BENDER ELEMENTS AND BENDING DISKS FOR MEASUREMENT OF SHEAR AND COMPRESSIONAL WAVE

VELOCITIES IN LARGE SAND SPECIMENS

A Thesis Presented

by

Remzi Oguz Deniz

to

The Department of Civil and Environmental Engineering

in partial fulfillment of the requirements

for the degree of

Master of Science

in

Civil Engineering

in the field of

Geotechnical and Earthquake Engineering

Northeastern University

Boston, Massachusetts

08/2008

i

ABSTRACT

This thesis reports on research that is part of a larger project funded by the

National Science Foundation Grant Number CMS-0509894 aimed at evaluating induced-

partial saturation in sands as an effective liquefaction mitigation measure. The focus of

this thesis is using bender elements and bending disks for shear and compressional wave

velocity measurements in large sand specimens to be used in shaking table tests.

Shear wave velocity, Vs, and compressional wave velocity, Vp, are two very

important parameters used in geotechnical earthquake engineering analysis. The use of

bender elements and bending disks in large soil specimens, typically tested in shaking

table tests, poses significant challenges. The wave form generated by a source transducer

is three dimensional and attenuates quickly as the distance between the source and

receiver transducer gets larger. Moreover, due to complex wave forms, wave travel

paths, boundary effects, and soil properties it gets harder to obtain reliable accurate test

results.

Many challenges were experienced during this research starting from

manufacturing piezoelectric transducers to get the maximum efficiency to improving the

data acquisition and interpretation of the results. Bender elements were found to be

suited well for measurement of shear wave velocities in large specimens. For

measurement of compressional waves, it was determined that bending disks were more

suitable. A special setup was devised including a signal generator, power amplifier, and a

multi-channel digital oscilloscope that permitted accurate measurements of simultaneous

readings of bender elements and bending disks responses

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This thesis presents, the details of the devised experimental setup, preparation of

bender elements and bending disks, and example measurements of Vs and Vp in fully and

partially saturated sands. A summary and a set of conclusions are presented regarding the

challenges of using bender elements and bending disks.

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ACKNOWLEDGEMENTS

I would like to thank my advisor Professor Mishac Yegian for providing me such

a wonderful opportunity to work in this research and for his constant support and

encouragement and invaluable guidance. I feel privileged to know him who has been

beyond an academic advisor to me. I also appreciate the support of the National Science

Foundation for this research program.

I express my gratitude to Ece Eseller Bayat Ph.D candidate at Northeastern

University for helping me in all aspects of this research. I appreciate her assistance and

friendship from the first day to date. I would like to express my sincere thanks to David

Whelpley for astonishing me with the limits of his abilities. Also I am grateful to Seda

Gokyer for her valuable help and useful discussions. It was a pleasure to be a graduate

student in Civil and Environmental Engineering Department at Northeastern University

and working with all those great people there. I appreciate the support that Professor

Sheahan, Acting Chair of the Department, provided me throughout my studies at

Northeastern University.

I would like to thank Professor Erhan Karaesmen at Middle East Technical

University for providing me this opportunity for a graduate study at Northeastern

University.

Many thanks to all my friends Gokce Gulsoy, Salih Saran, Musa Umut Sirma,

Emre Tuncel, Cihan Yilmaz and Bilgehan Donmez for their infinite friendship and

understanding. Special thanks go to my beloved one Gulbin Ozcan for bearing with me

over the last four years.

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Finally, this thesis is dedicated to my parents, Sukriye and Ethem Yavuz Deniz

for their endless love, care and patience. I am indebted to them for everything I have.

v

TABLE OF CONTENTS

ABSTRACT……………………………………………………………………………….i

ACKNOWLEDGEMENTS………………………………………………………………iii

LIST OF FIGURES……………………………………………………………………..viii

1. INTRODUCTION……………………………………………………………………...1

2. PIEZOELECTRIC TRANSDUCERS………………………………………………….4

2.1. Piezoelectric Ceramics……………………………………………………………4

2.2. Bender Elements………………………………………………………………….5

2.2.1. Properties of Bender Elements……………………………………………..6

2.2.2. Types of Bender Elements…………………………………………………8

2.3. Bending Disks…………………………………………………………………..10

2.3.1. Properties of Bending Disks………………………………………………11

2.3.2. Types of Bending Disks…………………………………………………..12

2.4. Application of Piezoelectric Transducers in Geotechnical Engineering………..13

2.5. Instrumentation………………………………………………………………….14

2.5.1. Function Generator………………………………………………………14

2.5.2. Power Amplifier…………………………………………………………15

2.5.3. Digital Oscilloscope & Software………………………………………...17

2.5.4. Cyclic Simple Shear Liquefaction Box (CSSLB)……………………….18

3. SHEAR WAVE VELOCITY MEASUREMENT…………………………………...20

3.1. Introduction……………………………………………………………………...20

3.2. Design and Manufacturing Bender Elements…………………………………...21

3.2.1. Wiring……………………………………………………………………21

vi

3.2.2. Waterproofing……………………………………………………………23

3.2.3. Housing…………………………………………………………………..24

3.2.4. Grounding………………………………………………………………..26

3.3. Sand Tested and Specimen Preparation…………………………………………28

3.4. Typical Test Results and Observations………………………………………….29

3.4.1. Signal Interpretation and Analysis……………………………………….29

3.4.2. Test Results with Different Specimens…………………………………..34

3.4.2.1. Test Results for Different Degrees of Saturation………………...34

3.4.2.2. Test Results for Different Void Ratios…………………………..37

3.4.2.3. Test Results for Different Effective Stresses…………………….40

3.4.3. Effects of Modifiable Parameters Dependent on Testing Apparatus…….45

3.4.3.1. Effect of Frequency………………………………………………45

3.4.3.2. Effect of Distance………………………………………………..51

3.4.3.3. Effect of Box……………………………………………………..55

4. COMPRESSIONAL WAVE VELOCITY MEASUREMENT……………………...57

4.1. Introduction……………………………………………………………………...57

4.1.1. Extender Elements……………………………………………………….57

4.2. Design and Manufacturing of Bending Disks…………………………………..61

4.2.1. Wiring……………………………………………………………………61

4.2.2. Waterproofing……………………………………………………………62

4.2.3. Housing…………………………………………………………………..62

4.2.4. Grounding………………………………………………………………..64

4.3. Typical Test Results and Observations………………………………………….66

vii

4.3.1. Signal Interpretation and Analysis……………………………………….66

4.3.2. Test Results with Different Specimens…………………………………..73

4.3.2.1. Test Results for Different Degrees of Saturation………………...73

4.3.2.2. Test Results for Different Effective Stresses…………………….80

4.3.3. Effects of Modifiable Parameters Dependent on Testing Apparatus…….83

4.3.3.1. Effect of Frequency………………………………………………83

4.3.3.2. Effect of Distance………………………………………………..86

5. SUMMARY AND CONCLUSIONS………………………………………………..87

REFERENCES…………………………………………………………………………..90

APPENDIX A: MATERIALS USED FOR MANUFACTURING PIEZOELECTRIC

TRANSDUCERS………………………………………………………92

APPENDIX B: OTTAWA SAND SPECIFICATIONS…………………………………95

viii

LIST OF FIGURES

Figure 2.1 Response of a piezoelectric ceramic when exposed to an electric current….4

Figure 2.2 Typical Bender Element…………………………………………………….6

Figure 2.3 Typical Bender Element Wiring, Polarization and Displacement…………..7

Figure 2.4 Bender Element Part Numbers……………………………………………...8

Figure 2.5 Typical Bending Disk……………………………………………………...10

Figure 2.6 Series Wired X-poled Bending Disk………………………………………11

Figure 2.7 Bending Disk Part Numbers……………………………………………….12

Figure 2.8 HP/Agilent 33120A Function/Waveform Generator………………………15

Figure 2.9 Piezo Linear Amplifier (Model EPA-104-115)……………………………16

Figure 2.10 Peak Voltage Delivered to Capacitive Load at Peak Current Rating as a

Function of Operating Frequency…………………………………………..16

Figure 2.11 Digital Oscilloscope & Data Recorder (Yokogawa–DL 750)……………..18

Figure 2.12 CSSLB Front Elevation View……………………………………………..19

Figure 3.1 Shear Wave Propagation…………………………………………………..20

Figure 3.2 Wiring Process of Bender Elements……………………………………….22

Figure 3.3 Coating Process of Bender Elements……………………………………...24

Figure 3.4 Housing Unit for a Bender Element……………………………………….25

Figure 3.5 Combining the Bender Element and the Brass Fitting…………………….26

Figure 3.6 Grounded Bender Element………………………………………………...27

Figure 3.7 Index Properties of Ottawa Sand (Holtz and Kovacs, 1981,

Modified after Hough, 1969)………………………………………………29

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Figure 3.8 Bender Element Test Setup………………………………………………..30

Figure 3.9 Bender Element Configuration within the CSSLB………………………..32

Figure 3.10 Output of Waveform Viewer for a Typical Shear Wave Measurement….33

Figure 3.11 Shear Wave Velocity Measurement of a Fully Saturated Specimen with

Dr=0.21, σ`=9.5 kPa, Vs=63 m/s ………………………………………………………………35

Figure 3.12 Shear Wave Velocity Measurement of a Partially Saturated Specimen with

