Application of Piezoelectric Sensors in Soil Property Determination

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APPLICATION OF PIEZOELECTRIC SENSORS

IN SOIL PROPERTY DETERMINATION

by

LEI FU

Submitted in partial fulfillment of the requirements

for the degree of Doctor of Philosophy

Dissertation Advisor:

Prof. XIANGWU ZENG

Department of Civil Engineering

CASE WESTERN RESERVE UNIVERSITY

August, 2004


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CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the dissertation of

______________________________________________________

candidate for the Ph.D. degree *.

(signed)_______________________________________________

(chair of the committee)

________________________________________________

________________________________________________

________________________________________________

________________________________________________

________________________________________________

(date) _______________________

*We also certify that written approval has been obtained for any

proprietary material contained therein.

Lei Fu

David Gurarie

Adel S. Saada

J. Ludwig Figueroa

Robert Mullen

07/09/2004

Xiangwu Zeng


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DEDICATION

I love you all


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i

TABLE OF CONTENTS

TABLE OF CONTENTS iLIST OF TABLES iv

LIST OF FIGURES vi

ACKNOWLEDGEMENTS xi

ABSTRACT xii

CHAPTER 1 INTRODUCTION 1

1.1 Introduction 11.2 Laboratory Measurement of Soil Properties 1

1.2.1 Introduction 11.2.2 Element Tests 31.2.3 Model Tests 51.2.4 Centrifuge Tests 7

1.2.4.1 Introduction 71.2.4.2 Scaling Laws 91.2.4.3 Limitations of Centrifuge Modeling 121.2.4.4 CWRU Centrifuge 16

1.3 Field Determination of Soil Properties 221.3.1 Introduction 221.3.2 Seismic Methods 23

1.3.2.1 Crosshole Method 241.3.2.2 Downhole Method 261.3.2.3 Shear Wave Refraction Method 271.3.2.4 SASW Method 28

1.3.3 Cone Penetration Tests (CPT) 291.3.4 Standard Penetration Tests (SPT) 30

1.4 Piezoelectric Sensors and Their Applications 311.4.1 Introduction 31

1.4.2 Piezo Motors 331.4.3 Piezo Generators 341.4.4 2-Layer Elements 34

1.4.4.1 Bender Elements 341.4.4.2 Extender Elements 37

1.1.1 Series and Parallel Operation 371.1.2 Application of Piezoelectric Sensors in Soil Property

Determination 39


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CHAPTER 2 LITERATURE REVIEW 41

2.1 Review of Piezoelectric Sensors in Soil Property Measurement 412.2 Review of Soil Property Measurement in Centrifuge tests 442.3 Research Objectives and Outline 52

2.3.1 Research Objectives 522.3.2 Outline 53

CHAPTER 3 BENDDER ELEMENTS IN CENTRIFUGE MODEL TESTS

---DRY SPECIMEN TESTS 54

3.1 Introduction 54

3.2 Bender Elements 55

3.3 Nevada Sand 56

3.4 Experimental Setup 583.5 Description of the Model 61

3.6 Model preparation 633.7 Test Procedures 66

3.8 Experimental Results and Analysis 66

3.9 Conclusions 79

CHAPTER 4 BENDER ELEMENTS IN CENTRIFTGUE MODEL TESTS

---SATURATED SPECIMEN TESTS 80

4.1 Introduction 80

4.1.1 Evaluation Liquefaction Potential of Soils 804.1.2 Content of This Chapter 86

4.2 Test Equipment 864.3 Input Earthquake Motion 864.4 Transducer Description 87

4.4.1 Water-proof Bender Elements 874.4.2 Accelerometers 88

4.4.3 Pore Pressure Transducers 884.5 Preparation of Saturated Models 90

4.5.1 Description of the Models 90

4.5.2 Preparation of the Models 92

4.5.3 Pore Fluid 954.5.4 Saturation of specimen 97

4.6 Centrifuge Testing Procedure 98

4.7 Test Results 101

4.7.1 Shear Wave Velocities 101

4.7.2 Pore Pressures 1064.7.3 Accelerations 106


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4.7.4 Examination of Liquefaction Criteria Based on Shear

Wave Velocities 1074.8 Conclusions 116

CHAPTER 5 PIEZO CONE PENETROMETER 118

5.1 Introduction 118

5.2 Piezo Cone Penetrometer Structure 119

5.3 Experimental setup 123

5.4 Principle of the Tests 1255.5 Field Test Procedure 126

5.6 Typical Laboratory Test Results 127

5.6.1 Soil Description 127

5.6.2 Test Procedure 128

5.6.3 Test Results 1285.7 Conclusions 135

CHAPTER 6 ODOMETER FOR GRAVELLY MATERIAL STIFFNESS

MEASUREMENTS 136

6.1 Introduction 136

6.2 Equipment Description 140

6.3 Experimental Setup 143

6.4 Typical Test Results 1446.4.1 Soil Description 144

6.4.2 Test Procedures 1456.4.3 Test Results 145

6.5 Conclusions 148

CHAPTER 7 SUMMARY OF CONCLUSIONS AND SUGGESTIONSFOR FUTURE STUDY 149

7.1 Introduction 1497.2 Summary of Observations and Conclusions 151

7.2.1 Application of Bender Elements in Centrifuge Tests 151

7.2.2 Piezo Cone Penetration for Pavement Field Tests 153

7.2.3 Odometer for Gravelly Material Stiffness Measurements 1547.3 Suggestions for Future Study 155

REFERENCES 159


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LIST OF TABLES

Table 1.1 Relative Quality of the Laboratory Technique for Measurement

of Dynamic Soil Properties (after Silver, 1981) 4

Table 1.2 Scaling Factors for Centrifuge Tests (after Taylor, 1995) 12

Table 1.3 Comparison of Methods for Centrifuge Earthquake MotionSimulation (after Whitman, 1988) 18

Table 3.1 Bender Element Performance (Source: Piezo Systems, Inc.) 56

Table 3.2 Index Properties of Nevada Sand (after Arulmoli, 1994) 57

Table 3.3 Locations of the Bender Elements in Models 62

Table 3.4 Shear Save Velocities Measured during Spin-up of the Centrifuge

(Dr = 30%) 68

Table 3.5 Shear Wave Velocities Measured during Spin-up of the Centrifuge

(Dr = 48%) 69

Table 4.1 Specifications of Accelerometer 89

Table 4.2 Calibrations of Accelerometers 89

Table 4.3 Specifications of Pore Pressure Transducers 90

Table 4.4 Calibrations of Pore Pressures Transducers 90

Table 4.5 Locations of Sensors 92

Table 4.6 Physical Properties of METHOCEL(Source: Dow Chemical Company) 96

Table 4.7 Shear Wave Traveling Time 102

Table 4.8 Shear Wave Velocities (Spin-up) 102

Table 4.9 Shear Wave Velocities (after the First Earthquake) 103

Table 4.10 Shear Wave Velocities (after the Second Earthquake) 103


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Table 5.1 Types of the Elements 120

Table 5.2 Index Properties of Two Soils 127

Table 5.3 Test Results on Nevada Sand 130

Table 5.4 Test Result on Delaware Clay 130

Table 5.5 Summary of the Results of CBR Tests 134


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LIST OF FIGURES

Figure 1.1 Range and Applicability of Dynamic Laboratory Tests(after Das, 1993) 4

Figure 1.2 Sketch of the Mechanics Relating to the Two Types of Centrifuges 6

Figure 1.3 Takenaka Corporation Centrifuge (Source: Takenaka Corporation) 8

Figure 1.4 Stresses in Model and Prototype 10

Figure 1.5 Stress Variation with Depth in a Centrifuge Model

(after Taylor, 1995) 14

Figure 1.6 CWRU Laminar Box (after Dief, 2000) 21

Figure 1.7 Crosshole Method 25

Figure 1.8 Downhole Method 26

Figure 1.9 Shear Wave Refraction Method 27

Figure 1.10 Spectral-Analysis-of-Surface-Waves Method 29

Figure 1.11 Sketch of a Cone Penetrometer 30

Figure 1.12 SPT Test (after Kovacs et al., 1981) 31

Figure 1.13 Peizoceremic Material 32

Figure 1.14 Sketch of a Motor 33

Figure 1.15 Sketch of a Generator 34

Figure 1.16 Structure of a 2-Layer Piezo Element 35

Figure 1.17 Bender Element Transmitter 36

Figure 1.18 Bender Element Generator 36

Figure 1.19 A 2-Layer Bender Element Poled for Series Operation 38


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Figure 1.20 A 2-Layer Bender Element Poled for Parallel Operation 38

