AN INNOVATIVE SENSING TECHNOLOGY TO MEASURE THIN
INTERFACES FOR GEOTECHNICAL APPLICATIONS
by
QUAN GAO
Submitted in partial fulfillment of the requirements
For the degree of Doctor of Philosophy
Dissertation Advisor:
Professor Xiong (Bill) Yu
Department of Civil Engineering
Case Western Reserve University
May, 2016
CASE WESTERN RESERVE UNIVERSITY
SCHOOL OF GRADUATE STUDIES
We hereby approve the thesis/dissertation of
Quan Gao
Candidate for the degree of Doctoral of Philosophy.
Committee Chair
Xiong Yu
Committee Member
Adel Saada
Committee Member
Xiangwu Zeng
Committee Member
Weihong Guo
Date of Defense
3/11/2016
*We also certify that written approval has been obtained
for any proprietary material contained therein.
DEDICATION
To my wife Yang Long
TABLE OF CONTENTS
LIST OF TABLES ............................................................................................................V
LIST OF FIGURES ........................................................................................................ VI
ACKOWLEDGMENTS ................................................................................................. XI
ABSTRACT .................................................................................................................. XIII
NOTATION .................................................................................................................... XV
CHAPTER 1 INTRODUCTION ......................................................................................1
1.1
Background and Motivation ................................................................................ 1
1.1.1 Bridge Scour ............................................................................................ 2
1.1.2 Water Film in Layered Soil...................................................................... 3
1.2
Research Objectives ............................................................................................. 7
1.3
Organization of the Dissertation .......................................................................... 8
CHAPTER 2 THEORETICAL BASICS OF TIME DOMAIN REFLECTOMETRY
TECHNOLOGY ............................................................................................10
2.1
Introduction ........................................................................................................ 10
2.2
Technical Fundamentals of Time Domain Reflectrometry ............................... 11
2.3
Interpretation of TDR Signal ............................................................................. 14
2.4
Mixing Model for Dielectric Permittivity .......................................................... 17
2.5
Typical Dielectric Constant of Material ............................................................ 18
2.6
Review of Existing Design for TDR Probe ....................................................... 20
2.6.1 Probe Classification ............................................................................... 20
2.6.2 Material and Length of Probes ............................................................... 27
I
2.6.3 Spacing and Diameter of Probes ............................................................ 29
2.6.4 Installation and Spatial Sensitivity......................................................... 30
2.7
Summary and Conclusions ................................................................................ 33
CHAPTER 3 DESIGN AND EVALUATION OF THE NEW SPIRAL TDR
SENSOR WITH HIGH SPATIAL RESOLUTION ...................................34
3.1
Introduction ........................................................................................................ 34
3.2
The Concept of Spiral-shaped TDR Sensor ....................................................... 35
3.3
Computer-aided Design of Spiral TDR Probe ................................................... 36
3.3.1 Electric Field Distribution around a TDR Probe ................................... 36
3.3.2 Effective Sampling and Sensing Area of TDR Probe ............................ 37
3.3.3 Implementation of Computational Simulations ..................................... 39
3.3.4 Simulation Results Analysis .................................................................. 41
3.4
Design and Fabrication of Spiral Sensor ........................................................... 45
3.5
Performance Evaluation of Spiral TDR Sensor ................................................. 46
3.5.1 Comparison with Traditional Two Rod TDR Probe .............................. 47
3.5.2 Effect of Superhydrophobic Coating ..................................................... 49
3.5.3 Sensitivity of Spiral TDR Probe ............................................................ 51
3.6
Summary and Conclusions ................................................................................ 58
CHAPTER 4 ASSESSMENT OF THE HIGH RESOLUTION SPIRAL TDR
SENSOR FOR SIMULATED BRIDGE SCOURING................................60
4.1
Introduction ........................................................................................................ 60
4.2
Review of Bridge Scour Monitoring Technology ............................................. 61
4.2.1 Sonars ..................................................................................................... 62
II
4.2.2 Magnetic Sliding Collar ......................................................................... 63
4.2.3 Float-Out Devices .................................................................................. 65
4.2.4 Tilt Sensors ............................................................................................ 66
4.2.5 Sounding Rods-BRISCO Monitors ....................................................... 68
4.2.6 Fiber Bragg Grating Sensors .................................................................. 69
4.2.7 “Smart Rock” Technology ..................................................................... 71
4.2.8 Time Domain Reflectrometry ................................................................ 73
4.3
Principle of Bridge Scour Depth Estimation with TDR .................................... 77
4.4
Design and Fabrication of Spiral-shaped Sensor ............................................... 80
4.5
Calibration of Spiral-shaped Sensor .................................................................. 82
4.5.1 Calibration with Liquid .......................................................................... 83
4.5.2 Calibration using wet soil with known water moisture ......................... 85
4.6
Simulated Scouring Experiment Using New Spiral TDR Probe ....................... 89
4.6.1 Experimental Program ........................................................................... 89
4.6.2 Experimental Materials .......................................................................... 89
4.6.3 Experiment Results Analysis and Discussion ........................................ 90
4.6.4 Comparison with Straight TDR Scour Probe......................................... 97
4.7
Summary and Conclusions ................................................................................ 99
CHAPTER 5 DETERMINATION OF THIN WATER FILM DUE TO VOID
REDISTRIBUTION USING SPIRAL TDR SENSOR .............................101
5.1
Introduction ...................................................................................................... 101
5.2
Review of Water Film Due to Void Redistribution ......................................... 102
5.2.1 Water Film due to Void Redistribution ............................................... 102
III
5.2.2 Previous Investigations on Water Film ................................................ 104
5.3
Sensor Configuration and Calibration ............................................................. 115
5.4
Water Film Detection in Static Experiments ................................................... 118
5.4.1 Deployment of Experiment Apparatus ................................................ 118
5.4.2 Testing Materials ................................................................................. 120
5.4.3 Experiment Procedure .......................................................................... 121
5.4.4 Interpretation of Testing Signals .......................................................... 123
5.4.5 Measurement of Water Interlayer Thickness .......................................... 125
5.5
Water Film Measurement in Dynamic Shaking Table Test............................. 130
5.5.1 Experimental Program ......................................................................... 130
