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 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)
______
______
______
______
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(date) ______
*We also certify that written approval has been obtained for any proprietary material contained therein.
DEDICATION
To my parents To my wife, Xiaoli To my daughter, Katherine
I love you all
TABLE OF CONTENTS
TABLE OF CONTENTS i LIST OF TABLES iv LIST OF FIGURES vi ACKNOWLEDGEMENTS xi ABSTRACT xii
CHAPTER 1 INTRODUCTION 1
1.1 Introduction 1 1.2 Laboratory Measurement of Soil Properties 1 1.2.1 Introduction 1 1.2.2 Element Tests 3 1.2.3 Model Tests 5 1.2.4 Centrifuge Tests 7 1.2.4.1 Introduction 7 1.2.4.2 Scaling Laws 9 1.2.4.3 Limitations of Centrifuge Modeling 12 1.2.4.4 CWRU Centrifuge 16 1.3 Field Determination of Soil Properties 22 1.3.1 Introduction 22 1.3.2 Seismic Methods 23 1.3.2.1 Crosshole Method 24 1.3.2.2 Downhole Method 26 1.3.2.3 Shear Wave Refraction Method 27 1.3.2.4 SASW Method 28 1.3.3 Cone Penetration Tests (CPT) 29 1.3.4 Standard Penetration Tests (SPT) 30 1.4 Piezoelectric Sensors and Their Applications 31 1.4.1 Introduction 31 1.4.2 Piezo Motors 33 1.4.3 Piezo Generators 34 1.4.4 2-Layer Elements 34 1.4.4.1 Bender Elements 34 1.4.4.2 Extender Elements 37 1.1.1 Series and Parallel Operation 37 1.1.2 Application of Piezoelectric Sensors in Soil Property Determination 39
i CHAPTER 2 LITERATURE REVIEW 41
2.1 Review of Piezoelectric Sensors in Soil Property Measurement 41 2.2 Review of Soil Property Measurement in Centrifuge tests 44 2.3 Research Objectives and Outline 52 2.3.1 Research Objectives 52 2.3.2 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 58 3.5 Description of the Model 61 3.6 Model preparation 63 3.7 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 80 4.1.2 Content of This Chapter 86 4.2 Test Equipment 86 4.3 Input Earthquake Motion 86 4.4 Transducer Description 87 4.4.1 Water-proof Bender Elements 87 4.4.2 Accelerometers 88 4.4.3 Pore Pressure Transducers 88 4.5 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 95 4.5.4 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 106 4.7.3 Accelerations 106
ii 4.7.4 Examination of Liquefaction Criteria Based on Shear Wave Velocities 107 4.8 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 125 5.5 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 128 5.7 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 144 6.4.1 Soil Description 144 6.4.2 Test Procedures 145 6.4.3 Test Results 145 6.5 Conclusions 148
CHAPTER 7 SUMMARY OF CONCLUSIONS AND SUGGESTIONS FOR FUTURE STUDY 149
7.1 Introduction 149 7.2 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 154 7.3 Suggestions for Future Study 155
REFERENCES 159
iii 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 Motion Simulation (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
iv 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
v 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
vi 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 Measured during 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
vii 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 First Earthquake 109
Figure 4.14 Pore Pressure History of the Bottom Point during the First Earthquake 110
Figure 4.15 Pore Pressure History of the Top Point during the Repeated Earthquake 110
viii Figure 4.16 Pore Pressure History of the Middle Point during the Repeated Earthquake 111
Figure 4.17 Pore Pressure History of the Bottom Point during the Repeated Earthquake 111
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 First Earthquake 112
Figure 4.20 Acceleration History of the Bottom Point during the First Earthquake 113
Figure 4.21 Acceleration History of the Top Point during the Repeated Earthquake 113
Figure 4.22 Acceleration History of the Middle Point during the Repeated Earthquake 114
Figure 4.23 Acceleration History of the Bottom Point during the Repeated Earthquake 114
Figure 4.24 Case history of Liquefaction with Centrifuge Model Test Data Added Based on Shear Wave Velocity 115
Figure 4.25 CRR Values and Overburden Stress-Corrected Shear Wave Velocities 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
ix 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 kPa for 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
x 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.
xi 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
xii 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.
xiii 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
1 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.
2 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.
3 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 Young’s Material Effects of number Attenuations
Modulus Modulus Damping of Cycles
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 —
4 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).
5
ω
ω
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.
6 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 prototype’s 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.
7 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:
z Centrifuge radius: the platform radius is 7.0m;
z Usable payload dimensions: 2.0 m× 2.0 m × 1.1 m (width × depth ×
height);
z 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.
z Electrical slip-rings: 214 electrical slip-rings.
Figure 1.3 Takenaka Corporation Centrifuge (Source: Takenaka Corporation)
8 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:
2 a=Reω =Ng (1.1)
9 where, a = centrifugal acceleration
Re = effective length of the centrifuge arm
ω = angular velocity
N = scaling factor
g = earth’s gravity (9.81 m/sec2).
ω
σp
σm= σp
ω
Model Prototype
Figure 1.4 Stresses in Model and Prototype (after Taylor, 1995)
10 Then the vertical stress, σvm at depth hm in the model is:
σvm = ρNghm (1.2) where, ρ = mass density of the soil
hm = depth of the point below soil surface in the model.
In the corresponding prototype, the stress σp is
σp = ρghp (1.3) where, hm = Depth of the point below soil surface in the prototype
Thus for
σm = σp or
ρghp = ρNghm then
1 hm = hp N
1 The scaling factor for linear dimensions is . Since the model is a linear scale N representation of the prototype, then the displacement will also have a scaling
1 1 factor of . It follows therefore that the strain has a scaling factor of , and the N 1 stress-strain curve mobilized in the model will be identical to the prototype. More scaling factors of parameters are listed in Table 1.2.
11
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 N3
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
12 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 Earth’s 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
13 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.
Prototype Stress
h/3 2h/3 Maximum Under-stress h Centrifuge Model
Maximum Over-stress Depth
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.
14 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 = 2ωV (1.4) where, ω = centrifuge angular velocity
V = velocity of moving mass.
The centrifugal acceleration is:
A = ωv (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 V<5%v. For high velocities such as in dynamic events, V>2v (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
15 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
16 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
17 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 Very Very Simple Poor ------Springs Low Piezoelectric Low Simple Good ------
Explosive Low Simple Moderate ------
Bumpy Road High Complex Moderate ------
Hydraulic Very Very Complex Very Good ------High
(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
18 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
19 materials have also been applied to the inner wall of the container to reduce the influence of incident waves (Taylor, 1995).
CWRU’s 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).
20
Figure 1.6 CWRU Laminar Box (after Dief, 2000)
21 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 Young’s 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.
22 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
23 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, Poisson’s 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 Poisson’s 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
24 velocity layers exist nearby. In some situations, thin low-velocity layers may be missed.
Figure 1.7 The Crosshole Method (Source: Olson Instruments, Inc.)
25 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
26 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.)
27 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.
28
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.
29
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
30 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
31 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
32 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)
33 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.
34
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.
35
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)
36 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.
37 Input Force
Piezo Layers
Shape before Deformation
Output Electric Field Original Polarization Field V out
Figure 1.19 A 2-Layer Bender Element Poled for Series Operation
Output Force Shape after Deformation
Input Electric Field V out
Shape before Deformation Piezo Layers Original Polarization Field
Figure 1.20 A 2-Layer Bender Element Poled for Parallel Operation
38 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:
2 Gmax = ρ(vs) (1.7)
where, ρ = the mass density of the soil.
39 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:
2 E = ρ(vp) (1.9)
Wave Generator
Top Cap Transmitter
Soil Specimen Digital Oscilloscope Driving Signal Receiver Signal
Receiver Pedestal
Figure 1.21 Setup for Incorporating Bender Elements in the Resonant Column Apparatus (after Dyvik, 1985)
40 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
41 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
42 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
43 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 ¼ ~ 4 wavelengths, which can be estimated from λ= 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
44 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
45 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
46 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
47 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)
48 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)
49 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 Earth’s gravity.
50
Mini-air Piston
Figure 2.3 In-Flight Shear Wave Measurement (after Arulnathan et al., 2000)
51 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
52 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.
53 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.
54 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
55 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 (±µm) ±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.
56 Grain Size Distribution 100 t 90 80 70 60 50 40 30 20
Percent FinerPercent by Weigh 10 0 1 0.1 0.01 Diameter (mm)
Figure 3.2 Grain Size Distribution of Nevada Sand (after Rokoff, 1999)
Table 3.2 Index Properties of Nevada sand (after Arulmoli, 1994)
Parameter Value
D50 0.17 mm
D10 0.09 mm
Cu 2.0
Cc 1.0
Specific gravity 2.67
Maximum dry density 17.33 kN/m3
Minimum dry density 13.87 kN/m3
Maximum void ratio 0.887
Minimum void ratio 0.511
57 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.
58 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.
59
Agilent 33120A Agilent 54624A Oscilloscope Wave Generator
Wires
Keithley MB38-02 Signal-Conditioning Modules Slip Rings
Receivers
Transmitters Arm Counterweight Skirt Laminar Box Main Shaft
Foundation
Figure 3.3 Experimental Setup
Figure 3.4 Test Equipment in the Laminar Box
60 3.5 Description of the Model
Altogether, three models of Nevada sand were tested with relative densities of Dr=30% (model 1), 31% (model 2) and 48% (model 3). The heights of the models were 15.3, 15.2, and 14.7 cm, respectively. Locations of the bender elements are shown in Figure 3.5. An accelerometer was installed at the base of laminar box. The locations of the bender elements are listed in Table 3.3
Z
Bender Element Holding Column
S1 R1
S2 R2 S3 R3 Y 0
Nevada Sand
X S1,S2,S3------Bender Element Transmitters R1,R2,R3------Bender Element Receivers
Figure 3.5 Bender Elements in Soil Model
61 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
Model 1 R1 0 50 107
R2 0 50 57
R3 0 50 8
S1 0 -50 107
S2 0 -50 53
S3 0 -50 9
Model 2 R1 0 50 107
R2 0 50 53
R3 0 50 9
S1 0 -50 109
S2 0 -50 55
S3 0 -50 10
Model 3 R1 0 50 109
R2 0 50 55
R3 0 50 10
Note: the coordinates of each element refer to lower front corner point of the element
62 3.6 Model Preparation
The model was prepared by a dry pluviation method using a sand hopper.