S=0.77, Dr=0.18, σ`=9.3 kPa, Vs=59 m/s………………………………….36

Figure 3.13 Shear Wave Velocity Measurement of a Fully Saturated Specimen with

Dr=0.21, σ`=3.1 kPa, Vs=53 m/s…………………………………………..38

Figure 3.14 Shear Wave Velocity Measurement of a Fully Saturated Specimen with

Dr=0.72, σ`=3.0 kPa, Vs=70 m/s…………………………………………..39

Figure 3.15 Shear Wave Velocity Measurement of a Fully Saturated Specimen with

Dr=0.21, σ`=2.1 kPa, Vs=46 m/s…………………………………………..41

Figure 3.16 Shear Wave Velocity Measurement of a Fully Saturated Specimen with

Dr=0.21, σ`=3.1 kPa, Vs=49 m/s…………………………………………..42

Figure 3.17 Shear Wave Velocity Measurement of a Fully Saturated Specimen with

Dr=0.21, σ`=9.5 kPa, Vs=64 m/s…………………………………………..43

Figure 3.18 Shear Wave Velocity Measurement of a Fully Saturated Specimen with

Dr=0.21, σ`=12.7 kPa, Vs=73 m/s…………………………………………44

Figure 3.19 Near-Field Effect for r=15.5 cm (r/λ≈1.2)…………………………………47

Figure 3.20 Near-Field Effect for r=27 cm (r/λ≈2.5)…………………………………...48

Figure 3.21 Natural Frequency Determination by a Physical Impact…………………..50

Figure 3.22 Top View of the Box with S-wave Paths………………………………….52

x

Figure 3.23 Effect of Distance in the S-wave Tests………………………………...53-54

Figure 3.24 Bender Element Test in the Empty Box…………………………………...56

Figure 4.1 Compressional Wave Propagation………………………………………...57

Figure 4.2 Typical Extender Element Wiring, Polarization and Displacement………58

Figure 4.3 Compressional Wave Velocity Measurements for Fully Saturated Specimen

with σ`=1.5 kPa…………………………………………………………...60

Figure 4.4 Housing Unit and Final Design of the Bending Disk……………………...63

Figure 4.5 Typical Test Result of Poorly Grounded Bending Disks………………….65

Figure 4.6 Typical P-wave Measurement Test Result for a Fully Saturated

Specimen……………………………………………………………….68-69

Figure 4.7 Typical P-wave Measurement Test Result of a Partially Saturated Specimen

with S=0.82…………………………………………………………….71-72

Figure 4.8 Comparison of Test Results for Different Degrees of Saturation……...74-79

Figure 4.9 Variation of observed P-wave velocity with Degree of Saturation………..80

Figure 4.10 P-wave Velocity Measurement of a Partially Saturated Specimen; S=0.97,

σ`=3.2 kPa, Vp=712 m/s…………………………………………………...81

Figure 4.11 P-wave Velocity Measurement of a Partially Saturated Specimen; S=0.97,

σ`=9.6 kPa, Vp=732 m/s…………………………………………………...82

Figure 4.12 Wave Forms for the Same Specimen with Different Source

Frequencies……………………………………………………………..84-85

Figure 4.13 Different Wave Attenuations due to Different Wave Paths……………….86

1

1. INTRODUCTION

Nondestructive sample quality assessment is a comparatively new developing

area. Sample disturbance and its detrimental effects have been very well known in

geotechnical engineering practice. In the past few years, researchers have focused their

efforts to develop nondestructive test methods to determine the effect of sample

disturbance on soil properties. Measurement of wave velocities has been the preferred

method to evaluate change in wave velocities as a measure of sample disturbance. It is

also recognized that such techniques can provide small strain dynamic soil properties

needed in seismic response evaluations of soils.

At the present, piezoelectric ceramics are used in such nondestructive methods.

Although piezoelectric motors and sensors were first discovered to utilize in electrical

devices, later on scientists found ways of adapting them in geotechnical engineering. For

more than a quarter century piezoelectric ceramics have been successfully utilized to

measure velocities of waves propagating through soil specimens. Special designs with

piezoelectric transducers are used to transmit vibrating signals in the form of shear and

compressional waves. The reason for this is shear and compressional waves can give

some hints about the elastic properties of the medium where they travel; the small strain

shear modulus (Gmax) is related to shear wave velocity and small strain constrained

modulus (Mmax) is related to compressional wave velocity.

Since Shirley and Hampton (1978) introduced this method, many researchers tried

different ways of using piezoelectric instruments to determine S-wave and P-wave

velocities. Bender elements, a certain type of piezoelectric transducers, are used to

determine shear wave velocity. It is becoming widely used in laboratory testing

2

equipments. On the other hand, there are different applications of piezoelectric

instruments for measuring P-waves. Using bending disks is one of the most convenient

way for determination of P-wave velocity. Owing to their piezoelectric properties bender

elements and bending disks can operate in two ways, both as a motor and a sensor. When

used as a motor, benders can create shear waves and when used as a sensor, they can

receive shear waves in the specimen. The same relation is valid for bending disks and P-

waves.

Although piezoelectric transducers are highly sensitive, they are not powerful

enough to send high energy waves which may have trouble when propagating at long

distances. Mostly bender elements and bending disks are utilized at S-wave and P-wave

measurements within small specimens so that quality test results can be obtained easily.

However, small specimens do not represent the properties of the real situation.

The purpose of this research is to develop an experimental setup for measurement

of shear and compressional waves by the help of bender elements and bending disks in

large sand specimens. There are certain common problems which researchers using

piezoelectric transducers may face based on their setup. Moreover testing waves in large

sand specimens also raises other issues having negative effects on the performance of

testing equipment. Due to the fundamentals of attenuation, the longer the distance is, the

more rapidly waves lose energy. Also sand specimens are composed of granular particles

and it is more difficult to provide coupling (soil/bender contact) between the piezoelectric

transducers and the medium.

On the other hand, properties of the specimen and testing parameters also affect

the measurements. Often, because of these effects, experience and good knowledge are

3

required to interpret the data correctly. Although still there are many challenges in the

interpretation and analysis of bender element and bending disk test results, they are

getting resolved as more research is conducted on the use of these instruments.

This thesis describes techniques developed for manufacturing of bender elements

and bending disks, and a setup devised to measure accurately wave velocities in large

sand specimens using multiple bender elements and bending disks. The thesis also

includes results from example tests performed on fully and partially saturated sands to

demonstrate the applicability of the devised techniques and setup in the measurement of

shear and compressional wav velocities in relatively large sand specimens.

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2. PIEZOELECTRIC TRANSDUCERS

2.1. Piezoelectric Ceramics

A piezoelectric material generates an electrical output when subjected to mechanical

deformation or vice versa, and changes its shape when an electrical field is applied to it.

Piezoelectricity can be found in nature in quartz and tourmaline crystals. In industrial

applications, it is often obtained artificially with certain ceramics such as lead zirconate

titanate, barium titanate, and lead titanate. Activation of the piezoelectric property in

ceramics, typically called polarization, is obtained by applying a high DC voltage

between a pair of electrode faces. Most of the piezoelectric ceramics are used in various

areas related to electronics as in piezo valves, choppers, modulators, fans and

microscopes. Soil testing is one of the latest aspects of this comparatively new area.

Figure 2.1 Response of a piezoelectric ceramic when exposed to an electric Current (Piezo Systems, Inc.)

5

2.2. Bender Elements Bender elements are very sensitive tiny plates made of piezoelectric ceramics.

They can provide small deformations which is the most important advantage in terms of

soil assessment. By the help of necessary instruments, a bender element can vibrate and

generate shear waves in the medium. Simply, generating shear waves using bender

elements is based on sending an electrical pulse to the bender element to make it vibrate

which will cause a shear wave propagation in the soil. On the other hand, a bender

element can also be used as a receiver in case a shear wave leads to a mechanical

deformation and triggers an electrical signal due to piezoelectric properties of the

transducer. The reason for this bending motion is differential elongation and contraction

depending on the polarity of the charge. A simple bender element is composed of two

piezo layers and a metal shim between them. Also, thin conductive layers (electrodes)

have to be applied externally to the bender to provide an equal charge distribution. The

metal shim separates the ceramic piezo layers and also provides a reinforcement

increasing the strength of the bender element. Due to the orientation of the piezoelectric

ceramic, one side of the bender element either elongates or contracts and the other side

does the opposite. As long as they are fixed to each other, the composite motion turns

into bending motion. In order to benefit from this bending motion, bender should be

embedded in the soil and mounted to a stiff member of the setup so it can operate like a

cantilever beam stimulating the particles to move perpendicular to the surface of the

element and creates a shear wave.

6

Most researchers dealing with bender elements have focused on clay specimens

within short distances. Method for generating and receiving shear waves by using bender

elements was first developed by Shirley and Anderson (1978). Subsequently, Horn

(1981), Schultheiss (1981), de Alba et al. (1984), Dyvik and Madshus (1985),

Richardson (1987), Dyvik and Olsen (1989), Agarwal and Ishibashi (1991), Viggiani and

Atkinson (1995), Jovičić et al. (1996), Arulnathan et al. (1998), Santamarina et al. (2001),

and Leong et al. (2005) conducted more experiments and advanced the state-of-the-art on

bender element data analysis.

2.2.1. Properties of Bender Elements As it was mentioned, polarity, which is established during the manufacturing

process, assigns the direction of the motion, therefore changing orientation of the polarity

leads to a different characteristic property of the bender element. There are two types of

Figure 2.2 Typical Bender Element

7

bender elements discussed in the literature which are used for different purposes. If two

ceramics are put together with the same direction shown as in the Figure 2.3(a), then it is

called Y-poled bender element, inversely, if the polarity is opposite as in the Figure 2.3(b),

then it is called X-poled. Thus, these two versions differ due to the electrical connection

of the two polarized plates.

Parallel connection is required for Y-poled benders to drive voltage to the

piezoceramics in opposite directions. In order to achieve this purpose, one of the poles

coming from the circuit has to be split into two and each needs to be attached to the outer

surfaces of the bender while the other pole should be connected to the center shim. To

reach the center shim, a small portion of the piezoceramics on one side needs to be

scraped in order to uncover the shim. Although all benders act two ways, as Brignoli,

Gotti, and Stokoe (1996) explained it is better to use parallel connection with Y-poled as

Figure 2.3 Typical Bender Element Wiring, Polarization and Displacement; (a) Y-poled, (b) X-poled (Piezo Systems, Inc.)