Figure 1.21 Setup for Incorporating Bender Elements in the Resonant

Column Apparatus (after Dyvik, 1985) 40

Figure 2.1 Experimental System (after Shibata et al., 1991) 48

Figure 2.2 Layout of Bender Source and Receiver (after Gohal and Finn, 1991) 49

Figure 2.3 In-Flight Shear Wave Measurement (after Arulnathan et al., 2000) 51

Figure 3.1 Dimension of the Bender Element 55

Figure 3.2 Grain Size Distribution of Nevada Sand 57

Figure 3.3 Experimental Setup 60

Figure 3.4 Test Equipment in Laminar Box 60

Figure 3.5 Bender Elements in Soil Model 61

Figure 3.6 Traveling Pluviation Apparatus 65

Figure 3.7 Typical Recorded Signal 67

Figure 3.8 Effect of Relative Density on Shear Wave Velocity Measuredduring Spin-up of the Centrifuge 70

Figure 3.9 Repeatability of Shear Modulus Determined during Spin-up of

Two Different Centrifuge Models 71

Figure 3.10 Change of Shear Save Velocity with Acceleration during Spin-up

of the Centrifuge 71

Figure 3.11 Comparison between Test Results and Results from

Empirical Equation 74

Figure 3.12 Shear Modulus during Spin-up and Spin-down of the Centrifuge 75

Figure 3.13 Comparison of Gmax by Resonant Column Tests and Bender

Element Tests during Spin-up of the Centrifuge

(Dr= 30%) 77

Figure 3.14 Time History of Base Acceleration Scaled to Prototype Values 77


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Figure 3.15 Effect of Earthquake Shaking on Shear Modulus Measured

during Spin-down of the Centrifuge 78

Figure 4.1 Relationship between Cyclic Stress Ratios Causing Liquefaction

and (N1)60 Values (after Seed et al., 1975) 84

Figure 4.2 Liquefaction Relationship Recommended for Clean, Uncemented

Soils (after Andrus and Stoloe, 2000) 85

Figure 4.3 Prototype Acceleration of Base Input Motion 87

Figure 4.4 Locations of Sensors in Centrifuge Model 91

Figure 4.5 Schematic of the Chamber with an Air Tight Lid (after Dief, 2000) 94

Figure 4.6 Effect of Pore Fluid Viscosity on Pore Pressures in Centrifuge

Model Tests (after Dief, 2000) 96

Figure 4.7 Model Saturation System (after Dief, 2000) 98

Figure 4.8 Shear Wave Velocity Vs Acceleration

(Spin-up, before Earthquake) 104

Figure 4.9 Variations of Shear Wave Velocity with Depth in the Model(Spin-up, before Earthquake) 104

Figure 4.10 Shear Wave Velocities before and after the First Earthquake 105

Figure 4.11 Comparison of Shear Wave Velocities after the First and

Second Earthquakes 105

Figure 4.12 Pore Pressure History of the Top Point during the

First Earthquake 109

Figure 4.13 Pore Pressure History of the Middle Point during the


Figure 4.14 Pore Pressure History of the Bottom Point during theFirst Earthquake 110

Figure 4.15 Pore Pressure History of the Top Point during the

Repeated Earthquake 110


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Figure 4.16 Pore Pressure History of the Middle Point during the


Figure 4.17 Pore Pressure History of the Bottom Point during the


Figure 4.18 Acceleration History of the Top Point during the First Earthquake 112

Figure 4.19 Acceleration History of the Middle Point during the


Figure 4.20 Acceleration History of the Bottom Point during the


Figure 4.21 Acceleration History of the Top Point during theRepeated Earthquake 113

Figure 4.22 Acceleration History of the Middle Point during the


Figure 4.23 Acceleration History of the Bottom Point during the


Figure 4.24 Case history of Liquefaction with Centrifuge Model Test DataAdded Based on Shear Wave Velocity 115

Figure 4.25 CRR Values and Overburden Stress-Corrected Shear WaveVelocities before and after the First Earthquake 116

Figure 5.1 Detailed Schematic of the Piezo Penetrometer 121

Figure 5.2 Photo of the Piezo Cone Pentrometer 122

Figure 5.3 Experimental Setup for Laboratory Tests 123

Figure 5.4 Experimental Setup for Field Tests 124

Figure 5.5 Experimental Principal 125

Figure 5.6 Typical Bender Element Test Results 129

Figure 5.7 Typical Extender Element Test Result 129

Figure 5.8 Test Results on Nevada Sand (Dry Density=1600 kg/m3) 131


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Figure 5.9 Test Results on Delaware Clay (Dry Density = 1590 kg/m3) 131

Figure 5.10 CBR Test Results on Delaware Clay (Dry Density =1557 kg/m3) 133

Figure 5.11 CBR Test Results on Nevada Sand (Dry Density =1610 kg/m3) 134

Figure 6.1 Shear Modulus in Different Plane (after Zeng and Ni, 1999) 137

Figure 6.2 Relationship between Shear Moduli in Different Shear Planes:

(a) Theory; (b) Experimental Data (Vertical Stress Is 60 kPafor Inner Ellipse and Is Increased by 60 kPa for each Ellipse,

Pool Filter Sand) (after Zeng and Ni, 1999) 139

Figure 6.3 Detailed Schematic of the Odometer 141

Figure 6.4 Photo of the Odometer 142

Figure 6.5 Loading and Displacement Measurement System 143

Figure 6.6 Particle Size Distribution Curves of the Two Soils 144

Figure 6.7 Shear Moduli during One Cycle of Loading (Soil with 25%

Gravel, Cycle No. 1) (by Zeng, Wolfe, and Fu) 146

Figure 6.8 Settlement of the Soil Sample under Repeated Loading

(Soil with 50% Gravel) (by Zeng, Wolfe, and Fu) 147

Figure 6.9 Comparison of Test Results of Two Soils

(by Zeng, Wolfe, and Fu) 147

Figure 7.1 An Automatic Piezo Cone Penetrometer System 157


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ACKNOWLEDGEMENTS

The author would like to express his sincere and heartfelt appreciation to

his advisor, Professor Xiangwu Zeng, for his valuable guidance and

encouragement in academic and personal life. It was his idea which originated

this research.

The author is thankful to Professor Adel S. Saada, Professor J. Ludwig

Figueroa, and Professor Robert L. Mullen for serving on the graduate committee

and for their invaluable instructions.

The author is also thankful to Professor David Gurarie for being a member

of the graduate committee.

The author is indebted to Judy Wang for her proof reading of this

dissertation, Gang Liu for his help in centrifuge tests, and Yunyi Zou for his

friendly help in many aspects.

Many thanks are extended to Kathleen Ballou, Sheila Campbell, and

Bernie Strong for their support.

Finally, the study reported here was founded under NSF Grant No.

01960166. The author is deeply grateful to Dr. Clifford Astill (NSF Program

Manager) for his support.


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APPLICATION OF PIEZOELECTRIC SENSORS

IN SOIL PROPERTY DETERMINATION

Abstract

by

LEI FU

Piezoceramic as a smart or adaptive material has been widely used in

engineering measurement and control. When used in soil testing, the material can

work as a wave transmitter or a wave receiver. Among the piezoelectric sensors,

the bender element and the extender element are the most widely used. While the

bender element is used to generate and receive shear waves, the extender element

is used to produce and detect P-waves.

One application of piezoelectric sensors is to measure shear wave

velocities in centrifuge tests. Measurement techniques for both dry and saturated

specimens were developed. A series of centrifuge model tests were performed.

Bender element tests were carried out during the spin-up, spin-down, and in-

flight stages of a centrifuge. Dynamic centrifuge tests were conducted on both

dry and saturated models to investigate the influence of earthquake motions.

Shear wave traveling times, accelerations, and pore water pressures were

monitored during the tests. Based on the test results presented in this study, the

current shear wave velocity-based liquefaction evaluation criteria were examined.

Piezoelectric sensors were also used to develop a new piezo cone

penetrometer. The piezo cone penetrometer is equipped with one set of bender


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elements and one set of extender elements. The equipment is designed for the

purposes of measuring stiffness of the subgrade and the sublayer of a pavement

in the field. Compared to the conventional CBR test, this method is quick and

simple as well as being theoretically sound. The results in the laboratory have

shown it to be a promising tool.

