applying a transient excitation to the
surface of the aggregate test pad with a hammer. Receivers placed on the
surface of the test pad in a linear array were used to measure the velocity of
Raleigh-type surface waves passing between the receivers. This general
arrangement is illustrated in Fig. 7.1. The tests were conducted with the
receivers placed at various spacings in the linear array which allowed
sampling of a range of depths in the test pad. Through a forward modeling
procedure, a profile of shear wave velocity with depth was obtained. A
105
complete discussion of the SASW procedure for use in characterizing
geotechnical materials can be found in Stokoe et al. (1994).
RecordingEquipment
Receiver 2Receiver 1
ActiveSource
d1
d2
Fig. 7.1. Basic Configuration for SASW Testing (from Stokoe et al. 1994)
7.3 Non-Linear Moduli
It can be shown that material stiffness in shear decreases with
increasing strain amplitude as illustrated in Figs. 7.2 and 7.3. Small-strain
shear moduli below 0.001 % strain are considered to be independent of strain
amplitude. These shear moduli are typically denoted as Gmax or G0. Because
106
the SASW procedure produces strains in the material less than 0.001 %, the
shear modulus obtained from these tests is independent of strain amplitude.
.
Shea
ring
Stre
ss, t
Shearing Strain, γ, %
GmaxG1 G2 G3 G4
MonotonicLoading Curve
00.05 0.10 0.150
Fig. 7.2. Relationship between the Monotonic Loading Curve and Material Stiffness in Shear of a Geotechnical Material
107
Gmax
10-3 10-2 10-110-40
gte=
G2
G3G4
G1
1
Nc = 1 cycleso = Constant
threshold strain below which Young's modulus is constant
10-5
Strains Generatedin Field Seismic Tests
Shearing Strain, γ, percent
Shea
r Mod
ulus
, G
Fig. 7.3. Variation in Material Stiffness in Shear with Increasing Strain Amplitude as Determined from Fig. 7.2
This range of strain amplitude (< 0.001%) is referred to as the linear or small-
amplitude range. There is evidence to suggest that, many times, strains under
working loads in geotechnical materials are also within the small-strain range
(Burland 1989). Of course, the strain amplitude depends on the conditions of
loading and the proximity to the load point or loaded area. It is important to
have a good idea of the strain amplitude being produced in the material under
observation so that the appropriate modulus can be used in characterizing the
material. A discussion of the relative magnitude of strains induced in the
seismic tests and the plate-load tests in the Georgetown, Texas test pad is
included in Chapter 8.
108
7.4 Determination of Small-Strain Shear Modulus
Shear modulus is defined as the shearing stress divided by the shearing
strain. The small-strain shear modulus, Gmax, may be determined from shear
wave velocity measurements according to the following relationship:
Gmax = ρVs2 .............................................................. (7.1)
where Gmax = small-strain shear modulus,
ρ = mass density (total density divided by acceleration due to
gravity), and
Vs = shear wave velocity.
7.5 Determination of Small-Strain Equivalent Spring Constant
The stiffness of the material may be described in terms of an
equivalent spring constant, keff, which is represented in units of force divided
by units of length (displacement). The theoretical equivalent spring constant
(stiffness) of a geotechnical material experiencing a uniform load under a
circular plate is defined in terms of the shear modulus as shown below:
109
keff = 4Gro/(1-ν) ........................................................ (7.2)
where keff = equivalent spring constant,
G = shear modulus,
ro = radius of plate, and
ν = Poisson’s ratio.
If the strains in the material beneath the plate are in the small-strain
range, then G in Eq. 7.2 is simply Gmax. The relationship between Vs (hence
Gmax) and keff expressed by Eq. 7.2 is presented graphically in Fig 7.4 for an
average total unit weight of 138 lb/ft3 (21.7 kN/m3), a plate radius of 0.5 ft
(15.2 cm) and a small-strain Poisson’s ratio of the material (granular base) of
0.25.
110
8
7
6
5
4
3
2
1
02500200015001000500
Shear Wave Velocity (VS), ft/sec
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
800600400200
Shear Wave Velocity (VS), m/sec
γ = 138 lb/ft 3
ro = 0.5 ftν = 0.25
Fig. 7.4. Equivalent Spring Constant, keff, Determined from Shear Wave Velocity for Strain Amplitudes in the Small-Strain Range
7.6 Shear Wave Velocity Profiles
SASW testing and the associated data reduction produces a profile of
shear wave velocity with depth in the material being tested. Two such velocity
profiles for the Georgetown test pad at the plate-load test locations are shown
in Figs. 7.5 and 7.6. The shear wave velocity profile for the drier material (w ~
4.7 %) is shown in Fig. 7.5 and the shear wave velocity profile for the wetter
material (w ~ 6.1 %) is shown in Fig. 7.6.
111
30
20
10
0
-10
-20
150010005000
Shear Wave Velocity, Vs, ft./sec
50
40
30
20
10
0
5004003002001000
Shear Wave Velocity, Vs, m/sec
Subgrade
Lift 1
Lift 2
Fig. 7.5. Shear Wave Velocity Profile of the Test Pad for the Drier Material (w ~ 4.7 %)
30
20
10
0
-10
-20
150010005000
Shear Wave Velocity, Vs, ft./sec
50
40
30
20
10
0
5004003002001000
Shear Wave Velocity, Vs, m/sec
Lift 1
Subgrade
Lift 2
Fig. 7.6. Shear Wave Velocity Profile of the Test Pad for the Wetter Material (w ~ 6.1 %)
112
The near-surface material [depth < 5 in. (12.7 cm)] in a wetter state
can be seen to be much softer than the near-surface material in a drier state as
shown in Figs. 7.5 and 7.6. The wetter material at a depth of 5 to 12 in. (12.7
to 30.5 cm) is only slightly softer than the drier material at the same depth.
Below a depth of 12 in. (30.5 cm), the small-strain shear stiffness is the same
for both materials (wetter state and drier state).
It can be observed from Fig. 7.6 that the near surface material in the
wetter state [depth < 5 in. (12.7 cm)] is considerably less stiff than the deeper
material. This is not true of the material in a drier state as observed in Fig. 7.5.
It is believed that the negative capillary stresses in the drier material had a
stiffening effect on the material. It was also observed that the increase in
stiffness due to negative capillary stresses causes the stiffness of the near-
surface material to be even greater than the stiffness of the material at a depth
of 5 in. (12.7 cm) for the drier material.
113
7.7 Measured Small-Strain Stiffness
The small-strain equivalent spring constant was calculated from the
shear wave velocity for both the drier and wetter material under the condition
of no external (surface) load. The stiffness was calculated using the average
shear wave velocity in the top 12 in. (30.5 cm) (one plate diameter) of the test
pad. The small-strain equivalent spring constants are presented in Table 7.1. Table 7.1. Average small-strain stiffness for an effective depth of 12 in. (30.5 cm) (one plate diameter)
Material Moisture Condition
Average Shear Wave Velocity, Vs
Small-Strain Equivalent Spring Constant, k
(Stiffness) ft/sec m/sec lb/in. kN/m
Drier (w ~ 4.7 %) 1300 396 1.7 X 106 0.30 X 106 Wetter (w ~ 6.1 %) 900 274 0.79 X 106 0.14 X 106
The material near the surface exhibited more than a 50% reduction in
stiffness due to the wetting as shown by the SASW data. This reduction in
stiffness was not detected by changes in density. The average value of the
density for the drier material is 131 pcf (20.6 kN/m3), and the average density
of the wetter material is 135 pcf (21.2 kN/m3). This change in density is small
compared to the change in seismic stiffness. In addition, the measurement of
dry density depends on measurement of the moisture content which is only a
rough estimate of the actual moisture content of the material when measured
with the NDG.
114
115
7.8 Adjustment to the Small-Strain Stiffness for Variations in
the State of Stress
The state of stress in compacted granular materials depends on a
number of factors which include the effective horizontal state of stress and the
effect of negative capillary stresses. The development of negative capillary
stresses produces an all-around increase in the state of stress; the process of
compaction locks in horizontal stresses of unknown magnitude; and finally,
increases in the vertical load produce increases in the state of stress.
The only variable mentioned above which was measured in this study
was the vertical load. Quantifying increases in the state of stress due to
locked-in horizontal stresses is difficult and was not attempted in this study. It
has been shown, however, that locked-in horizontal stresses can exceed the
vertical overburden stress. Negative capillary stresses can also have a very
significant impact on the state of stress at low levels of vertical effective
stress. However, negative capillary stresses were also not evaluated. The
application of a vertical load on a circular plate also produces a stress
distribution under the plate which varies with depth from the surface which
was only estimated in this study.
CHAPTER EIGHT
COMPARISON OF STIFFNESS VALUES FROM PLATE-
LOAD AND SEISMIC TESTS
8.1 Introduction
The stiffness measurements made in plate-load and seismic tests are
compared and discussed in this chapter. This discussion is divided into two
major categories: small-strain comparisons and large strain comparisons. A
method for determining strain amplitude, and an explanation of the reduction
in shear modulus for increasing strain amplitude are discussed before the
small and large strain comparisons are presented.