8

a transmitter because it gives the largest deformation for a given input. This performance

is important when you have a low intensity supply source. As a feature of parallel

connection, the available voltage is not divided between the two plates so each ceramic is

excited by the same voltage. X-poled bender with series wiring performs better as a

receiver and provides higher output for a given distortion. Unlike parallel connection, for

series connection the voltage is equal to the sum of the potentials available to the

electrodes of each ceramic element.

2.2.2. Types of Bender Elements

The behavior of the bender element is characterized by certain parameters. They

all have influence on the capability of the whole apparatus and purpose of the use. There

are many commercially available piezoelectric instruments including bender elements.

The bender elements used for our research were purchased from Piezo Systems, Inc of

Cambridge, MA. The specific bender element part number is given in the Figure 2.4.

All of these headings have varied options referring to different properties. The

first one “T” stands for “transducer only” which means it doesn’t include a mount and

wires. Although, there are also “quick-mounted” types which are pre-mounted and wired

Figure 2.4 Bender Element Part Numbers

9

on one end, they are not suitable for our specific setup. Moreover, they are pretty costly

compared to the plain ones. According to the definition a bender element has 2 piezo

layers however there are other products made of piezoelectric ceramics having more than

2 layers. “20” defines the total thickness of the bender as 0.020 inches where thickness is

inversely proportional to the maximum deflection. There are slight differences between

the ceramic materials. H4 is used for PSI-5H4E an industry type piezoceramic. It has a

high motion/volt and charge/newton rating, which is useful when voltage or force is

limited. For the reinforcement material blank space means standard brass shim is used for

larger deflections. According to the size designation “303” length is 1.25 inches and

width is 0.5 inches. As it is X-poled, series connection was implemented.

Different types of bender elements have different performance levels and also

their limitations vary depending on their properties. The three most important limitations

are rated voltage, free deflection and blocked force. Rated voltage assigns the maximum

voltage driven to the bender to excite the motion. Higher amplitude results in larger

deflections, however this specific bender can have 180 V utmost. Any voltage higher

than this amount can damage the piezoceramics. During the preliminary stage of this

research we considered the free deflection as a priority for bender element selection. We

decided to use the one having the maximum deflection. It has a free deflection capacity of

±250 μm. When a bender element tries vibrating in the soil it has to overcome the

blocking force due to the pressure of the soil. Therefore we could not exceed the

maximum blocking force which is 0.28 N. To confirm the performance of the bender

elements, the capacitance can be checked after the manufacturing process. For the

10

maximum efficiency it is supposed to be kept close to 24 nF, however after preparing it

for the test setup the capacitance deviates from the original one.

2.3. Bending Disks

Just like bender elements, bending disks have the similar properties with a

significant difference of purpose. Their function for soil testing is creating P-waves in the

specimen. Bending disks have a shorter history in the literature even compared to bender

elements. They are not widely used in civil engineering. Although, they function based

on the same elongation and contraction principles as benders do, the application includes

many distinctions. Bending disks bow in and out (like a drum head) when actuated.

Due to properties of piezoelectric ceramics, bending disks can be used as both

wave source and receiver, too. Unlike bender elements the bonding layer in between the

Figure 2.5 Typical Bending Disk

11

piezo layers is not utilized for strength. They are produced only X-poled, and parallel

wiring is unavailable for this element. Working on bending disks is a more challenging

project as there is not much published experience in the literature. Although they are

supposed to be similar to bender elements in many ways, from design to analysis bending

disks have very different properties.

2.3.1. Properties of Bending Disks

The only way of wiring a disk is series as shown in Figure 2.6. It is exactly the

same as for X-poled bender elements. One pole of the circuit goes to one side and the

other pole goes to the other side of the disk. The mounting is totally different compared

to bender elements, because bender elements are restrained at one side, fixed like a

cantilever beam, however bending disks are restrained like hinged around the

circumference not to prevent the motion in the other directions. When a disk is excited,

one side elongates and the other contracts which leads to a bowing motion. The body

moves in a way that the center goes back and forth and applies an impact into the

Figure 2.6 Series Wired X-poled Bending Disk (Piezo Systems, Inc.)

12

material standing in front of the surface. This impact is transformed into P-wave in the

medium and travels through the soil.

2.3.2. Types of Bending Disks

All the part numbers for bender elements are also valid for bending disks,

however as the application for disks is narrower there are less options available for each

property. The total thickness of a disk is 0.016 inches and the diameter is 1.25 inches. It

uses PSI-5A4E industry type piezoceramic with no shim reinforcement which makes the

element weaker. Although there is no alternative polarization, it is specified that this

bending disk is an X-poled one.

The maximum free deflection corresponding to the maximum rated voltage (180 V)

is 119 μm. Applying higher voltages do not result in higher deflections, it will burn the

bending disk. The capacitance is 27 nF which decreases after the soldering process during

manufacturing. Another important point is the blocked force which is 2.4 N. If the

pressure due to the soil above it applies a higher force, the response of a bending disk will

fade.

Figure 2.7 Bending Disk Part Numbers

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2.4. Application of Piezoelectric Transducers in Geotechnical Engineering

Most commonly available techniques for determining soil properties invariably

disturb the specimen.. The benefit of using piezoelectric transducers in geotechnical

engineering is that they provide a nondestructive method, thus avoiding effects of sample

disturbance. By the help of required equipment, one can measure the velocity of shear

and compression wave propagation by using pulse transmission method. Especially for

small scale geotechnical experiments, piezoelectric crystals can be used effectively.

Standard S-wave piezoelectric transducers are not adequate to measure shear wave

velocity in soils due to weak S-wave directivity, poor coupling with soil and high

operating frequency but bender elements resolve these problems. Bender elements were

first introduced by Shirley (1978) in laboratory testing and Schultheiss (1981) has

described their use in triaxial apparatus. In 1984, The Norwegian Geotechnical Institute

compared bender test results with those from more conventional resonant column

technique, and observed similar results within the limits of experimental error limits.

Generally, adequacy and accuracy of bender element tests are influenced by two factors.

First one is the reliability of the bender element setup itself, and second one is the

reliability of the interpretation method used in analyzing test data. Many researchers

including Viggiani and Atkinson (1995), Jovicic et al. (1996), Arulnathan et al. (1998),

Santamarina et al. (2001) conducted their work to solve these problems and improve

bender element application for better results. However, P-wave measurements with

piezoelectric elements have not been very successful for dry granular materials since the

energy dissipation through the material is very large. Various researchers have expressed

difficulties encountered with P-wave velocity measurements using piezoelectric disks

14

through dry and moist granular media (De Alba et al. (1984)). On the other hand, a

bender element that mainly creates shear displacements will also generate small

compressive displacements.

Clearly, it is not easy to use piezoelectric transducers with ordinary setups.

Therefore, researchers have needed special test setups having suitable spaces for their

piezoelectric instruments. Although bender elements are more widely used compared to

bending disks, they are still mostly utilized at laboratory tests.

2.5. Instrumentation

2.5.1. Function Generator

When a bender element is exposed to a voltage difference it creates shear waves

due to the bending motion. That voltage difference can be provided by sending certain

electrical signals to the circuit which is wired to the bender element. For this purpose a

function/waveform generator (Figure 2.8) was used throughout the S-wave and P-wave

measurements. The abilities of a function generator are extremely important for wave

measuring tests as they can excite the transducers with various signals to get the best

results.

Different signals have different effects on the system, and therefore properties of

the signals have great influence on the test results. The three most important properties of

a signal are waveform, amplitude, and frequency. Although our function generator can

send signals in different waveforms, the advantage of using sinusoidal waves among

others (sawtooth and square) is ease of interpreting the received data and preventing

possible damages to the equipment. The maximum amplitude of an output signal is ±10

V which needs to be amplified to transmit higher energy to the benders, especially if the

15

source and received transducers are quite apart. For shear wave measurements

comparatively lower frequencies were used within a range of 100 hz to 1 khz. For

compressional wave measurements the frequency range of the source signal was wider, 3

khz to 20 khz, due to the characteristics of P-waves. Also different features of the

function generator helped us with improved testing techniques. It enabled us to send any

signal once, continuously or continuously with specified time intervals.

2.5.2. Power Amplifier

Due to the shortfall of the output voltage of the function/waveform generator, a

power amplifier (Figure 2.9) is needed to amplify the voltage. The maximum voltage our

piezoelectric transducers can take is ±180 V, however the function generator can go up to

±10 V. The purpose of the power amplifier is receiving and amplifying the voltage of the

signal coming from the function generator and going to the source bender element.

Figure 2.8 HP/Agilent 33120A Function/Waveform Generator

16

It is a low noise generating power amplifier which can go up to ±200 V by

multiplying the original voltage. However it causes a distortion on the high frequency

signals. The maximum voltage it can provide decreases as the frequency of the signal

passes beyond limits as shown in Figure 2.10. This model does not cause any lag time

during the amplifying process which is very important for velocity measurement type of

tests.

Figure 2.9 Piezo Linear Amplifier (Model EPA-104-115)

Figure 2.10 Peak Voltage Delivered to Capacitive Load at Peak Current Rating as a Function of Operating Frequency

17

2.5.3. Digital Oscilloscope & Software

A receiver bender element can feel the waves in the soil and convert the motion of

that wave into electrical signals. An oscilloscope can exhibit those signals in waveforms.

The digital oscilloscope and data recorder, called scopecorder, shown in Figure 2.11 can

show the received signals real time and also record it. Basically, it converts analog

signals to digital data which can be used in ASCII form. By the help of its official

software, this data can be downloaded to a computer and used with different applications.