Finally, a large odometer was developed for testing gravelly materials.

The advantages of the device include that it can measure the stiffness of a soil

with large grain sizes and can measure moduli in different planes.

In conclusion, measurement of soil properties using piezoelectric sensors

is direct and accurate. The technique is theoretically sound. The application of

the technique is limited to low strain levels, which are in the elastic range of soil

deformations.


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CHAPTER ONE

INTRODUCTION

1.1 Introduction

Geotechnical tests are used to investigate soil properties, provide

parameters for analyses, and evaluate the performance of a particular prototype.

Measurements of stiffness of soils are an important part of soil tests.Generally,

the test methods fall into two categories, field testing and laboratory testing. In

laboratory tests, either a specimen is tested to represent a point with a given initial

stress state in the field, or a model is tested to study the behavior of a prototype

under specific working condition. The ability of laboratory tests to provide

accurate measurements of soil properties depends on their ability to replicate the

initial stress conditions and loading conditions of the problems investigated. In

field tests, all the measurements are carried out in the existing state of the soil.

The influences of stress history, structural conditions of the soil body, thermal

conditions, and chemical conditions are reflected in the test results.

1.2 Laboratory Tests

1.2.1 Introduction

Currently lab tests provide material properties that are difficult to

measure by means of in-situ tests, such as high-strain modulus and high-strain


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damping. Nagarai (1993) cites the advantages of determining the mechanical

properties of soils in the laboratory, including:

(1)Total control over test conditions, including boundary conditions can be

attained;

(2)Control can be exercised over the choice of material to be tested;

(3)Tests can be carried out under simulated field conditions or can be very

different from the in-situ conditions, e.g., environmental factors such as

temperature and humidity can be simulated;

(4)Laboratory testing permits the examination of a great variety of other

conditions which may be relevant to further changes in environmental and

other stress conditions;

(5)Tests can be carried out on reconstituted (destructured or remolded) and

processed materials under different stress conditions;

(6) Laboratory test data enable the understanding or the basic mechanisms of

material behavior.

There are two types of laboratory tests, element tests and model tests.

Element tests are usually performed on relatively small specimens that are

assumed to be representative of elements which are subjected to uniform initial

stresses and undergo uniform changes in stress and strain conditions. Model tests

may be used to evaluate the performance of a particular prototype or verify

predictive theories.


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1.2.2 Element Tests

Static and dynamic tests are performed to measure soil properties with

respect to different controlled conditions. For measuring the of stiffness of soils, it

is argued (Woods,1994), however, that we should no longer distinguish between

dynamic and static properties as they are indeed a continuum, and we should,

rather, distinguish properties on the basis of strain level. Soil stiffness

measurements methods include seismic wave tests (ultrasonic pulse tests), cyclic

triaxial tests, resonant column tests, and cyclic simple shear tests, etc. Saada and

Townsend (1981) pointed out that the thin long hollow cylinder apparatus

complemented by the true triaxial apparatus with rigid boundaries, driven by the

proper controls, can simulate most of the conditions met in the field. The

magnitudes of modulus and damping are functions of the shear strain amplitude.

Figure 1.1 shows the amplitude of shear strain levels, types of applicable dynamic

tests, and the areas of applicability of the test results. Table 1.1 gives a summary

of the parameters measured in dynamic laboratory tests.


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Figure 1.1 Range and Applicability of Dynamic Laboratory Tests (after Das,

1993)

Table 1.1 Relative Quality of the Laboratory Technique for Measurement of

Dynamic Soil Properties (after Silver, 1981)

Relative Quality of Test Results

Shear

Modulus

Youngs

Modulus

Material

Damping

Effects of number

of Cycles

Attenuations

Resonant Column Good Good Good Good

With adaptation Fair

Ultrasonic pulse Fair Fair Poor

Cyclic triaxial Good Good Good

Cyclic simple shear Good Good Good

Cyclic torsional shear Good Good Good


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1.2.3 Model Tests

In other laboratory tests, specimens are tested as models. A model is a

reduced scale simulation of the prototype. Model tests may be used to evaluate the

performance of a particular prototype or to study the effects of different

parameters on a general problem. Model tests usually attempt to reproduce the

boundary conditions of a particular problem by subjecting a small-scale physical

model of a full-scale prototype structure. Commonly used model tests include the

centrifuge test and the shake table test.

The Geotechnical centrifuge test benefits from the additional centripetal

force acting on a model while the centrifuge is rotating. As it increases the self-

weight of the soil and thus creates a stress distribution in the soil sample that is

comparable to prototype. It is well known that soil behavior is a function of stress

level and stress history. It is this reason that centrifuge modeling of major use to

the geotechnical engineering. In principle, the stress conditions at any point in a

model should be identical to those at the corresponding point in a prototype. Then,

it is assumed that the overall behavior of the model, such as displacements and

failure, should also be identical to the prototype.

There are two types of centrifuges: the beam centrifuge with a swinging

basket and the drum centrifuge with a fixed channel (Figure 1.2).


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Figure 1.2 Sketch of the Mechanics Relating to the Two Types of Centrifuges

A shake table test models the response of field structures during an

earthquake in 1 g environment. Shake tables of many sizes have been used in civil

engineering research. Some are quite large, allowing models with dimensions of

several meters to be tested. In geotechnical earthquake engineering, the shake

table test has been used with great success in modeling the dynamic effect of

structures. But, in the shake table model, with densities kept constant while linear

dimensions reduced, the same the stress field as that of the prototype can not be

produced. For this reason, the shaking table test is less successful for soil

mechanics problems.


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Model tests share certain drawbacks, among the most important of which

are similitude and boundary effects. Boundary effects are usually associated with

the metallic boxes in which shake table and centrifuge models are usually

constructed. The side walls can restrain soil movement and reflect energy that

would radiate away in the prototype problem. The industrial filler material

Duxseal has been used as an absorbent wall lining with some success (Steedman,

1991).

1.2.4 Centrifuge Tests

1.2.4.1 Introduction

The centrifuge test is one type of model test that is used to study

prototype problems. By spinning the soil package and testing the model at a high

speed, an artificial gravity is induced. The increase in gravity allows the stress,

strain, and strength to be modeled in a scaled soil model. The conclusions

regarding the prototypes behavior can be made by observing the model in similar

circumstances. In order to replicate the gravity-induced stresses of a prototype in

a 1/n reduced model, it is necessary to test the model in a gravitational field n

times larger than that of prototype. This idea was applied for the first time in

1930s, in the field of geotechnical engineering by Bucky (1931) and Pokrovsky

(1932). Since then, a number of geotechnical centrifuges have been developed all

over the world as an important research tool. The centrifuge has proven valuable

both in the soil property investigation and the modeling of prototype.


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The main features of a centrifuge include payload capacity, arm radius,

maximum acceleration, and payload size. Figure 1.3 shows one of the most

powerful centrifuges in the world, the Takenaka centrifuge. It has the following

specifications:

Centrifuge radius: the platform radius is 7.0m;

Usable payload dimensions: 2.0 m 2.0 m 1.1 m (width depth

height);

Performance: maximum payload is 5000 kg; acceleration at

maximum payload is 100 g; payload at maximum acceleration is

2000 kg; and acceleration range is 10 g and 200 g.

Electrical slip-rings: 214 electrical slip-rings.

Figure 1.3 Takenaka Corporation Centrifuge (Source: Takenaka

Corporation)


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Possible geotechnical centrifuge studies include: 1) modeling of a

prototype. A model being constructed to be geometrically similar to the prototype

using the same material, the prototype behavior can be simulated in the centrifuge;

2) investigation of new phenomena; 3) parametric studies; 4) validation of

numerical models (Takemura et al., 1998).

Two key issues in centrifuge tests are scaling laws and scaling errors.

Scaling laws can be used by dimensional analysis. Centrifuge modeling is often

criticized as having some scaling errors due to the non-uniform acceleration field

and the difficulty of representing sufficient detail of the prototype in a small-scale

model. In physical modeling studies, it is seldom possible to replicate precisely all

the details of the prototype and some approximations have to be made.

1.2.4.2 Scaling laws

The basic scaling law derives from the need to ensure stress similarity

between the model and the corresponding prototype. The following scaling law

analyses were given by Taylor (1995).