8.1.1 Estimation of Strain Amplitude
Comparison of seismic and working-load stiffness measurements for
the purpose of predicting displacement requires evaluating the strain
amplitudes generated in SASW and plate-load testing. The shearing strain
produced during seismic testing is less than 0.001% as discussed in Chapter 7.
The modulus of the material is well within the linear range at these levels of
strain. No measurement of internal displacements were made below the plate
during plate-load tests. However, vertical strains can be estimated from
115
measured vertical displacements of the plate if an effective depth of influence
is assumed.
A procedure for estimating the strain distribution in granular material
under the center of a loaded circular plate was developed by Schmertmann
(1970). The strain estimation consists of a bi-linear idealization of the
distribution of strain with depth as shown in Fig. 8.1. The effective depth is
assumed to be two plate diameters, with the maximum strain occurring at a
depth of 0.5 diameter. The strain influence factor Iz from Fig. 8.1 is used in
Eq. 8.1 to estimate vertical strain at any depth under the center of the plate:
εv = Iz (q/Es) ..............................................................(8.1)
where:
εv = vertical normal strain,
Iz = influence factor,
q = applied pressure at the surface, and
Es = Young’s modulus of the granular base material.
116
2.0
1.5
1.0
0.5
0.0
0.70.60.50.40.30.20.10.0
Vertical Strain Influence Factor, IZ Fig. 8.1. Variation of Vertical Normal Strain with Depth Beneath a Circular Plate on Sand after Schmertmann (1970)
8.1.2 Adjustments to Small-Strain Shear Modului for Increase
in Strain Amplitude and Increase in State of Stress
Young’s modulus of the material is estimated from the stiffness
measurements back-calculated from the plate-load tests. The equivalent
spring constant, keff, at small strains, is evaluated from the average slope of
the unload-reload loops at each general load zone. The equivalent spring
117
constant is related to the shear modulus, G, by the expression shown in Eq.
7.2. Young’s modulus can then be determined from the shear modulus as
shown in Eq. 8.2.
E = k(1+ν)(1-ν)/2r0 ................................................... (8.2)
where:
E = Young’s modulus,
k = equivalent spring constant,
ν = Poisson’s ratio, and
r0 = radius of the plate.
An average curve illustrating the reduction in normalized shear
modulus with increasing shearing strain amplitude for sands (Seed et al.,
1987) is shown in Fig. 8.2. It is recognized from Fig. 8.2 that stiffnesses
evaluated by seismic tests may be slightly greater than the stiffness of a
granular base course material under working loads due to the fact that
working load strains may be somewhat above the boundary which defines the
linear range of stiffness (γ = 0.001%).
118
1.2
1.0
0.8
0.6
0.4
0.2
0.010-5 10-4 10-3 10-2 10-1 100
Shearing Strain, γ, %
Seed et al. (1986) (For Sands) Range Mean
Fig. 8.2. Illustration of the Reduction in Shear Modulus with Increases in Strain Amplitude
A second factor affecting the measured stiffness between the seismic
tests and the plate-load tests is that they are determined at different states of
stress. The initial state of stress during seismic testing is due to the weight of
the material, locked-in horizontal stresses, and negative capillary stresses.
The initial state of stress in the plate-load test includes a significant additional
vertical stress from loading of the plate. As a result, the material becomes
stiffer under plate-loading due to the increased confinement of the material.
119
The effects of strain amplitude and vertical effective stress counteract
one another in this case, but they do not have equal influences. For this
reason, each factor must be accounted for separately.
8.2 Small-Strain Stiffness Comparisons
Spectral-Analysis-of-Surface-Waves (SASW) tests yielded profiles of
shear wave velocity with depth for the aggregate base course. Profiles of
shear modulus or Young’s modulus with depth were evaluated from these
seismic measurements. The strains induced during seismic testing (SASW)
are sufficiently low that the calculated stiffness values are within the linear
range. The same is not true for stiffness values calculated during plate-load
testing, because strains induced in the aggregate base can be in the linear or
nonlinear range, depending upon the applied load and proximity to the load
plate. It is convenient to first evaluate those plate-load stiffness values which
were measured within or very near the linear range. The nine groups of small
unload-reload loops [four in Test B1(drier test) and five in Test C1(wetter
test)] meet this criterion and are discussed below. The adjusted load-
settlement curves are included again for convience in Figs. 8.3 and 8.4 for the
drier and wetter aggregate base conditions, respectively.
120
100
80
60
40
20
01086420
Force (kips)
2.5
2.0
1.5
1.0
0.5
0.0
403020100Force (kN)
AB1BB1
CB1DB1
Plate Diameter: 12 in. (305 mm)
Fig. 8. 3. Adjusted Load-Settlement Curve with Unload-Reload Loops for Test B1; Incremental Plate-Load Test from 0 to 8.3 kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7 %)
100
80
60
40
20
01086420
Force (kips)
2.5
2.0
1.5
1.0
0.5
0.0
403020100Force (kN)
BC1
AC1
CC1DC1EC1
Plate Diameter: 12 in. (305 mm)
Fig. 8.4. Adjusted Load-Settlement Curve with Unload-Reload Loops for Test C1; Incremental Plate-Load Test from 0 to 8.6 kips (38.3 kN) on Wetter Material (Moisture Content ~ 6.1 %)
121
8.2.1 Adjustment to Small-Strain Stiffnesses for Increased
Strain Amplitude
The maximum and average strains were calculated for each group of
unload-reload loops in Test B1 (drier base course) and Test C1 (wetter base
course) assuming a value of 0.25 for Poisson’s ratio. An influence factor of
0.6 was selected from Fig. 8.1 for the maximum strain in each group of
unload-reload loops, while an average influence factor of 0.325 was used over
an effective depth of two plate diameters to estimate the average strain for
each group of unload-reload loops in the plate-load tests. Strains experienced
during initial loading are not included in this discussion, because they are well
outside the small-strain range due, in large part, to the high degree of volume
change during compression. The average and maximum strain amplitudes for
each group of unload-reload loops are presented in Table 8.1.
122
Table 8.1. Estimated Strain Amplitudes for Small-Strain, Unload-Reload Loops in Tests B1 and C1
Moisture Condition of Base Course
Unloading-Reloading Loops
Maximum Vertical Normal
Strain, εv-max
Average Vertical Normal
Strain, εv-ave % %
Drier AB1 0.0041 0.0022 (w ~ 4.7 %) BB1 0.0035 0.0019
CB1 0.0028 0.0015 DB1 0.0060 0.0032
Wetter AC1 0.0084 0.0046 (w ~ 6.1 %) BC1 0.0033 0.0018
CC1 0.0005 0.0003 DC1 0.0024 0.0013 EC1 0.0031 0.0017
The estimated strain ranges induced during the application of the
cyclic unload-reload loops in the plate-load tests have plotted with the Seed et
al. (1986) curve for both the wetter base course material and the drier base
course material in Fig. 8.5. It should be noted that the shearing strain, γ, was
determined from the axial strain following Eq. 8.3.
γ = (1 + ν)εv .............................................................(8.3)
where:
γ = shearing strain,
ν = Poisson’s ratio (0.25 for this case), and
εv = vertical normal strain.
123
1.2
1.0
0.8
0.6
0.4
0.2
0.010-5 10-4 10-3
γ10-2 10-1 100
Shearing Strain, , %
Seed et al. (1986) (For Sands) Range Mean
10-5 10-4 10-3 10-2 10-1 100
Shearing Strain, γ, %
Drier Material - Max. Strain
Drier Material - Ave. Strain
Wetter Material - Max. Strain
Wetter Material - Ave. Strain
Fig. 8.5. Illustration of Strain Ranges Observed from Multiple Series of Cyclic Unload-Reload Loops During Plate Load Testing
124
For these tests, the magnitude of the stiffness reduction observed for
the granular base course material varied from about 0-27 % depending on
whether the maximum strain or the average strain was considered. There is
little variation in the value of this reduction between the tests on drier material
and the tests on wetter material.
8.2.2 Adjustment to Small-Strain Stiffnesses for Increased
State of Stress due to Wetting and due to Increasing the Load
on the Plate
The Young’s modulus values calculated from plate-load tests and
seismic tests are presented in Table 8.2. It can be observed that the base
course material became softer as a result of wetting the test pad from the
surface. However, the softening effect was observed only when there were
relatively low loads on the plate [< 2 or 3 kips (8.9 to 13.3 kN)]. This
corresponds to an average pressure directly under the plate of 17.7 to 26.5 psi
(122 to 183 kPa). This result was observed for unload-reload groups applied
during the overall loading cycle and the during overall unloading cycle. The
softening effect was diminished when the load on the plate was increased.