It is a multi-purpose, multi-channel scopecorder which has interchangeable

modules for different specific purposes. Each module has two channels and receiver

bender elements are connected to these channels. It has a 10 MS/s sampling rate which is

split among the functioning channels. It has different signal capturing modes. Either real

time data can be shown for each transducer or just significant data can be captured by a

wide range of triggering functions. Triggering value can be adjusted to get rid of

unnecessary signals. Display of the channels can be changed to emphasize the important

parts. By the help of zooming properties, test results can be observed clearly during tests.

There are math functions like filtering and FFT which are important to identify and pick

specific waves by their frequencies or other properties. The stacking feature is very useful

to average the received data. The accuracy of our modules is as low as 10-6 V. The noise

effects between the modules are avoided which is important for low amplitude

measurements. It is confirmed that this device does not cause any lag time during data

acquisition. Although it can be connected to a computer from USB outlet, it has also a

small printer apparatus.

18

2.5.4. CSSLB

All the shear and compressional wave measurements were made in a special

container called Cyclic Simple Shear Liquefaction Box (CSSLB). It is a large

liquefaction box designed for testing fully and partially saturated sand specimens under

simple shear types of deformations. It allows testing of large soil samples, permits the

application of large overburden stresses, controls water drainage conditions, provides

space for elaborate instrumentation, and minimizes box sidewall boundary effects

(Ortakci, 2007).

As shown in Figure 2.12, there are holes on each wall at three different heights for

fixing bender elements and bending disks. Therefore, shear and compressional waves can

be measured under different effective stresses. Also width and length dimensions of the

Figure 2.11 Digital Oscilloscope and Data Recorder (Yokogawa–DL 750 ScopeCorder)

19

box give the opportunity to make measurements at different distances. This way

uniformity of the specimen can be checked.

Figure 2.12 CSSLB Front Elevation View (Ortakci, 2007)

20

3. SHEAR WAVE VELOCITY MEASUREMENT

3.1. Introduction

Also called as “S-wave” or “Secondary Wave”, shear waves cause particles to

oscillate perpendicular to the direction in which it moves through the body of an object,

which is the soil for geotechnical engineering purposes. Granular materials such as sands

are formed of discrete particles and considered to behave like an elastic continuum under

a confined stress state. In such a case, propagation of shear waves is related to the elastic

properties of the material. In geotechnical engineering, small shear strain modulus (Gmax)

of soils is convenient for measuring soil stiffness. The value of Gmax can be determined

by the help of shear wave velocity measurements using bender elements according to the

following equation:

( )22max tLVG s ρρ ==

where ρ=soil total density; Vs= shear wave velocity; L=effective length and t=travel time.

For our particular test setup, the effective length is the tip-to-tip distance between source

and receiver bender elements.

Figure 3.1 Shear Wave Propagation

21

3.2. Design & Manufacturing of Bender Elements

Designing a new test setup for a challenging application (testing relatively large

sand specimens) was time consuming and a difficult task of the research. Whenever a

new problem arose, it was necessary to change or improve the design. The most

important part of this research was figuring out solutions to overcome the problems. In

order to have accurate and reliable results from the tests, all the instruments and

equipments of the setup had to be prepared with utmost care. The first thing to achieve

was having bender elements working properly. A comprehensive literature search helped

us to understand the basic principles of bender elements. As in any experimental work,

most of the improvements and solutions to problems were achieved by trial and error

method.

3.2.1. Wiring

Bender elements are highly sensitive pieces and need great care during production

process. Based on the description of piezoelectric transducers, benders are used as a

member of an electric circuit. As wave source, our benders have an input limit of 180V.

However, when used as a receiver, they need to read the data at mV range. Considering

the ambient charge in the medium and around the setup, it is absolutely necessary to

prevent those exterior factors already creating noise within the same range. For accurate

and clear test results, the cable has to be shielded to prevent ambient noise. The shield

eliminates the magnetic effects of the equipment around. For this purpose, a special type

of cable was used for connecting sensors and actuators to controllers. During our research

we tried using different cables including unshielded / shielded cables and coaxial cables.

The best results were gathered with the one shown in Figure 3.2(a). It is “Xtra-Guard

22

shielded continuous flex data cable multiconductor” manufactured by Alpha Wire

Company. The advantage of using this kind of a cable is the effective shielding layer and

ease of grounding. On the other hand, oscilloscope and function generator outlets are

suitable for BNC connectors. Therefore, while one end of the cable is soldered to the

bender, the other end is soldered to a coaxial cable which has a BNC connector.

Positive and Negative Poles

Grounding

Figure 3.2 Wiring Process of Bender Elements: (a) Cable Preparation, (b) Soldering

(a)

(b)

23

As the bender element functions symmetrically, there is no difference between

two sides. Positive and negative poles of the cable are supposed to be soldered to each

side of the bender for series connection. The important point for this process is there

should not be any conductive connection between the wires. It is better to have the solder

near the edge to have a longer effective length, but if it touches the other side and

connects them, there will be a short circuit. Soldering has to be performed very carefully.

Firstly, flux has to be applied to the area where solder sticks. This helps to control the

solder easily with the hot iron. A small portion of the shield has to be kept intact for

grounding. After soldering, the element has to be cleaned by washing it under tap water

gently to get rid of the residual flux.

3.2.2. Waterproofing

As the bender elements are used in saturated specimen, they have to be

waterproofed as a member of the circuit. Waterproofing is one of the most important

requirements for this kind of experiment. Basically, it is achieved by covering the bender

element with a coating material. Among different coating materials, we decided to use an

air drying polyurethane coating, after many trials. It has a lot of benefits for the system.

Firstly, it protects the material against corrosion and increases the durability of the

members. Secondly, it provides a shield for mechanical impacts and makes it stronger.

The last but not the least, it isolates the element from undesired charges.

After soldering the bender element, we dipped it into a container full of

polyurethane and kept it in the fluid for a few seconds as shown in Figure 3.3. Then took

it out and held it vertically for the excess fluid to drip of the element. When we had only

a thin layer of polyurethane on the bender, we held it horizontally for a few minutes to let

24

the fluid spread equally and dry on the bender element. After the polyurethane sets, it was

easy to hang it on a stand horizontally for 24 hours for the polyurethane to dry. It is better

to repeat this procedure five times for a thicker layer.

3.2.3. Housing

There is a need for an extra piece to keep the bender element fixed in the

specimen. The first thing to do was designing a housing unit according to the need of the

setup and the application. The advantage of our design is that with a few modifications it

can be used as a common way of holding the bender element in a regular box or

container. Our box has 12 female threaded holes. The housing unit for the bender element

is just a piece of a brass pipe modified to be male threaded at one end as shown in the

Figure 3.4. So if you have a ready to use bender element in a brass fitting, you can easily

assemble it into the holes of any container from the outer walls.

Figure 3.3 Dipping Bender Elements into the Polyurethane

25

The installation of a bender element into the brass fitting is a tricky process, as it

is a manual operation. After the polyurethane on the bender element dried, we needed to

place the element into the housing unit. Positioning of the bender is significantly

important so that facing benders can head to each other perfectly. For locating the bender

in the brass fitting accurately we designed a special mold made of plexiglass, as shown in

Figure 3.5 . To have enough sensitivity and maximum deflection, nearly two thirds of the

bender element protruded from the threaded end of the fitting. However the soldered area

needed to stay in the fitting. First, bender element should be placed in the gap as shown

in Figure 3.5(a) and then the mold can be assembled firmly (Figure 3.5 (b)). The

openings around the bender can be closed by taping to prevent any possible leak. Brass

fitting was put into the hole at the correct orientation and pushed hard. It was important to

keep the grounding wire out of the fitting. The mold was holding both the bender and the

fitting stable so we were able to pour another filling material into the fitting

(Figure3.5(c)). The empty space in the fitting was filled with Devcon 5 minute epoxy and

Figure 3.4 Housing Unit for a Bender Element

26

waited till it dried. After epoxy hardened, the mold was dissembled to release the bender

element with the fitting (Figure 3.5(d)).

3.2.4. Grounding

The most difficult part of preparing a bender element setup was figuring out how

to ground the bender elements. The ground (literally earth) is zero charged so it

assimilates all the charges having a contact by a conductor. The grounding wire shown in

Figure 3.2 (a) sticks out of the brass fitting and also touches the shield which goes all the

(a) (b)

(c) (d)

Figure 3.5 Combining the bender element and the brass fitting; (a) placing the bender element, (b) assembling the mold, (c) brass fitting full of epoxy, (d) dissembling the mold

27

way to the other end of the cable. At this end the shield of the cable has to be attached to

the grounding member of an equipment. For our case, earth ground of the oscilloscope

was used for this purpose. The more complex part is the other end of the cable where

bender element is located. Although it is covered by polyurethane, the magnetic field

affects the bender element and induces undesired electric signals. In order to eliminate

these signals, we needed to benefit from Faraday’s cage which serves as an electrical

shielding. This can be achieved by creating a circle made of conductive materials around

the bender element. For this purpose silver paint was applied on the bender like drawing a

continuous strip (Figure 3.6) which was also extended to touch the grounding cable. Any

excess charges deposited on the inner surface of the Faraday cage migrated to the outer

surface of the cage, where they could produce no electric fields within the enclosure. By

the help of grounding wire, all those free charges could be removed.

Both source and receivers should be grounded in a setup for better test results.

Unless the elements are perfectly grounded, crosstalk can be observed. Crosstalk results

from a signal transmitted on a channel which creates undesired effects. It is usually

Silver Paint

Figure 3.6 Grounded Bender Element

28

caused by inductive or conductive coupling and magnetic field around the bender. When

crosstalk occurs, the receiver bender element picks a signal exactly at the same time

source is excited. Since it has to take time for a physical wave to travel a distance,

anything shown at zero time at the receiving end can not be a wave.