5.5.2 Fundamentals of Estimation Water Film during Shaking Events ........ 132
5.5.3 Experiment results analysis.................................................................. 137
5.6
Summary and Conclusions .............................................................................. 144
CHAPTER 6 CONCLUSIONS AND FUTURE WORKS .........................................146
6.1
Summary and Conclusions .............................................................................. 146
6.1.1 Design and Evaluation of the New Spiral TDR Sensor with High Spatial
Resolution
147
6.2.2 Assessment of the New Sensor for Bridge Scour ................................ 148
6.2.3 Determination of Water Film Thickness in Multi-Layered Soil Profile
with the New Sensor .................................................................................................. 149
6.2
Recommendations for Future Work................................................................. 150
REFERENCES ...............................................................................................................152
IV
LIST OF TABLES
Table 2-1. Dielectric constant of some typical materials ................................................. 19
Table 3-1. Configurations of simulation parameters ........................................................ 40
Table 3-2. Comparison of two sensors in air and water ................................................... 48
Table 3-3. Measurement results of two probes with micrometer caliper ......................... 56
Table 4-1. Comparison of existing instruments for monitoring bridge scour .................. 75
V
LIST OF FIGURES
Fig. 1-1. Some effects caused by soil liquefaction. (a) Tilting of buildings due to
liquefaction during the 1964 Niigata Earthquake; (b) Sand boils ejected to the ground
surface during the 2011 Christchurch Earthquake. ............................................................. 4
Fig. 1-2. Schematic illustration of void redistribution mechanism in stratified soil profile
(modified from Malvick et al. 2006)................................................................................... 5
Fig. 2-1. a) Schematic diagram of a typical TDR system; b) An example of TDR output
signal (Drnevich et al. 2001) ............................................................................................. 12
Fig. 2-2. TDR waveform (b) for a wet sand and its first derivative with respect to time; (a)
and corresponding bifilar TDR probe; (c) with rod spacing, S, and rod diameter; (d) the
dashed vertical lines denote two reflection points, corresponding times t1 and t2 (Evett
2000). ................................................................................................................................ 15
Fig. 2-4. The TDR waveform (bottom) and its first derivative (top) with features identified
by Baker and Allmaras (1990) .......................................................................................... 17
Fig. 2-5. Examples of TDR coaxial cell probe (Cataldo et al. 2008; Topp et al. 1980; Xiong
and Vincent 2004) ............................................................................................................. 22
Fig. 2-6. Schematic diagram of typical straight TDR waveguide .................................... 24
(a) two-leg; (b) three-leg; (c) four-leg; (d) seven-leg; (e) two-plate; (f) three-strip ......... 24
Fig 2-7. Distribution of electric field intensity for a variety of TDR probe designs.
Configurations include (a) two-rod; (b) three-rod; (c) four-rod (d) seven-rod; (e) two
parallel plates (Robinson et al. 2003) ............................................................................... 25
Fig. 2-8. Some examples of non-straight TDR probe (serpentine and spiral waveguide)
(Bittelli et al. 2004; Selker et al. 1993; Vaz and Hopmans 2001) .................................... 27
VI
Fig. 3-1. Schematic illustration of working principle for the spiral TDR sensor ............. 35
Fig. 3-2. Schematic diagram of spiral probe for FEM analysis ........................................ 39
Fig. 3-3. Mesh grid of computation domain ..................................................................... 41
Fig. 3-4. Electric potential (contour and color) and electric field (red arrow) distribution
(filled in water) ................................................................................................................. 42
Fig. 3-5. Electric energy density (color), effective sampling area with 90% level (contour)
and electric field (red arrow) distribution (filled in water) ............................................... 42
Fig. 3-6. Influence of wire distance on sample area ......................................................... 44
Fig. 3-7. Influence of wire diameter on sample area ........................................................ 44
Fig. 3-8. Photo of spiral-shaped TDR probe..................................................................... 46
Fig. 3-9. Comparison of traditional and spiral TDR probe (a- in the air; b- totally
submerged in the water) .................................................................................................... 48
Fig. 3-10. Comparison of spiral TDR probe with and without superhydrophobic coating
(a- with coating; b- without coating) ................................................................................ 51
Fig. 3-11. Photo of converted micrometer ........................................................................ 52
Fig. 3-12. Output signals of two-rod straight and spiral probe at different water levels .. 55
Fig. 3-13. Relationship between scaled length and water level (air-water interface) for two
sensors ............................................................................................................................... 57
Fig. 4-1. Schematic diagram of sonar scour monitoring system (Hunt 2009) .................. 63
Fig. 4-2. Schematic diagram of a magnetic sliding collar monitoring system (Hunt 2009)
........................................................................................................................................... 64
Fig. 4-3. Schematic diagram of a float-out device and float-out sensors (Hunt 2009)..... 66
Fig. 4-4. Schematic diagram of a float-out device and float-out sensors (Hunt 2009)..... 67
VII
Fig. 4-5. Schematic diagram of a sounding-rod monitoring system (Haas et al. 1999) ... 69
Fig. 4-6. The FBG scour monitoring system (a) model I (b) model II (Lin et al. 2004) .. 71
Fig. 4-7. The “smart rocks” scour monitoring system (Chen et al. 2014) (a) (b) working
principle of “smart rocks”; (c)(d) smart rocks; ................................................................. 72
Fig. 4-8. Schematic diagram of bridge scouring measurement with TDR technique ....... 78
Fig. 4-9. Comparison of straight TDR probe and spiral-shaped TDR probe ................... 81
Fig. 4-10. Effects of coating on the dielectric constant (  is the dielectric constant of
coating) ............................................................................................................................. 82
Fig. 4-11. Output signals of spiral sensor in liquid (a- in standard solvent; b- in ethanol-DI
water mixture ) .................................................................................................................. 84
Fig. 4-12. Relationship between measured and real dielectric constant ........................... 85
Fig. 4-13. Calibration of spiral TDR probe with moisture sand ....................................... 86
Fig. 4-14. Output signals of TDR with spiral probe in moisture sand.............................. 88
Fig.4-15. Calibration of spiral probe with moisture sand ................................................. 88
Fig. 4-16. Grain size distribution of two types of testing materials ................................. 90
Fig. 4-18. Relationship between dielectric constant and sediment thickness (a - fine soil; b
– coarse soil) ..................................................................................................................... 95
Fig. 4-19. Measured and predicted sediment layer thickness (a - fine sediment; b – coarse
sediment) ........................................................................................................................... 96
Fig. 4-20. Relationship between sediment layer thickness and apparent length (a – straight
probe; b – spiral probe) ..................................................................................................... 98
Fig. 5-1. Sketch of void redistribution in submerged layered infinite slope (Malvick et al.