The setup of the traveling pluviation apparatus is shown in Figure 3.6. The sand deposition was performed by moving the hopper and the tube manually over the area of the model. In the dry pluviation method, the relative density of the model is defined by the drop height and the speed at which the sand is poured. Before pluviation, the two aluminum columns with the bender elements were fixed at prescribed positions within the laminar box. Sand pouring was carried out in thin layers by raising the tube by an amount equivalent to the thickness of each layer to obtain a constant height of pluviation. Chen et al. (1998) indicated that any type of traveling loop might be used without significant influence on the relative density.
The air pluviation technique consists of pouring consecutive dry soil layers through a fixed drop height and then saturating the specimen. The major factors affecting the relative density of air pluviated specimens are the height of particle drop and the pouring volume rate (Vaid and Negussey, 1984). Based on the results obtained by their tests, Chen at al. (1998) proposed the relationship between the relative density, drop height, and rigid tube diameter using the following expression:
m n Dr = D0+αh d (3.1) where, Dr = relative density
63 D0 = minimum relative density of the soil
d = tube diameter
h = falling height of the soil
α, m, n = constants depending on the soil.
The height of the sand hopper was adjustable in order to keep the outlet of tube at the desired heights. After pluviation, the height of the specimen and the weight of the sand used were measured. In the tests, the drop heights were 20, 20 and 70 cm, respectively, leading to relative densities of 30% (Model 1), 31%
(Model 2), and 48% (Model 3).
64
Figure 3.6 Traveling Pluviation Apparatus
65 3.7 Test Procedures
Before starting the centrifuge testing, the profile of the model was measured and the bender element test corresponding to the 1 g stress condition was performed. The centrifuge was then swung up in steps of 10g, 20g, 40g, and
50g measured in the middle of the sand layer. At each step, a total of nine wave velocity measurements, recording the shear wave velocity between the transmitter
Si to the receiver Ri (i = 1, 2 and 3), were performed. Then the centrifuge was swung down at a step sequence of 40g, 20g, 10g, and 1g. Again, at each step, the bender element tests were performed as before, and at 1g, the profile of the model was measured. After the “static” sequence of wave velocity measurements, tests to investigate the effect of an earthquake were carried out. The model was accelerated to 50g, and a synthetic earthquake was applied at the base of the model to investigate the change of soil properties after shaking. After the earthquake, the centrifuge was swung down in steps and further measurements of shear wave velocities were carried out. At 1g, the vertical settlements of the model surface were measured.
3.8 Experimental Results and Analysis
Typical signals recorded on the oscilloscope are shown in Figure. 3.7. The dashed line shown in the figure indicates signals obtained by the same sensor when the polarity of the source signal was reversed. The first reversed point of the two curves was considered to be the initial arrival of the shear waves.
66 5 25 20 3 15 Arrival of Shear Wave 10 1 5 0 -1 -5 -10 Received Signal (V) Signal Driving Received Signal (mV) Signal Received -3 Received Signal (Input Signal Reversed) -15 Driving Signal -20 -5 -25 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 Time (ms)
Figure 3.7 Typical Recorded Signals
Shear wave velocities measured in the horizontal shear planes and inclined shear planes in the models corresponding to relative densities of 30% (Model 1) and 48% (Model 3) are summarized in Tables 3.4 and Table 3.5, respectively. For the shear wave velocities in horizontal planes (or vii; i =1, 2, 3) there is a clear trend of increase in the shear wave velocities as the centrifugal acceleration increases. It is also clear that the deeper the element is located, the higher the speed is a consequence of the increased effective confining pressure. For the shear wave velocities in the inclined directions (or vij; i = 1, 2, 3, j = 1, 2, 3, and i ≠ j), the influence of centrifugal acceleration is the same. However, the relative magnitude between the vij values and in comparison to vii values is less obvious
67 due to two factors. Firstly, in the direction of the wave path, the magnitude of the
effective confining pressure changes. Therefore, the measured wave velocity is an
average over the entire stress path. Secondly, due to stress-induced anisotropy
(Zeng and Ni, 1999), the wave velocity on an inclined shear plane is higher than
in the horizontal shear plane under the same effective confining pressure.
Table 3.4 Shear Wave Velocities Measured during Spin-up of the Centrifuge
(Dr = 30%)
Acceleration (g) 1 10 20 40 50
v11 78.1 122.0 125.0 142.9 158.2
v12 76.4 119.2 117.6 139.7 159.9
v13 81.6 126.0 132.5 160.7 177.2
v21 68.4 95.6 120.3 153.8 163.5
Velocity* v22 76.9 130.2 143.7 177.3 191.6
(m/s) v23 73.8 117.9 143.9 179.4 194.4
v31 71.3 115.3 140.3 159.8 165.8
v32 74.9 111.2 142.3 174.5 188.7
v33 96.2 135.1 167.8 209.2 222.2
* vij : wave velocity between transmitter i and receiver j.
68 Table 3.5 Shear Wave Velocities Measured during Spin-up of the Centrifuge
(Dr = 48%)
Acceleration (g) 1 10 20 40 50
v11 86.2 123.5 136.6 153.8 159.2
v12 83.2 116.5 136.1 155.6 192.5
v13 87.3 133.7 146.3 171.3 177.2
v21 74.3 110.1 145.2 155.6 161.4
Velocity(m/s)* v22 84.7 130.2 176.1 185.2 195.3
v23 80.2 123.1 143.9 176.9 193.0
v31 92.6 137.2 158.2 189.1 195.0
v32 80.2 128.6 188.7 228.5 230.5
v33 104.2 136.6 193.8 252.5 266.0
* vij : wave velocity between transmitter i and receiver j.
Figure 3.8 shows the profiles of shear wave velocities in the soil layer in
Model 1 and Model 3 during spin-up of the centrifuge. It is clear that wave
velocities increase with depth and with centrifugal acceleration. It is also obvious
that the higher density in Model 3 leads to higher shear wave velocities at the
same depth under the same centrifugal acceleration. The results of Models 1 and
Model 2, which had about the same relative densities, are presented in Figure 3.9,
clearly showing a good repeatability of experimental results. Figure 3.10
summarizes the change of shear wave velocity with acceleration levels, which are
69 related to overburden stress levels, during the spin-up phase of the centrifuge test.
The trend of the variation in shear velocity agrees with the theoretical relationship that the shear velocity increases approximately as the fourth root of the stress or g-level.
Shear Wave Velocity (m/s) 50 100 150 200 250 300 0 1g(Dr=48%) 10g(Dr=48%) 0.03 20g(Dr=48%) 40g(Dr=48%) 50g(Dr=48%) 0.06 1g(Dr=30%) 10g(Dr=30%)
Depth (m) 0.09 20g(Dr=30%) 40g(Dr=30%) 50g(Dr=30%) 0.12
0.15
Figure 3.8 Effect of Relative Density on Shear Wave Velocity Measured during Spin-up of the Centrifuge
70 Shear Modulus (MPa)
0 1020304050607080 0 1 g(Dr=30%) 10g(Dr=30%) 0.03 20g(Dr=30%) 40g(Dr=30%) 50g(Dr=30%) 0.06 1g(Dr=31%) 10g(Dr=31%) 20g(Dr=31%) 0.09 40g(Dr=31%) Depth (m) Depth 50g(Dr=31%)
0.12
0.15
Figure 3.9 Repeatability of Shear Modulus Determined during Spin-up of Two Different Centrifuge Models
300 S1-R1(Dr=31%,Spin-up) S2-R2(Dr=31%,Spin-up) S3-R3(Dr=31%,Spin-up) 250 S1-R1(Dr=48%,Spin-up) S2-R2(Dr=48%,Spin-up) S3-R3(Dr=48%,Spin-up) 200
150 Shear Wave Velocity (m/s) Wave Shear
100
50 0 1020304050
Acceleration (g)
Figure 3.10 Change of Shear Wave Velocity with Acceleration during Spin- up of the Centrifuge
71 Based on the shear wave velocities measured and using Equation (1.7), shear moduli of the soil in the model can be calculated. The results are shown in
Figure 3.11. The dashed lines in the figure show the shear moduli calculated by the following empirical equation proposed by Hardin and Richart (1963):
2 1 6908(2.17 − e) 2 G = σ (3.2) max 1+ e 0
1 σ0 = (1+2K0) σv (3.3) 3 where, e = void ratio
σ0 = mean effective stress
σv = vertical effective stress and
K0 = at-rest earth pressure coefficient, which can be estimated using:
K0 = 1-sinθ (3.4)
where, θ = the friction angle with a value of 32 degrees as obtained through
triaxial testing of Nevada sand, Arulmoli (1994).
Figure 3.11 shows that the experimental results and the computed results agree with each other quite well. The test results are typically higher near the bottom of the model, which can be explained by the theoretical stress distribution
72 in a centrifuge model as shown in Figure 1.5. For about one-third of the model height, there exists a maximum under-stress, so the measured shear moduli would be smaller than those calculated. Near the bottom of the model, an over-stress state exists (Taylor, 1995), which leads to a higher measured shear moduli. The tests results thus show that the bender element technique can serve as a reliable and accurate shear wave velocity measurement tool in centrifuge tests.
Figure 3.12 shows the change of shear moduli during the spin-up and spin- down stages of the model. It is obvious that after experiencing a high stress at a centrifugal acceleration of 50g, the stiffness of the specimen increased. This is likely due to the lock up of horizontal effective stresses as the resulting of the plastic deformation of the soil, a commonly encountered soil behavior during a loading and unloading cycle.
73 Shear Modulus (MPa)
0 1020304050607080 0 1 g(Test Results) Relative Density Dr=30% 10g(Test Results) 20g(Test Results) 0.03 40g(Test Results) 50g(Test Results) 1g(H & R Equation) 0.06 10g(H & R Equation) 20g(H & R Equation) 40g(H & R Equation) 50g(H & R Equation)
Depth (m) Depth 0.09
0.12
0.15
Shear Modulus (Mpa) 0 20 40 60 80 100 120 0 1 g(Test Results) Relative Denstiy Dr=48% 10g(Test Results) 20g(Test Results) 0.03 40g(Test Results) 50g(Test Results) 1g(H & R Equation) 0.06 10g(H & R Equation) 20g(H & R Equation) 40g(H & R Equation) 50g(H & R Equation)
Depth (m) 0.09
0.12
0.15
Figure 3.11 Comparison between Test Results and Results from Empirical Equation
74 80 Relative Density Dr=30% 70
60
50
40
30 S1-R1(Spin-down) Shear Modulus(MPa) Shear 20 S2-R2(Spin-down) S3-R3(Spin-down) S1-R1(Spin-up) 10 S2-R2(Spin-up) S3-R3(Spin-up) 0 0 102030405060 Acceleration(g)
120 S1-R1(Spin-down) S2-R2(Spin-down) 100 S3-R3(Spin-down) S1-R1(Spin-up) S2-R2(Spin-up) 80 S3-R3(Spin-up)
60
40 Shear Modulus(MPa)
20 Relative Density Dr=48%
0 0 102030405060 Acceleration(g)
Figure 3.12 Shear Modulus during Spin-up and Spin-down of the Centrifuge
75 The observed behavior clearly demonstrates the importance of measuring the modulus during the centrifuge flight at the specified centrifugal acceleration.