125
Table 8.2. Young’s Modulus Values Calculated Directly from Unload-Reload Loops in Plate-Load Tests and from Small-Strain Seismic Tests
Moisture Condition of
the Base Course
Test Number
Average Load on Plate
During Cyclic Unloading-Reloading
Young’s Modulus, E 1
kips kN (psi) (kPa) Drier AB1 1.5 6.7 1.38 X105 9.51 X 105
(w = 4.7 %) BB1 3.7 16.5 1.68 X 105 11.6 X 105 CB1 3.2 14.2 1.96 X 105 13.5 X 105 DB1 1.6 7.1 0.95 X 105 6.55 X 105 SASWB1 1.26 X105 8.69 X 105
Wetter AC1 2.2 9.8 0.70 X 105 4.83 X 105 (w = 6.1 %) BC1 3.9 17.3 1.80 X 105 12.4 X 105
CC1 8.1 36.0 11.0 X105 75.8 X 105 DC1 3.6 16.0 2.32 X105 16.0 X 105 EC1 2.3 10.2 2.08 X 105 14.3 X 105 SASWC1 0.60 X 105 4.14 X 105
1 Young’s moduli calculated from seismic tests have not been adjusted for strain amplitude and stress-state effects.
The stiffnesses determined from the unload-reload cycles in the plate-
load test are approximately equal for the the material in the drier state and in
the wetter state under loads larger than 2 to 3 kips (8.9 to 13.3 kN). In fact,
the stiffnesses of the wetter material appear to be slightly higher than the
stiffnesses of the drier material in some cases. For example, the stiffness
determined from unload-reload group BC1 (wetter base course) is slightly
higher that the stiffness determined from BB1 (drier base course) despite the
126
fact that they were determined at nearly the same load range. This is because
the load on the plate was slightly higher for unload-reload group BC1 (wetter
base course) than for group BB1 (drier base course). The same result can be
observed by comparing Groups CB1-DC1 and DB1-EC1. This indicates that the
load on the plate (or the confinement of the material) has a much more
significant effect on the stiffness of the material than the moisture content
does at these states of stress.
In an effort to adjust seismic stiffness measurements to account for the
increased state of stress during plate loading, the observed stiffnesses were
plotted against the pressure applied to the plate as shown in Fig. 8.6.
Reduction of the seismically determined moduli was performed using the
average Seed et al. (1987) curve before determining the increase in stiffness
due to increased confining pressure. Considerable scatter is observed over the
nine points for which small-strain stiffnesses were measured in the plate-load
test. A trend line through the data should cross the vertical axis at 1.0.
However , no convenient correlation was found to account for the effect of
increasing the confining pressure in this material. Additional data may better
define a trend between the applied pressure and the increase in seismically
predicted stiffnesses. Future tests should include seismic testing under the
loaded plate in order to better explain the change in material properties due to
changes in mean effective stress.
127
89
1
2
3
4
56789
10
2
3
10 2x101 3 4 5 6 7 8
Applied Pressure Under Plate (psi)
7 8 9100
2 3 4 5
Applied Pressure Under Plate (kPa)
Group Applied During Loading Group Applied During Unloading
AB1
BB1
CB1
DB1
AC1
BC1
CC1
DC1EC1
Fig. 8.6 Relationship Between Pressure Applied to the Plate and Observed Increase in Small-Strain Stiffness
8.2.3 Conclusions From Small-Strain Moduli Comparisons
Based on previous theoretical and experimental studies, the mean
effective stress in an unbound granular base course material has a significant
effect on the stiffness. The mean effective stress depends on the following
two factors.
128
(1) Horizontal stresses locked-in during compaction and
negative capillary stresses developed during drying are
significant in defining the initial stiffness of the material. This
initial state of stress in the material governs the measurement
of shear wave velocities in seismic tests.
(2) The increase in mean effective stress due to increased load
on the plate during plate-load testing depends on the
distribution of vertical stress with depth as well as the degree
to which horizontal stresses are maintained after the material is
unloaded.
Improving the determination of the state of stress at any point before,
during, or after loading will aid in quantifying the effects of stress state on
seismically determined moduli. Despite its limitations, seismic testing has
been used to show material behavior not previously observed in granular
bases such as the significant stiffening effect of negative capillary stresses.
Further research in determining small-strain stiffnesses under pavement
surfaces during loading will help to improve the prediction of working load
displacements with seismic tests.
8.3 Large-Strain Stiffness Comparisons
Stiffness measurements from plate-load tests were taken under a
variety of loading conditions. Throughout the tests, it was observed that the
measured equivalent spring constant, keff, was influenced by the magnitude of
129
the load, duration of loading, moisture content, stress history, and strain
amplitude. Although the material response discussed below involves strain
amplitude outside the linear range and is influenced by the aforementioned
factors simultaneously, the relative magnitude of the stiffnesses offer some
useful insight about the material behavior.
8.3.1 Short Duration Load to Failure
The deformational properties of the compacted material can be
observed through a range of loading states from the results of Test A4 in
which the material was subjected to a 40 kip (178 kN) load after having
undergone 85 mils (2.2 mm) of permanent deformation from the three
previous tests. This displacement corresponds to an average strain on the
order of 0.4 % when an effective depth of two plate diameters is assumed.
The stress history may be considered analogous to the “conditioning” imposed
by compaction of an asphalt cement concrete surface course over an unbound
base course.
The load was applied over a period of approximately 7 minutes and
released over a period of 3 minutes. The continuous load-settlement curve has
been replotted in Fig. 8.7 for convenience. For a loading range from 0 to
about 18 kips (0 to 80 kN), the material exhibited the same approximately bi-
linear stiffness behavior observed during loading in the large amplitude cyclic
tests on both the wetter and drier material (Tests A3 and C2). At a load of 18
kips (80 kN) which corresponds to a pressure of 159 psi (1096 kPa), the
130
material began to soften, and the plate displacements began to increase.
While it is not clear that this point should be called failure, it is a significant
point of interest in the deformational behavior of the material. The maximum
load was less than about 11 kips (49 kN) or 97 psi (669 kPa) in all of the other
plate-load tests performed on the Georgetown test pad. It should also be
noted that the pressure on the base course in a layered pavement system would
not be expected to reach 159 psi (1196 kPa) under even the most severe
loading as previously illustrated in Fig. 4.1. The increased displacement at
the end of the loading cycle was the result of maintaining the 40-kip (178 kN)
load on the plate for 2 minutes.
131
160
140
120
100
80
60
40
20
0403020100
Force (kips)
4
3
2
1
0
200150100500Force (kN)
AA4
BA4
CA4
Fig. 8.7. Illustration of Material Response Under Load to “Failure”; Test A4, Loading from 0 to 40 kips (0 to 178 kN) in 6 Minutes and Unloading to Zero
The failure load was also estimated using bearing capacity theory. For
an effective friction angle, φ’, of 45 degrees, the bearing capacity was
calculated to be about 132 psi (910 kPa) which corresponds to 15 kips (67 kN)
on a 1 ft (30.5 cm) diameter loading plate. This is near the load at which the
material began to soften during the plate-load test as shown in Fig. 8.7.
132
8.3.2 Stiffness Under Large-Amplitude, Short-Duration Cyclic
Loading
The base course material was tested under cyclic loads of 8 or 9 kips
(36 or 40 kN) in both the drier and the wetter state. The duration of loading
was varied from 11 seconds to 3.7, minutes with most cycles lasting less than
one minute. The continuous load-settlement curves from Test A3 (drier
material) and Test C2 (wetter material) are plotted again for convenience in
Figs. 8.8 and 8.9, respectively.
It was observed that the cyclic plate-load tests showed a 65-70 %
reduction in stiffness during loading from the dry test to the wet test. This is
shown graphically in Fig. 8.10 where loop 5 for the test on drier material (Test
A3) and loop 5 for the test on wetter material (Test C2) have been plotted
together. The reduction in stiffness was observed for both the initial and final
sections of the loading curve.
133
30
2520
15
105
0121086420
Force (kips)
0.8
0.6
0.4
0.2
0.0
50403020100Force (kN)
Plate Diameter:12 in. (305 mm)Effective Plate Area:107 in.2 (690 cm2)
Loop 30Loop 25
Fig. 8.8. Continuous Force-Displacement Plot from Test A3; 32 Cycles of 0 to 9 kips (40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %)
30
2520
15
105
0121086420
Force (kips)
0.8
0.6
0.4
0.2
0.0
50403020100Force (kN)
Plate Diameter: 12 in. (305 mm)
Fig. 8.9. Continuous Force-Displacement Plot from Test C2; 5 Cycles of 0 to 8 kips (35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%)
134
0.6
0.4
0.2
0.0
403020100Force (kN)
30
25
20
15
10
5
01086420
Force (kips)
Loop 5 - Test A3 - Drier Base Course
Loop 5 - Test C2 - Wetter Base Course
Fig. 8.10. Comparison of Stiffness Under Large Amplitude Cyclic Loading; Loop 5 from Tests A3 (Drier Material) and C2 (Wetter Material)
The seismically determined stiffnesses were compared to the
stiffnesses determined during the large-amplitude cyclic loading cycles in the
plate-load tests. The stiffness data for loop 5 from Test A3 (drier material)
and for loop 5 from Test C2 (wetter material) are presented in Table 8.3. The
seismically determined stiffness values are also presented graphically for
comparison in Figs. 8.11 and 8.12 for the drier base course and wetter base
course, respectively.