2006) ............................................................................................................................... 103
VIII
Fig. 5-2. Photos of shaking table tests on layered slope with embedded silt layer (Boulanger
et al. 2014; Kokusho 1998) ............................................................................................. 106
Fig. 5-3. Excess pore water pressure redistribution pattern during liquefaction in layered
soils (Brennan and Madabhushi 2005) ........................................................................... 108
Fig. 5-4. Post-shaking photos of centrifuge models having identical initial relative density
but different underlying sand layer thicknesses; (Kulasingam et al. 2004) .................... 111
Fig. 5-5. Two examples of void redistribution simulation for slopes with low permeable
silt interlayer using PM4Sand model; a) post-shaking slope with sand permeability of 0.012
m/s, b) post-shaking slope with sand permeability of 0.06 m/s, c) slope geometry before
shaking event (Kamai and Boulanger 2012) ................................................................... 113
Fig. 5-6. Excess pore water pressure ratio time history at different depth using DEM
(Zeghal and El Shamy 2008) .......................................................................................... 114
Fig. 5-7. Configuration of new spiral TDR sensor ......................................................... 116
Fig. 5-10. Testing setup for static experiment (a- sketch diagram; b- photo of test device)
......................................................................................................................................... 119
Fig. 5-11. Particle size distribution of testing soil .......................................................... 121
Fig. 5-12. Procedures of static testing to measure water film ........................................ 122
Fig. 5-13. Comparison of TDR output signal with and without water interlayer ........... 124
Fig. 5-14. Schematic diagram of test for water interlayer thickness measurement ........ 125
Fig. 5-15. Output signals of TDR with different thickness of water interlayer .............. 128
Fig. 5-16. Comparison of measured and actual water interlayer thickness .................... 129
Fig. 5-17. Schematic experimental setup for dynamic shaking table test ...................... 131
Fig. 5-18. Particle size distribution of soil sample for dynamic experiments ................ 132
IX
Fig. 5-19. Schematic diagram of water film measurement in one soil layer system using
TDR sensor (a- the initial state; b- at any given time during shaking process) .............. 133
Fig. 5-20. Schematic illustration for the onset and elapse of water interlayer during shaking
event ................................................................................................................................ 135
Fig. 5-21. Output signals of the new spiral TDR for shaking test .................................. 138
Fig. 5-22. Variation of apparent length and dielectric constant ..................................... 138
Fig. 5-23. Screen shots from testing video capturing the development process of water film
interlayer ......................................................................................................................... 141
Fig. 5-24. Comparison of the water interlayer measurement from the spiral TDR sensor
and testing videos ............................................................................................................ 142
Fig. 5-25. Photo of failure for clay layer during shaking test ......................................... 143
X
ACKOWLEDGMENTS
I would like to express my sincerest gratitude to my advisor, Professor Xiong Yu,
for his valuable mentoring, patience, continuous encouragement and support for my
research as well as my personal life. I am so grateful to Professor Yu for offering me so
many opportunities to participate in national and international workshops and conferences,
from which I benefited both professionally and personally.
I feel extremely grateful to Professor Adel S. Saada for his imparting knowledge,
consistent guidance and dedication, especially his financial support for my graduate studies
during the past few years at CWRU.
I also want to sincerely thank Professor Xiangwu Zeng and Professor Weihong Guo
for their extraordinary teaching and for serving on my graduate committee.
I also appreciate the assistance and support I received from Mr. Jim Berilla with
regards to the experiment system setup and development of the TDR sensors. I would like
to thank Nancy Longo who is always available to provide suggestions and assistance over
the years. Many thanks are also extended to all faculty members, staffs, and my fellow
graduate students and friends: Dr. Zhen Liu, Dr. Junliang Tao, Dr. Hao Yu, Dr. Ye Sun,
Yuru Li, Jin Qin, Guangxi Wu, Jianying Hu, Saman Sabzehzar, Kamil Nizamiev, Yang
Yang, Chanjuan Han, Yuan Guo, Shaoyang Dong, Jiale Li and Xuefei Wang. Their support
helped make my life at CWRU very meaningful and memorable.
This dissertation work is also supported by National Science Foundation (CMMI1131295). I am grateful for the financial support throughout this project.
XI
Last, but most importantly, my appreciation should be given to my parents, parentsin-law and other family members, and especially my wife, Yang Long, for her
understanding and love over the past few years. Her everlasting support and encouragement
to me, consistent efforts and contributions to our family are in the end what made me
complete my dissertation work successfully.
XII
An Innovative Sensing Technology to Measure Thin Interfaces for Geotechnical
Applications
ABSTRACT
By
QUAN GAO
Time Domain Reflectrometry (TDR) is a useful and effective technique for the
detection of discontinuities or interfaces. It has been extensively applied for geotechnical
applications by detecting air-water or soil-water interface, such as monitoring reservoir
water level and bridge scour. But the current TDR sensor (e.g., conventional straight
waveguide) would lose capability for some applications involving detection of very thin
interfaces, for instance, the bridge scour surveillance with scouring in the range of
centimeters, the measurement of water film due to void redistribution in multiple-layered
soil profile, which is even in the range of millimeters. This makes it imperative to further
improve the resolution and sensitivity of the TDR waveguide.
The concept of the spiral TDR probe is proposed in this dissertation study. It means
designing the traditional straight waveguide into a spiral shape to increase the effective
propagation path of EM wave per unit length along the direction of the sensor. A FEM
analysis is conducted for the optimization design of the new sensor. The effect of geometric
configurations on the sampling area is also analyzed, including waveguide diameter and
spacing distance, etc. Several spiral TDR sensors are fabricated and evaluated using a series
of laboratory experiments. Its performance is also compared with the conventional straight
probes.
XIII
The new spiral TDR sensor is calibrated using several standard liquids or solvents
with known dielectric information. A series of simulated scouring tests with twocentimeter sediment scouring are performed with the new sensor and traditional straight
probe. The performance of the two sensors and the advantage of the new probe is analyzed
and evaluated.
The new spiral TDR sensor is then applied for the detection and measurement of
water film due to void redistribution in the layered soil column. A group of static and
dynamic shaking table tests are carried out in the laboratory to assess the performance of
the new sensor. The results from both experiments indicate that the new spiral sensor is
capable to detect and measure the water film within millimeter in layered ground. However,
further refinements and improvements are still required to explore applications of the new
spiral sensor in future studies.