Also, it is obvious that the effect of spin-up and spin-down on shear moduli is more significant in the loose sample.
The comparison of the shear modulus obtained in this study with the maximum shear moduli from resonant column tests is shown in Figure 3.13. It is clear that the strain levels were in the elastic range in the tests, and the supporting columns had little effect to the bender element test results.
To study the influence of earthquake vibration on the stiffness of a dry sand layer, a sinusoidal wave shaking with a prototype frequency of 6 Hz was applied to the model at 50g. The time history of the “earthquake” input is shown in Figure 3.13. The number of the cycles is 90. After the earthquake was applied, shear moduli at different depths and different centrifugal accelerations were measured. Comparisons between the shear moduli measured before and after the earthquake both during spin-down are shown in Figure 3.15. It is clear that the vibration significantly increased the shear modulus of the models. Based on the model profile measured after the tests, the settlement of the models were 1.6, 1.4 and 1.27 mm, and relative densities increased from 30%, 31%, and 48% to 35%,
35%, and 52% respectively.
76 80
70
60
50
40
30 Shear Modulus (MPa) Shear Modulus
20 Resonant Column Tests
10 Bender Element Tests
0 0.0 5.0 10.0 15.0 20.0 Stress (kPa)
Figure 3.13 Comparison of Gmax by Resonant Column Tests and Bender Element Tests during Spin-up of the Centrifuge (Dr = 30%)
150
100
50
0
-50 Acceleration(% g) -100
-150 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Time(Second)
Figure 3.14 Time History of Base Acceleration Scaled to Prototype Values
77 100 S1-R1(After E.Q.) Relative Density Dr=30% S2-R2(After E.Q) S3-R3(After E.Q.) 80 S1-R1(Before E.Q.) S2-R2(Before E.Q.) S3-R3(Before E.Q.)
60
40 Shear Modulus (Mpa) Shear Modulus
20
0 0 1020304050 Acceleraton (g)
140 S1-R1(After E.Q.) Relative Density Dr=48% S2-R2(After E.Q.) 120 S3-R3(After E.Q.) S1-R1(Before E.Q.) 100 S2-R2(Before E.Q.) S3-R3(Before E.Q.) 80
60
Shear Modulus (Mpa) Modulus Shear 40
20
0 0 5 10 15 20 25 30 35 40 45 50 Acceleraton (g)
Figure 3.15 Effect of Earthquake Shaking on Shear Modulus Measured during Spin-down of the Centrifuge
78 3.9 Conclusions
This chapter presented the successful application of the bender element technique to measure the shear modulus of soils during the spin-up, in-flight and spin-down stages of a centrifuge. The technique is accurate and reliable. During the centrifuge spin-up, the shear modulus increases with the centrifugal acceleration. When the centrifuge is spinning down, the shear modulus is much higher than it is during the spin-up stage at the same centrifugal acceleration; this indicates some degree of soil deformation. This technique can also be used to study the influence of earthquake excitation on the shear modulus of soils. The measured shear modulus agrees well with calculated values from a commonly used empirical formula, and the repeatability of experimental results is very good.
The measured stiffnesses or shear wave velocities show that the acceleration field in the centrifuge model is not uniform. While it has the correct stress field at about one-third depth of the model, it is over-stressed at the bottom and under-stressed near the surface of the model. To get better results in a numerical simulation of the model, the effects should be considered.
One difficulty encountered during this research was the electric-cross talking between channels in the slip rings because of the high current used in triggering the transmitters, which in some cases significantly affects the quality of data received. This difficulty can be avoided if an onboard data acquisition system is used.
79 CHAPTE FOUR BENDER ELEMENTS IN CENTRIFUGE TESTS--- SATURATED SPECIMEN TESTS
4.1 Introduction
4.1.1 Evaluation of Liquefaction Resistance of Soil
Under dynamic loads, such as earthquakes, traffic loads, or machine vibrations, loose and saturated cohesionless soils tend to compact and decrease in volume. This results in an increase of pore water pressures in the saturated soils.
Once the pore water pressure reaches the same magnitude as the effective confining pressure, the soil loses its strength and turn into a liquid-like state. This phenomenon is called the liquefaction of soil.
Both laboratory and field tests are used to evaluate the liquefaction resistance of soil. Laboratory test methods include the cyclic triaxial test, cyclic simple shear test, and cyclic torsional shear test. All these test methods have some limitations in reproducing field stresses and boundary conditions.
The shake table test is better at simulating free-field boundary conditions, but it is limited to test specimens at 1 g conditions. The centrifuge model test is the most appropriate method to simulate free-field stresses and boundary conditions. It is widely used to study liquefaction related problems, such as the
VELACS project (Arulanandan, 1993) used dynamic centrifuge tests to verify various procedures in liquefaction analysis.
80 To avoid the difficulties encountered in simulating field conditions and
sampling undisturbed granular soils in laboratory tests, field tests have been used
for liquefaction investigation. Different criteria have been developed to evaluate
the liquefaction properties of soil in the field (Youd, et al., 2001):
1) Criteria based on standard penetration tests (SPT);
2) Criteria based on cone penetration tests (CPT);
3) Criteria based on shear wave velocity measurements;
4) Criteria based on the Becker penetration test for gravelly soil;
To estimate the liquefaction resistance of soil, two variables are required:
CSR (cyclic stress ratio) and CRR (cyclic resistance ratio). A ground motion can be converted to CSR by a simplified procedure introduced by Seed and Idriss
(1971) as:
CSR=0.65 (amax/g) (σv0/σ′v0) rd (4.1) where, amax = peak acceleration of the motion
g = acceleration of gravity
σv0 = total vertical overburden stress
σ′v0 = total effective vertical overburden stress
rd = stress reduction coefficient. It can be estimated by the following
equations:
rd = 1.0 – 0.00765 z , for z ≤ 9.15m
rd = 1.174 – 0.0276 z, for 9.15 m < z ≤ 23m
where, z = depth below ground surface.
81 CRR curves for the SPT method and shear-wave velocity method are shown in Figure 4.1 and Figure 4.2, respectively. In Figure 4.2, the overburden stress-corrected shear wave velocity, Vs1, is used. It is defined as (Sykora, 1987):
0.25 Vs1 = Vs (Pa/σ′v0) (4.2) where, Vs1 = overburden stress-corrected shear wave velocity
Vs = shear wave velocity
Pa = atmospheric pressure
σ′v0 = initial effective vertical stress.
Andrus and Stokoe (1997, 2000) developed liquefaction resistance criteria from field measurements of shear wave velocity Vs. The advantages of using shear velocity include (Andrus and Stokoe, 1997, 2000): (1) Vs measurements are possible in soils that are difficult to penetrate with CPT and SPT, in soils in which it is difficult to extract undisturbed samples, such as gravelly soils, and at sites where boring or soundings may not be permitted; (2) Vs is a basic mechanical property of soil materials, directly related to the small-strain shear modulus; and
(3) the small-strain shear modulus is a parameter required in analytical procedures for estimating dynamic soil response and soil structure interaction analysis. Figure
4.2 shows data from liquefaction case history information for magnitude 5.9 – 8.3 earthquakes.
82 The above in-situ case history-based criteria evaluate the liquefaction potential of soil layers in terms of in situ tests parameters, such as SPT values and shear wave velocities. The field tests are conducted on the soils that are known to have liquefied or not liquefied during earthquakes in the United States and other countries. The limitations of the in-situ case history criteria include:
z Some soil properties were from measurements performed before the
earthquake, others followed the earthquake. For the parameters
measured after the earthquake, they in fact represent post-earthquake
soil properties. It is well known that earthquake motions can densify
soil layers and as a result, the stiffness, shear wave velocities, and
liquefaction resistance of the soils will be improved. Therefore, one
problem of the in-situ case history-based criteria is to evaluate the
liquefaction potential of soils base on the post earthquake soil
properties. The ideal criteria should be based on the initial soil states
before earthquakes.
z The occurrence of liquefaction was based on the surface evidence,
such as sand boils, ground cracks, and ground settlement. This
approach is not reliable. The damages may not be caused by
liquefactions.
z In some cases, σv or σv′ was estimated using the typical values of soil
densities, not the tested values.
83 z The specific properties (amplitude, frequency, and duration) of each
earthquake were not considered.
In this chapter, the curves will be examined by dynamic centrifuge test results.
Figure 4.1 Relationship between Cyclic Stress Ratios Causing Liquefaction and (N1)60 Values (after Seed et al., 1985)
84
Figure 4.2 Liquefaction Relationship Recommended for Clean, Uncemented Soils (after Andrus and Stoloe, 2000)
85 4.1.2 Content of This Chapter
In this chapter, a series of dynamic centrifuge tests at a scale of N g’s were conducted on water saturated models to investigate dynamic problems, such as liquefaction properties of soil layers during earthquakes. Wave velocities were measured during spin-up and spin-down, before and after the earthquakes were applied. Variations of shear modulus of soils and effects of earthquakes and repeated earthquakes on the soil properties were investigated.
Based on the dynamic centrifuge test results, the Vs criteria for evaluation of liquefaction resistance were examined and discussed.
4.2 Test equipment
As in the dry model tests, the Case Western Reserve University centrifuge was used in the saturated specimen tests. Seismic simulation of a designed earthquake was produced by the electro-hydraulic shaker. Accelerations and pore pressures in different locations of the model were measured.
4.3 Input Earthquake Motion
One of VELACS acceleration records, VELACS50, was chosen to be the input earthquake motion for the dynamic centrifuge tests. The wave in prototype is shown in Figure 4.3.