3.3. Sand Tested & Specimen Preparation

Pluviation is one of the sample preparation methods used by other researchers to

prepare soil samples with different relative densities and gradation. Pluviation can be

performed in water (wet pluviation) or in the dry (dry pluviation). For wet pluviation at

first a certain height of water was poured into the box. Then water and soil were poured

together with the same flow rate to keep the excess water height constant. This excess

water needs for the soil to spread in the box slowly and uniformly. Pouring soil from a

funnel which has a screen at the tip helps controlling the flow rate of soil.

Ottawa sand was used throughout this research for shear and compressional wave

measurements. The index properties of Ottawa sand are given in Figure 3.7. (Ottawa sand

specifications are given in Appendix B) The void ratio for the prepared loose Ottawa

sand specimen was calculated as 0.74. The maximum and the minimum void ratios of the

Ottawa sand were measured to be 0.5 and 0.8 respectively. Relative density calculations

were made according to the following equation;

2.05.08.0

74.08.0

minmax

max =−−

=−−

=ee

eeDr

29

3.4. Typical Test Results & Observations

The ultimate goal of this research was to develop a working bender element test

setup. To demonstrate the achievement of this goal, example tests were run and results

are presented with discussions.

3.4.1. Signal Interpretation and Analysis

Signal interpretation and analysis of bender element tests have been research

topics for many researchers. There are some controversial issues about benders which

have not yet been resolved. One of the problems, maybe the most important, is

determining the travel time for the shear wave between emerging from source and

arriving at the receiver. There are different methods used by various researchers. The one

we used in this research was detecting the first arrival in output signal and taking the time

between start of the source and first arrival of the received signals. According to

Arulnathan, Boulanger and Riemer (1998), there are some difficulties to detect the first

Figure 3.7 Index Properties of Ottawa Sand (Holtz and Kovacs, 1981, Modified after Hough, 1969)

30

arrival in most cases because the output signal from the receiving bender element

measures a complex interaction of incident and reflected waves. Measured Vs using

bender elements can be significantly affected by the choice of the interpretation method.

The test setup also includes assisting equipments to utilize from bender elements

as explained in Chapter 2. For the ease of understanding, the scheme shown in Figure 3.8

explains the order of the process for testing the specimen. Firstly, a certain pulse is

generated by the function generator and sent to the power amplifier to increase the

voltage. This signal is amplified to a required voltage and sent both to the source bender

element and the oscilloscope simultaneously. The importance of sending a duplicate of

Figure 3.8 Bender Element Test Setup

31

the source signal to the oscilloscope is necessity of acquiring the starting time of the

source.

When the source is excited, it generates a shear wave which goes all the way to

the receiver. As the pulse arrives, the receiver sends a signal to the oscilloscope instantly.

Therefore, there will be sent and received signals captured at different channels. After the

oscilloscope stops acquiring data, we can download it to a computer. The data on the

computer (Figure 3.9) can be analyzed by the oscilloscope software.

For similar applications, any possible time lag problem should be checked.

Sometimes instruments and/or test equipment may cause time lag which may lead to

erroneous the shear wave velocity results. To eliminate this situation, bender elements

were tested tip-to-tip touching each other. Determining the travel time equal to zero when

travel distance is zero proves that bender elements and the system works well without a

lag.

A simple illustration of the box with bender elements is shown in Figure 3.9.

Bender elements are inserted into the soil in a vertical position pointing each other. This

helps a bender having the same stresses on both sides and same orientation for higher

efficiency. Also one can see numbering for each wall of the box corresponding to the

channels for each test as the bender element on the wall-1 is shown at channel 1. There

are two different levels where transducers are located and at the same level there is one

source and three receivers. It is easier to differentiate the benders by the help of their

position. For example, the Figure 3.10 shows that the bender element on wall-1 is the

source and the others are receivers. Channel 3 shows the receiver facing the source and

channels 2 and 4 shows the ones on the sides. The signal is supposed to be received better

32

at the facing bender (channel 3) than at the diagonally located ones (channels 2 and 4).

By the help of time cursors on the left-down corner of the window, the travel time can be

obtained. Facing benders give more reliable results for shear wave velocity calculations

as the orientation of the transducers and wave orientation are same. On the other hand, it

is useful to figure out the diagonal ones for a better understanding of the wave

characteristics.

Figure 3.9 Bender Element Configuration within the CSSLB

33

1st ch

anne

l

2nd ch

anne

l

3rd ch

anne

l

4th ch

anne

l

Tim

e D

ispl

ay

Am

plitu

de

Dis

play

Figu

re 3

.10

Out

put o

f Wav

efor

m V

iew

er fo

r a T

ypic

al S

hear

Wav

e M

easu

rem

ent

34

3.4.2. Test Results with Different Specimens 3.4.2.1. Test Results for Different Degrees of Saturation

Shear wave motion is transmitted through elastic media and the main restoring

force comes from the shear effects. Therefore, change in degree of saturation does not

have an effect on the shear wave velocity. For this particular controlled test, two

specimens with different degrees of saturation were compared. First one is a fully

saturated specimen and the other is a partially saturated specimen with same effective

stress. Only two channels, source and facing receiver, are shown in the following two

figures (Figure 3.11, Figure 3.12) to make the similarity distinctive. Shear wave

velocities are pretty close however they are not exactly same due to some frequency

effects. Also it is acceptable to have some variation at different trials. Although both

source signals have the same frequency (600 hz), response of the soil to the wave

propagation changes as the soil properties change. The difference in the received signal

amplitudes and patterns depends on all of these factors. It can be inferred that fully

saturated specimen shows more stability while partially saturated specimen has a

tendency to vibrate due to a pulse. Both of the patterns are common shear waves gathered

by bender elements. As one can see it is not easy to pick the start of the arriving signal.

According to the method we use, the point where the signal starts deviating from the

original axis is assumed to be the first point.

35

Figu

re 3

.11

She

ar W

ave

Vel

ocity

Mea

sure

men

t of a

Ful

ly S

atur

ated

Spe

cim

en w

ith D

r=0.

21, σ

`=9.

5 kP

a, V

s=63

m/s

36

Figu

re 3

.12

She

ar W

ave

Vel

ocity

Mea

sure

men

t of a

Par

tially

Sat

urat

ed S

peci

men

with

S=0

.77,

Dr=

0.18

, σ`=

9.3

kPa,

Vs=

59 m

/s

37

3.4.2.2. Test Results for Different Void Ratios

Shear wave velocity is considerably affected when relative density changes.

Figure 3.14 is the test result of the specimen after tapping the sample for which the

results were shown in Figure 3.13. Tapping the specimen resulted in increase in the

relative density and a denser sand. Also densification by tapping improved the coupling

between the sand and the bender elements. For this specific situation, it is obvious that

the first sample is looser so the ability to transmit pulses is weaker. After getting denser

not only shear wave velocity increased but also the amplitude of the signal got higher. To

be consistent, in both tests the same source signal was used.

38

Figu

re 3

.13

She

ar W

ave

Vel

ocity

Mea

sure

men

t of a

Ful

ly S

atur

ated

Spe

cim

en w

ith D

r=0.

21, σ

`=3.

1 kP

a, V

s=53

m/s

.

39

Figu

re 3

.14

She

ar W

ave

Vel

ocity

Mea

sure

men

t of a

Ful

ly S

atur

ated

Spe

cim

en w

ith D

r=0.

72, σ

`=3.

0 kP

a, V

s=70

m/s

.

40

3.4.2.3. Test Results for Different Effective Stresses

Effective stress applied on a soil specimen is another distinctive property in terms

of shear wave velocity. The liquefaction box, CSSLB has holes for instruments at

different depths providing the advantage of testing the same soil with different effective

stresses. Besides, additional weights can be added on top of the specimen to increase the

effective stress. In order to compare shear wave velocities under different effective stress

conditions other parameters were kept constant.. All the tests were done on the same

specimen and the only difference was in the effective stresses that the sand felt at

different depths in the liquefaction box. The higher the effective stresses on the soil in

higher shear wave velocities are. Also increasing effective stress improves the contact

forces between the sand particles therefore amplitude of the received pulse increases.

As can be seen in the Figures 3.15 through 3.18, before S-waves there are some

other pulses which may be due to P-waves responses of the bender element. To pick the

start of the received S-wave we need to recognize the common bender element S–wave

pattern. The frequency of the received wave needs to be similar to the sent wave. This

way the faster waves coming before S-waves can be easily differentiated. Under higher

effective stresses the soil gains a more stable situation that has less ambient vibrations so

that shear waves get more distinctive. Moreover, the reflected S-waves start showing up

as seen in Figure 3.17. They travel the same distance three times as the first S-waves do

so it takes three times for reflected S-waves to reach the receiver.

41

Figu

re 3

.15

She

ar W

ave

Vel

ocity

Mea

sure

men

t of a

Ful

ly S

atur

ated

Spe

cim

en w

ith D

r=0.

21, σ

`=2.

1 kP

a, V

s=46

m/s

42

Figu

re 3

.16

She

ar W

ave

Vel

ocity

Mea

sure

men

t of a

Ful

ly S

atur

ated

Spe

cim

en w

ith D

r=0.

21, σ

`=3.

1 kP

a, V

s=49

m/s

43

Ref

lect

ed S

hear

Figu

re 3

.17

Sh

ear W

ave

Vel

ocity

Mea

sure

men

t of a

Ful

ly S

atur

ated

Spe

cim

en w

ith D

r=0.

21, σ

`=9.

5 kP

a, V

s=64

m/s

44

Figu

re 3

.18

She

ar W

ave

Vel

ocity

Mea

sure

men

t of a

Ful

ly S

atur

ated

Spe

cim

en w

ith D

r=0.