XIV
NOTATION
2D
Two Dimensional
3D
Three Dimensional
BNC
Bayonet Neill-Concelman
DEM
Discrete Element Method
DI
Deionized
EM
Electromagnetic
FBG
Fiber Bragg Grating
FDM
Finite Differential Method
FEM
Finite Element Method
MSC
Magnetic Sliding Collars
NCHRP
National Cooperative Highway Research Program
TDR
Time Domain Reflectrometry
TEM
Transverse Electromagnetic
XV
CHAPTER 1 INTRODUCTION
1.1
Background and Motivation
Many applications in civil engineering involve the detection of different
discontinuities or interfaces, such as rock joints, cracks in some construction materials (e.g.,
concrete and asphalt), and air-water or soil-water interface, etc. Rock joints could impact
the mechanical behavior of rock mass (Fathi et al. 2016) and the stability of infrastructures
(Satıcı and Ünver 2015). Cracks in concrete is a stubborn adversary to engineers, since it
will decrease the concrete strength significantly and consequently influence the safety of
structures (Hamrat et al. 2016; Han et al. 2016). Measuring and preventing the development
of concrete cracks is an essential mission for civil engineers (Alam et al. 2010; Bazant and
Oh 1983; Yiran et al. 2013).
A variety of soil erosional processes also often occur at the soil-water interfaces.
Detecting and measuring the variation of soil-water interface is recognized as a viable
approach to capture the information of these erosion process. Two examples selected in
this dissertation study include the measurement of the bridge scouring process and water
film due to void redistribution in layered soil profile. The bridge scour can be monitored
by measuring the elevation variation of the streambed-water interface, whereas the
development of water film, acting as a shear band in layered soil profile, can also be
determined via detecting the location of the soil-water interface directly and indirectly.
1
1.1.1
Bridge Scour
Bridge scour has been identified as the major cause for bridge failures in the United
States, accounting for more than half of the reported bridge failures. It could induce
millions of economic loss in the United States every year due to direct cost of restoring and
repairing these destroyed structures, indirect transportation system disruption, and worst
situation, loss of lives (Tao 2013; Yu et al. 2013). One recent example is I-35W Bridge
located at Minneapolis-ST Paul, Minnesota Twin Cities metropolitan area. The collapse of
this bridge, in 2007, resulted in approximately an economic loss of $ 71,000 to $220,000 a
day because of the transportation issue (Xie and Levinson 2011).
Monitoring or surveillance of the scouring process around bridge foundations is an
important and effective countermeasure. It is monitored by detecting and measuring the
elevation variation of the stream bed, i.e., soil-water interface, using the direct or indirect
method. The stream bed elevation will decrease when scouring occurs, otherwise rise
during refilling or sedimentation process. Therefore, the location of the soil-water interface
can be treated as an indicator of bridge scour. The existing monitoring technologies for
bridge scour include sonar (Hayes and Drummond 1995; Mason and Sheppard 1994),
sliding collar (Yankielun and Zabilansky 1999) , dropping weights (Lefter 1993) and other
advanced techniques, such as neutral buoyancy “fish” and “smart rocks” by Zabilansky
(1996) and Radchenko et al. (2013). These technologies, while having merits, also have
limitations due to the heavy weight, large volume or power supply issues.
TDR is another alternative option to monitor bridge scour with advantages of being
automatic and inexpensive. Previous researchers have developed a few generations of TDR
2
bridge scour monitoring systems (Yu and Yu 2010; Yu et al. 2013; Zhang et al. 2010).
These studies have proved the viability of TDR to monitor the process of bridge scour,
however, it still possess some limitations or insufficiencies. For example, the conventional
straight TDR probe adopted in their studies can be able to sense the sediment layer varying
within centimeter range (4 cm or 10 cm). It might lose the capability to detect scouring
when the scouring thickness is smaller than that range. This limitation constitutes a strong
motivation for this dissertation: improving the resolution and sensitivity of current TDR
sensors to measure the scouring process more accurately.
1.1.2
Water Film in Layered Soil
Soil liquefaction is the extreme manifestation of excess pore water pressure
generation when subjected to cyclic loading (e.g., seismic earthquake loading). The buildup
of excess pore water pressure will induce a substantially loss of soil stiffness and strength,
causing the soil to behave as liquid-like materials and eventually giving rise to devastating
(a)
3
(b)
Fig. 1-1. Some effects caused by soil liquefaction. (a) Tilting of buildings due to
liquefaction during the 1964 Niigata Earthquake; (b) Sand boils ejected to the ground
surface during the 2011 Christchurch Earthquake.
failure of structure foundations, levees, embankments and other infrastructures, such as
1964 Niigata earthquake (Kishida 1966), 1989 Loma-Prieta earthquake and 2011
Christchurch earthquake (e.g., Fig. 1-1).
Liquefaction in uniform soils has been extensively studied. The conclusions from
these studies, however, may not be applicable to stratified soil conditions. This is because
for stratified soil profile with embedded lower permeability interlayer (e.g., Fig. 1-2), a
unique phenomenon called void redistribution might occur, i.e., a portion of the liquefied
soil locally loosens whereas another portion densifies. This will subsequently contribute to
the formation of a thin water film or shear band beneath the low permeable soil layer, and
4
eventually lead to the failure of “sand boils” (Fig. 1-1b), lateral spreading or postliquefaction (Kamai and Boulanger 2012; Kokusho and Kojima 2002; Kulasingam et al.
2004; Malvick et al. 2006; Yang and Elgamal 2001).
Fig. 1-2. Schematic illustration of void redistribution mechanism in stratified soil profile
(modified from Malvick et al. 2006)
Water film due to void redistribution has been observed in a number of laboratory
studies (Kokusho 1999; Kulasingam et al. 2004; Malvick et al. 2008; Malvick et al. 2006).
It was found that the formation of water film at the interface area between liquefied soil
and the soil layer of low permeability can cause significant loss of shear strength during
and after an earthquake (Kulasingam et al. 2004; Malvick et al. 2008; Malvick et al. 2006).
This is one of the most likely failure mechanisms for mild slopes (slope inclined angle <5°)
or embankments made of stratified soil layers (Boulanger et al. 2014). Over the years,
investigators have implemented a variety of experimental studies, trying to verify this
5
mechanism. Kulasingam et al. (2004) conducted a group of centrifuge tests on seismic
stability of a sand slope with or without a layer of low permeability silt. Based on the
recorded excess pore pressure and deformation, they concluded that this mechanism is
probably the right one. However, the variation of water film thickness or extent of void
redistribution has not been directly quantified in these investigations. In the 1-g shaking
table test, the thickness of water film during and after shaking events are determined with
a measuring grid or ruler and recorded testing videos (Kokusho 1998; Kokusho 1999;
Kokusho and Kabasawa 2005). But this does not work for centrifuge model experiments,
and it can be only relying on the indirect estimation by inferring from pore pressure
measurements using pore pressure transducers placed at different depths within the layered
soil models.