86
0.2
0.15
0.1 0.05
0 0 2 4 6 8 10 12 14 16 18 -0.05
Acceleration (g) -0.1
-0.15
-0.2 Time (Second)
Figure 4.3 Prototype Acceleration of Base Input Motion
4.4 Transducer Description
4.4.1 Water-proof Bender Elements
General piezoelectric sensors can not be used in wet specimen tests.
Procedures as the following were developed to produce water-proof sensors:
1) Prepare the sensors’ surface by making them clean and dry;
2) Apply Devcon epoxy gel evenly on the surfaces of the sensors;
3) After about 8 hours, add another layer of the epoxy gel onto the
sensors;
4) Coat the sensors with a layer of Performix plastic dip.
87 The sensors treated by the above procedures worked very well in the saturated specimen tests.
4.4.1 Accelerometers
Accelerators of model type 353B17 produced by PCB Piezotronic, Inc. were used. They are capable of high frequency vibration measurements. The accelerations’ specifications are listed in Table 4.1. Their calibrations are listed in
Table 4.2.
4.4.2 Pore Pressure Transducers
The pore pressure transducers used were Druck PDCR81 (maker: Druck
Ltd. UK). The transducers’ specifications are listed in Table 4.3. Their calibrations are listed in Table 4.4.
88 Table 4.1 Specifications of Accelerometer
Useful Acceleration Range ± 500g
Resolution 0.01 g
Resonant Frequency 74 kHz
Useful Frequency Range 1-10000 Hz
Temperature Range -54/+120 °C
Voltage Sensitivity 10 m V/g
Transverse Sensitivity 15- 3.6%
Output Bias Level 9.3 V
Weight 1.7 gm
Size (Height × Hex) 14× 7.1 mm
Table 4.2 Calibrations of Accelerometers
Accelerometers Calibration Factor (mV/g)
A1 10.19
A2 10.1
A3 10.21
89 Table 4.3 Specifications of Pore Pressure Transducers
Resolution Infinitely small
Sensitivity 1.8 kPa/mV
Temperature Range -20/+20 °C
Weight 2 gm
Size (Height × Diameter) 11.4 × 5.8 mm
Table 4.4 Calibrations of Pore Pressure Transducers
Accelerometers Calibration Factor (psi/V)
U1 3.608
U2 3.755
U3 3.762
U4 3.764
4.5 Preparation of Saturated Models
4.5.1 Description of the Model
A model of Nevada sand was tested with a relative density of Dr=55%.
The heights of the models were 15.3 cm. A sketch of the model and the location of sensors are shown in Figure 4.4. The locations of the bender elements are listed in Table 4.5.
90
Z
Bender Element
Holding Column S1 U1 A1 R1
A2 U4 S2 U2 R2 S3 A3 R3 U3 Y 0 Nevada Sand
X
S1,S2,S3------Bender Element Transmitters R1,R2,R3----- Bender Element Receivers A1,A2,A3----- Accelerometers U1,U2,U3,U4----Pore Pressure Transducers
Figure 4.4 Location of Sensors in Centrifuge Model
91 Table 4.5 Locations of Sensors
Sensors X(mm) Y(mm) Z(mm)
S1 0 -35 86
S2 0 -35.5 51
S3 0 -36 13
Bender Element R1 0 35 86
R2 0 35.5 51
R3 0 36 13
A1 25.4 35 86
Accelerometer A2 25.4 35 51
A3 25.4 35 13
U1 25.4 -35 86
Pore Pressure U2 25.4 -35 51
Transducer U3 25.4 -35 13
U4 -25.4 -35 86
Note: the coordinates of each bender element refer to the lower front corner point of the element, and the coordinates of accelerometers and pore pressure transducers refer to the center points of their front surfaces.
4.5.2 Preparation of the Models
Nevada sand as described in Chapter three was used in these tests.
Different methods of preparing saturated soil specimens, such as tamping, air
pluviation, and wet pluviation, are compared.
92 The moist tamping technique consists of pouring consecutive soil layers of a specified thickness and tamping each layer of soil with a specified force before the next layer is placed. Cone penetration test results (Miura et al., 1984) show considerable non-uniformity of specimens prepared by this method.
For the wet pluviation method, dry sand is poured into water while vibrating the mold until the desired density is achieved (Kuerbis and Vaid, 1988).
Particle size segregation during pluviation of sands is a problem for both air and water pluviation techniques, but it is worse in water pluviation (Vaid and
Negussey, 1984; Kuerbis and Vaid, 1988).
The air pluviation has been introduced before. The major factors affecting the relative density of air pluviated specimens are the height of particle drop and the pouring volume. The air pluviation method produces more uniform specimens, so this method was used for this research.
The setup for air pluviation is shown in Figure 3.6. The height of the sand hopper is adjustable to keep the outlet of tube at the desired height. A sealed wooden box with an airtight cover is used as a chamber for the model during preparation of the specimen. The airtight covers have pipe connections in order to saturate the soil as shown in Figure 4.5.
Three accelerometers, four pore water pressure transducers, and six bender elements are embedded at selected locations during the process of pouring sands.
The pore water pressure transducers are saturated by soaking in deaired water for two days prior to the sample preparation.
93
Figure 4.5 Schematic of the Chamber with an Air Tight Lid (after Dief, 2000)
94 4.5.3 Pore Fluid
The use of pore fluid is important in ensuring the time scaling factors of
centrifuge modeling. A solution of water and hydroxypropyl methylcellulose
powder, such as METHOCEL Cellulose Ethers by DOW Chemical Company, is
used as pore fluid by some researchers (Dief, 2000). The viscosity of a solution
made with this product depends on the concentration of hydroxypropyl
methylcellulose and the temperature. The METHOCEL solution has virtually the
same density of water. Some other physical properties of the METHOCEL
product are listed in Table 4.6. Two similar dynamic centrifuge tests on Nevada
sand at 70% relative density saturated either with deaired water of 60 centistokes
hydroxypropyl methylcellulose solution were conducted at 60 g by Dief (2000).
The soil sample represented a soil deposit 7.6 m in depth. The horizontal
acceleration time history at the base of the box was identical to the VELACS
record used. Figure 4.6 shows a comparison between the excess pore fluid
pressures for the water and the hydroxypropyl methylcellulose saturated samples
measured. There is not much difference in the first 0.16 seconds, where the
accumulation of the excess pore pressure is not affected by pore fluid viscosity.
However, the viscosity of the fluids influences the rate of the dissipation of the
pore pressure.
95 Table 4-6 Physical Properties of METHOCEL (Source: Dow Chemical Company) Appearance White to slightly off-white powders Specific Gravity of 1% solution at 4˚C 1.0012
Specific Gravity of 5% solution at 4˚C 1.0117
Apparent Density 0.25-0.70 g/cm3
Freezing point of 2% solution 0.0˚C
Figure 4.6 Effect of Pore Fluid Viscosity on Pore Pressures in Centrifuge Model Tests (after Dief, 2000)
96 In the research presented in this chapter, the soil properties in the
centrifuge models were measured before and after an earthquake applied. The
post-earthquake measurements were carried out after excessive pore pressures had
dissipated, so it was assumed that the post-earthquake soil properties were the
same for the deaired water and the fluid specimens. Deaired water was used in
saturating the specimens in tests.
4.5.4 Saturation of Specimens
The procedure introduced by Dief (2000) was adopted to saturate the
specimen. After pluviation, valves V2, V8, V3, and V5 as shown in Figure 4.7
were opened to replace the air in the soil by carbon-dioxide, which dissolves
easily in the water. Then, all of the valves were closed and de-aired water of 2 m
water head difference were allowed to pass slowly into the soil from the bottom to
the top by opening valves V4, V7, and V5. After the soil was immerged by the
deaired water completely, valves V4, V7, and V5 were closed, and V6 and V3
were opened to induce a vacuum. A high degree of saturation of the specimen
could be achieved by maintaining the vacuum for about 6 hours.
97
Figure 4.7 Model Saturation System (after Dief, 2000)
4.6 Centrifuge Testing Procedure
The followings are the procedures for the saturated specimen tests:
1) After saturation is finished, the laminar box is carefully moved from the saturation box and fastened on the shake table of the centrifuge. The counter weight is added to the other side of the swing arm. All of the transducers are
98 properly connected. Before starting the centrifuge, a complete checkup of all equipment and connections on the arm is done.
2) As in the dry specimen tests, before the centrifuge test is started, the profile of the model is measured, and bender element tests corresponding to the 1 g stress condition are performed. The centrifuge control program is started, and the parameters are set to desired values.
3) The centrifuge is then swung up in steps of 10g, 20g, 40g, and 50g
(measured in the middle of the sand layer). At each step, a total of nine wave velocity measurements, recording the shear wave velocity between the transmitter
Si to the receiver Ri (i = 1, 2 and 3), are taken.
4) At 50g, to operate the shake table, the 16-channel shake table control program is enabled to set up the waveform data, date acquisition configurations, and the wave form generation parameters. The earthquake test is performed by
(Dief, 2000):
• Turning on the hydraulic power supply for 10-15 seconds, enabling
the servo valve voice coil power signals for another 10 seconds,
followed by enabling the actuator position servo-loop for another 10
seconds and finally,
• Inputting the desired waveform, VELCS50, to the shake table by
pressing the Run Test button in the run test panel.
99 • Both the actuator position servo valve and the servo valve voice coil
power signals are disabled, and finally the hydraulic power supply is
turned off.
• Data collected from the 16 channels is displayed on the computer
screen and saved in a separate file.
5) After the dynamic centrifuge test, bender elements tests are performed at a 50g level. Then the centrifuge is swung down at a step sequence of 40g, 20g, 10g, and 1g. Again, at each step, the bender element tests are performed as before. At 1g, the vertical settlements of the model surface are measured.
6) After the oil was pumped out of the shake table, the centrifuge is spun up to 50g directly, and at this g level, the same earthquake motion is applied to the soil model to investigate the effects of the repeated earthquake to the stiffness and liquefaction properties of the soil.
7) After the second dynamic centrifuge test, the centrifuge is swung down at a step sequence of 50 g, 40 g, 20 g, 10 g, and 1 g. At each step, bender element tests are performed. At 1 g, the vertical settlements of the model surface are measured again.
100 4.7 Experimental Results and Analysis
4.7.1 Shear Wave Velocities
Shear wave velocities measured during spin-up of the centrifuge before earthquake, spin- down of the centrifuge after the first earthquake, and spin-down the centrifuge after the second earthquake are listed in Table 4.1, Table 4.2, and
Table 4.3, respectively.