By rotating a package in the centrifuge at high speeds, an acceleration

normal to the package is achieved (see Figure 1.4). The relationship is given by:

a=Re2=Ng (1.1)


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Model

Prototype

m=p

p

where, a = centrifugal acceleration

Re = effective length of the centrifuge arm

= angular velocity

N = scaling factor

g = earths gravity (9.81 m/sec2).

Figure 1.4 Stresses in Model and Prototype (after Taylor, 1995)


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Then the vertical stress, vm at depth hm in the model is:

vm

= Nghm

(1.2)

where, = mass density of the soil

hm = depth of the point below soil surface in the model.

In the corresponding prototype, the stress p is

p = ghp (1.3)

where, hm = Depth of the point below soil surface in the prototype

Thus for

m = p

or

ghp = Nghm

then

hm =N

1 hp

The scaling factor for linear dimensions isN

1. Since the model is a linear scale

representation of the prototype, then the displacement will also have a scaling

factor ofN

1. It follows therefore that the strain has a scaling factor of

1

1, and the

stress-strain curve mobilized in the model will be identical to the prototype. More

scaling factors of parameters are listed in Table 1.2.


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Table 1.2 Scaling Factors for Centrifuge Tests (after, Taylor, 1995)

Parameter Model Prototype

Acceleration N 1

Density 1 1

Stress 1 1

Strain 1 1

Velocity 1 1

Length 1 N

Area 1 N2

Volume 1 N3

Force 1 N2

Energy 1 N

3

Time (static) 1 1

Time (dynamic) 1/N 1

Time (dissipation) 1/N2

1

1.2.4.3 Limitations of Centrifuge Modeling

In physical modeling studies, it is seldom possible to replicate precisely all

of the details of the prototype, and some approximations have to be made. The

limitations involved in the modeling are: 1) errors in the centrifugal acceleration


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field; 2) grain size effects; 3) difficulty in modeling the actual site, i.e., aging,

sophisticated subsoil conditions; 4) inconsistency of scaling factors with time

((Takemura et al., 1998).

(1) Particle Size Effects

In the centrifuge test, the dimensions of a prototype is scaled down by a

factor of N, but generally, the soil particles can not be scaled down at the same

scale. This will produce grain size effects. An index used to show the effects is

the ratio of the representative length of the model (B) to the average grain

diameter (D50). For circular foundations, the critical ratio is 15 (Oveson, 1979).

Some researcher suggested that it is more appropriate to examine the particle size

effect by considering the ratio of particle size to shear band width (Tatsuoka et al.,

1991)

(2) Acceleration Field Scaling Errors

1) Variation in Vertical Direction

The Earths gravity is uniform for soil deposits in prototypes. When using

a centrifuge to generate the high acceleration field, there is a slight variation in

acceleration through the model (Taylor, 1995). Figure 1.5 shows there is exact

correspondence in stress between model and prototype two-thirds of the model

depth, and the maximum under-stress and the maximum over-stress exist at one-

third of the height of the model and at the bottom of the model, respectively. For


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most centrifuge models, hm/Re is less than 0.2, and therefore the maximum error

in the stress profile is generally less than 3% of the prototype stress.

Figure 1.5 Stress Variation with Depth in a Centrifuge Model (after Taylor,

1995)

2) Lateral Acceleration Component

In the centrifuge model, the acceleration is directed towards the center of

rotation and hence in the horizontal plane. There is a change in its direction

relative to the vertical across the width of the model. There is, therefore, a lateral

component of acceleration. To minimize this effect, it is good practice to ensure

that the major events occur in the central region of the model where the error due

to the radial nature of the acceleration field is small.

Maximum Over-stress

Depth

h

2h/3

h/3

Prototype

Centrifuge Model

Maximum Under-stress

Stress


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3) Coriolis Acceleration

Coriolis acceleration occurs when changing the reference system of

observation. The Coriolis effect may be observed in a centrifuge model, such as in

the modeling of a explosion, when the movement of the mass is in the plane of

rotation.

The Coriolis acceleration, ac can be expressed as:

ac = 2V (1.4)

where, = centrifuge angular velocity

V = velocity of moving mass.

The centrifugal acceleration is:

A = v (1.5)

where, v = velocity of centrifuge.

It is assumed that for low velocity of moving mass, Coriolis effects become

neglectable if ac/a < 10%. This implies V2v (Taylor, 1995).

(3) Boundary Conditions

In a centrifuge test, a model is built inside a container. For dynamic tests,

the excitation has to be transmitted through this container. The model container

imposes artificial boundaries and leads to potential boundary effects. Three major

boundary effects may be caused by a model container, namely the effects on the

stress field, on the strain field, and on the seismic waves (Taylor, 1995). The basic


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requirements for the containers of dynamic tests are that the end walls function as

shear beams with the same shear stiffness as the adjacent soil, and that the end

walls should have the same friction as the adjacent soil. Of the many containers,

the equivalent shear beam container (Zeng and Schofield, 1996) is the one close

to satisfying the requirements. This container is built from rectangular frames of

dural separated by rubber layers as to achieve the same dynamic stiffness as the

soil. To sustain the complementary shear stresses induced by base-shaking, a

flexible and in-extensible friction sheet was attached to the end walls.

1.2.4.4 CWRU Centrifuge

The Case Western Reserve University geotechnical centrifuge has a dual

platform with an effective radius of 1.37m. The centrifuge payload capacity is 20

g-ton with a maximum acceleration of 200g for static tests and 100g for dynamic

tests. The centrifuge is equipped with a hydraulic shaker designed by the TEAM

Corporation. The laminar box used in this test consists of 13 rectangular

aluminum rings separated by linear bearings. The internal dimensions of the box

are 53.3 cm (length) 24.1 cm (width) 17.7 cm (height). The following details

of the centrifuge were reported by Figueroa et al. (1998).

The centrifuge driving system consists of a 15 HP premium efficiency AC

motor and torque control inverter which powers the centrifuge arm through a belt

drive. The support structure consists of the main shaft, rotational bearings,

bearings housings, a triangular shaped support skirt, and three footings. The


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imbalance force as well as dead loads is transmitted to the foundation through this

structure. The centrifuge arm is balanced by adjusting the counterbalance weights

on the swing platform which opposes the testing platform. The dynamic

imbalance force is monitored at one of three support footings with a sensitive

LVDT which is connected to the centrifuge control computer.

The centrifuge is controlled using a program. The computer is configured

with two data acquisition boards which send and receive analog and digital

signals to and form the centrifuge.

The centrifuge data acquisition system is designed to accommodate a wide

variety of static and dynamic tests. The signal conditioning is performed by the

signal conditioning chassis which rides on the centrifuge arm in the

instrumentation rack mounted over the center of rotation. The digital analog lines

for the signal conditioning chassis are connected to a multifunction data

acquisition and control board. The conditioned analog signal is then passed

through the slip rings and on to the AT M10 16E.

(1) Electro-Hydraulic Shaker

In the centrifuge test, earthquake motions are simulated by the shake table

installed on the arm. This is an ideal method for modeling the responses of field

structures during the earthquakes.

Many different techniques have been introduced to generate motions of

the shake table. Table 1.3 is a comparison of the techniques. It is clear that the


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electro-hydraulic method is considered superior to other methods because of the

large forces, which can be generated by the hydraulic actuators as well as its

versatility in producing pre-programmed motions (Ko, 1994). The centrifuge

shaker of CWRU is the electro-hydraulic type.

Table 1.3 Comparison of Methods for Centrifuge Earthquake Motion

Simulation (after Whitman, 1988)

Cost Simplicity Adjustability Frequency Range

Low High

Cocked

Springs

Very

Low

Very Simple Poor --------------

Piezoelectric Low Simple Good ------

Explosive Low Simple Moderate ------------

Bumpy Road High Complex Moderate ------------

Hydraulic Very

High

Very Complex Very Good ------------------------

(2) Model Container

In a dynamic centrifuge test, the soil model in the container should

simulate the behavior of free field of the continuous soil horizon in the field

during an earthquake. The container may affect stress field, strain field, and

seismic waves. The boundary effects of the model container are considered a

major potential source of error. The design criteria for an ideal container as

following (Taylor, 1995):

1) The end walls function as shear beams with the same dynamic

stiffness as the adjacent soil, so as to achieve strain similarity and


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to minimize the interaction between the soil and the end walls and

hence minimize the generation of compression waves.

2) Each end wall should have the same friction as the adjacent soil so

that it can sustain the complementary shear stresses induced by

base-shaking and thus the same stress distribution as in the

prototype shear beam can be achieved.