The context in section 1.1.1 has revealed that TDR can be utilized to monitor the
bridge scour, since it is capable to accurately detect and measure the soil-water interface
during the course of scouring. This feature, thus, enables TDR technique as a potential
method to directly measure the onset and development of water film during and after the
shaking process. But considering the thickness of water film, which is in the range of
millimeters, for example, it is assumed tens of diameter 𝐷50 (particle size where 50% of
soil particles are smaller than the size) (Malvick et al. 2006), a new TDR sensor with higher
resolution is required to be designed and developed. This constitutes another motivation
for this dissertation.
6
1.2
Research Objectives
TDR is an effective technique for numerous geotechnical applications via detecting
and measuring the soil-water interface. The previous contexts have illustrated the
limitations or inadequacies of current TDR sensors on the application for bridge scour, as
well as the urgent demand of new waveguides with higher resolution to directly quantify
the thickness of water film and the extent of void redistribution in layered ground. This
dissertation study is an effort to address this problem, the objectives of which include but
not limit to:

To provide a comprehensive summary and review on the advancement of
TDR technology, especially the state-of-art for the design of the TDR
waveguide;

To propose and develop an innovative TDR sensor with higher resolution
and sensitivity with the assistance of computational simulation analysis;

To evaluate the performance of the new TDR sensor from several aspects
and compare it with the traditional straight waveguides;

To appraise the applicability of the spiral TDR sensor on measuring bridge
scour process and its advantages over the conventional straight probe;

To assess the viability and applicability the new sensor has on the water
film thickness determination in the stratified soil profile due to void
redistribution;
7
1.3
Organization of the Dissertation
This dissertation explores an innovative spiral TDR sensor with high resolution for
some geotechnical applications by detecting and measuring the variation of soil-water
interface. It is organized into the following six chapters.
Chapter 1 introduces the background information pertaining to this research. Two
typical scenarios are illustrated to pave a way for the research motivation statement. Also
included are five specific objectives to be addressed and organization of this dissertation
study.
Chapter 2 provides a synthetic summary of the TDR technology, i.e., the technical
background, signals interpretation method, mixing model for dielectric permittivity and
dielectric information of some typical materials. In addition, the state-of-art for the current
TDR waveguide design is reviewed meticulously in this chapter.
Chapter 3 presents the concept and design of the innovative spiral TDR sensor.
Finite element simulation is conducted to assist the geometrically optimization design for
the new sensor. Several pilot sensors are fabricated with the spiral spacing distance of 2
mm. A series of experiments are implemented to evaluate its performance in the laboratory,
and compared with the traditional straight probes.
Chapter 4 reviews the current monitoring methodologies and techniques for bridge
scour as well as their application scope and limitations. Also reported are a group of
simulated bridge scouring tests using both the conventional straight TDR probe and the
new spiral probe designed in Chapter 3.
8
Chapter 5 presents the previous studies and state-of-art on the water film in
stratified soil profile due to void redistribution. A new TDR sensor with spiral spacing
distances of 1 mm is utilized for measuring water film thickness variation in static and
dynamic shaking table tests. The testing results from the new sensor and the measuring
ruler are compared.
Chapter 6 summarizes the significant findings and conclusions of this dissertation,
along with some recommendations for future work.
9
CHAPTER 2 THEORETICAL BASICS OF TIME DOMAIN REFLECTOMETRY
TECHNOLOGY
2.1
Introduction
TDR is an effective and efficient nondestructive technique, featuring the
advantages of being automatic, real time and inexpensive. Although it was originally
developed to locate the faults or breaks for electrical cables, it has already been extensively
applied for a variety of civil and environmental applications during recent decades, such as
characterizing properties for soils and concrete (Drnevich et al. 2001; Hager III and
Domszy 2004; O'Connor and Dowding 1999; Topp and Davis 1985; Xiong and Vincent
2004), monitoring infrastructure conditions (Chen et al. 2004; Lin et al. 2005; Su and Chen
1998; Yu et al. 2013), contaminants transportation (Haridy et al. 2004), detecting
freeze/thaw behaviors of soils (Liu et al. 2012) and monitoring seepage processes in the
embankment (Zhang et al. 2010), etc.
In order to present the development and applications of the new TDR sensor in the
following chapters, the author firstly introduces the technical background of the TDR
technique, including the working principle of TDR, the interpretation method of TDR
signals, the mixing model for dielectric permittivity and typical dielectric properties of
several materials. Additionally, a comprehensive review of the TDR waveguide is
presented. In this section, the author categorizes the existing TDR probes into three types:
coaxial cell probe, straight-leg probe and non-straight probe. Also included in the review
10
on the TDR probe are the selection of fabrication materials, sensor installation, the probe
design and its influence on the spatial sensitivity performance of the sensor.
2.2
Technical Fundamentals of Time Domain Reflectrometry
The TDR technique works by generating a small-magnitude pulse to the
transmission cable and then probes and receiving the echoes and reflection signals from
the measured materials. Fig. 2-1 (a) shows the schematic of a TDR system, which typically
consists of a pulse generator, coaxial cable, a sensing probe and control station such as by
PDA, laptop or datalogger.
As shown in Fig. 2-1(a), the pulse generator produces a fast rising electromagnetic
(EM) pulse (with rise time of hundred picoseconds to allow for high resolution in the
interface detection). When this signal reaches the beginning of the probe, due to the
impedance mismatch between the cable and the soil probe, a portion of the signal is
reflected back to the device. When the rest of the signal reaches the air-soil interface and
the end of the probe, two more reflections of the signal occur. These three reflections cause
three discontinuities in the resulting signal, illustrated in Fig. 2-1 (b) (Ledieu et al. 1986;
Yu and Drnevich 2004). The time difference between the last two discontinuities is the
time (t) the signal requires to travel back and forth from the soil surface and the probe end,
i.e., twice the length (L) of the probe in the soil. Therefore, the EM wave propagation
velocity, v, in the soil surrounding the TDR probe can be determined by equation (2-1):
𝑣=
𝑐
(2-1)
√𝐾𝑎
11
(a)
(b)
Fig. 2-1. a) Schematic diagram of a typical TDR system; b) An example of TDR output
signal (Drnevich et al. 2001)
12
where
v = the velocity of an electromagnetic wave in measured materials;
c = the velocity of an electromagnetic wave in free space (2.998 × 108 𝑚/𝑠);
Ka = the dielectric constant of the material;
And the time for the signal to propagate from air-soil interface to the probe end is
given by equation (2-2), provided that the length of the probe in the soil is assumed to be
Lp.