Figure 4.8 and Figure 4.9 show the change of shear wave velocities with g-level and depth in the saturated model. As in the dry specimen tests, the velocities increase with increasing of g-level and depth.
Figure 4.10 compares the shear wave velocities before and after the first earthquake applied. The velocities are obviously improved. This indicates that after the earthquake, the soil was densified, and the stiffness of the soil was improved.
Figure 4.11 compares the shear wave velocities of the model after the first and the second earthquakes. The curves show that the second earthquake did not improve the shear wave velocities of the model. This means that the repeated earthquake did not densify the same soil layer, and that the soil layer will not liquefy under the repeated earthquake.
101 Table 4.7 Shear Wave Traveling Time
Traveling Time Tij (µs) Distance Transmitter Receiver (cm) 1g 10 g 20 g 40g 50 g
S1 R1 7 1530 1315 1085 944 880
S1 R2 8 1670 1343 1113 952 915
S1 R3 11.38 2230 1370 1117 1000 941
S2 R1 8 1958 1315 1094 944 888
S2 R2 7.1 1434 1021 874 768 736
S2 R3 7.53 1714 1002 855 736 721
S3 R1 11.38 2332 1389 876 950 906
S3 R2 7.53 1664 1214 920 888 871
S3 R3 7.2 1395 947 824 711 686
Table 4.8 Shear Wave Velocities (Spin-up)
Acceleration (g) 1 10 20 40 50
v11 46 53 65 74 80
v12 48 60 72 84 87
v13 49 83 102 114 121
Shear Wave Velocity v21 41 61 73 85 90
(m/s) v22 50 70 81 92 96
v23 44 75 88 102 104
v31 49 82 130 120 126
v32 45 62 82 85 86
v33 52 76 87 101 105 * vij : wave velocity between transmitter i and receiver j.
102 Table 4.9 Shear Wave Velocities (after the First Earthquake)
Acceleration (g) 1 10 20 40 50
v11 58 78 86 89 86
v12 80 96 91 88 89
v13 66 106 116 125 125 Shear Wave Velocity v21 54 85 97 99 99
(m/s) v22 58 87 88 91 102
v23 59 101 117 122 122
v31 68 100 116 126 125
v32 60 112 82 110 96
v33 65 107 115 121 117
Table 4.10 Shear Wave Velocities (after the Second Earthquake)
Acceleration (g) 1 10 20 40 50
v11 67 67 89 92 88
v12 80 93 109 104 99
v13 70 103 106 128 127 Shear Wave Velocity v21 56 75 75 103 100
(m/s) v22 71 83 102 102 102
v23 62 90 92 115 118
v31 98 90 94 129 130
v32 76 102 101 91 83
v33 78 105 104 118 120
103 120
) 100
80
60
S1-R1 40 S2-R2
S3-R3 20 Shear Wave Velocity Wave (m/s Shear
0 0 102030405060 Acceleration (g)
Figure 4.8 Shear Wave Velocity Vs Acceleration (Spin-up, before Earthquake)
Shear Wave Velocity(m/s) 0 20 40 60 80 100 120 0 1 g 0.02 10 g 0.04 20 g 40 g 0.06 50 g
0.08
Depth(m) 0.1
0.12
0.14
0.16
Figure 4.9 Variations of Shear Wave Velocity with Depth in the Model (Spin- up, before Earthquake)
104 120 ) 100
80
60 S1-R1(After the first earthquake) S2-R2(Afterthe first earthquake) 40 S3-R3(After the first earthquake) S1-R1(Before earthquake)
Shear Wave Velocity (m/s 20 S2-R2(Before earthquake) S3-R3(Before earthquake) 0 0 102030405060
Acceleration (g)
Figure 4.10 Shear Wave Velocities before and after the First Earthquake
140
) 120
100
80
60 S1-R1(After the first earthquake) S2-R2(After the first earthquake) 40 S3-R3(After the first earthquake) S1-R1(After the second earthquakes) 20 S2-R2(After the second earthquakes) Shear WaveVelocity (m/s S3-R3(After the second earthquakes) 0 0 102030405060 Acceleration (g)
Figure 4.11 Comparison of Shear Wave Velocities after the First and Second Earthquakes
105 4.7.2 Pore Pressures
Figure 4.12, Figure 4.13, and Figure 4.14 present the excess pore pressures during the first earthquake recorded by the transducers located at top, middle and bottom of the model. The maximum values of the pore pressure rates are 1.0, 1.0, and 0.85, respectively. They indicate that, from middle to top, the soil layers were liquefied during the earthquake.
Figure 4.15, Figure 4.16, and Figure 4.17 show the excess pore pressures during the second earthquake as measured by the pore pressure transducers located at the top, middle, and bottom of the model. The maximum values of the pore pressure rates are less than 0.1. This indicates that the model did not liquefy during the second earthquake.
4.7.3 Accelerations
Figure 4.18, Figure 4.19, and Figure 4.20 show histories of accelerations during the first earthquake as measured by accelerometers located at the top, middle, bottom, and base of the model. The peak accelerations decay from bottom to top, as the result of soil liquefaction.
Figure 4.21, Figure 4.22 and Figure 4.23 show histories of accelerations during the second earthquake as recorded by accelerometers located at the top, middle, bottom, and base of the model.
106 4.7.4 Examination of Liquefaction Criteria Based on Shear Wave Velocities
According to the acceleration histories and the measured shear wave velocities during the first earthquake, the CRR curves in Figure 4.2 can be examined. It should be point out that in equation (4.2), it is implicitly assumed that Vs is measured with both particle motion and wave propagation polarized along principle stress directions and one of those direction is vertical (Andrus, et al., 2000). For the both particle motion and wave propagation polarized along horizontal direction (the case of this research), the measured shear wave velocity is horizontal shear wave velocity VSH. It can be converted to vertical shear wave velocity VSV by the following equation (Zeng and Ni, 2000):
n/4 VSV = VSH/(K0) (4.3) where, K0 = at-rest earth pressure coefficient, which can be estimated by equation
(3.4)
n = soil constant equal to 0.5 for sand.
Then the overburden stress-corrected shear-wave velocity VS1 can be estimated from horizontal shear wave velocity by following equation:
0.25 n/4 VS1 = CV VSV = CV K VSH = (Pa/σv′) (K0) VSH
(4.4)
0.25 where, CV = (Pa/σv′) , which is a factor to correct measured shear-wave velocity
for over-burden pressure
107 n/4 K = (K0) , which is a factor to convert horizontal shear-wave velocity to
vertical shear wave velocity
Pa = atmospheric pressure
σ′v = initial effective overburden stress.
Figure 4.24 is modified from Figure 4.2 by adding the values of CSR and
VS1 into it. It shows that the two liquefied points, the points located at the top and middle of the model, are in the region with data indicative of liquefaction. But the non-liquefied bottom point is also located in this region. As shown in the figure, many field cases without liquefaction are included in the region without liquefaction. The positions of the CRR curves, which separate regions liquefied from the regions not liquefied, need to be further verified or modified using more case history points or model test data. Dynamic centrifuge model tests can serve as powerful tools for this work. Series centrifuge model tests using various sands and different earthquake motions can be extensively tested in the future.
Figure 4.25 shows the CRR values and overburden stress-corrected shear wave velocities before and after the application of the first earthquake to the soil model. It is clear that the shear wave velocities are improved. This means that the liquefaction resistance of the soil is improved. Based on the post earthquake soil properties, the in-situ case history-based criteria may overestimate the liquefaction resistance of soils.
108 1.2 U1 1
0.8
0.6
0.4
0.2
0
Excess Pore Water Pressure Ratio Excess Pore Water 0 0.2 0.4 0.6 0.8 -0.2
Time (Second) Figure 4.12 Pore Pressure History of the Top Point during the First Earthquake
1.2 U2 1
0.8
0.6
0.4
0.2
0
Excess Pore Water Pressure Ratio Excess Pore Water 0 0.2 0.4 0.6 0.8 -0.2
Time (Second)
Figure 4.13 Pore Pressure History of the Middle Point during the First Earthquake
109 1.2 U3 1
0.8
0.6
0.4
0.2
0 0 0.2 0.4 0.6 0.8 Excess Pore Water Pressure Ratio Excess Pore Water -0.2 Time (Second) Figure 4.14 Pore Pressure History of the Bottom Point during the First Earthquake
1 U1 0.8
0.6
0.4
0.2
0 0 0.2 0.4 0.6 0.8 Excess Pore Water Pressure Ratio Pressure Water Pore Excess -0.2 Time (Second)
Figure 4.15 Pore Pressure History of the Top Point during the Repeated Earthquake
110 1 U2 0.8
0.6
0.4
0.2
0 00.20.40.60.8 Excess Pore Water Pressure Ratio Pressure Water Pore Excess -0.2 Time (Second)
Figure 4.16 Pore Pressure History of the Middle Point during the Repeated Earthquake
1 U3 0.8
0.6
0.4
0.2
0 0 0.2 0.4 0.6 0.8 Excess Pore Water Pressure Ratio Pressure Water Pore Excess -0.2 Time (Second)
Figure 4.17 Pore Pressure History of the Bottom Point during the Repeated Earthquake
111 0.4 A1 0.3
0.2
0.1
0 0 0.1 0.2 0.3 0.4 0.5 0.6 Acceleration(g) -0.1
-0.2
-0.3 Time (Second)
Figure 4.18 Acceleration History of the Top Point during the First Earthquake
0.4 A2 0.3 0.2 0.1 0 -0.1 0 0.2 0.4 0.6 0.8 1
Acceleration(g) -0.2 -0.3 -0.4 Time (Second) Figure 4.19 Acceleration History of the Middle Point during the First Earthquake
112 1 A3 0.8 0.6
0.4 0.2
0 Acceleration(g) 0 0.1 0.2 0.3 0.4 0.5 0.6 -0.2
-0.4 Time (Second)
Figure 4.20 Acceleration History of the Bottom Point during the First Earthquake 0.2 A1 0.15
0.1
0.05
0 0 0.1 0.2 0.3 0.4 0.5 0.6 -0.05 Acceleration(g)
-0.1
-0.15
-0.2 Time (Second)
Figure 4.21 Acceleration History of the Top Point during the Repeated Earthquake
113 0.2 A2 0.15 0.1 0.05 0 -0.05 0 0.1 0.2 0.3 0.4 0.5 0.6
Acceleration(g) -0.1 -0.15 -0.2 Time (Second)
Figure 4.22 Acceleration History of the Middle Point during the Repeated Earthquake
0.2 A3 0.15 0.1 0.05 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -0.05 -0.1 Acceleration(g) -0.15 -0.2 -0.25 Time (Second)
Figure 4.23 Acceleration History of the Bottom Point during the Repeated Earthquake
114
Figure 4.24 Case History of Liquefaction Based on Shear Wave Velocity with Centrifuge Model Test Data Added
115 0.3 Before The First Earthquake 0.29 After The First Earthquake 0.28
0.27
0.26 Cyslic Stress Ratio, CRR
0.25 100 110 120 130 140 150 160
Overburden Stress-Corrected Shear Wave Velocity, Vs1 ( m/s)
Figure 4.25 CRR Values and Overburden Stress-Corrected Shear Wave Velocities before and after the first Earthquake.