3) The side walls should be frictionless so that no shear stress is

induced between the side walls and soil during base-shaking to

create the same two-dimensional condition as in the prototype.

4) The model containment should be rigid statically to achieve a zero

lateral strain condition, and after shaking to maintain its initial size.

5) The fictional end walls should have the same vertical settlement as

the soil layer contained during the spin-up of a centrifuge to avoid

initial shear stresses on the boundary.

Containers with different types of boundaries have been developed over

the years. By far, the most successfully device is a stack of ring or laminar box

(Whitman et al., 1981; Hushmand, et al., 1988; Zeng and Schofield, 1996). The

laminar box consists of rectangular frames stacked together with low friction

bearings between the frames. The idea is that the box would be essentially

massless and frictionless; the response of the soil to input motion at its base would

be controlled by the soil rather than the box properties. Energy absorbing


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materials have also been applied to the inner wall of the container to reduce the

influence of incident waves (Taylor, 1995).

CWRUs laminar box consists of 13 rectangular aluminum rings separated

from one another by linear motion anti-friction bearings. The internal dimensions

of the box are 53.3 cm 24.1 cm 17.7 cm (length width height). The

laminar box is shown in Figure 1.6. Detailed performance of the box under

dynamic loads can be found in the thesis of Dief (2000).


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Figure 1.6 CWRU Laminar Box (after Dief, 2000)


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1.3 Geotechnical Field Tests

1.3.1 Introduction

The conventional approach to characterize the engineering properties of

soils consists of a chain of events involving the overall appraisal of the problem,

sampling, testing, and analysis. Where these materials are too difficult to sample,

likely to be severely disturbed by the sampling process, or could not be sampled

due to structural safety, in-situ methods are used for engineering property

evaluation.

Geophysical techniques are normally used to determine the Youngs

modulus or shear modulus of the soil through measurement of the compression

wave and shear wave velocities, respectively. Penetration tests, such as standard

cone penetration test (SPT) and cone penetration test (CPT), are also widely used

in the field to evaluate soil properties, including stiffness, density, etc.

The measurement of soil properties by field tests has a number of

advantages:

1) Field tests do not require sampling, which can alter the stress, and

structural conditions in soil specimens. The problem becomes very acute for soils

such as very loose sand and peat which are difficult to sample without

considerable disturbance. Intensifying the need for in-situ determination of

dynamic properties is that these soils which are difficult to sample are also the

type of soils which are often of the most concern in dynamic site response

analysis.


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2) Many field tests measure the response of relatively large volumes of

soil, thereby minimizing the potential for basing property evaluation upon small,

unrepresentative specimens.

3) Furthermore, it is often not possible to accurately simulate the in-situ

stress conditions in the laboratory due to equipment limitations.

Field tests have some shortcomings however, such as the fact that they

do not allow the effects of conditions other than the in-situ conditions to be

investigated easily. In many field tests, the specific soil property is not measured

but is determined indirectly by empirical equations.

Field methods range from relatively simple penetration test to small-scale

loading tests to extensive nondestructive tests. Some field tests can be performed

on the ground surface, while others require the drilling of boreholes or the

advancement of a probe into the soil. The followings are some field measurement

methods of soil elastic modulus and other parameters.

1.3.2 Seismic methods

In situ measurements of the propagation behavior of low-amplitude stress

(seismic) waves within geologic media provides valuable geotechnical site-

characterization information. Seismic wave methods have proven to be both

effective and theoretically-sound in the determination of the low-strain material

stiffnesses of soil layers. The material properties measured from seismic methods

can be directly applied to low strain problems, such as vibrations of machine


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foundations. Seismic methods combined with other high strain tests, such as

triaxial tests can provide stiffness and damping values for high strain applications,

such as earthquake response analysis of earth structures.

There are four primary field methods routinely utilized to measure the

shear wave velocity: (1) downhole method, (2) crosshole method, (3) surface

refraction method, and (4) SASW method. In general, all of these techniques have

a common limitation: they provide velocity measurements only at low strain

levels (generally less than 10-4 percent).

Soil properties that influence wave propagation and other phenomena

include stiffness, damping, Poissons ratio, and density. Of these, stiffness and

damping are the most important.

1.3.2.1 Crosshole Method

The crosshole method involves generating a shear wave or compression

wave in one borehole, and at the same depth in one or more adjacent boreholes

measuring the average travel time for the waves, as shown in Figure 1.7. Based on

the seismic velocities, shear modulus, Young modulus and even Poissons ratio

can be determined. By testing at various depths, a velocity profile of the soil layer

can be obtained. The depth of test can reach 30 to 60 m.

The major shortcomings are that more than one borehole is needed. The

measured velocities may not be equal to the actual velocities when the high


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velocity layers exist nearby. In some situations, thin low-velocity layers may be

missed.

Figure 1.7 The Crosshole Method (Source: Olson Instruments, Inc.)


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1.3.2.2 Downhole method

The downhole method involves the generation of shear waves or

compressive with an impulse source at the ground surface adjacent to borehole.

The travel time of the down-propagating shear wave is measured at one or more

multi-axis geophones clamped in the borehole at various elevations (see Figure

1.8). The profile of shear wave or compression wave can be obtained. This test

requires one borehole, so it is a low cost test compared with the corsshole method.

Figure 1.8 The Downhole Method


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1.3.2.3 Shear Wave Refraction Method

In shear wave refraction test, horizontal geophones are employed with the

sensitive axis of the sensors aligned in a horizontal plane transverse to the

direction of wave travel (see Figure 1.9). The energy source may be sledge

hammer blows in extremely shallow search surveys (less that 10 meters), a

shotgun source when overburden conditions allow, or explosives where depth

and/or energy attenuation is a deciding factor. This is a non-intrusive method.

Measurements are performed on the ground surface without the use of boreholes,

so it is also economic. The test results can provide information for preliminary

planning purposes and feasibility studies. But, the accuracy of the method is

restrained in complicated multilayered deposits. It is accurate only under

conditions where velocities increase with depth;

Figure 1.9 The Shear Wave Refraction Method (Source: Frontier

Geosciences, Inc.)


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1.3.2.4 SASW (Spectral-analysis-of-surface-waves method )

The SASW method is a nonintrusive technique that employs surface waves

of the Rayleigh type to determine the layer thicknesses and stiffnesses of

subsurface profiles. The SASW technique is based on the dispersive property of

surface waves propagating in a layered system. In a layered system, the velocity

of Rayleigh waves varies with the wavelength of the surface waves. The variation

of velocity with wavelength depends on the subsurface stiffness. In the

application of the SASW technique, the stiffness profile is determined by first

measuring the dispersion curve (variation in surface wave velocity with

wavelength or frequency) and then through either an inversion or forward

modeling process, determining the layer thickness and their stiffness properties

(Stephen et al., 1994) (Figure 10). This method is relatively rapid and

inexpensive. The disadvantages arise due to difficulty of interpretation and lack of

specific stratigraphic information. Currently it is considered as secondary site

investigation tools for determining dynamic geotechnical properties. Like the

shear save refraction method, the SASW has particular application advantages to

evaluate material properties in sites that are difficulties to penetrate.


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Figure 1.10 Spectral-Analysis-of-Surface-Waves Method

(from http://www.geovision.com/SASW.htm)

1.3.3 Cone Penetration Test (CPT)

A cone penetrometer consists of the cone, friction sleeve and measuring

system as shown in Figure 1.11. The cone penetrometer is pushed into the ground

at a constant rate and continuous measurements are made. During the penetration,

the cone resistance and the friction are measured. The results from a cone

penetration test can be used to evaluate: soil type, soil density, stiffness, and shear

strength parameters. It permits the incorporation of other sensors, such as pore

water pressure transducer and temperature gage.


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Figure 1.11 Sketch of a CPT (after Baldi et al., 1988)

1.3.4 Standard Penetration Test (SPT)

The Standard Penetration Test (SPT) provides a measure of the resistance

of the soil to penetration, in term of number of blows, N (Figure 1.12). During the

test, a disturbed soil sample can be obtained. The sample can be used for

classification and index tests. The SPT N value, which gives an indication of the

soil stiffness, can be empirically related to many engineering properties, such as

relative density, stiffness, shear strength, compressibility, and liquefaction


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potential. The test is easy to execute and convenient both above and below the

water table.