𝑡=
2𝐿𝑝
(2-2)
𝑣
Submitting equation (2-1) into (2-2) and defining apparent length, 𝐿𝑎 = 𝑐𝑡/2,
which can be determined from the TDR output signal (Fig. 2-1 (b)), equation (2-2) is
yielding to equation (2-3)
2
𝐿
𝐾𝑎 = (𝐿𝑎 )
(2-3)
𝑝
where
𝐿𝑎 = apparent length;
𝐿𝑝 = probe length;
From equation (2-3), the dielectric properties of the material can be determined
from TDR signal. Therefore, with the approach described above, TDR can be employed
for measuring the dielectric properties of materials.
13
2.3
Interpretation of TDR Signal
TDR is a useful approach for characterizing soil properties, such as dielectric
permittivity, bulk electrical conductivity, water content and density, however, the accuracy
or even success of this method is highly dependent on the graphical interpretation of the
output signals, i.e., to accurately determine the reflection points on the waveform. Despite
its essential importance in this method, only a few papers have been published to elaborate
this issue (Baker and Allmaras 1990; Evett 2000; Heimovaara 1993; Topp et al. 1982).
Topp et al. (1982) first proposed a method to interpret TDR output waveforms
captured on paper using a chart recorder or by photographing on an oscilloscope screen.
This method includes two graphical algorithms. Take the output waveform of a bifilar TDR
probe totally embedded in wet soil as an example (Fig. 2-2), Fig. 2-3 illustrates this two
graphical algorithms: 1) draw a horizontal line across the top of the first peak, and draw
another line tangent to the descending limb of the first peak; the intersection of the two
lines defines the reflection time at the probe head (starting point of probe in wet sand), t1;
2) draw a horizontal line tangent to the base line between the first peak and second
inflection, and draw another line tangent to the second inflection; this intersection of the
latter two lines defines the second reflection at the end of the probe, t2. The travel time of
the pulse in the portion of the waveguide that is buried in the soil is thus defined as tt which
is tt = t2 − t1. Besides, the reflection point for the impedance discontinuity of the coaxial
cable to the probe head can also be determined with the same algorithm, which is
corresponding to time t1.bis in Fig. 2-2. In Topp et al. (1982) method, peaks and inflections
are subjectively identified by eye and no computer codes or algorithms are implemented.
14
(a)
(b)
(c)
Fig. 2-2. TDR waveform (b) for a wet sand and its first derivative with respect to time;
(a) and corresponding bifilar TDR probe; (c) with rod spacing, S, and rod diameter; (d)
the dashed vertical lines denote two reflection points, corresponding times t1 and t2
(Evett 2000).
15
Fig. 2-3. Example of TDR output waveform from TACQ. The bottom curve is the TDR
output waveform, while the top curve is the first derivative of the bottom curve. Vertical
lines denote times t1.bis, t1, and t2. A horizontal line, drawn tangent to the waveform
base line at the far left, intersects with a line drawn tangent to the first rising limb of the
waveform to define t1.bis. A horizontal line drawn tangent to the peak intersects with a
line drawn tangent to the descending waveform after the peak to define t1. (Evett 2000)
By following the principle described by Topp et al. (1982), Baker and Allmaras
(1990) developed a computer program, TACQ, for interpretation of TDR output
waveforms, which can automatically capture the reflection point and determine the
travelling time of EM wave in the measured medium. In the TACQ program, Baker and
Allmaras (1990) also explained the use of the first derivative of the waveform to find the
16
location of the inflection point, which is of importance for the determination of the tangent
line (Fig. 2-4).
Fig. 2-4. The TDR waveform (bottom) and its first derivative (top) with features
identified by Baker and Allmaras (1990)
2.4
Mixing Model for Dielectric Permittivity
To quantitatively describe the dielectric property of mixtures, Birchak et al. (1974)
proposed a semi-empirical volumetric mixing model to correlate the bulk dielectric
constant of the mixture to its components using equation (2-4).
17
(𝐾𝑚 )𝛼 = ∑𝑛𝑖=1 𝑣𝑖 (𝐾𝑖 )𝛼
(2-4)
where
𝑣𝑖 = the volumetric fraction of each component;
𝐾𝑖 = the dielectric permittivity of each component;
𝐾𝑚 = the dielectric constant of mixture;
n = the nth component of the mixture;
α = exponent coefficient;
For example, the dielectric constant of some porous medium, such as soil, concrete,
asphalt or even rock, are correlated with each constitute.
Since soil is typically considered as a three-phase system, i.e., solid particles as
skeleton, air and water in the porous space, the dielectric property of the soil consists of
three components. Birchak et al. (1974) and Ledieu et al. (1986) suggested that the
exponent 𝛼 can be empirically chosen as 𝛼 = 0.5 for geotechnical applications.
2.5
Typical Dielectric Constant of Material
The dielectric properties of materials vary significantly due to their different
mineral compositions. Table 2-1 illustrates the dielectric information of some typical
geomaterials at 1 atm atmosphere and 20 ℃ (Hubbard et al. 1997). For instance, the
dielectric constant of pure water is around 81, while it is just about 1 for air, and the
18
discrepancy between different types of soil is very prominent. In addition, the dielectric
constant of saturated soils is much higher than dry soils, but lower than pure water, which
is because the additive of water into dry soil could result in significant increments of the
soil-water mixture (saturated soil) based on the mixing model described in the section 2.4.
Table 2-1. Dielectric constant of some typical materials
Material
Dielectric Constant
Material
Dielectric Constant
air
1
water
80.4
sand (dry)
3-6
sandy soil (saturated)
19
sand (saturated)
20-30
clayey soil (dry)
2
silt
5-30
clayey soil (saturated)
15
shale
5-15
sandstone (saturated)
6
clay
5-40
limestone (dry)
7
humid soil
30
limestone (saturated)
4-8
cultivated soil
15
basalt (saturated)
8
rocky soil
7
granite (dry)
5
sandy soil (dry)
3
granite (saturated)
7
19
2.6
Review of Existing Design for TDR Probe
Ferré et al. (2000) presented three primary functions of a TDR probe: connection
to a coaxial line from a cable tester, transmission of a voltage pulse through a sample, and
termination at the end of the probe. People mostly focus on the influence of the probe
design on the pulse propagation through the sample.