4.8 Conclusions
In this chapter, a bender element technique for saturated centrifuge model tests was introduced. Procedures of the bender element test were described in detail. Dynamic model tests were performed to investigate the effects of earthquakes on soil properties. Various parameters, including shear wave traveling times, pore pressures, accelerations and settlement were monitored.
Conclusions can be drawn from the test results as follows: z The bender element technique developed in this chapter is effective in
measuring soil properties in saturated specimen tests. z The shear wave velocities in saturated specimens increase with g-level and
depth. The increases are caused by increases in confining pressures.
116 z At 50 g, the model was liquefied by the action of the first earthquake, and
after the earthquake the shear wave velocities were improved. This means the
stiffness of the model increased. The vibration had densified the model. z The histories of the pore pressures recorded during the first earthquake show
the peak values of excess pore pressure ratios from the middle to the top of
the model reached 1.0. They indicate that the upper part of the model
liquefied during the earthquake. z During the second earthquake, the peak values of excess pore pressure ratios
from the bottom to the top of the model is less than 0.1 far away from 1.0.
The model was not liquefied during repeated earthquake, or the repeated
earthquake could not densify the soil. z The shear wave velocities measured after the repeated earthquake are the
same as those measured after the motion applied at the first time. This means
the stiffness of the soil did not change after the repeated earthquake, which
verifies the above conclusion based on pore pressures. z The CRR curves developed from the post earthquake soil properties, may
overestimate the liquefaction resistance of soils. More case history points or
model test data are needed to further verify or modify the curves.
117 CHAPTER FIVE PIEZO CONE PENETROMETER
5.1 Introduction
The stiffnesses of base, subbase, and subgrade layers are very important parameter in pavement design and evaluation. Measurements of stiffnesses of base and subgrade layers are required by the new design guidelines proposed by
AASHTO. Currently the most widely used technique to determine the stiffnesses of pavement layers is to the California Bearing Ratio (CBR) test, which is done on soil samples prepared in the laboratory. The resilient modulus of soil, MR, is calculated by using empirical expressions. One example is the method recommended by AASHTO:
MR = 10340 CBR (kPa) (5.1)
There are a number of limitations in this method. Firstly, the specimens are prepared in the laboratory using compaction procedures different from what the soils are subjected to in the field. Therefore, the laboratory specimens may have stiffnesses different from the soil in the field. Secondly, the CBR test does not provide enough information as needed by engineers to determine whether or not the stiffnesses of subgrade, subbase, and base soil of a pavement under construction meets design requirements. Thirdly, for an existing pavement where the subgrade, subbase, and base soils have gone through years of weather cycles
118 and traffic load applications, the CBR alone can not provide a realistic measurement of the pavement’s stiffness. Therefore, there is a need to develop an in-situ, non-destructive, accurate, and economical method for to measure stiffness of soils for pavement engineering applications.
In this chapter, a recently developed piezo cone penetrometer is described. The penetrometer is designed to measure the material properties of the underlayers of pavement. It measures the shear modulus, Young’s modulus, and
Poisson’s ratio during and after construction. Two small cone penetrometers are equipped with one set of bender elements and one set of extender elements. The penetrometers can be pushed into sublayers of a pavement under construction.
The stiffness of the sublayers can be determined in a short time. The equipment is theoretically sound, and the measurements and computations are direct and simple.
This device is mainly aimed towards pavement engineering field measurements, but it can also be used in other fields of geotechnical engineering.
5.2 Piezo Cone Penetrometer Structure
The piezo cone penetrometer is shown in Figure 5.1. It consists of four piezoelectric sensors, two pushing sleeves and two connection bars. The sensors installed are two bender elements designated S1 and R1, and two extender elements designated S2 and R2. The types of the elements are listed in Table 5.1.
These elements can be coated with epoxy to make them water-tight, allowing their use in a saturated environment. Similarly, all the electrical connections
119 within the penetrometer can be made waterproof. Because of this unique setup, the shear modulus, Young’s modulus, and Poisson’s ratio can be determined simultaneously. The length of each pushing sleeve is about 70 cm with an outside diameter of 1.91 cm. The horizontal distance between the two sleeves is adjustable.
Table 5.1 Types of the Elements
Sensor Function Type
S1 Transmitter Bender element, Q220-A4-303Y
R1 Receiver Bender element, Q220-A4-303X
S2 Transmitter Extender element, Q220-A4-303YE
R2 Receiver Extender element, Q220-A4-303XE
120
Figure 5.1 Detailed Schematic of the Piezo Penetrometer
121
Figure 5.2 Photo of the Piezo Cone Pentrometer
122 5.3 Experimental setup
The experimental setups for laboratory and field tests are shown in
Figure 5.3 and Figure 5.4, respectively. A wave generator is needed to produce source signals and the received signals are displayed and stored by an oscilloscope.
Figure 5.3 Experimental Setup for Laborory Tests
123
Digitizing
Oscilloscope
Wave Generator
Penetrometers Base, Subbase, or Subgrade Layers
Bender Elements
Extender Elements
Figure 5.4 Experimental Setup for Field Tests
Figure 5.4 Experimental Setup for Field Tests
124 5.4 Principle of the Test
Motion Motion
Receiver Transmitter S-wave
Bender Element Test
Motion Motion
P-wave Transmitter Receiver
Extender Element Test
Figure 5.5 Experimental Principle
From the traveling time of shear waves between the top bender element transmitter (S1) and the top bender element receiver (R1) (see Figure 5.5), the shear wave velocity and shear modulus can be determined by:
Vs = L/ts (5.2)
2 Gmax = ρVs (5.3)
125 From the traveling time of the P-wave between the top extender element transmitter (S2) and the top extender element receiver (R2), the P-wave velocity and constrained modulus can be determined by:
Vp = L/tp (5.4)
2 M = ρVp (5.5)
Using the values of the shear modulus and the constrained modulus at the same depth of the underlayers of the pavement, Poisson’s ratio can be calculated by:
µ= [(M/Gmax-2) / (2M/Gmax-2)] (5.6)
5.5 Field Test Procedure
The piezo penetrometer can be pushed directly into the sublayers of a pavement under construction to measure the stiffness of sublayer materials. The continuous profile of the stiffnesses of the sublayers of the pavement can be obtained by pushing the penetrometer and doing the measurements step by step.
The test is simple and quick. The results can be displayed in a few minutes, allowing the device to be used to monitor compaction quality.
For an existing pavement, two holes can be cored through the upper asphalt concrete or Portland cement layer, and the penetrometers can be pushed into the underlying layers gradually to measure the velocities at different depths of the pavement. Thus the device can be used to check the mechanical properties
126 of the sublayers of an existing pavement. The test does very little disturbance to underlayers of a pavement, so reliable and highly accurate results can be expected.
5.6 Typical Laboratory Test Results
Two soils were tested in the laboratory. CBR tests were also performed for comparison purposes.
5.6.1 Soil Description
The soils used in the tests are Delaware clay and Nevada sand. Their index properties of are listed in Table 5.2.
Table 5.2 Index Properties of Two Soils
Soil Delaware clay Nevada sand
D10 (mm) 0.09
D30 (mm) 0.13
D60 (mm) 0.92
Liquid limit 33.6%
Plastic limit 20.5%
Soil classification Lean clay Poorly graded sand
3 (γd)max (kN/m ) 18.7 17.3
3 (γd)min (kN/m ) 13.9
127 5.6.2 Test Procedure
Laboratory tests were conducted on specimens of soil prepared in a steel
container with a diameter of 25.4 cm and a height of 50.8 cm. The steel container
has enough lateral stiffness to create a K0 stress condition that is typical in the
field. Specimens were prepared by pouring the soils into the container using a
hopper. After the specimen was ready, the penetrometer was pushed into the soil
slowly until the piezoelectric sensors reached the specified depth. Bender element
tests and extender element tests were then conducted to measure S-wave and P-
wave velocities. After the tests were finished, the penetrometers were pushed to
deeper positions to perform more measurements. After all the tests were finished,
S-wave velocities, P-wave velocities, shear moduli, and constrained moduli
corresponding to different measurement positions were calculated. Poisson’s
ratios were further calculated by using the shear modulus and constrained
modulus at the same depth.
5.6.2 Test Results
Figure 5.6 and Figure 5.7 are signals recorded by oscilloscope for bender
element and extender element tests. Compared to the signal of the bender element
receiver, the signal of the extender element has a higher frequency, lower
amplitude, and shorter traveling time.