135
Table 8.3. Comparison of Stiffness Values Determined from Large Amplitude Plate-Load Tests and from Seismic Tests
Test/Moisture Condition Equivalent Spring Constant, keff, (Stiffnesses), lb/in.
Initial Portion of Loading
Curve From Plate-Load
Test 1
Final Portion of Loading Curve From Plate-Load
Test 1
SASW Adjusted for
Strain Amplitude 2
Test A3 - Drier Material 0.45 X 106 0.78 X 106 1.53 X 106 Test C2 - Wetter Material
0.16 X 106 0.65 X 106 0.67 X 106
Test/Moisture Condition Equivalent Spring Constant, keff, (Stiffnesses),
kN/m Initial
Portion of Loading
Curve From Plate-Load
Test 1
Final Portion of Loading Curve From Plate-Load
Test 1
SASW Testing Adjusted for
Strain Amplitude 2
Test A3 - Drier Material 0.078 X 106 0.14 X 106 0.27 X 106 Test C2 - Wetter Material
0.028 X 106 0.11 X 106 0.12 X 106
1 Working-load stiffness values were determined from large-amplitude cyclic plate-load tests. The bi-linear stiffness values from loop 5 in Test A3 (drier material) and from loop 5 in Test C2 (wetter material) were used for comparison. 2 Seismic stiffnesses were adjusted for strain amplitude, but were not adjusted for increased state of stress from loading of the plate.
136
0.6
0.4
0.2
0.0
403020100Force (kN)
30
25
20
15
10
5
01086420
Force (kips)
Slopes NearlyParallel
SeismicallyDeterminedStiffnesskeff = 1.53 X 106 lb/in.(0.27 X 106 kN/m)
Fig. 8.11. Comparison of Seismically Determined Stiffness with Plate-Load Stiffness for Large Amplitude Cyclic Plate-Load Tests; Loop 5, Test A3 - 32 Cycles of 0 to 9 kips (40.0 kN) in 20 Minutes on Drier Material (Moisture Content ~ 4.7 %)
0.6
0.4
0.2
0.0
403020100Force (kN)
30
25
20
15
10
5
01086420
Force (kips)
Slopes NearlyParallel
SeismicallyDeterminedStiffnesskeff = 0.67 X 106 lb/in.(0.12 X 106 kN/m)
Fig. 8.12. Comparison of Seismically Determined Stiffness with Plate-Load Stiffness for Large Amplitude Cyclic Plate-Load Tests; Loop 5, Test C2 - 5 Cycles of 0 to 8 kips (35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%)
Stiffness calculations from the unloading curves showed considerably
more scatter than those from the loading curves. It was therefore difficult to
make meaningful conclusions from observation of the stiffness during
unloading. It can be observed, however, that the material was stiffest at the
beginning of the rebound curve. This is presumed to be the result of locked-in
horizontal stresses from the loading portion of the cycle.
Finally, it was observed that the large-amplitude cyclic load-settlement
curves began to “close” or plot on top of one another after a short number of
cycles as shown in Fig. 8.13 for the drier material and in Fig. 8.14 for the
wetter material. However, the displacement began to increase more rapidly if
even a slight increase in loading was applied to the plate. It was observed in
Test A3 on the drier material that the displacement periodically stabilized for
a few cycles, and then increased for a few cycles. Loops 23 and 24 are plotted
in Fig. 8.15 to illustrate this point. The loops in Fig. 8.15 have “closed”,
however the maximum displacement is significantly greater than that
observed for the two loops in Fig. 8.13 which were recorded earlier in the
same test (Test A3).
139
30
25
20
15
10
5
01086420
Force (kips)
0.6
0.4
0.2
0.0
403020100Force (kN)
Loop 5Loop 6
Loop 7
Fig. 8.13. Closure of Cyclic Loops From Plate-Load Test A3; 32 Cycles of 0 to 9 Kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
Loop 4
Loop 5
Fig. 8.14. Closure of Cyclic Loops From Plate-Load Test C2; 5 Cycles of 0 to 8 Kips on Wetter Material (w ~ 6.1 %)
140
30
25
20
15
10
5
01086420
Force (kips)
0.6
0.4
0.2
0.0
403020100Force (kN)
Loops 23 and 24
Fig. 8.15. Closure of Cyclic Loops From Plate-Load Test A3 After Accumulated Displacement from Application of Previous Loops; 32 Cycles of 0 to 9 Kips on Drier Material (w ~ 4.7 %)
8.3.3 Stiffnesses From Incremental Plate-Load Tests
Two nearly identical incremental plate-load tests were performed, one
on the drier material (B1) and one on the wetter material (C1). A maximum
force of 8.3 to 8.6 kips (36.9 to 38.3 kN) was applied to the plates over
approximately 3 to 3.5 hours. The maximum displacement with the drier
material was 51 mils (1.3 mm), and the maximum displacement with the
wetter material was 91 mils (2.3 mm). The permanent displacement from the
test on the drier material was approximately 67 % of the maximum
displacement, while the permanent displacement from the test on the wetter
material was 73 % of the maximum. The stiffness of the wetter material was
141
61 % less than that of the drier material at the beginning of loading, but only
20 % less during the latter part of the loading curve. This is slightly different
from the behavior observed in the short duration cyclic tests in which the
stiffness at every point during loading was reduced 65-70% due to wetting.
The adjusted load-settlement curves are plotted in Chapters 5 and 6
without zeroing the displacement measurement after application of the seating
load. Both curves are replotted in Figs. 8.16 and 8.17 without the small
unloading-reloading loops and with re-zeroing to the displacement measured
after the seating load was applied.
The overall stiffnesses for the incremental tests were the lowest
observed among all of the plate-load tests conducted on the test pad. These
overall stiffnesses are not particularly meaningful in terms of the displacement
expected from normal traffic loads, but may be relevant for predicting
displacement due to stationary pavement loads on parking areas and cargo
staging facilities. In addition, the moduli determined at a pressure of 10 psi
(69 kPa) in the incremental plate-load tests are the values used in rigid
pavement design procedures (AASHTO, 1986) as noted in Figs. 8.16 and
8.17. This pressure corresponds to a load of 1131 lb (5.0 kN) on the 1 ft (30.5
cm) diameter plate.
The modulus of the material at a pressure of 10 psi (69.0 kPa) is
referred to as the modulus of soil reaction, ku’. The modulus is determined
from the load-settlement plot after zeroing for the seating load. The values of
modulus of soil reaction as determined by the procedure given in AAHSTO
142
T-222 (1986) are recorded in Table 8.3 for reference. A 70% reduction in
modulus of soil reaction was observed as a result of wetting the near-surface
material. Table 8.4 AASHTO T-222 Modului of Soil Reaction for Georgetown Crushed Limestone Test Pad
Test Modulus of Soil Reaction, ku’ (lb/in3) (MN/m3)
B1, Drier Material 2141 581 C1, Wetter Material 635 172
8.3.4 Sensitivity of the Material to Duration of Loading
The stiffness of the unbound granular base material has been shown to
be dependent on the duration of loading. This is again illustrated in Fig. 8.18
for the drier material and in Fig. 8.19 for the wetter material. The initial
loading curves for the cyclic test and the incremental test were plotted
together on one graph for each moisture condition of the base course. The
plots show the time-dependent displacement behavior observed during plate-
load testing. It should be noted that the cyclic tests were conducted after other
plate-load tests had been conducted at the same location. The displacements
are, therefore, slightly less than those which would be expected had no
previous load been applied to the plate. It should be noted that the seismically
determined stiffnesses fit the end of the cyclic loading curves well especially
for the later loops after much of the initial volume change in the material had
taken place.
143
100
80
60
40
20
01086420
Force (kips)
2.5
2.0
1.5
1.0
0.5
0.0
403020100
Force (kN)
Plate Diameter: 12 in. (305 mm)
ku' determined at10 psi (69 kPa)1.1 kips (4.9 kN)
Fig. 8.16. Long-Term, Adjusted Load-Settlement Curve; Test (B1) on Drier Material (w ~ 4.7 %)
100
80
60
40
20
01086420
Force (kips)
2.5
2.0
1.5
1.0
0.5
0.0
403020100
Force (kN)
Plate Diameter 12 in. (305 mm)
ku' determined at10 psi (69 kPa)1.1 kips (4.9 kN)
Fig. 8.17. Long-Term, Adjusted Load-Settlement Curve; Test (C1) on Wetter Material (w ~ 6.1 %)
144
50
40
30
20
10
01086420
Force (kips)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
403020100Force (kN)
Plate Diameter: 12 in. (305 mm)Effective Plate Area: 107 in.2 (690 cm2)
Duration of LoadingCycle = 0.94 minutes(Test A3 - cyclic loading)Duration of Loading
Cycle = 97 minutes(Test B1 - incremental test)
SeismciallyDeterminedStiffness 1
Fig. 8.18. Illustration of the Effect of Duration of Loading on Unbound Granular Base Course Material; Plate-Load Tests at Location C on Drier Material (Moisture Content ~ 4.7%) 1 Seismically Determined Stiffness Corrected for Strain Amplitude, but not for State of Stress
80
60
40
20
01086420
Force (kips)
2.0
1.5
1.0
0.5
0.0
403020100Force (kN)
Plate Diameter: 12 in. (305 mm)
Duration of LoadingCycle = 2.7 minutes(Test C2 - cyclic test)
Duration of LoadingCycle = 125 minutes(Test C1 - incremental test)
Seismically Determined Stiffness 1
Fig. 8.19. Illustration of the Effect of Duration of Loading on Unbound Granular Base Course Material; Plate-Load Tests at Location C on Wetter Material (Moisture Content ~ 6.1%) 1 Seismically Determined Stiffness Corrected for Strain Amplitude, but not for State of Stress
8.4 Summary of Stiffness Comparison
The results of plate-load and seismically-determined stiffness
measurements show unbound granular material to be sensitive to duration of
loading and moisture content. It was observed that the material was more
sensitive to moisture content at low loads [< 2 or 3 kips (8.9 to 13.3 kN] than
at high loads. This threshold corresponds to an average pressure directly
under the plate of 17.7 to 26.5 psi (122 to 183 kPa). Significant softening was
observed at low loads in both types of tests with increased wetting.