21, σ

`=12

.7 k

Pa, V

s=73

m/s

45

3.4.3.Effects of Modifiable Parameters Dependent on Testing Apparatus

Bender element’s performance is based on various parameters and to have high

quality data they have to be considered and adjusted if possible. Frequency of the signal,

travel distance and the box holding the specimen are some of most important ones having

significant influences on test results. Having a control of them gives the researcher a

great opportunity to maximize the amplitude of the received signal and helps to interpret

data reliably.

3.4.3.1. Effect of Frequency

Although bender elements are not designed to create P-waves, they induce some

weak P-waves due to compression effect of the vibration. Low frequency source is more

suitable for S-waves therefore formation of high frequency P-waves is minimized.

Moreover, P-waves fade faster than S-waves as high frequency waves dissipate easier

than low frequency waves. Also S-waves are slower which prevents the interference of

shear and compression waves. However test results show some traces belonging to the

effect of distorted P-waves. Besides, the existence of near-field effect can mislead the

travel time measurements.

Near-field effect is a phenomena related with the wavelength and frequency of the

signal. It has been extensively studied by many researchers and is experimentally

observed, when ratio of r (distance between transducers) to λ (wavelength) is between 1

and 2 as stated by Y.H. Wang (2007). It can be easily detected right before the start of S-

wave. The existence of near-field effect can bias the travel time determination even if it is

identified by the first direct arrival in output signal. Near-field effects are potentially

46

more complicated in a specimen bounded by a container like the liquefaction box

CSSLB as the spherically spreading waves that are generated by the source transducer

can reflect from the boundaries and travel between benders by indirect paths. Near-field

effect starts fading when r/λ > 2, however it can be prolonged to a further distance, r/λ >

3.5. Figure 3.19 shows the near-field effect observed when r/λ≈1.2 where tip-to-tip

distance is 15.5 cm and frequency is 800 hz. If the length is longer and/or frequency gets

higher, near-field effect will increase as shown in Figure 3.20. Although there are

different test results with different source signals at different frequencies under different

conditions, mostly single sinusoidal waves around 600 hz were used for S-wave

measurements.

47

Figu

re 3

.19

Nea

r-Fi

eld

Effe

ct fo

r r=1

5.5

cm (r

/λ≈1

.2)

Nea

r-Fi

eld

Effe

ct

48

Nea

r-Fi

eld

Effe

ct

Effe

ct o

f P-w

aves

Figu

re 3

.20

Nea

r-Fi

eld

Effe

ct fo

r r=2

7 cm

(r/λ≈2

.5)

49

The resonant frequency of the bender element is a very important parameter for

near field effect and travel time determinations. Also it has a significant effect on the

amplitude of the signal transmitted through the soil. The resonant frequency of the system

is not constant. For a bender element in air (no soil around), it can be predicted by

analytical solutions for a cantilever beam considering the boundary conditions. Also it

can be determined experimentally as shown in Figure 3.21. The mounted bender element

in air was subjected to a mechanical impact and its respond was recorded. As it can be

seen, after the impact the bender tends to vibrate freely at a constant frequency around

600 hz. However, the resonant frequency of the mounted bender element embedded in

soil depends on the cantilever beam properties, anchoring conditions, soil density and

stiffness. Therefore, the resonant frequency of the system varies with effective stresses. It

can be determined experimentally by checking different frequencies during the test. This

way, higher amplitude data can be gathered for each situation.

50

Free

Vib

ratio

n

Figu

re 3

.21

Nat

ural

Fre

quen

cy D

eter

min

atio

n by

a P

hysi

cal I

mpa

ct

51

3.4.3.2. Effect of Distance

As an S-wave created by a bender element travels away from the source, the

energy it contains dissipates rapidly. This is called attenuation. Attenuation causes

reduction in amplitude and density of the signal significantly. There are two sources of

attenuation; radiational damping and internal damping. Radiational damping is based on

distribution of the same amount of energy to greater volumes. Internal damping is related

with the characteristics of the material through which the waves are traveling. To date,

most applications of bender elements are in triaxial setup. As the total volume of the

specimen is not large, it is more convenient for the bender to create enough energy for the

S-wave to reach the receiver in small specimens. However, our purpose is testing bender

elements in large specimens. The box we used provides a large volume for S-waves to

spread in three dimensions. Therefore, we worked on bender elements to make them as

efficient as we could. The amount of energy needed to excite the source is much higher

than the amount of energy receiver produces. Even when there are two transducers in the

air touching each other, one source and one receiver, the energy send to the source to

excite it can not be close to the energy received from the other transducers. To overcome

this problem, received signals were expanded to identify the waves. The amplitude of the

source signal can be hundred thousand times larger than the amplitude of received signal.

Usually, figures from the oscilloscope have different zoom ratios for each channel as the

travel distances and wave paths are different. Also effective stress, void ratio and

saturation degree affects the amplitude of the signal but radiational damping is the most

dominant attenuation source. Figure 3.22 shows the wave paths for each source and

52

receiver. There are two different direct paths (a long distance and a short distance)

between facing benders and four identical diagonal paths.

Figure 3.23 shows influence of distance on S-wave tests. In the short distance,

near-field effect is more considerable. On the other hand, in the long distance effect of P-waves

gets more noticeable due to the shape of the box. This effect on P-waves will be

explained in detail in Chapter 4. Amplitude of the received signal at the short distance is

much higher than at the long distance. Although the source signals are same, the pattern

of the received signals differs due to distance-wavelength ratio.

Figure 3.22 Top View of the Box with S-wave Paths; Long Distance=27cm, Short Distance=15.5cm, Diagonal Distance=15.6cm

53

Figu

re 3

.23

(a)

Effe

ct o

f Dis

tanc

e in

the

S-w

ave

Test

s, L=

15 c

m

54

Figu

re 3

.23

(b)

Effe

ct o

f Dis

tanc

e in

the

S-w

ave

Test

s, L=

27 c

m

55

3.4.3.3. Effect of Box

For all similar tests using piezoelectric transducers, it is necessary to eliminate all

signals coming through the box itself. When a signal is sent to the source even in an

empty box, receiver can still pick some undesired wave components. As shown in Figure 3.24,

the first portion, which is very high frequency, occurs due to sound waves traveling in air.

Frequency of the second part is lower than sound waves but higher than the source signal.

The reason of this effect is the impacts of the bender on the walls of the box due to free

vibration. When the box is filled with sand, it hinders sound waves as it envelops the

bender element. Also the soil covering the bender prevents free vibration as it holds the

soil. Therefore these high frequency components are eliminated by filling the box.

56

Soun

d W

aves

V

ibra

tion

thro

ugh

the

Box

Figu

re 3

.24

Ben

der E

lem

ent T

est i

n th

e Em

pty

Box

57

4. COMPRESSIONAL WAVE VELOCITY MEASUREMENT 4.1. Introduction

Figure 4.1 Compressional Wave Propagation

Also called as “P-wave” or “Compression Wave”, compressional waves cause

particles to oscillate in the direction the wave propagates. Like shear waves, propagation

of compressional waves is related to the elastic properties of the material which is soil for

geotechnical purposes. By the help of compressional wave velocity (Vp) small strain

constrained modulus (Mmax) can be determined according to the following equation:

22max )( tLVM p ρρ ==

where ρ=soil total density; Vp= compressional wave velocity; L=effective length and

t=travel time. For this setup, the effective length is the distance between source and

receiver bending disks.

4.1.1. Extender Elements

Properties of bender elements are explained in Chapter 2. It was specially

emphasized that series connection is used for X-poled bender elements and likewise

parallel connection is used for Y-poled bender elements. This way, while one of the

58

piezoelectric ceramics elongates, the other one contracts. However, if a Y-poled bender

element is wired in series as in Figure 4.2(a) or an X-poled bender element is wired in

parallel as in Figure 4.2(b) then both piezoelectric ceramics elongate or contract. Due to

this coupled action the body gains extension ability instead of bending and therefore this

new type of transducer is referred as extender element. Unlike bender elements, extender

elements create P-waves as they induce an impact in the direction of the wave during

extension. This application allows us utilizing them in two ways which means a bender

element can also be used as an extender element by the help of a control box which can

switch parallel connection to series and vice versa.

Although there are different types of extender elements for both motors and

generators, for the ease of application it is more advantageous using the same pieces as

bender/extender elements for the reason that they are made of same materials with the

same design. All the manufacturing steps for preparing bender elements to use in our

Figure 4.2 Typical Extender Element Wiring, Polarization and Displacement; (a) Y-poled, (b) X-poled (Piezo Systems, Inc.)

59

setup are also valid for extender elements. There is no distinguishing difference in their

physical appearance. The only difference is the functionality due to contrast wiring.

According to M. L. Lings (2001), bender/extender elements are capable of

transmitting and receiving S-waves and P-waves providing clear signals that are easy to

interpret. Our tests show that extender elements give reliable results in fully saturated

specimens, however it has significant deficiencies in measuring P-waves in partially

saturated sands. Firstly, the surface pushed into the soil during extension is very small so

the amount of energy dispersed in the medium is insufficient. Even in fully saturated

specimen, amplitude of the received signal is pretty small compared to the test results in

which bending disks were used. Secondly, the maximum deflection of a source extender

element is extremely small again compared to that of a source bending disk.

Resonant frequency of an extender element is much higher than resonant

frequency of a bending disk therefore extenders are more suitable for sending square

pulse as shown in Figure 4.3. Square waves make easy the travel time determinations.

Briefly, bender/extender elements facilitates shear and compressional wave

measurements however they are not effective enough to work in large distances with

partially saturated granular soils. Fine soils provide more coupling which improves the

ability of extenders sending P-waves. Using extender elements did not meet the

expectations of our research where bending disks gave more satisfactory results in large

sand specimens.