Figure 1.12 SPT Test (after Kovacs et al., 1981)

1.4 Piezoelectric Sensors and Their Applications

1.4.1 Introduction

Piezocelectric sensors are made of piezo ceramic material. When a

piezoelectric sensor is electrically stressed by a voltage, its dimensions change.

When it is mechanically stressed by a force, it generates an electric charge. If the

electrodes are not short-circuited, a voltage associated with the charge appears. A


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+

-

piezoelectric sensor is therefore capable of acting as either a sensing or

transmitting element or both.

Figure 1.13 shows a piece of piezo ceramic material, in which P is the

original polarization field within the ceramic established during manufacture by a

high DC voltage that is applied between the electroded faces to activate the

material. The polarization vector P is represented by an arrow pointing from the

positive to the negative poling electrodes.

The relationship between the applied forces and the resultant responses

depend upon the piezoelectric properties of the ceramic, the size and shape of the

piece, and the direction of the electrical and mechanical excitation. Most

information about piezoelectric sensors of this section is from the website of

Piezo System, Inc.

Figure 1.13 Peizoceremic Material


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1.4.2 Piezo Motors

Piezo motors convert voltage and charge to force and motion. When an

electrical field which has the same polarity and orientation as the original

polarization field is placed across the thickness of a single sheet of piezoceramic,

the piece expands in the thickness or "longitudinal" direction (along the axis of

polarization) and contracts in the transverse direction (perpendicular to the axis of

polarization) (see Figure 1.14). When the field is reversed, the motions are

reversed. However, the motion of a sheet in the thickness direction is extremely

small (on the order of tens of nanometers). On the other hand, the transverse

motion along the length is generally larger (on the order of microns to tens of

microns) since the length dimension is often substantially greater than the

thickness.

Figure 1.14 Sketch of a Motor (Source: Piezo System, Inc)


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1.4.3 Piezo Generators

When a mechanical stress is applied to a single sheet of piezoceramic in

the longitudinal direction (parallel to polarization), a voltage is generated which

tries to return the piece to its original thickness (see Figure 1.15).

Figure 1.15 Sketch of Generator (Source: Piezo System, Inc)

1.4.4 2-Layer Elements

Two-layer elements can be made to elongate, bend, or twist depending on

the polarization and wiring configuration of the layers. A center shim laminated

between the two piezo layers adds mechanical strength and stiffness but reduces

motion. "2-layer" refers to the number of piezo layers as shown in Figure 1.16.

The "2-layer" element actually has nine layers, consisting of four electrode layers,

two piezoceramic layers, two adhesive layers, and a center shim.


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Figure 1.16 Structure of a 2-Layer Piezo Element

1.4.4.1 Bender Elements

Figure 1.17 illustrations common bending configurations. A 2-layer

element produces curvature when one layer expands (the top layer in Figure 1.17)

while the other layer contracts (the bottom layer in Figure 1.17). These

transducers are often referred to as bender elements. Bender motion on the order

of hundreds to thousands of microns and bender force from tens to hundreds of

grams are typical. When the direction of the electric field is changed continuously,

the direction of the curvature of the element deformation will change

continuously. Thus, the element will vibrate and work as a wave generator.


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Figure 1.17 Bender Element Transmitter (Source: Piezo System, Inc)

On the other hand, when a mechanical force causes a suitably polarized 2-

layer element to bend, one layer is compressed, and the other is stretched. Charge

develops across each layer in an effort to counteract this deformation. This

arrangement is good for a wave receiver (see Figure 1.18).

Figure 1.18 Bender Element Generator (Source: Piezo System, Inc)


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1.4.4.2 Extender Elements

A 2-layer element behaves like a single layer when both layers expand or

contract together. If an electric field is applied which makes the element thinner,

extension along the length and width results. Extender motion on the order of

microns to tens of microns and forces from tens to hundreds of Newtons are

typical. When a mechanical stress causes both layers of a suitably polarized 2-

layer element to stretch or compress, a voltage is generated which tries to return

the piece to its original dimension.

1.4.5 Series and Parallel Operation

The element arranged in series as shown in Figure 1.19 can generate a

total output voltage two times the voltage generated by an individual layer. This

arrangement is good for a receiver. On the other hand, for the same motion, a 2-

layer element arranged for parallel operation (Figure 1.20) needs only half the

voltage required for series operation. An applied electrical field causes maximum

deformation, making this arrangement suitable for a transmitter.


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Figure 1.19 A 2-Layer Bender Element Poled for Series Operation

Figure 1.20 A 2-Layer Bender Element Poled for Parallel Operation

Shape after Deformation

Vout

Input Electric Field

Shape before Deformation

Original Polarization Field

Output Force

Piezo Layers

V out

Output Electric Field

Input Force

Piezo Layers

Original Polarization Field

Shape before Deformation


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1.4.6 Application of Piezoelectric Sensors in Soil Property Determination

The piezoelectric sensor with its smart or adaptive structure has many

engineering applications, such as control transducers for aerospace systems and

health monitorings of structures.

The bender element technique enables geotechnical engineers to

determine Gmax of a soil by measuring wave velocity through a porous media. An

advantage of the test is the measurements and computations are more direct and

simpler than those in a resonant column test. The bender element may be

incorporated into other laboratory tests, such as resonant column, triaxial or

odometer tests. One experimental setup used by Dyvik and Madshus (1985) is

shown in Fig. 1.21. The shear wave velocity (vs) in the soil specimen can be

determined by:

vs = L/t (1.6)

where, L = the distance between the tip of the transmitter and the tip of the

receiver

t = the travel time of the shear wave through the distance L.

The elastic shear modulus (Gmax) is determined by:

Gmax = (vs)2

(1.7)

where, = the mass density of the soil.


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In Figure 1.21, the bender elements can be replaced by a set of extender

elements. Then P wave velocity vp can be measured as:

vp = L/t (1.8)

and elastic modulus can be calculated by:

E = (vp)2

(1.9)

Figure 1.21 Setup for Incorporating Bender Elements in the Resonant

Column Apparatus (after Dyvik, 1985)

Pedestal

Receiver

Receiver Signal

Driving Signal

Digital Oscilloscope

Top Cap

Soil Specimen

Transmitter

Wave Generator


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CHAPTER TWO

LITERATURE REVIEW

2.1 Review of Piezoelectric Sensors in Soil Property Measurements

Piezoelectric crystals were first introduced to soil tests by Lawrence (1963,

1965). He used the crystals to send and receive shear and compression waves in

sand and clay. Latter, Bender elements were used by some researchers in

measuring shear wave velocities (Shirley and Hampton, 1978; Shirley and

Anderson, 1978a & b). Horn (1980) used piezoelectric transducers comprised of a

stack of six bender elements connected together in saturated soil tests. The

elements coated by epoxy resin were used both to generate and receive shear

waves. Howarth (1985) used piezoelectric transducers in measuring compression

and shear wave velocities through rock specimens in a triaxial cell. Tarun et al.

(1991) used a triaxial-piezoelectric device to measure compression and shear

wave velocities of a granular material, a glass sphere assembly. They used very

high voltages to generate enough energy in granular media to have measurable

amplitude signals at the receiving transducers. The P-wave was generated by

applying 400 to 600 volts of a single pulse to compression wave transmitters. The

shear wave transmitters were actuated with a voltage of 80 to150 volts.

Lings and Greening (2001) introduced a single hybrid element termed

bender/extender, capable of transmitting and receiving both S and P waves

using a single pair of elements mounted across a dry sand sample. A 10 kHz


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single sinusoidal pulse with peak-to-peak amplitude of 20 Volts was used as

source signal. The received signals were connected directly to a digital

oscilloscope without using a charge amplifier. The test results showed that the

bender/extender could provide clear signal that are easy to interpret.

Bender elements have been incorporated into conventional geotechnical

test devices, such as triaxial, odometers, and direct simple shear devices. Since

specimens are not disturbed during bender elements tests, the specimens can be

subsequently tested for other soil properties. Dyvik and Madshus (1985)

combined piezoelectric tests into triaxial tests. A parallel connected bender

element was used as transmitter, and a series connected element was used as the

receiver of shear wave. For the series connected element, when used as a receiver,

it is twice as effective as a parallels connected element. On the other hand, a

parallels connect bender element is twice as effective as a series connected

element when used as a motor. Square waves of amplitude 10 Volts were used

as input signals. The maximum shear strain for the tests was estimated to be on

the order of 10-3

%. This is in the elastic range of soil deformation. The bender

element test results compared with those of resonant column tests showed general

agreement.