Seismic tests have the advantage of being able to show the softening
effects of wetting or surface disturbance without damaging the pavement.
Seismically determined stiffness measurements show promise in the
prediction of working load displacements if adjusted for increases in material
stiffness during loading. The importance of the adjustment may be minimized
significantly if seismic tests are performed on a layered pavement system,
because smaller pressures and smaller strains will be induced in the granular
material under a pavement wearing course.
147
CHAPTER NINE
SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS
9.1 Summary of Testing Program
Plate-loading and seismic tests were performed on a test pad
constructed at the Capitol Aggregates quarry in Georgetown, Texas. The test
pad was constructed to determine whether or not the crushed limestone base
course material could be compacted in single lifts thicker than 6 to 8 in. (15.2
cm to 20.3 cm) while still achieving the same material properties as would be
achieved by compacting in thinner single lifts. Plate-load tests and seismic
tests were conducted on the surface of the Georgetown test pad to evaluate the
use of seismic stiffness measurements for predicting working-load
displacements.
The test pad was constructed of unbound crushed limestone which is
commonly used in the construction of pavement base courses. The material
had a nominal maximum particle size of 1.5 in. (3.8 cm), a modified Proctor
maximum density of 141 pcf (22.1 kN/m3), and an optimum moisture content
of 6.5 %. The fines were non-plastic. The portion of the test pad used for
plate-load and seismic testing was constructed in two thick lifts and was
compacted with a vibratory pad foot roller. The first lift was 12 in. (30.5 cm)
thick and the second lift was 23 in. (58.4 cm) thick. Nuclear density gauge
measurements were made before the plate-load and seismic tests, and
149
laboratory moisture content specimens were collected from beneath the plate
at the conclusion of each series of plate-load tests.
The plate-load tests were conducted using the mechanical loading
mechanism of the Rolling Dynamic Deflectometer (RDD) developed at The
University of Texas at Austin (Bay 1997). The RDD was used in a stationary
mode to deliver static loads to a plate on the surface of the test pad. The
loading mechanism of the RDD also allowed the application of short duration
cyclic loads to the plate, and was used to apply small amplitude [1 kip (4.4
kN)] and large amplitude [9 kip (40 kN)] cyclic loads with a loading duration
of less than one minute. The time-dependent deformational behavior of the
unbound crushed limestone was observed from the results of the plate-load
tests conducted with different loading rates.
Continuous measurements of load and displacement were made during
the plate-load tests using the computer-based data acquisition system installed
in the RDD. The load applied to the plate was measured with a load cell
mounted on the loading frame of the RDD. The displacement of the plate was
measured with Linear Variable Differential Transformers (LVDTs) which
were held in place with an aluminum framework constructed specifically for
this application.
Seismic surface wave tests were conducted on the surface of the test
pad directly before the plate-load tests were conducted. The Spectral-
Analysis-of-Surface-Waves (SASW) test was used to determine profiles of
150
shear wave velocity with depth. Shear stiffness and axial stiffness profiles
were calculated from the SASW results.
The softening effect of adding moisture to the unbound aggregate base
course was evaluated by performing plate-load and seismic tests on both drier
base course (moisture content ~ 4.7%) and wetter base course (moisture
content ~ 6.1%). Plate-load and seismic tests were first conducted on the test
pad in a drier state and later conducted near the same location on the test pad
after adding moisture to the test pad from the surface.
9.2 Summary of Observations
The unbound granular base material used to construct the test pad in
the Capitol Aggregate quarry exhibited time-dependent settlement under
sustained loading conditions. Although the granular base contained only 12%
material passing the #40 (0.425 mm) sieve, and the fines were non-plastic, the
loading plate continued to displace with time under a constant load. This
response under loading is more commonly associated with somewhat
cohesive-type material. This time-dependent behavior suggests significant
variation in the load-displacement performance depending on the duration of
loading.
It was observed that plate-load testing in the range of working loads
similar to those induced by 18 kip (80 kN) Equivalent Single Axle Loads
(ESALs) produced surface displacements which corresponded to strain
amplitudes in the unbound aggregate base course that fall in the nearly linear
151
to mildly non-linear range of stiffness. It is estimated that an adjustment to
the small-strain modulus determined by seismic tests is necessary to account
properly for the difference in strain amplitude between seismic tests and static
plate-load tests. This adjustment is made by multiplying the small-strain
(seismic) modulus by a factor which ranges from 0.75 to 0.95.
Factors such as natural cementation, negative capillary stresses,
locked-in horizontal stresses during compaction, and locked-in horizontal
stress during unloading had a stiffening effect on the unbound granular
material tested at the Georgetown, Texas test site. The addition of moisture
from the surface of the test pad was found to have a softening effect on the
unbound granular base material. This is presumably due mainly to the relief
of negative capillary stresses, but may also be due to reducing any
contribution from natural cementation. The softening effect when moisture
was added was observed in both the plate-load tests and the seismic surface
wave tests.
Seismic test results were also used to show that the material near the
surface of the compacted test pad was significantly softer than the material at
a depth of 6 in. (15 cm) or greater immediately after compaction. However,
the seismic tests also showed that this softer zone became just as stiff as (or
stiffer than) the underlying material once it dried. Compression of the softer,
near-surface material when the base course was tested in a wetter state is felt
to have contributed significantly to the displacement of the loading plate
during plate-load testing. It has been shown by Bueno et al. (1998) that the
152
disturbed layer near the surface of an unbound aggregate base course is later
compacted when another layer is compacted on top of the initially disturbed
material. For this reason, it is expected that displacements measured in the
plate-load test would be significantly smaller if the test pad had been paved
with asphalt concrete or Portland cement concrete wearing course, even if the
pressure delivered to the granular base course layer was the same as for the
plate-load tests on the unpaved test pad.
Paving the test pad would also have the effect of reducing the strain
amplitude in the granular base course layer. This would improve the
prediction of surface displacements using seismically determined stiffness
values.
9.3 Conclusions from Plate-Load and Seismic Tests
Seismic tests show potential for predicting pavement surface
displacements under working loads. However, fundamental differences exist
between seismic tests and plate-load tests which must be taken into account
when predicting settlement from the seismic test measurements. The strain
amplitudes induced by plate-load testing ranged from slightly greater to much
greater than those induced by seismic tests. Estimates of strain amplitudes
were made from small, unload-reload cycles [1 kip (4.4 kN)] during plate-load
tests on the unbound aggregate test pad. These strain amplitudes were found
to be slightly above the linear range. This increased strain amplitude
153
corresponded to a 5-25% reduction in stiffness between seismically measured
stiffnesses and stiffness under working traffic loads.
Larger amplitude unload-reload loops [9 kips (40.0 kN)] showed
greater surface displacement and thus greater strain amplitudes than the
smaller unload-reload loops [1 kip (4.4 kN)]. However, no constant vertical
load was applied to the material during the larger unload-reload cycles as was
the case for the smaller unload-reload loops. Compression of the less-stiff,
near-surface material accounted for a large part of the displacement under the
larger magnitude cyclic loading. It was observed that the softening effects of
wetting and the effect of the presence of a softer layer near the surface of the
test pad were both diminished significantly when the load on the plate was
increased above 2 or 3 kips (8.9 to 13.3 kN). This corresponds to a pressure
directly beneath the plate of about 18 to 27 psi (124 to 186 kPa).
Additional adjustment to the small-strain stiffnesses measured
seismically is necessary in this test pad material if displacements under
working traffic loads are to be predicted. The difference in the state of stress
in the material under load must be accounted for in the prediction.
Theoretical solutions for displacements under working loads will also have to
account for the effects of locked-in horizontal stresses, any natural
cementation, and negative capillary stresses.
Despite the fact that stiffnesses measured with seismic tests must be
adjusted for strain amplitude and state of stress, the SASW test has been
shown to be very effective in detecting the relative softening of granular
154
155
material due to wetting or disturbance near the surface. These changes in
stiffness could not be detected by field tests which measure density.