Water moisture measurement for soil and other porous materials is one of typical
applications for TDR technology, since the reliable relationship between the permittivity
of a material and its water content has been developed by Topp et al. (1980), which is also
validated by numerous studies. The initial probe design for this application is coaxial cells
(Topp et al. 1980). However, due to the impracticality of installing coaxial probes into soil,
Topp et al. (1982) introduced twin parallel rod probes, and later Zegelin et al. (1989)
demonstrated that three-rod probes approximated more closely to the behavior of a coaxial
cell.
During the past three decades, a number of designs of the TDR waveguide have
been developed. These new TDR probes have also been used to explore other new
applications, such as bridge scour, liquid level measurement, and monitoring the movement
of landslides, etc. In the following section, the existing designs of the TDR probe will be
categorized into three types: coaxial cell probe, straight- and non-straight-leg probe, and a
brief review on these TDR probes will be presented.
2.6.1
Probe Classification
1) Coaxial cell probe
20
Fig. 2-5 shows some examples of currently used coaxial cell probe, including the
one designed by Topp et al. (Fig. 2-5 (a)). In Topp’s research, soil sample is prepared in
the cylinder (inner diameter equals to 5 cm) composed by the two outer conductors, and
the inner conductor is fixed at the center of the soil sample. Porous ceramic are used to
inject/remove water into/from the soil sample, so that the water content can be accurately
controlled during the experiment. Note that the device is horizontally deployed and the
inner conductor is buried in advance to avoid the disturbance of the soil sample.
Derived from the model of Topp, some altered probes were developed, as shown in
Fig. 2-5 (b) and (c) (Cataldo et al. 2008; Xiong and Vincent 2004). In these two designs,
the outer conductor is not separated but as a whole. For the design in Fig. 2-5 (b), the soil
with certain water content is vertically prepared and the inner conductor is then inserted
into the soil sample. A four-leg connector is used to connect the outer and inner conductor,
coaxial cable and the TDR unit. This device is much more convenient for testing but still
cannot avoid the disturbance of the soil sample. Also, both of these two coaxial cell probes
can only be used in the laboratory. However, Cataldo et al. (2008) and Chung et al. (2013)
developed a similar coaxial cell probe but with some modifications (Fig. 2-5 (c)). They
developed it for the hydrological applications, measuring and monitoring the water level
in some difficult field conditions, such as underpasses, tunnels, culverts or sewers, etc. In
their design, the outer steel pipe conductor is perforated to facilitate the circulation of the
flow and air during the course of the probe insertion and the inner conductor is fixed at the
center of the pipe. The results of their research show that the water level can be reliably
measured and monitored. This sensor can also be utilized for the measurements of granular
or non-gravel materials with fine particles, such as sand, silt and clay, etc.
21
(a)
(b)
(c)
Fig. 2-5. Examples of TDR coaxial cell probe (Cataldo et al. 2008; Topp et al. 1980;
Xiong and Vincent 2004)
22
2) Straight-leg probe
The above descriptions of coaxial cell probes indicate that the coaxial cell probe
will become a straight-leg or multi-wire probe if the outer conductor is divided into several
slices in the direction of the cylinder center axis. The quantity of the outer conductor is
typically set as three, four, five, seven or even more (Campbell 1990; Heimovaara 1994;
Zegelin et al. 1989), but if the outer conductor is approximately replaced with only one rod,
the probe will become a traditional two-leg probe, shown in Fig. 2-6. Also presented in
Fig. 2-6 are models of a three-, four-, seven-leg probe, two-parallel plate and three-strip
probes (Robinson and Friedman 2000; Yu et al. 2013; Zegelin et al. 1989).
The two-leg probe has the advantage of minimal soil disturbance, but produces an
unbalanced signal, giving rise to unwanted noise and signal loss, which requires a balun
transformer embedded in the probe head to reduce and resolve. The three- or more-rod
probes provide much more stable and balanced signals, avoiding the use of balun but at the
expense of some additional soil disturbance. The probe legs can be permanently connected
to the coaxial cable as shown in Fig. 2-6, or designed separately with the coaxial cable. For
the latter case, another linker should be prepared to connect the probe legs and coaxial
cable (similar to connect shown in Fig. 2-5 (b)). The parallel strip or plate probe, on one
hand, might be a useful alternative probe for the measurement in the laboratory and field,
but it needs to be buried in the materials to be measured before testing. In the study of Yu
et al. (2013), the author attached the flexible strip probe to a supportive rod and successfully
applied this probe in the field for bridge scour monitoring. On the other hand, the pliable
strip or plate probe can be adopted in some specific applications, such as seepage
monitoring for levees and embankments (Woersching et al. 2006; Zhang et al. 2010).
23
Fig. 2-6. Schematic diagram of typical straight TDR waveguide
(a) two-leg; (b) three-leg; (c) four-leg; (d) seven-leg; (e) two-plate; (f) three-strip
As the dominant mode of EM wave in a TDR waveguide is usually assumed to be
Transverse Electromagnetic (TEM) wave mode, the electrical field distribution of probes
can be numerically solved (Knight et al. 1997). Fig. 2-7 shows the electrical field
distribution of some typical straight-leg TDR probes in the direction perpendicular to the
probe axis. It indicates that an increasing number of outer electrode leads to a much better
approximation to the ideal coaxial cell in which the equipotential lines are concentric
circles centered at the inner conductor. The use of the plate gives a more even and uniform
distribution of electromagnetic energy within the soil volume sampled and reduces the so
called “skin effect” where the electromagnetic energy is concentrated close to the surface
of the electrodes (Robinson and Friedman 2000).
24
Fig 2-7. Distribution of electric field intensity for a variety of TDR probe designs.
Configurations include (a) two-rod; (b) three-rod; (c) four-rod (d) seven-rod; (e) two
parallel plates (Robinson et al. 2003).
3) Non-straight probe
Even though straight probes are the priority choice for such applications as soil
water moisture measurement, some novel non-straight TDR probes have also been
designed and developed recently and they have been widely extended to some new
applications.