128
12 Source Signal 10 Received Signal 8 Received Signal(Source Signal 6 Reversed) SSil 4 2 for received signal) for received 0
Voltage (V for input mv signal, -2 0123 Time (ms)
Figure 5.6 Typical Bender Element Test Results
12 r 10
8 Received Signal Input Signal 6
4
received signal) received 2
0 Voltage (V for source signal, fo mV source Voltage for (V -2 0 0.5 1 1.5 2 2.5 Time (ms)
Figure 5.7 Typical Extender Element Test Results
129 Table 5.3 Test Results on Nevada Sand
Shear Modulus Constrained H-B Equation Poisson's Depth(cm) (MPa) Modulus(MPa) Results (MPa) Ratio 6.4 6.8 6.6 9.5 7.1 8.1 12.7 9.6 41.2 9.3 0.35 15.9 10.2 43.2 10.4 0.35 19.1 12.1 45.9 11.4 0.32 22.2 12.1 43.2 12.6 0.31 25.4 13.9 43.7 13.2 0.27 28.6 52.9 31.8 43.7
Table 5.4 Test Results on Delaware Clay
Shear Modulus Constrained H-B Equation Poisson's Depth(cm) (MPa) Modulus(MPa) Results (MPa) Ratio 6.4 10.3 8.0 9.5 11.2 9.9 12.7 11.6 47.2 11.4 0.34 15.9 12.3 50.9 12.7 0.34 19.1 13.1 53.7 13.9 0.34 22.2 13.2 53.7 15.1 0.34 25.4 13.7 54.4 15.9 0.33 28.6 54.9 31.8
130 60 0.6 Gmax(Test Results) Gmax(H-R Equation) 50 Constrained Modulus M(Test Results) 0.5 Poisson's Ratio 40 0.4
30 0.3 Poisson's Ratio Poisson's
Modulus (Mpa) 20 0.2
10 0.1
0 0 0 5 10 15 20 25 30 35
Depth (cm)
Figure 5.8 Test Results on Nevada Sand (Dry Density=1600 kg/m3)
60 0.6
50 0.5
40 0.4
30 Gmax(Test Results) 0.3 Gmax(H-D Equation)
Constrained Modulus M(Test Results) Ratio Poisson's Modulus (Mpa) 20 0.2 Poisson's Ratio 10 0.1
0 0 0 5 10 15 20 25 30 35
Depth (cm)
Figure 5.9 Test Results on Delaware Clay (Dry Density = 1590 kg/m3)
131 Figure 5.8 and Figure 5.9 are test results on Nevada sand and Delware clay. The results show that both the constained modulus and the shear modulus increase with depth. Also shown in the figures are the results of shear moduli calculated using two commonly used empirical equations, the Hardin and Richart
(1963) equation, for sand and the Hardin and Drnevich (1972) equation for clay, which show very good agreement with the experimental results.
From the shear and constained moduli, Poisson’s ratios were also calculated and shown in the two figures. For the Delaware clay, under the test conditions, the Poisson’s ratio is about 0.34. For the Nevada sand, the measured
Poisson’s ratios decrease from 0.35 to 0.27 when the depths increase from 12.7 cm to 25.4 cm. These are reasonable values for the soils studied.
To compare the test results presented above with those from the traditional CBR test, two samples were prepared using the same method described above. CBR test results are shown in Figure 5.10 and Figure 5.11, and corresponding resilient moduli are listed in Table 5.5. For Nevada sand, the average constrained modulus from the CBR tests is 40.1 MPa, which is close to the constrained modulus of 41.7 MPa measured at a depth of 12.5 cm using the piezo cone penetrometer. For the Delware clay, the modulus from the CBR test is
23.4 MPa, while the modulus from piezo penetrometer test at depth of 12.5 cm is
46.5 MPa. The CBR test measures the average modulus from the soil in the foundation with a dominant influence of the soil near the surface. The piezo
132 penetrometer can measure a continuous profile of the elastic modulus of the subgrade.
400
350
300 250
Test1 200 Test2 150
Resistance (kPa) 100
50
0 0123456789 Penetration (mm)
Figure 5.10 CBR Test Results on Delaware Clay (Dry Density = 1557 kg/m3)
133
350
300
250
200 Test1 Test2 150
Resistance (kPa) 100
50
0 01234567 Penetration (mm)
Figure 5.11 CBR Test Results on Nevada Sand (Dry Density = 1610 kg/m3)
Table 5.5 Summary of the Results of CBR Tests
Delaware Clay Nevada Sand
CBR Mr (MPa) CBR Mr (MPa)
Test1 2.46 25.4 4.18 43.2
Test2 2.06 21.3 3.58 37.0
Average 23.4 40.1
134 5.7 Conclusions
z The piezo cone penetrometer described in this chapter can be used in in-
situ measurement of soil properties, such as the measurement of base and
subgrade layer stiffnesses and Poisson’s ratio during and after
construction of a pavement.
z The system is mobile and can be used in the field. It offers a superior
technique for the field control of construction quality.
z The test method is simple, quick, economic, and reliable.
z Compared to determination of a resilient modulus from CBR test based
on an empirical equation, the piezo cone penetromter is theoretically
sound.
135 CHAPTER SIX ODOMETER FOR GRAVEL MATERIAL STIFFNESS MEASUREMENT
6.1 Introduction
Soil stiffness is an important design parameter in many geotechnical problems. Traditionally, elastic soil properties are measured using resonant column tests or cyclic triaxial tests in the laboratory, and crosshole and downhole tests in the field. For laboratory tests, due to limitation of the sizes of the soil specimens, it is impossible to measure the soil properties with large particle sizes, such as gravel soils. Therefore, the developments of new devices for large specimens are necessary.
Generally, in the field, soil is in anisotropic status. The anisotropies of a soil may come from the fabric of the soil, or may be stress induced. The elastic modulus of soil depends on the properties of the minerals as well as the confining pressure. Hardin and Blandford (1989) established an equation showing shear modulus in different planes as follows (see Figure 6.1):
k n (OCR) Sij G = P 1 − n ( σ σ ) 2 (6.1) ij F(e)2(1+ν ) a i j
2 (6.2) Fe()=+03 . 07 . e
136 where, Gij = maximum shear modulus in shear plane containing principal stress σi,
σj
OCR = over consolidation ratio
e = void ratio
n = elastic constant
Sij = dimensionless elastic stiffness coefficient of soil in shear plane
containing principal stress σi, σj
Pa = atmosphere pressure.
σα σ 1
τ α
G13 (GV )p la n e v α3 v 13 σ 3
Gα plane
σ 2 v 23
G23 (GH )p la n e α
Direction of wave propagation Direction of p article vibration
Figue 6.1 Shear Modulus in Different Planes (after Zeng and Ni, 1999)
137 The above equation shows that the elastic shear modulus depends on the normal stresses in the shear plane and is independent of the normal stresses in the orthogonal direction.
Zeng and Ni (1998b) suggested a relationship between the shear modulus in a nonprincipal stress plane, Gα, and the shear moduli in the principal stress plane, GV and GH, as follows:
GV GH Gα = 2 2 (6.3) GH sin α + GH cos α
where, α = inclination angle of Gα plane with respect to horizontal plane
GV = maximum shear modulus in vertical stress plane
GH = maximum shear modulus in vertical stress plane.
This is the equation of an ellipse with major and minor semi-axes of
GV and GH as shown in Figure 6.2. The figure indicates that shear modulus in the vertical direction is the largest and in the horizontal direction is at a minimum.
The odometer developed in this chapter takes advantage of the bender element technique. It can measure shear wave velocities in different planes in a soil specimen. The shear moduli are related to the shear wave velocities by equation (1.6). Thus, the shear moduli in different planes can be determined.
138
Figure 6.2 Relationship between Shear Moduli in Different Shear Planes: (a) Theory; (b) Experimental Data (Vertical Stress Is 60 kPa for inner Ellipse and Is Increased by 60 kPa for each Ellipse, Pool Filter Sand)(after Zeng and Ni, 1999)
139 6.2 Equipment Description
The experimental setup is shown in Figure 6.3. The odometer has an inside diameter of 30.48cm, a thickness of 2.54 cm, and a height of 23.5cm is made of aluminum. The odometer is rigid enough to form K0 conditions during tests. A Teflon sheet is stuck on the inside surface to reduce friction. One bender element was installed at the base of the odometer as wave transmitter, and three receivers were placed at the top to measure signals from different directions, one from the vertical direction and two from the inclined directions. The bender element types Q220-A4-303Y (transmitter) and Q220-A4-303X (receiver) were used. Under a K0 condition, the shear wave velocities in the different directions are different, which reflects the anisotropy of stiffness induced by an anisotropic stress condition (Zeng and Ni, 1999).
140 α
Figure 6.3 Detailed Schematic of the Odometer
141
Figure 6.4 Photo of the Odometer
142 6.3 Experimental Setup
The odometer is installed in a loading frame system as shown in Figure
6.5. The vertical force is applied by two parallel air pistons. The vertical
deformation of the sample is measured by a LVDT. The triggering signal, a
square pulse, is
LVDT Driving Signal Receiver Signal
Digital Oscilloscope Odometer
Soil Sample
Air Piston Wave Generator
Figure 6.5 Loading and Displacement Measurement System
143
produced by an Agilent 54624A wave generator and is sent to the transmitters.
Vibrations of the transmitters produce shear waves that propagate through the soil and are recorded by the receivers. The recorded signals are displayed and stored by an Agilent 33120A oscilloscope.
6.4 Typical Test Results
6.4.1 Soil Description
Two types of soils were used in the tests. One has about gravel content of
25%, and the other has a gravel content of 50%. The particle size distribution curves of the two soils are shown in Figure 6.6. The maximum grain size is about
4.8 mm.
25% gravel % Finer
50% gravel 020406080100 10 1 0.1 0.01 Diameter (mm)
Figure 6.6 Particle Size Distribution Curves of the Two Soils
144 6.4.2 Test Procedures
For each type of soil tested, two identical tests were conducted. During
each test, the vertical load was applied in steps to a maximum load corresponding
to a vertical stress of 160 kPa. Then the load was reduced in the same series of
steps to the initial effective stress due to self-weight of the soils. At each load
step, shear wave velocities in the vertical direction and the two-inclined
directions which correspond to inclined angles of approximately 30 and 45
degrees were measured. The settlement of the sample was measured continuously,
and the distances between the wave transmitter and the receivers were updated
for each step so as to calculate the shear wave velocity accurately. At the same
time, the void ratio after each step was calculated. Then the shear moduli in the
three directions were determined based on the shear wave velocities and the
updated mass density of the soil. Then the same load cycles were repeated for up
to 20 times to study the influence of repeated loading on the stiffness of the soils.
6.4.3 Test Results
A typical result of the shear modulus during one load cycle is shown in
Figure 6.7. As shown in the figure, the shear modulus of the gravely soil
increases gradually with confining pressure. During unloading, the shear
modulus is always higher than that during loading at the same stress level,
indicating the influence of the stress history on stiffness of gravelly soils. The
figure also indicates that shear modulus in the vertical direction is the highest,
145 followed by the value at 30 degrees. The shear modulus at 45 degrees direction is
the lowest among the three values. This can be explained by Equation (6.3).
900000
800000 0 Degrees Loading 0 Degrees Unloading 700000 30 Degrees Loading 30 Degrees Unloading 600000 45 Degrees Loading 45 Degrees Unloading 500000
400000 Gmax (kPa) Gmax 300000
200000
100000
0 0 50 100 150 200 Axial Stress (kPa)
Figure 6.7 Shear Moduli during One Cycle of Loading (Soil with 25% Gravel, Cycle No. 1) (by Zeng, Wolfe, and Fu)
Figure 6.8 shows the settlement of the soil sample under repeated loading.