60

Figu

re 4

.3 C

ompr

essi

onal

Wav

e V

eloc

ity M

easu

rem

ent f

or F

ully

Sat

urat

ed S

peci

men

with

σ`=

1.5

kPa

61

4.2. Design and Manufacturing of Bending Disks

Bending disks are similar to bender elements in terms of materials however the

purpose of the use is different. As the shape of a bending disk is circular and the surface

should face the other bending disk, the design for inserting the disks in the liquefaction

box had to be changed. Gaining some experience in bender element test setup design, a

partially improved new design was used for bending disks. Due to their similar properties

some of the materials used to prepare these instruments were common. The process of

manufacturing bending disks to use in our setup is explained in this chapter.

4.2.1. Wiring

Bending disks are only wired in series because they are produced as X-poled. P-waves

dissipate faster than S-waves, therefore the amplitude of the received signals are lower.

To interpret P-waves successfully, the received signal has to be zoomed in by a large

scale. This will also result in amplifying the ambient noise of the signal in the display. In

order to distinguish the P-waves from noise there should be a significant difference

between them. Thus the noise level has to be kept as low as possible in the data during

recording. For this purpose a high quality cable is necessary to prevent noise. We chose

“Xtra-Guard shielded continuous flex data cable multiconductor” especially for P-wave

measurement as it is more critical than S-wave measurement.

The application is similar to the bender element preparation. One of the wires was

soldered on one side of the disk and the other wire goes to the other side. Again the

grounding cable plays a crucial role here. Without grounding, none of these instruments

can work properly. All the wires had to be kept long enough to fit in the housing unit.

62

The other end of the cable was soldered to a coaxial cable like it was done for bender

element preparation.

4.2.2. Waterproofing

Disks have to be covered with a waterproofing material after soldering the cables.

They were dipped in polyurethane and held in air to dry. To get stronger members this

step had to be repeated five times just as it was done for bender elements.

4.2.3. Housing

Designing a housing unit for bending disks was the most challenging part of

preparing the P-wave measurement setup. There were two important difficulties we had

to overcome. Firstly, diameter of a bending disk was larger than diameter of the holes

made for the instruments on the liquefaction box. Secondly, it needed to have threads so

that it could be fixed into the holes before preparing the sand specimen in the box.

The housing unit is comprised of two parts; a body which is originally used as a

reducing bushing piece for PVC pipes and male threads used for mounting the bending

disk into the box. Diameter of top of the reducing bushing is equal to the diameter of the

disk.. There is a groove for the thin wire which is soldered to the top surface of disk. Also

holes were made on the side of the bushing for the soil to fill the inside of the mount. The

reason for this is to balance the pressure in and out of the mount when the box is filled

with sand specimen. Then threads taken from another PVC coupler was fixed to the back

of the reducing bushing. Regular epoxy was used to hold them together firmly. The next

step was placing the disk on to the mount. Firstly, the cables were passed through the

center of the combined piece. Silicon was applied on top of the body all around the

63

circumference where the disk was be seated. Trying to keep the disk horizontal was

necessary for higher wave amplitudes. After the silicone hardened, the bottom empty

space inside the threaded part was filled with silicone fully without leaving a bubble. The

important point was not to fill the back of the disk so soil could get in. There were two

reasons for using silicone to adhere the disk to the mount. Silicone is flexible enough to

let the disk expand and contract perpendicular to the direction of waves when disk is

excited. Also it absorbs the vibration which would have been transmitted to the walls of

the box.

Groove for the wires

Threads for mounting

Silver Paint

Figure 4.4 (above) Housing Part, (below) Final Design of the Bending Disk

64

Unlike bender elements, mounting this piece had to be done from the inside face

of the walls of the liquefaction box. Therefore, all the threads needed to be covered with

vinyl tape to fill the hole totally to prevent any possible leakage from a saturated

specimen.

4.2.4. Grounding

Grounding process of bending disks was similar to grounding bender elements.

Before fixing the disks to the housing, silver paint was applied around the disks as shown

in Figure 4.4. Also the grounding cable had to meet the silver paint to discharge the

magnetic field effects. It was easier to stick the grounding cable on the housing unit and

extend the silver paint to the cable.

Grounding for P-wave measurements is more critical than that of S-waves as the

amplitude of the received signal is lower. Grounding is a useful treatment for decreasing

the noise level. Also the magnetic field in the box created by the electric flow leads to an

effect called cross-talk. It induces undesired signals on the receiver transducer. Figure 4.5

shows that the most distinctive property of a cross-talk signal is it comes simultaneously

with the source as it is not a physical wave traveling through the soil. Although it can be

easily distinguished from the other waves, when it overlaps with P-waves the start of the

P-wave can not be easily interpreted.

Higher frequencies allow cross-talk happen at higher amplitudes. That also makes

P-wave measurements more vulnerable as the source is supposed to send higher

amplitude waves. A perfectly waterproofed and grounded bending disk should not permit

cross-talk formation however any deficiency occurred during the manufacturing

processes or due to being worn out may lead to inaccurate results.

65

Cro

ss-ta

lk

Figu

re 4

.5 T

ypic

al T

est R

esul

t of P

oorly

Gro

unde

d B

endi

ng D

isks

66

4.3. Typical Test Results & Observations

Analogous to S-wave measurements, P-wave measurements were made to

determine wave velocities under different conditions.

4.3.1. Signal Interpretation and Analysis

Unlike S-wave measurements, there is no contradiction for travel time

determination in P-wave measurements as long as the data is clear enough to interpret.

However it is more difficult getting reliable data for P-wave measurements. The main

reason for this issue is the fast dissipation of compressional waves traveling through

partially saturated soils. Therefore larger recording scales had to be used for channels of

received signals. Only disks facing each other were considered for travel time

determination. Although disks located diagonally do not give reliable results in terms of

P-wave velocity calculations, they give some information about the homogeneity of the

specimen as they are supposed to give pretty similar patterns. The difference usually

arises from not manufacturing the bending disk instruments exactly identical as it is a

manually controlled process.

Sending square wave signals to the source would be more effective as the

receiving disks give more explicit outcomes. However, square waves at high amplitudes

were observed to damage the disk. They impose high intensity energy at a very short

instant. When we sent continuous or repeated signals within short time intervals, disks

started burning slightly. Therefore, sending sinusoidal signals are assumed to be the best

choice to be sent to the source.

High frequency signals are more proper for sending P-waves which are faster than

S-waves, so the time interval of the data recording is much shorter than S-wave

67

measurements. As shown in Figure 4.6 (a), the whole recording at channel 4 includes a

high frequency and then a low frequency respond where only the first portion stands for

P-waves. Besides Figure 4.6 (b) points out two different forms of P-waves; fast P-wave

and slow P-wave. The circles correspond to each other where the second one is the

expanded version of the first one. It is easier to distinguish these two different P-wave

components. Fast P-wave comes faster but the amplitude is lower. It shows the

characteristics of commonly used regular P-waves. On the other hand, according to K.

Nakagawa (1996) the slow P-wave is slower as it travels through the soil skeleton. The

purpose of this research fast P-wave velocities were measured.

68

Figu

re 4

.6

Typi

cal P

-wav

e M

easu

rem

ent T

est R

esul

t for

a F

ully

Sat

urat

ed S

peci

men

;

(

a) fo

r a re

cord

leng

th o

f 10

ms

P-w

aves

69

Fast

P-w

aves

Sl

ow P

-wav

es

Figu

re 4

.6

Typi

cal P

-wav

e M

easu

rem

ent T

est R

esul

t for

a F

ully

Sat

urat

ed S

peci

men

;

(b) f

or a

reco

rd le

ngth

of 1

ms.

70

As the amplitude of the received signals was very low and close to the noise level

stacking was applied to the data which decreased the effect of noise. By the help of

function generator a specific number of signals were sent with defined time intervals. The

digital oscilloscope recorded all signals separately and then averaged the data. Stacking is

not necessary for S-wave measurements as the amplitude of the signal is adequate,

however for P-wave measurements stacking was applied to 32 to 256 data depending on

the clarity of the test results. As the noise is an ambient sourced signal averaging weakens

the amplitude of noise and can recover a weak hidden wave signal. Also travel time of P-

wave is very short compared to S-waves so in order to interpret the start of the received

signals both horizontal and vertical scales needed to be expanded.

Figure 4.7 shows both the whole recording and the zoomed in data of a partially

saturated specimen. Although the start of a P-wave is very distinct in a fully saturated

specimen, it gets indistinct for partially saturated specimens. The very first significant

deflection from the original axis of the signal can be assumed as the start of the P-wave

effect. There is no need to worry about the near-field effects when considering

compressional waves as the frequency is high.

71

Figu

re 4

.7 T

ypic

al P

-wav

e M

easu

rem

ent T

est R

esul

t of a

Par

tially

Sat

urat

ed S

peci

men

with

S=0

.82;

(a)

for a

reco

rd le

ngth

of 1

0 m

s

72

Figu

re 4

.7 T

ypic

al P

-wav

e M

easu

rem

ent T

est R

esul

t of a

Par

tially

Sat

urat

ed S

peci

men

with

S=0

.82;

(b)

for a

reco

rd le

ngth

of 1

ms

73

4.3.2. Test Results with Different Specimens

4.3.2.1. Test Results for Different Degrees of Saturation

One of the most important aspects of the larger research project is to establish a

relationship between P-wave velocity and degree of saturation in a large sand specimen.

It is widely known that P-wave velocity decreases with decreasing degree of saturation. If

the specimen is fully saturated as shown in Figure 4.8 (a), P-waves travel at maximum

velocity which is the P-wave velocity in water. On the other hand, even small amounts of

gas in a soil increases the compressibility and as a result the fast P-wave velocity drops

drastically. Figure 4.8 explains the change in P-wave velocity with decreasing degree of

saturation. “The theoretical analysis made by Kitsunezaki (1986) predicts that when

degree of saturation changes from 100% to 99.99% fast P-wave velocity decreases

approximately 30%.” (Nakagawa, K., Soga, K., Mitchell, J.K., 1996) It is not only

velocity but also wave pattern changes as the amount of gases in the specimen increases.