Thomann and Hryciw (1990) performed bender element tests in a large

odometer to measure Gmax under Ko condition. Zeng and Ni (1999) applied the

bender element technique to investigate the stress-induced anisotropy in Gmax of

sands. In their tests, bender element receivers were located at different directions


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in an odometer with respect to transmitters. Thus, shear wave velocities in

different planes of a specimen were measured and shear moduli were calculated

from the shear wave velocities. Zeng et al. (2002) developed a new test device

called the bender element cone penetrometer to measure the stiffness of base and

subgrade layers in a pavement.

Besides the measurement of stiffnesses of soils, the bender element

technique has also been used in investigating the liquefaction properties of the

soils based on the measured shear wave velocities. Shirley and Anderson (1978a

& b) used single bender element crystals as shear wave transmitter and receiver.

They performed shear wave propagation experiments on a saturated specimen

under undrained condition. The liquefaction was introduced by applying a sudden

increase in chamber pressure. They noticed that the disappearance of shear wave

was observed near liquefaction stage. De Alba et al. (1984) used piezoelectric

transducers in a triaxial specimen to investigate the liquefaction property of sands

and its relationship to shear wave velocities. The transducers were an array of four

cantilevered bender elements.

The factors that affect the bender element test results include the first

arrival time of the received signal, frequency of source signal, and rising time of

source signal etc. The first arrive time of the received signal is a main factor that

may affect test results. It is common practice to locate the first arrival of the shear

wave at the point of first deflection of the received signal. Reversal of the polarity

of the received signal as the polarity of the input signal is reversed is often taken


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as demonstration the arrival of the shear wave (Abbiss, 1981). However,

theoretical studies by Salinero et al. (1986) showed that the first deflection of the

signal may not corresponding to the arrival of the shear wave but to the arrival of

the so-called near-field component which travels with the velocity of a

compression wave. The near-field effect may mask the arrival of the shear wave

when the distance between the source and the receiver is in the range of ~ 4

wavelengths, which can be estimated from = Vs/f where f is the mean frequency

of the received signal (Viggiani and Atkinson, 1995). Regards to the length of the

wave, Thill et al. (1968) reported that a wavelength approximating the average

grain size resulted in almost complete signal attenuation and therefore made the

detection of wave arrival almost impossible. They recommended a wavelength

approximately 10 times the average grain size for low attenuation of propagated

waves. Their tests were conducted on rock samples. Zeng and Ni (1999) studied

the effect of the rising time of source signal on the test results. Square waves of

different rising time were used. They observed that the change in rising time of

the electric pulse did not affect the travel time for shear waves. But if the rising

time is too large, the vibration of the transmitter will be too weak to make a well-

defined first arrival of the wave.

2.2 Review of Soil Property Measurements in Centrifuge Tests

Centrifuge testing has gradually become a routine experimental method in

geotechnical engineering throughout the world given the fact that it can be used to


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study a wide range of problems. Centrifuge modeling provides engineers with a

cost effective experimental tool to investigate phenomena of concern at full-scale

stress conditions on a small-scale model. Data from centrifuge tests can be used to

study the mechanisms of complex problems, to validate numerical models, and to

verify new design methods. However, centrifuge modeling is also a complex

experimental method. Like many other experimental methods, centrifuge

modeling can have inherent inaccuracies and difficulties arising from factors such

as boundary conditions imposed by the model container; inability to satisfy all the

scaling laws in certain situations; system limitations of equipment, transducers;

and data acquisition, and the measurement of soil properties under centrifugal

acceleration during in-flight conditions. The usefulness and accuracy of testing

data depend critically on how well the effects of these problems are understood

and addressed. In recent years, a significant amount of research has been

conducted to study problems of transducer response (Kutter et al., 1990; and Lee,

1990), boundary effects in earthquake centrifuge tests (Hushmand, et al., 1988;

and Zeng and Schofield, 1996), the use of viscous pore fluids (Zeng et al., 1998;

Ko and Dewoolkar, 1998), and the influence of variation of centrifugal

acceleration and model container size on the accuracy of centrifuge test (Zeng and

Lim, 2002).

One of the challenges in centrifuge modeling is the measurement of soil

properties during the centrifuge flight. In most cases, soil properties in a model

are measured before and/or after a test under a 1g condition. However, as


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mechanical properties of soils such as strength and stiffness are highly stress

dependent, one can expect that these properties can be significantly different

during centrifuge flight. Without direct measurements, some important soil

properties, such as Gmax and K0, in the centrifuge model are usually assumed or

obtained by other test methods, including monotonic or cyclic triaxial tests,

monotonic or cyclic direct simple shear tests, or resonant column tests. This

creates a difficult situation for numerical modelers in the simulation of

experimental results. For example, in the VELACS project (Arulanandan and

Scott 1993), the values of Gmax and K0 for the same models used by different

predictors for numerical simulation of liquefaction problems varied significantly

for the same sand (Zeng and Arulanandan 1994). The differences in soil

parameters used by different predictors could have contributed significantly to the

reported differences in the numerical simulation results. Therefore, a reliable

measurement of soil properties during the flight of a model is necessary in order

to get a good numerical simulation of the test phenomena and to have a clear

understanding of the test results.

Due to the uncertainties and errors exit in centrifuge tests as previously

discussed, soil property measurements in in-flight centrifuge tests are important.

The investigation of samples can be conducted before, during, and after the test.

This research will focus on an investigation carried out in-flight. The

investigations before and after a centrifuge test can follow the same procedures as

for full scale field tests. In-situ investigation tools have been scaled down to


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conduct comparable tests in-flight, such as vane tests, T-bar tests, cone

penetration tests and seismic method tests.

In recent years, in-flight measuring devices have been developed to

provide more reliable soil property measurements in centrifuge tests. For example,

cone penetrometer tests are performed to determine soil strength or to check

homogeneity of the soil in the model. A test is carried out by measuring the

penetration resistance on the cone and, if possible, including the measurement of

pore water pressure. To use the penetration test data, empirical relationships for

their correlation with fundamental soil properties must be developed (Ferguson,

1985). The inter-laboratory variability of test results was assessed by five

European laboratories (Renzi et al., 1994). A comparison showed that the

difference in test results for sand was of the order on 20%. Katagiri and Okamura

(1998) proposed a cone penetration test manual for centrifuge tests.

Shibata et al. (1991) measured shear wave velocities in-flight. A

piezoelectric oscillator is used for generating seismic waves. The accelerometers

of piezoelectric type are placed at two different points to detect seismic motions

propagated in the soil. The accelerometers are embedded at the same depth as that

of the oscillator and are aligned with the oscillator (see Figure 2.1). The driving

signal of a rectangular waveform is produced by a function generator. The

frequency of the signal is 10 KHz, and double amplitude is 10 V. Before it is sent

to the oscillator, the signal is amplified 10 times. The signals from the

accelerometers are processed through high-pass filter, with a cut-off frequency at


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1.5 KHz. The phase shifts brought by the filter are assumed to be the same for the

two receivers. From the distance between the generator and the receiver, and the

traveling time difference between them, the shear wave velocity is determined.

Figure 2.1 Experimental System (after Shibata et al., 1991)


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Gohal and Finn (1991) reported measurements of the shear wave velocity

in centrifuge tests. Their experimental setup is shown in Figure 2.2. The elements

were attached to bearing plates and lined up vertically. A 10 volt single

amplitude, 30 Hz square wave pulse was used as the source signal. The received

signal was first amplified, then passed via the centrifuge slop rings to a data

acquisition system. The difficulty of the setup was to accurately determine the

location of the receivers during the test. A loose and a dense sample of one kind

of sand were tested and the shear wave velocities at different depths of the model

were obtained.

Figure 2.2 Layout of Bender Source and Receiver (after Gohal and Finn,

1991)


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Arulnathan et al. (2000) used a mini-air hammer to generate shear waves.

The propagation of shear waves in the model was recorded in-flight by a vertical

array of four accelerometers placed at different depths (Figure 2.3). The hammer

consisted of a hollow aluminum cylinder 47 mm long. A 25 mm long piston fit

inside the cylinder. The piston was fired towards the end of the cylinder by

applied air pressure, and the motion of the cylinder produced the shear wave.

Models of Nevada sand at 80 g were tested. The shear wave measured were

compared with those from piezoceramic bender element tests in a triaxia device

and got excellent agreement. Models of Nevada sand at 80 g were tested. The

shear waves measured were compared with those from bender element tests in a

triaxial device and were in excellent agreement.