Under repeated loading, the settlement of the sample increased continually but the rate of increase reduced as the number of cycles increased. Most of the displacement occurred in the first several cycles. A comparison of the results from the two soils is shown in Figure 6.9. It seems that change of gravelly content has little effect on shear moduli.
146 0.53
0.51
0.49
Ratio Void 0.47
0.45 1 10 100 1000 Axial Stress (kPa)
Figure 6.8 Settlement of the Soil Sample under Repeated Loading (Soil with 50% Gravel) (by Zeng, Wolfe, and Fu)
800 25% Gravelly
50% Gravelly 600
(MPa) 400
max G
200
0 0 50 100 150 200
Axial Stress (kPa) Figure 6.9 Comparison of Test Results of Two Soils (by Zeng, Wolfe, and Fu)
147 6.5 Conclusions
A large odometer equipped with piezoelectric sensors has been developed
in the laboratory. It is capable of measuring the elastic modulus of gravelly soils
in different planes.
Two gravelly soils were tested to study the properties of the soils under repeated loading conditions. The test results show that the elastic modulus increases with confining pressure. During unloading, the measured modulus was significantly higher, indicating the influence of stress history. The test results also show that change of gravelly content has little effect on shear moduli.
148 CHAPTER SEVEN SUMMARY OF CONSLUSIONS AND SUGGESTIONS FOR FUTURE STUDY
7.1 Introduction
Piezoceramic as a smart material has been widely used in engineering
measurement and control. The piezoelectric sensor is made of piezoceramic
material which will either vibrate when an electric field is applied or will produce
charges when it is deformed by a force. Based on these properties, it can work as
a wave transmitter or a wave receiver in the measurement of soil property.
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.
The shear modulus and Young’s modulus of the soil are related to the S-wave
velocity and the P-wave velocity, respectively. Other soil properties may also be
estimated from measured wave velocities, such as the liquefaction resistance of a
soil deposit.
In this thesis, piezoelectric sensors were first used to measure shear wave
velocities in centrifuge tests. Techniques were developed for both dry and
saturated specimen tests. The centrifuge is a powerful tool in modeling
geotechnical problems, especially earthquake-related problems, but it also suffers
from some shortcomings, such as effects of boundary conditions and non-
uniform acceleration fields in the model. The direct measurement of soil
149 properties in an in-flight centrifuge model is very important, on the one hand, measured data can provide insights about the centrifuge test itself, on the other hand, the data can provide parameters for numerical simulation and analysis.
Piezoelectric sensors were also used to develop a new piezo cone penetrometer. The piezo cone penetrometer is equipped with one set of bender elements and one set of extender elements. It can measure the shear modulus,
Young’s modulus, and Poisson’s ratio of the soil. The equipment is aimed towards measurement of stiffness of subgrades and sublayers of pavements in field, but it can be used in the stiffness measurement of soils in other geotechnical fields.
Finally, a large odometer was developed for gravelly material tests. The advantages of the device include that it can measure the stiffness of soil with large grain sizes, which has limited the capacity of many conventional test methods, such as the resonant column test, triaxial test, torsional shear test, etc. It can measure moduli of specimen in different planes which are different for anisotropic specimens.
Generally speaking, the measurement of soil properties using piezoelectric sensors is simple, quick, and accurate, and the technique is theoretically sound. However, the applications of the technique are limited to the low-strain levels in the elastic range of soil deformations.
150 7.2 Summary of Observations and Conclusions
Several conclusions can be drawn from the techniques and equipment for
soil property determination with piezoelectric sensors.
7.2.1 Application of Bender Elements in Centrifuge Tests
The bender element technique for shear wave velocity measurement of
soil models in the in-flight centrifuge has been developed. The technique was
used in both dry and wet model tests. In the wet model tests, the sensors need to
be made waterproof. The bender element tests were carried out during the spin-
up, spin-down, and in-flight stages of a centrifuge, and before and after an
earthquake were applied to the model. Dynamic centrifuge tests were conducted
on both dry and saturated models to investigate the influence of the earthquake
motions. A repeated earthquake was also applied to a wet model. Three dry
models and two wet models of Nevada sand were tested. Shear wave traveling
times, accelerations, and pore water pressures were monitored during these tests.
Based on these test results, conclusions can be drawn as follows: z The bender element technique developed in this research is effective in
measuring soil properties during the spin-up, spin-down and in-flight stages
of a centrifuge. It can be used in both dry and saturated specimen tests. z The test results show good repeatability. Compared with the results of other
laboratory tests or empirical equations, they are also very accurate.
151 z The measured stiffness or shear wave velocity shows that the acceleration
field in the centrifuge model is not uniform. While it has the correct stress
field at about one-third depth of the model, it is over-stressed at the bottom
and under-stressed near the surface of the model. To get better results in a
numerical simulation of the model, the effects should be considered. z The shear wave velocities in both dry and saturated specimens increase with
g-level and depth. This is caused by the increase in confining pressures. z During the centrifuge spin-up, the shear wave velocity increases with the
centrifugal acceleration. When the centrifuge is spinning down, the velocity
is much higher than that during the spin-up stage at the same centrifugal
acceleration, indicating some degree of soil deformation z For both dry and saturated models, the models were densified by the vibration
of the earthquake. After the earthquake, the shear wave velocities were
improved. This means the stiffness of the model increased. The shear wave
velocities measured after the repeated earthquake were the same as those
measured after the motion applied at the first time. The repeated earthquake
could not improve the density of the soil. z The histories of the pore pressures recorded in the saturated model during the
first earthquake show that the peak values of excess pore pressure ratios from
the middle to the top of the model reached 1.0. They indicate that upper part
of the model liquefied during the earthquake.
152 z During the second earthquake, the peak values of the excess pore pressure
ratios from bottom to top of the model is less than 0.1 far away from 1.0. The
model was not liquefied during repeated earthquake, or the repeated
earthquake could not densify the soil. z The CRR curves, which were developed from field test data for the sites
which are known to have liquefied or not liquefied during earthquakes, need
to be further verified or modified by more case history points or model test
data.
7.2.2 Piezo Cone Penetrometer for Pavement Field Tests
The structure of a cone penetrometer was given in detail. The principle of
the technique was explained. Test procedures for both field and laboratory tests
were described. The equipment was examined by laboratory tests. Two soils,
Nevada sand and Delaware clay, were tested. CBR tests on the two soils were
also conducted for comparison purposes. The conclusions are:
z The piezo cone penetrometer described can be used in in-situ
measurement of soil properties, such as the measurement of base and
subgrade layer stiffness and Poisson’s ratio during and after construction
of a pavement. It offers a technique for field control of construction
quality.
153 z The equipment can measure the shear modulus, Young’s modulus, and
Poisson’s ratio at the same time. The continuous profiles of these
parameters can be obtained.
z Compared to the resilient modulus obtained from CBR tests based upon
empirical equations, the piezo cone penetromter test is theoretically sound.
z The test method is simple, quick, economic, and reliable.
z The test can be made mobile and be used in the field.
7.2.3 Odometer for Gravelly Material Stiffness Measurements
A large odometer equipped with piezoelectric sensors has been developed
in the laboratory. It is capable of measuring the elastic modulus of gravelly soils
in different directions. Its structure was described in detail and the experimental
setup for the test in the laboratory was presented as well. Two soils with different
gravelly content were tested using the equipment. The influence of the repeated
loading on the stiffness of the soils was studied. The stiffnesses at three
directions were measured. z The test results show that the elastic modulus increases with confining
pressure. During unloading, the modulus measured was significantly higher,
indicating the influence of stress history. z The shear modulus of the specimen is the largest in the vertical direction and
smallest in the horizontal direction for an anisotropic specimen.
154 z The test results also show that change in gravelly content has little effect on
the shear modulus for the two specimens tested.
7.3 Suggestions for Future Study z In the centrifuge test, the bender elements were fixed on the two columns
buried in the models. One of the main concerns is the interaction between the
measuring equipment with the soil, especially during dynamic model tests.
The effects on bender element test results and on model test results need to be
estimated. Bender elements and columns with smaller sizes could be used, or
numerical study could be performed to investigate these effects. Even a
different method to fix bender elements in the model could be designed in
future study. z The bender element technique combined with the shake table tests has been
shown to be promising in this study of the evaluation of liquefaction potential
of soil layers. Different sands and various earthquake motions could be used
to verify and develop shear wave velocity based liquefaction criteria in the
future. z The next version of the piezo cone penetrometer could be developed to
address the following problems:
1) The piezoelectric sensors are fragile. To be used in field tests, a protective
structure needs to be added to the current penetrometer. Using sensors of
different shapes, or even different but stronger sensors could be alternatives.
155 2) A method of pushing the penetrometer into the ground needs to be
designed. Attaching high frequency motors on top of the penetrometer and
driving it into ground by high frequency vibrations is under consideration. z Combining the penetrometer with other equipment can broaden the field of
the application of the equipment. For an example, when it is handled by a
robot, remote control tests can be performed in situations too dangerous for
human beings, or where it could be difficult for human beings to reach, such
as in tests of deep sea beds. z Automatic testing, data acquisition, and data processing system should be
developed. The basic idea is that the seismic test system should be composed
of one mobile computer plus the bender element test equipment. Signal
generation, data acquisition, signal identification, and data processing
(calculation of shear wave velocities and moduli) could be undertaken by one
computer. Figure 7.1 shows the idea of one of such setup. It depicts an
automatic system composed of a laptop plus the cone penetrometr used in the
pavement field tests.
156
Pavement
Figure 7.1 An Automatic Piezo Cone Penetrometer System
z Shear wave-based foundation design or soil liquefaction evaluation criteria
may be developed. The shear wave velocity is one of the basic properties of
soil layer. It mainly depends on the stress state and type of the soil. Many
parameters may be estimated from the shear wave velocities, such as the
stiffness and density of soil layer, the strength of the material, and the
157 liquefaction potential of a saturated soil. Shear wave velocity based
foundation design criteria or foundation quality evaluation criteria may also
be developed based on case histories, laboratory tests, field tests, or
centrifuge model tests. Field soil layer liquefaction resistance criteria based
on the shear wave velocity may also be developed. z Based on the measurements of shear wave velocities before an earthquake
(the first earthquake), after the first earthquake, and after a repeated
earthquake (the second earthquake), a model to predict soil properties after
the first earthquake and after the repeated earthquake may be established. z Investigation of other applications of the piezoelectric sensor in civil
engineering could be done, such as health monitoring of existing
infrastructure and development of smart structures.
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