Also the amplitude of the received signal gets lower so more attention is needed to

interpret the P-wave measurements for partially saturated specimens.

Although P-wave velocity changes significantly when the degree of saturation is

slightly decreases from 100%, it does not change much when degree of saturation

decreases further. Figure 4.9 shows that around 60% degree of saturation P-wave velocity

becomes stable and is pretty close to P-wave velocity for dry sand specimen. Inabilities

of the setup and slight differences between specimens define the variability in the test

results.

74

Figu

re 4

.8 (a

) C

ompa

rison

of T

est R

esul

ts fo

r Diff

eren

t Deg

rees

of S

atur

atio

n;

Ful

ly S

atur

ated

, Vp=

1755

m/s

75

Figu

re 4

.8 (b

) C

ompa

rison

of T

est R

esul

ts fo

r Diff

eren

t Deg

rees

of S

atur

atio

n;

S=0

.97,

Vp=

754

m/s

76

Figu

re 4

.8 (c

) C

ompa

rison

of T

est R

esul

ts fo

r Diff

eren

t Deg

rees

of S

atur

atio

n;

S=0

.945

, Vp=

644

m/s

77

Figu

re 4

.8 (d

) C

ompa

rison

of T

est R

esul

ts fo

r Diff

eren

t Deg

rees

of S

atur

atio

n;

S=0

.82,

Vp=

507

m/s

78

Figu

re 4

.8 (e

) C

ompa

rison

of T

est R

esul

ts fo

r Diff

eren

t Deg

rees

of S

atur

atio

n;

S=0

.53,

Vp=

480

m/s

79

Figu

re 4

.8 (f

) C

ompa

rison

of T

est R

esul

ts fo

r Diff

eren

t Deg

rees

of S

atur

atio

n;

Dry

, Vp=

425

m/s

.

80

4.3.2.2. Test Results with Different Effective Stresses

Figure 4.10 and Figure 4.11 shows the difference between the P-wave velocity

measurements for different effective stresses when other parameters are the same. Both

figures have time cursors where the first break on the signal is detected however it is not

very distinct as the amplitude is pretty low. When fast P-wave is considered, it is realized

that effective stress does not have an effect on P-wave velocity as it travels through pore

fluid. On the other hand, slow P-wave travels through the soil skeleton with

hydrodynamic interactions and thus the velocity depends on the compressibility of the

soil skeleton. Sometimes results may show some variation in P-wave velocities due to the

inaccuracy of the testing equipment. Also it can be inferred from following figures

amplitude of the received signal increases with effective stress.

0

500

1000

1500

2000

0 20 40 60 80 100Degree of Saturation, (%)

P-w

ave

Vel

ocity

, (m

/s)

Figure 4.9 Variation of observed P-wave velocity with Degree of Saturation

81

Figu

re 4

.10

P-w

ave

Vel

ocity

Mea

sure

men

t of a

Par

tially

Sat

urat

ed S

peci

men

;

S=

0.97

, σ`=

3.2

kPa,

Vp=

712

m/s

82

Figu

re 4

.11

P-w

ave

Vel

ocity

Mea

sure

men

t of a

Par

tially

Sat

urat

ed S

peci

men

;

S

=0.9

7, σ

`=9.

6 kP

a, V

p=73

2 m

/s

83

4.3.3. Effects of Modifiable Parameters Dependent on Testing Apparatus

Measuring P-waves at relatively large distances is a challenging operation with

bending disks. In order to have useful data controllable parameters need to be adjusted, if

possible. Otherwise, it would not be as easy as interpreting S-wave measurements due to

low amplitudes and/or inaccuracy of results.

4.3.3.1. Effect of Frequency

As the velocity of P-waves is quite high, near-field effect is not a problem for P-wave

measurements. Near-field waves are not supposed to be faster than P-waves, therefore

none of the reflected waves can reach the receiver bending disks with any irregular paths

before the waves coming directly. Although it was mentioned previously that for S-wave

measurement the first fluctuation of the received signal is assumed to be near-field effect

and skipped for the S-wave velocity determination, for P-wave velocity measurements

the first jump or break on the received signal is accepted as the arrival of P-wave.

Changing velocity does not have an effect on P-wave velocity however it affects

the pattern and amplitude of the received signals as shown in Figure 4.12. Sending higher

frequency signals to the source results in more high frequency less low frequency

component of the received signal. High frequency fast P-waves represent the commonly

used P-waves, so sending higher frequency source signals gives better results for

interpretation of the data.

84

(a)

(b)

85

(c)

(d)

Figure 4.12 Wave Forms for the Same Specimen with Different Source Frequencies; (a) 5 khz, (b) 8 khz, (c) 12 khz, (d) 15 khz.

86

4.3.3.2. Effect of Distance

P-waves are affected by attenuation as high frequency waves dissipate quickly

when traveling large distances. Triaxial testing setups use specimens which are long in

one direction but short in the other two directions. Therefore waves propagate more like

in a narrow path instead of spreading in 3-D medium. This feature prevents the energy

dispersion in a larger volume so density of energy reaching the receiving transducer is

preserved. However the liquefaction box, CSSLB used in our research has large

dimensions compared to triaxial apparatus and negative effects of length and width of the

specimen are more significant.

As shown in Figure 4.13 when the distance between the source and the facing

receiver is short then the wave spreads laterally more and energy intensity decreases due

to the large effective area. On the other hand, when the distance is large between the

source and facing receiver, this time wave attenuates more due to long distance. Our

observations show traveling large distance with more intense energy gives better results

in terms of the amplitude of received signal.

Figure 4.13 Different Wave Attenuations due to Different Wave Paths

87

5. SUMMARY & CONCLUSIONS

The focus of this research was to devise a nondestructive method for measuring

the shear and compressional wave velocities in fully and partially saturated large sand

specimens typically tested on a shaking table. Such measurements are to help determine

not only the dynamic material properties of the sands tested, but also evaluate the

uniformity of the density of the large sand specimens prepared in a special liquefaction

box used for testing on the shaking table. This research is part of a larger research

program funded by the National Science Foundation on using induced partial degree of

saturation as a measure for mitigating liquefaction-induced damages.

The nondestructive method developed included the use of piezoelectric ceramic

transducers referred to bender elements and bending disks. These transducers generate

different wave forms when excited by an electric current, and hence are used as wave

generators or transmitters. Similarly, the transducers generate low voltage current when

bent, thus acting as receivers that measure arriving waves.

Significant challenges and problems were encountered devising a working setup

that used bender elements and bending disks to accurately measure arrival times of shear

and compressional waves in large sand specimens. The final setup that was developed

included a digital signal generator, a power amplifier, a digital multi-channel

oscilloscope, and transducers that were housed in specially designed fittings.

One of the problems encountered was the inability of a standard signal generator

that sends typically ± 10 volt amplitude signals to generate enough energy in a bender

element to transmit a wave that could be detected with some reliance at the receiving

bender element placed at about 15 to 30 cm from the transmitting bender element. It was

88

evident that a power amplifier was required that could amplify the voltage of the signal

generator to about 200 volts.

The next hurdle was to develop a data acquisition system that could accurately

measure the arrival times of the ways at the receiving transducers. Initial attempts of

using a PC-based LabView software failed because of inability to accurately define the

zero time (time the transmitting bender transducer is excited). After many attempts, it

was decided to use a multi-channel digital oscilloscope that has the capability to

synchronize the sent and received signals and operate at a very reduce noise level.

Considerable amount of energy and time was spent in identifying the most

suitable piezoelectric ceramic transducers and in designing and manufacturing a housing

system that allowed the placement of the transducers on the side walls of the liquefaction

box that was used in the preparation of the sand specimens. Issues related to grounding,

waterproofing, cross-talk, box effects, had to be resolved before discernable signals could

be identified and accurate arrival times determined. This thesis presents details of the

solutions arrived for these various problems.

With regards to measurement of shear waves and compressional waves, it was

determined that bender elements were very well suited to measure shear wave arrival

times. However, bender elements generated very low amplitude compressional waves,

and hence could not be used for measurement of arrival times of compressional waves.

Bender elements can be configured to elongate and contract instead of bend. In such a

configuration they are referred to as extenders. It was determined that extenders did

generate adequate compressional waves in fully-saturated sands, but the intensities of the

89

waves were very low. Extenders were inadequate for measuring compressional waves in

partial saturated sands.

For compressional wave velocity measurements, bending disks were found to be

better suited than bender or extender elements. Since bending disks have different shapes

than bender elements, a new housing system was developed to permit the installation of

bending disks into the liquefaction box, prior to the preparation of large sand specimens.

To demonstrate that the primary goal of this research was achieved, sample tests

were run on fully and partially saturated sands, and shear and compressional wave

velocities were measured using the devised experimental setup and the bender elements

and bending disks prepared with their housings. The test results demonstrate the

functionality of the developed system.

While this research achieved its goal, it is important to note that it was not without

major challenges, frustrations and difficulties. Research on the use of bender elements

has been on the rise. It appears that there is heightened interest in using bender elements

in geotechnical research and even practice. It is noted that there are also significant

limitations for their use. Developing and using a properly working bender element

system, and most importantly correctly interpreting the signals generated and received,

require utmost care and expertise.

90

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Brignoli, E.G.M., Gotti, M., Stokoe, K.H.,II, (1996) “Measurement of Shear Waves in

Laboratory Specimens by Means of Piezoelectric Transducers” Geotechnical Tesitng

Journal, Vol. 19, No. 4, December 1996, pp. 384-397

92

APPENDIX A

MATERIALS USED FOR MANUFACTURING PIEZOELECTRIC

TRANSDUCERS

93

Polyurethane Coating

94

Devcon 5 Minute Epoxy

Silver Paint

Silicone

95

APPENDIX B

OTTAWA SAND SPECIFICATIONS

96

97