9.3 Recommendations for Future Work
Understanding of the behavior of unbound granular base courses under
working loads could be improved through in-situ seismic testing of complete
pavement systems. The state of stress under a compacted pavement is
expected to be higher than the state of stress in the granular base course test
pad built in Georgetown, Texas. Increasing the state of stress by adding a
confining layer of asphalt concrete or Portland cement concrete would
decrease displacements and strain amplitudes in the unbound granular base
course layer. It is expected that working loads applied to the pavement
wearing course would induce strains in the base course closer to the small-
strain range under which seismic tests are performed. This reduction in strain
amplitudes will improve the prediction of surface displacements using
seismically determined stiffness measurements.
Additional deflection testing under working loads would also add to
the understanding of the relationship between seismically determined
stiffnesses and working load displacements. Additional material types should
be tested to investigate the time-dependent characteristics under slow loading.
APPENDIX A
NUCLEAR DENSITY GAUGE DATA
155
Table A.1. Nuclear Density Gauge Data for Drier Material (w ~ 4.7 %); Collected by Gene Schlieker, Texas Transportation Institute Date: 11 Mar 98 Location A (drier test, moisture content ~ 4.7 %)
Station # (Location)
Depth DC MC Wet Density Dry Density M % Moisture
N#1 12 88 135.9 129.3 6.6 5.1(not used) 10 418 80 132.8 126.2 6.6 5.2
8 785 91 129.0 122.1 6.9 5.76 1345 88 123.4 112.8 6.6 5.74 2008 84 116.1 109.8 6.2 5.72 2414 90 104.5 97.7 6.8 7.0
Back Scatter N#1 12 217 91 135.6 128.7 6.9 5.4Second Test 10 402 89 134.2 127.4 6.7 5.3
8 793 91 128.6 121.7 6.9 5.76 1367 93 122.6 115.5 7.1 6.24 2045 95 115.1 107.7 7.3 6.82 2460 91 103.4 96.4 6.9 7.2
Back Scatter 720 96 101.4 95.0 6.4 6.8S#1 12 262 84 129.6 123.3 6.2 6.2
10 482 83 127.9 121.7 6.1 5.08 894 80 124.0 118.1 5.8 4.96 1499 85 118.5 112.2 6.3 5.64 2140 81 112.7 106.8 5.9 5.62 2479 87 102.9 96.4 6.5 6.8
Back Scatter 734 86 100.3 93.8 6.4 6.8
156
Table A.1. Continued
N#2 12 236 88 132.9 126.3 6.6 5.2
10 430 90 131.8 125.0 6.8 5.58 794 86 128.6 122.1 6.4 5.36 1362 85 122.8 116.5 6.3 5.44 2004 87 116.1 109.6 6.5 6.02 2431 89 104.1 97.4 6.7 6.9
Back Scatter 665 81 106.3 100.4 5.9 5.9S#2 12 248 89 131.3 124.6 6.7 5.4
10 436 87 131.3 124.8 6.5 5.28 785 92 129.0 122.0 7.0 5.76 1333 87 123.8 117.3 6.5 5.64 1956 88 117.4 110.8 6.6 6.02 2273 87 108.1 101.6 6.5 6.4
Back Scatter 681 87 104.8 98.1 6.7 6.8
Fig. 6.9. Variation of Displacement with Time; Test C2 - 5 Cycles of 0 to 8 kips (35.6 kN) in 9 Minutes on Wetter Material (Moisture Content ~ 6.1%)
157
158
Table A.2. Nuclear Density Gauge Data for Wetter Material (w ~ 6.1 %); Collected by Gene Schlieker, Texas Transportation
Institute
Date: 10 Apr 98 Location C (wetter test, laboratory moisture content ~ 6.1 %))
Station #
(Location) Depth DC MC Wet Density Dry Density M % Moisture
NW 12 226 149.0 139.6 9.4 6.7 10 398 150.1 140.0 10.2 7.3 8 729 149.0 138.5 10.5 7.5 6 1277 145.6 135.6 10.0 7.4 4 1907 141.7 131.8 9.9 7.5 2 2255 135.0 125.1 9.9 7.9 Back Scatter 660 135.3 125.6 9.7 7.7
SW 12 258 144.5 134.3 10.2 7.6 10 470 144.2 134.2 10.0 7.4 8 817 144.6 134.2 10.4 7.7 6 1368 142.5 132.8 9.7 7.3 4 2002 139.2 128.7 10.5 8.1 2 2309 133.6 123.7 9.9 8.0 Back Scatter 689 132.4 122.4 10.1 8.2
APPENDIX B
INDIVIDUAL LOADING CYCLE PLOTS FOR TEST A3
159
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.267 X 106 lb/in.(0.0468 X 106 kN/m)
k = 0.611 X 106 lb/in.(0.107 X 106 kN/m)
Fig. B.1. Test A3; Loop 1 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.864 X 106 lb/in.(0.151 X 106 kN/m)
k = 0.473 X 106 lb/in.(0.0828 X 106 kN/m)
Fig. B.2. Test A3; Loop 2 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.709 X 106 lb/in.(0.124 X 106 kN/m)
Fig. B.3. Test A3; Loop 3 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.356 X 106 lb/in.(0.0623 X 106 kN/m)
k = 0.723 X 106 lb/in.(0.127 X 106 kN/m)
Fig. B.4. Test A3; Loop 4 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.452 X 106 lb/in.(0.0792 X 106 kN/m)
k = 0.785 X 106 lb/in.(0.137 X 106 kN/m)
Fig. B.5. Test A3; Loop 5 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.399 X 106 lb/in.(0.0699 X 106 kN/m)
k = 0.868 X 106 lb/in.(0.152 X 106 kN/m)
Fig. B.6. Test A3; Loop 6 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.495 X 106 lb/in.(0.0867 X 106 kN/m)
k = 0.923 X 106 lb/in.(0.162 X 106 kN/m)
Fig. B.7. Test A3; Loop 7 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.451 X 106 lb/in.(0.0790 X 106 kN/m)
k = 0.726 X 106 lb/in.(0.127 X 106 kN/m)
Fig. B.8. Test A3; Loop 8 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.336 X 106 lb/in.(0.0588 X 106 kN/m)
k = 0.846 X 106 lb/in.(0.148 X 106 kN/m)
Fig. B.9. Test A3; Loop 9 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.556 X 106 lb/in.(0.0974 X 106 kN/m)
k = 0.843 X 106 lb/in.(0.146 X 106 kN/m)
Fig. B.10. Test A3; Loop 10 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.458 X 106 lb/in.(0.0802 X 106 kN/m)
k = 0.886 X 106 lb/in.(0.155 X 106 kN/m)
Fig. B.11. Test A3; Loop 11 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.440 X 106 lb/in.(0.0771 X 106 kN/m)
k = 0.827 X 106 lb/in.(0.145 X 106 kN/m)
Fig. B.12. Test A3; Loop 12 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.618 X 106 lb/in.(0.108 X 106 kN/m)
k = 1.32 X 106 lb/in.(0.231 X 106 kN/m)
Fig. B.13. Test A3; Loop 13 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.379 X 106 lb/in.(0.0664 X 106 kN/m)
k = 1.17 X 106 lb/in.(0.205 X 106 kN/m)
Fig. B.14. Test A3; Loop 14 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.465 X 106 lb/in.(0.0814 X 106 kN/m)
k = 1.10 X 106 lb/in.(0.193 X 106 kN/m)
Fig. B.15. Test A3; Loop 15 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.613 X 106 lb/in.(0.107 X 106 kN/m)
k = 1.23 X 106 lb/in.(0.215 X 106 kN/m)
Fig. B.16. Test A3; Loop 16 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.634 X 106 lb/in.(0.111 X 106 kN/m)
k = 1.52 X 106 lb/in.(0.266 X 106 kN/m)
Fig. B.17. Test A3; Loop 17 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 1.17 X 106 lb/in.(0.205 X 106 kN/m)
Fig. B.18. Test A3; Loop 18 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.593 X 106 lb/in.(0.104 X 106 kN/m)
k = 1.29 X 106 lb/in.(0.226 X 106 kN/m)
Fig. B.19. Test A3; Loop 19 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.501 X 106 lb/in.(0.0877 X 106 kN/m)