More recently, in-flight operating robots have been developed to conduct

sophisticated soil property measurements (Gaudin et al., 2002 and Ng et al., 2002).

In recent years, as micro machine-work and measuring technologies

advance, instrumentation applicable to centrifuge model tests is developing. A

wide variety of instrumentation is employed in centrifuge tests. The instruments

should be tested and calibrated over their work load using the model ground,

which is performed in a centrifuge or at the Earths gravity.


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Figure 2.3 In-Flight Shear Wave Measurement (after Arulnathan et al., 2000)

Mini-air Piston


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2.3 Research Objectives and Outline

2.3.1 Research Objectives

The primary objective of this research is to utilize piezoelectric sensors

in the determination of soil properties in the field and laboratory. The first

objective of the research is to develop a technique for soil property measurements

in the centrifuge. Then the technique will be used to measure shear wave

velocities in dry and saturated models of Nevada sand before and after

earthquakes during the spin-up, spin-down, and in-flight stage of a centrifuge. The

effects of repeated earthquakes on the liquefaction property of the soil will also be

investigated. Then, based on the test results, shear wave-based liquefaction

criteria will be examined.

Another objective of the research is to develop a new cone penetrometer

equipped with piezoelectric sensors. The equipment is aimed at in-situ stiffness

measurement of sublayers of existing pavements or construction projects. A series

of laboratory tests will be performed using the equipment, and the test results will

be compared with conventional CBR test results.

Finally, a large odometer equipped with piezoelectric sensors for

laboratory measurements of properties of gravelly materials will be developed.

Typical test results of the odometer will be presented


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2.3.2 Outline

Chapter 3 presents the use of bender elements in dry specimen centrifuge

tests. The bender element technique used is presented in detail. Sample

preparation methods and test procedures are described. The test results are

presented and compared with the results obtained by other methods.

Chapter 4 presents the use of bender elements in saturated specimen tests.

The bender element technique for wet soil specimen tests, sample preparation

methods and test procedures are described. The dynamic centrifuge test results on

Nevada sand will be presented. Shear wave-based liquefaction criteria will be

checked and discussed in this chapter.

Chapter 5 introduces a new piezo cone penetrometer. The device is

described in detail. Typical test results are presented and compared with the

results obtained by CBR tests.

Chapter 6 introduces a new odometers for gravel material tests. The

devices are described in details. Typical test results are presented.

Chapter 7 summarizes the significant findings of this research.

Suggestions for future research are also presented.


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CHAPTER THREE

BENDER ELEMENTS IN CENTRIFUGE TESTS---DRY SPECIMEN TESTS

3.1 Introduction

Due to the uncertainties and errors that exist in centrifuge tests as

discussed in section 1.2.4.3, the measurements in in-flight centrifuge tests are

important. The investigation of samples can be conducted before, during, and

after tests. This chapter presents and discusses in detail the bender element

technique in measuring soil properties during centrifuge tests. Models of Nevada

sand were tested in dry conditions.

The CWRU centrifuge was used in all of the tests. The centrifuge was

swung up in steps of 10g, 20g, 40g, and 50g. At each step, a total of nine bender

element tests were performed. At 50g, an earthquake was applied to the soil

model. After the earthquake, the centrifuge was spun-down at the step of 50g, 40g,

20g, 10g, and 1 g. Again, at each step, bender element tests were performed.

Parameters, such as accelerations and settlement were monitored.

From the test results, the shear wave velocities of the soil in different

stages of the tests were calculated. By further calculations, the profiles of the

stiffness of the models were obtained. The test results were discussed and were

compared with the results of the empirical equation proposed by Hardin and

Richart (1963), as well as the results of resonant column tests.


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3.2 Bender Elements

The bender element types Q220-A4-303Y (transmitter) and Q220-A4-

303X (receiver) used in these tests are produced by Piezo System Inc. with

dimensions of 34.7 12.7 0.5 mm (length width thickness) as shown in

Figure 3.1. The performance of the bender element transmitter Q220-A4-303Y is

listed in Table 3.1.

Figure 3.1 Dimensions of the Bender Element


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Table 3.1 Bender Element Performance (Source: Piezo Systems, Inc.)

Part Number Q220-A4-303Y

Piezo Material 5A4E

Weight (grams) 2.5

Stiffness (N/m) 843

Capacitance (nF) 50

Maximum Voltage ( Vp) 90

Resonant Frequency (Hz) 250

Free Deflection (m) 325

Blocked Force (N) 0.27

3.3 Nevada Sand

Nevada sand is used in the model tests. It was purchased from the Gordon

Sand Company of Compton, California. The sand has been widely used in

laboratories around US for liquefaction studies. It was used in the VELACS

project (Arulanandan and Scott, 1993) for dynamic centrifuge model tests.

Classification tests determining material properties for Nevada sand such as

specific gravity, grain size distribution, and the maximum and minimum void

ratios were previously performed by other researchers. The grain-size distribution

is plotted in Figure 3.2 and the corresponding index properties are shown in Table

3.2.


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3.4 Experimental Setup

The tests described in this paper incorporate bender elements into

centrifuge tests to measure shear wave velocities during the spin-up, in-flight, and

spin-down of the centrifuge. The experimental setup is shown in Figure 3.3. The

elements, which are fixed to the supporting columns which are placed in a laminar

box, are shown in Figure 3.4. There are six bender elements, three transmitters,

named S1, S2, and S3, respectively, and three receivers, designated R1, R2, and

R3, respectively. They are located approximately at one-third and two-thirds of

the model depth and near the bottom of the model. The distance between the

transmitting and receiving elements at each depth level is 10cm. In the setup, the

tips of the elements are 2.8 cm away from the columns, so the influence of the

columns on the stress states of the soil between the tips of the elements is small.

This can be seen from the comparison of the bender element tests results with

those by resonant column tests shown in Fig 3.14. A large model box, a all

column size, and large distance between the transmitters and receivers can reduce

the effects induced by columns.

The bender element types Q220-A4-303Y (transmitter) and Q220-A4-

303X (receiver) were used. The triggering signal, a square pulse, which was sent

to the transmitters in the laminar box, was produced by an Agilent 54624A wave

generator located in the control room. Vibrations of the transmitters produced

shear waves that propagate through the soil and were recorded by the receivers.


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The recorded signals were first amplified by Keithley MB38-02 signal-

conditioning modules and then transferred through the slip rings to an Agilent

33120A oscilloscope located in the control room. The traveling time of the shear

waves could be read from the oscilloscope directly, or the data could be

downloaded on disk for later processing. A multiple switch was devised in the

control room to schedule tests in the sequence of S1 to R1, S1 to R2, S1 to R3,

and then from S2 to R1, etc. For each test, the traveling time was measured based

on one pulse test. The test usually had good repeatability. The wave traveling

distances for the horizontal travel directions were measured from tip to tip, and

for non-horizontal travel directions, they were measured between the closest

corners of the elements.

Square waves of amplitude 10 volts were used as triggering signals in the

tests. Some researchers have used signals of the same amplitude, such as Dyvik

and Madshus (1984) and Gohl and Finn (1991). Dyvik and Madshus (1984) also

showed in their tests that the maximum shear strain was on the order of 10-3

%.

This is well within the elastic range of soils. Later, the Gmax values obtained by

bender element tests were compared with those by resonant column tests (see

Figure 3.13). The frequencies of the triggering signals used in the tests varied

from about 100 to 3000 Hz. The frequencies have no obvious effect on the

traveling time measured, but they can be changed to receive clear signals.


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Foundation

Main Shaft

Agilent 33120AOscilloscope

ArmCounterweight

Skirt

Agilent 54624A

Wave Generator

Wires

Slip Rings

Keithley MB38-02

Signal-Conditioning Modules

Receivers

Transmitters

Laminar Box

Figure 3.3 Experimental Setup

Figure 3.4 Test Equipment in the Laminar Box


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Table 3.3 Locations of the Bender Elements in Models

Model Transducer X(mm) Y(mm) Z(mm)

S1 0 -50 107

S2 0 -50 57

S3 0 -50 8

R1 0 50 107

R2 0 50 57

Model 1

R3 0 50 8

S1 0 -50 107

S2 0 -50 53

S3 0 -50 9

R1 0 50 107

R2 0 50 53

Model 2

Documents

Application of Piezoelectric Sensors in Soil Property Determination