k = 1.17 X 106 lb/in.(0.205 X 106 kN/m)
Fig. B.20. Test A3; Loop 20 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.386 X 106 lb/in.(0.0676 X 106 kN/m)
k = 1.19 X 106 lb/in.(0.208 X 106 kN/m)
Fig. B.21. Test A3; Loop 21 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.633 X 106 lb/in.(0.111 X 106 kN/m)
k = 1.40 X 106 lb/in.(0.245 X 106 kN/m)
Fig. B.22. Test A3; Loop 22 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.357 X 106 lb/in.(0.0625 X 106 kN/m)
k = 1.04 X 106 lb/in.(0.182 X 106 kN/m)
Fig. B.23. Test A3; Loop 23 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.594 X 106 lb/in.(0.104 X 106 kN/m)
k = 1.21 X 106 lb/in.(0.212 X 106 kN/m)
Fig. B.24. Test A3; Loop 24 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.595 X 106 lb/in.(0.104 X 106 kN/m)
k = 1.28 X 106 lb/in.(0.224 X 10 6 kN/m)
Fig. B.25. Test A3; Loop 25 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.433 X 106 lb/in.(0.0758 X 106 kN/m)
k = 1.02 X 106 lb/in.(0.179 X 106 kN/m)
Fig. B.26. Test A3; Loop 26 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.676 X 106 lb/in.(0.118 X 106 kN/m)
k = 0.939 X 106 lb/in.(0.164 X 106 kN/m)
Fig. B.27. Test A3; Loop 27 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.633 X 106 lb/in.(0.111 X 106 kN/m)
k = 0.827 X 106 lb/in.(0.145 X 106 kN/m)
Fig. B.28. Test A3; Loop 28 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.587 X 106 lb/in.(0.103 X 106 kN/m)
k = 1.14 X 106 lb/in.(0.200 X 106 kN/m)
Fig. B.29. Test A3; Loop 29 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.676 X 106 lb/in.(0.118 X 106 kN/m)
k = 1.61 X 106 lb/in.(0.282 X 106 kN/m)
Fig. B.30. Test A3; Loop 30 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 0.574 X 106 lb/in.(0.101 X 106 kN/m)
k = 1.09 X 106 lb/in.(0.191 X 106 kN/m)
Fig. B.31. Test A3; Loop 31 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
30
25
20
15
10
5
0121086420
Force (kips)
0.6
0.4
0.2
0.0
50403020100Force (kN)
k = 1.22 X 106 lb/in.(0.214 X 106 kN/m)
k = 0.695 X 106 lb/in.(0.122 X 106 kN/m)
Fig. B.32. Test A3; Loop 32 of 32 - 32 Loading Cycles from 0 to 9 kips on Drier Material (w ~ 4.7 %)
APPENDIX C
INDIVIDUAL UNLOAD-RELOAD LOOPS FOR TEST B1
16
14
2.22.01.81.61.41.21.0
Force (kips)
0.380.360.34
k = 0.82 X 106 lb./in.(0.14 X 106 kN/m)
16
14
0.380.360.34
k = 1.9 X 106 lb./in.(0.33 X 106 kN/m)
16
14
0.380.360.34
k = 1.6 X 106 lb./in.(0.28 X 106 kN/m)
16
14
0.380.360.34
k = 1.6 X 106 lb./in.(0.28 X 106 kN/m)
16
14
0.380.360.34
10987654
Force (kN)
k =2.2 X 106 lb./in.(0.39 X 106 kN/m)
Fig. C.1. Test B1, Individual Unload-Reload Loops, Group AB1
193
28
26
4.54.03.53.0
Force (kips)
0.72
0.70
0.68k = 4.5 X 106 lb./in.(0.79X 106 kN/m)
28
26
0.72
0.70
0.68k = 32.3 X 106 lb./in.(5.7 X 106 kN/m)
28
26
0.72
0.70
0.68k = 2.2 X 106 lb./in.(0.39 X 106 kN/m)
28
26
0.72
0.70
0.68k = 1.5 X 106 lb./in.(0.26 X 106 kN/m)
28
26
0.72
0.70
0.68
20181614
Force (kN)
k =1.0 X 106 lb./in.(0.18 X 106 kN/m)
Fig. C.2. Test B1, Individual Unload-Reload Loops, Group BB1
194
504846
4.03.83.63.43.23.02.82.62.4
Force (kips)
1.28
1.24k = 1.4 X 106 lb./in.(0.25 X 106 kN/m)
504846
1.28
1.24k = 2.2 X 106 lb./in.(0.39 X 106 kN/m)
504846
1.28
1.24k = 2.4 X 106 lb./in.(0.42 X 106 kN/m)
504846
1.28
1.24k = 2.8 X 106 lb./in.(0.49 X 106 kN/m)
504846
1.28
1.24
18161412
Force (kN)
k =2.8 X 106 lb./in.(0.49 X 106 kN/m)
Fig. C.3. Test B1, Individual Unload-Reload Loops, Group CB1
195
45
402.22.01.81.61.41.21.0
Force (kips)
1.16
1.12k = 1.2 X 106 lb./in.(0.21 X 106 kN/m)
45
40
1.16
1.12k = 1.2 X 106 lb./in.(0.21 X 106 kN/m)
45
40
1.16
1.12k = 1.3 X 106 lb./in.(0.23 X 106 kN/m)
45
40
1.16
1.12k = 0.86 X 106 lb./in.(0.15 X 106 kN/m)
45
40
1.16
1.12
1098765
Force (kN)
k =1.2 X 106 lb./in.(0.21 X 106 kN/m)
Fig. C.4. Test B1, Individual Unload-Reload Loops, Group DB1
196
Table C.1. Stiffnesses of Individual Small-Amplitude [1 kip (4.4 kN)] Unload-Reload Loops; Test B1, Incremental Plate-Load Test from 0 to 8.3 kips (36.9 kN) on Drier Material (Moisture Content ~ 4.7%)
Drier Material (moisture content ~ 4.7%)
ρ = 135 (lb/ft3) From nuclear density tests
ν = 0.25
ro = 0.5 (ft) Radius of plate
Cursors
Loop Number A B
Numpts in loop Slope k (from plt)
Average k for Each Group (from plt)
Relative Shear Wave Velocity, vsi (ft/sec)
k (from SASW)
Lbs/in Lbs/in k-4Gro/(1-ν)
First Set of Loops 1-1 75885 77691 1835 1.22 6.203+05
1-2 77491 79378 1887 0.53947 1.85E+06
1-3 79205 80927 1722 0.62856 1.59E+06
1-4 80715 82437 1722 0.643 1.56E+06
1-5 82074 83502 1428 0.446 2.24E+06 1.81 E+06 800 5.96 E+05
Second Set of Loops 2-1 114466 116186 1720 0.222 4.50E+06
2-2 115930 117449 1519 0.031 3.23E+07
2-3 117352 118605 1253 0.447 2.24E+06
2-4 118436 119912 1476 0.663 1.51E+06
2-5 119832 121112 1280 0.964 1.04E+06 8.31E+06 1100 1.13E+06
Third Set of Loops 3-1 247739 250068 2329 0.7337 1.36E+06
3-2 249871 251668 1797 0.45603 2.19E+06
3-3 251524 252869 1345 0.42034 2.38E+06
3-4 252727 254128 1401 0.35297 2.83E+06
3-5 254015 255081 1066 0.36267 2.76E+06 2.54E+06 #REF!
Fourth Set of Loops 4-1 316719 318471 1752 0.84551 1.18E+06
4-2 318282 319876 1594 0.824 1.21E+06
4-3 319638 321001 1363 0.788 1.27E+06
4-4 320777 322094 1317 1.17 8.65E+06
4-5 321903 323220 1317 0.847 1.18E+06 1.21E+06 #REF!
Note: Shaded boxes not used in the average
APPENDIX D
INDIVIDUAL UNLOAD-RELOAD LOOPS FOR TEST C1
50.049.048.0
3.02.82.62.42.22.01.81.6
Force (kips)
1.28
1.24
1.20
k = 1.0 X 106 lb./in.(0.18 X 106 kN/m)
50.049.048.0
1.28
1.24
1.20
k = 0.76 X 106 lb./in.(0.13 X 106 kN/m)
50.049.048.0
1.28
1.24
1.20
k = 0.95 X 106 lb./in.(0.17 X 106 kN/m)
50.049.048.0
1.28
1.24
1.20
k = 0.79 X 106 lb./in.(0.14 X 106 kN/m)
50.049.048.0
1.28
1.24
1.20
13121110987
Force (kN)
k = 1.1 X 106 lb./in.(0.19 X 106 kN/m)
Fig. D.1. Test C1, Individual Unload-Reload Loops, Group AC1
199
60.059.559.058.5
4.54.03.53.0
Force (kips)
1.52
1.48k = 2.8 X 106 lb./in.(0.49 X 106 kN/m)
60.059.559.058.5
1.52
1.48k = 1.5 X 106 lb./in.(0.26 X 106 kN/m)
60.059.559.058.5
1.52
1.48
k = 1.2 X 106 lb./in.(0.21 X 106 kN/m)
60.059.559.058.5
1.52
1.48
k = 2.8 X 106 lb./in.(0.49 X 106 kN/m)
60.059.559.058.5
1.52
1.48
20181614
Force (kN)
k = 2.9 X 106 lb./in.(0.51 X 106 kN/m)
Fig. D.2. Test C1, Individual Unload-Reload Loops, Group BC1
200
92.091.691.2
9.59.08.58.07.57.0
Force (kips)
2.352.342.332.32
k = 9.0 X 106 lb./in.(1.6 X 106 kN/m)
92.091.691.2
2.352.342.332.32
k = 32 X 106 lb./in.(5.5X 106 kN/m)
92.0
91.6
91.2
2.352.342.332.32k = 18.7 X 106 lb./in.
(3.3 X 106 kN/m)
92.091.691.2
2.352.342.332.32k = 11.5 X 106 lb./in.
(2.0 X 106 kN/m)
92.091.691.2
2.352.342.332.32
424038363432
Force (kN)
k = 3.7 X 106 lb./in.(0.65 X 106 kN/m)
Fig. D.3. Test C1, Individual Unload-Reload Loops, Group CC1
201
88.0
87.0
4.44.24.03.83.63.43.23.0
Force (kips)
2.232.222.212.20
k = 2.8 X 106 lb./in.(0.49 X 106 kN/m)
88.0
87.0
2.232.222.212.20
k = 12 X 106 lb./in.(2.1 X 106 kN/m)
88.0
87.0
2.232.222.212.20k = 3.1 X 106 lb./in.
(0.54 X 106 kN/m)
88.0
87.0
2.232.222.212.20
k = 3.3 X 106 lb./in.(0.58 X 106 kN/m)
88.0
87.0
2.232.222.212.20
20191817161514
Force (kN)
k = 2.8 X 106 lb./in.(0.49 X 106 kN/m)
Fig. D.4. Test C1, Individual Unload-Reload Loops, Group DC1
203
84.0
83.0
82.03.23.02.82.62.42.22.01.8
Force (kips)
2.12
2.10k = 1.5 X 106 lb./in.(0.26 X 106 kN/m)
84.0
83.0
82.0
2.12
2.10k = 2.9 X 106 lb./in.(0.51 X 106 kN/m)
84.0
83.0
82.0
2.12
2.10k = 2.1 X 106 lb./in.(0.37 X 106 kN/m)
84.0
83.0
82.0
2.12
2.10k = 2.4 X 106 lb./in.(0.42 X 106 kN/m)
84.0
83.0
82.0
2.12
2.10
141312111098
Force (kN)
k = 3.9 X 106 lb./in.(0.68 X 106 kN/m)
Fig. D.5. Test C1, Individual Unload-Reload Loops, Group EC1
204
Table D.1. Stiffness of Individual Small-Amplitude [1 kip (4.4 kN)] Unload-Reload Loops; Test C1, Incremental Plate-Load Test from 0 to 8.6 kips (38.3 kN) on Wetter Material (Moisture Content ~6.1%)
Wetter Material (moisture content ~ 6.1%)
ρ = 135 (lb/ft3) From nuclear density tests
ν = 0.25
ro = 0.5 (ft) Radius of plate
Cursors
Loop Number A B
Numpts in loop Slope k (from plt)
Average k for Each Group (from plt)
Relative Shear Wave Velocity, vsi (ft/sec) k-4Gro/(1-ν)
(lbs/in) (lbs/in) (lbs/in)
First Set of Loops 1-1 74032 75499 1467 1.002 9.98E+05
1-2 75407 76874 1467 1.32 7.58E+05
1-3 76740 77903 1163 1.0532 9.49E+05
1-4 77747 79305 1558 1.26 7.94E+05
1-5 79151 80597 1446 0.91 1.10E+06 9.20E+05 900 7.55E+05
Second Set of Loops 2-1 146504 147618 1114 0.35374 2.83E+06
2-2 147500 149771 2271 0.67153 1.49E+06
2-3 149513 151598 2085 0.82735 1.21E+06
2-4 151448 153114 1666 0.36158 2.77E+06
2-5 152962 154351 1389 0.34355 2.91E+06 2.50E+06 1100 1.13E+06
Third Set of Loops 3-1 241208 242314 1106 0.11127 8.99E+06
3-2 242169 244716 2547 0.0316 3.16E+07
3-3 244388 246109 1721 0.0535 1.87E+07
3-4 245982 247242 1260 0.00866 1.15E+07
3-5 247123 248521 1395 0.22416 3.65E+07 1.77E+07 0 0.00E+00
Fourth Set of Loops 4-1 313076 315398 2322 0.35754 2.80E+06
4-2 315153 316381 1228 0.083582 1.20E+07
4-3 316258 317850 1592 0.32177 3.11E+06
4-4 317689 318992 1303 0.29949 3.34E+06
4-5 318822 320553 1731 0.36424 2.75E+06 3.00E+06 1260 1.48E+06
Fifth Set of Loops 5-1 364570 366193 1623 0.666 1.50E+06
5-2 365988 368461 2473 0.344 2.91E+06
5-3 368355 370134 1779 0.47976 2.08E+06
5-4 370045 371369 1324 0.42574 2.35E+06
5-5 371270 372860 1590 0.25653 3.90E+06 2.81E+06 1030 9.88E+05
Note: Shaded boxes not used in the average
8
APPENDIX E
INDIVIDUAL LOADING CYCLE PLOTS FOR TEST C2
30
25
20
15
10
5
086420
Force (kips)
0.6
0.4
0.2
0.0
403020100Force (kN)
k = 0.145 X 106 lb/in.(0.0254 X 106 kN/m)
k = 0.531 X 106 lb/in.(0.0930 X 106 kN/m)
Fig. E.1. Test C2; Loop 1 of 5 - 5 Loading Cycles from 0 to 8 kips on Wetter Material (w ~ 6.1 %)
30
25
20
15
10
5
086420
Force (kips)
0.6
0.4
0.2
0.0
403020100Force (kN)
k = 0.552 X 106 lb/in.(0.0967 X 106 kN/m)
Fig. E.2. Test C2; Loop 2 of 5 - 5 Loading Cycles from 0 to 8 kips on Wetter Material (w ~ 6.1 %)
30
25
20
15
10
5
086420
Force (kips)
0.6
0.4
0.2
0.0
403020100Force (kN)
k = 0.111 X 106 lb/in.(0.0194 X 106 kN/m)
k = 0.469 X 106 lb/in.(0.821 X 106 kN/m)
Fig. E.3. Test C2; Loop 3 of 5 - 5 Loading Cycles from 0 to 8 kips on Wetter Material (w ~ 6.1 %)
30
25
20
15
10
5
086420
Force (kips)
0.6
0.4
0.2
0.0
403020100Force (kN)
k = 0.625 X 106 lb/in.(0.109 X 106 kN/m)
k = 0.191 X 106 lb/in.(0.0334 X 106 kN/m)
Fig. E.4. Test C2; Loop 4 of 5 - 5 Loading Cycles from 0 to 8 kips on Wetter Material (w ~ 6.1 %)
30
25
20
15
10
5
086420
Force (kips)
0.6
0.4
0.2
0.0
403020100Force (kN)
k = 0.648 X 106 lb/in.(0.113 X 106 kN/m)
k = 0.160 X 106 lb/in.(0.0280 X 106 kN/m)
Fig. E.5. Test C2; Loop 5 of 5 - 5 Loading Cycles from 0 to 8 kips on Wetter Material (w ~ 6.1 %)
REFERENCES
American Association of State Highway and Transportation Officials
(AASHTO) (1986), T 222-81, “Nonrepetitive Static Plate Load Test of Soils and Flexible Pavement Components, for Use in Evaluation and Design of Airport and Highway Pavements”.
American Association of State Highway and Transportation Officials
(AASHTO) (1986), AASHTO Guide for Design of Pavement Structures, 1993.
Ahtchi-Ali, F. and J.C. Santamarina (1994); “Settlement of Footings on
Granular Materials: Low and Large Strain Parameters”; Vertical and Horizontal Deformations of Foundations and Embankments: Proceedings of Settlement ‘94 / Texas A&M University, College Station, TX, June 16-18, 1994; edited by Albert T. Yeung and Guy Y. Felio. ASCE Geotechnical Special Publication No. 40, pp 1287-1297.
Bay, J.A. (1997), Development of a Rolling Dynamic Deflectometer for
Continuous Deflection Testing of Pavements, Dissertation, The University of Texas at Austin, Dec, 1997.
Bueno, J.L., K.H. Stokoe III, J.J. Allen (1998), “Density and Stiffness Results
for Thick Lift Sections”, Proceedings of the International Center for Aggregages Research Conference, St Louis MO, April 19-21, 1998.
Burland, J.B. (1989), “Small is Beautiful - the stiffness of soils at small
strains,” Ninth Laurits Bjerrum Memorial Lecture, Canadian Geotechnical Journal, Volume 26, pp. 499-516.
211
Huang, Y.H., (1969), “Influence Charts for Two-Layer Elastic Foundations,” Journal of the Soil Mechanics and Foundation Division, American Society of Civil Engineers (ASCE), Vol. 95, No. SM2, March, pp. 709-713.
Seed, H.B., Wong, R.T., Idriss, I.M., and Tokimatsu, K. (1986), “Moduli and
Damping Factors for Dynamic Analysis of Cohesionless Soils,” Journal of the Soil Mechanics and Foundation Division, American Society of Civil Engineers (ASCE), Vol. 112, No. SM11, pp. 1016-1032.
212
213
Stokoe, K.H.; S.G.Wright; J.A. Bay; J.M. Roesset (1994), “Characterization of Geotechnical Sites by SASW Method,” Technical Report: Geophysical Characterization of Sites, International Society of Soil Mechanics and Foundation Engineering (ISSMFE) Technical Committee 10, edited by R.D. Woods, Oxford Publishers, January, 1994.
Terzaghi, K.T. and R.B. Peck (1948), Soil Mechanics in Engineering Practice,
John Wiley and Sons, Inc. New York, Copyright, 1948.