Fig. 2-8 illustrates some efforts of new TDR probe designs. Selker et al. (1993)
proposed a two dimensional serpentine-shaped TDR waveguide for measuring water
25
content on the surface (Fig. 2-8 (a)), but the problem for this sensor still lies in the
disturbance of surface soil which will cause measurement errors. Bittelli et al. (2004) made
some revisions and improvements on the probe design to eliminate the influence of soil
disturbance on measuring results by using standard circuit board techniques. As shown in
Fig. 2-8 (c), the probe is constructed by etching spiral copper traces into a copper-clad
circuit board, and a thin epoxy solder mask with low dielectric permittivity of 4 covers the
wave guide as a coating layer. Their testing results indicate it is a reliable tool for the
measurement of surface water moisture. Nissen et al. (1998) presented a coiled TDR probe
to improve the resolution of TDR sensor. In this design, one rod of the TDR probe was
made in a spiral shape while the other one was kept as straight. Vaz and Hopmans (2001)
combined the coiled TDR probe with a penetrometer to measure the soil water content and
penetration resistance simultaneously (Fig.2-8 (b)). Katsura et al. (2008) utilized a coiltype TDR probe in a field monitoring program for the long term evolution of water content
in weathered granitic bedrock. The stainless wires were closely coiled without a gap
between the adjacent wires, which would lead to retain the moisture and compromise its
capability in real time detection of wetting and drying processes.
The appropriate selection of the TDR probe is largely dependent on the application
demand and functionality of each probe. It is difficult to state which type of probes is
absolutely better than the others. People should make wise decision to choose right probes
under specific circumstances.
26
(a)
(b)
(c)
Fig. 2-8. Some examples of non-straight TDR probe (serpentine and spiral waveguide)
(Bittelli et al. 2004; Selker et al. 1993; Vaz and Hopmans 2001)
2.6.2
Material and Length of Probes
Stainless steel has been chosen the dominant material for probes fabrication, despite
brass or copper is also an effective alternative, such as the coaxial cell probe used for field
water moisture measurement (Cataldo et al. 2008; Drnevich et al. 2001), various types of
straight commercial probes designed by (Campbell 2013), parallel strip probes (Yu et al.
2013; Zhang et al. 2010) and coiled probes (Vaz and Hopmans 2001). Stainless steel is the
first priority option for the design of these probes. However, sometimes a supportive frame
27
or rod is required for the design of probes. Davis (1979) used PVC pipes covered with
longitudinal, variable-width steel strips as electrodes. The design of the strip TDR probe
for field bridge scouring surveillance by Yu et al. (2013) includes a U-shaped E-glass frame.
To reduce or avoid the attenuation of EM pulse along the transmission line, some polymers
with low dielectric permittivity are often selected as a coating. In addition, people directly
choose the commercial electrical wires which itself has coatings, and make some
modifications to design and fabricate new TDR probes (Chung et al. 2013).
The determination of reflection points on TDR waveforms and calculation of
dielectric constant are highly dependent on the accuracy of apparent length, 𝐿𝑎 , in equation
(2-3), as the error of 𝐿𝑎 maybe influence the measuring results. Noborio (2001) presented
a comprehensive review on the length design of TDR probes. Stein and Kane (1983),
Reeves and Elgezawi (1992) indicated that short probes with probe length less than 0.1 m
might induce more errors. This is because shorter probes could create shorter 𝐿𝑎 and small
errors for the case of shorter 𝐿𝑎 will cause much larger relative uncertainties in dielectric
constant. Topp et al. (1984) compared the testing results for the water content measurement
in the field using probes with different length, which indicated that the errors via a 5 cm
long probe were much more significant than the probe with length larger than 10 cm. Topp
and Davis (1985) suggested the water content measurements in the field using probes with
length of 0.1–1.0 m show very good accuracy (within 2%). However, there are still
limitations for the length of the probe, since the attenuation of TDR signals along the probe
will impact the stability and accuracy of output waveform. Therefore, Dalton and Van
Genuchten (1986) suggested that a practical lower limit for the probe length is about 0.1
m. Most commercial straight probes of Campbell (2013) are almost around 0.3 m and the
28
length of the coiled probe by Nissen et al. (1998) is up to 0.295 m. Besides, with the aid of
coating material, the thin strip probe designed by Yu et al. (2013) can be as long as around
1 m. Also the coiled probes for surface water moisture measurement can be designed even
more than 1 m (Bittelli et al. 2004; Selker et al. 1993).
2.6.3
Spacing and Diameter of Probes
The probe diameter and spacing strongly influence the impedance of the probe,
which can be approximately expressed as equation (2-5) for a two-wire type probe (Kraus
1953).
𝑍=
120
√κ
𝑙𝑛
2𝑠
(2-5)
𝑑
where
𝑍 = characteristic impedance of the two-rod probe;
κ = the dielectric constant of a material surrounding the probe;
s = the spacing of rods;
d = the diameter of the rods;
The research on the effect of probe diameter on the measuring results is still limited,
but Topp and Davis (1985) indicated that the impedance mismatch due to different probe
diameters seemed not to affect too much the measurements. This might be verified by the
distribution comparison of the electrical field and energy storage for the three-rod probe
with and without the center rod twice the diameter of the outer rods (Robinson et al. 2003).
29
From the perspective of the probe installation, on the other hand, the probe diameter can
neither be too large nor too small, since the probe with a too small of a diameter is easy to
bend when inserted into the soil, and the insertion of the probe with the large diameter will
result in a higher disturbance of the soil, which might cause significant measuring errors.
Zegelin et al., (1989) utilized some three-rod probes with various spacing (2s=3 –
20 cm) to determine the dielectric constant of water, but his results indicated the influence
of the probe spacing distance on the measurements can be neglected. Knight (1992)
asserted a probe diameter should be appropriate for the spacing between the electrodes to
minimize the “skin effect”. Knight (1992) suggested the ratio of diameter to spacing for a
two- and three-leg straight probe should be larger than 0.1, since he found that compared
with the energy distribution (38%) of a two-leg probe with d = 1 cm and s = 20 cm, only
23% of the energy is contained within the two cylinders of the diameter 4 cm around the
probe for a probe with d = 2 cm and s= 20 cm. Ferré et al. (1998) reported the increase
of the rod diameter with a constant rod separation only results in a slight increase in the
sample area, which is of importance for probe sensitivity. In short, the effects of the
diameter and spacing between probes on the TDR response is still not fully understood,
therefore further systematic efforts and works need to be implemented in the future studies.
2.6.4
Installation and Spatial Sensitivity
Appropriate installation method is required to minimize the formation of air gaps
between the TDR probes and surrounding materials, since the air gaps may induce
significant errors (Annan 1977; Ferré et al. 1996; Knight et al. 1997). Ferré et al. (1996)
theoretically investigated the effects of air gaps and coated rods on the travel time of
30
electromagnetic waves. Rothe et al. (1997) reported that soil water content measurements
is much higher for the probe installation with pilot holes than probes installed by being
thrust, because the soil around the probes is 5–20% denser than other regions when the
probes are inserted directly into the soil. Knight et al. (1997) stated that the gaps filled with
low relative dielectric constant (such as air) have a greater impact on the measured relative
dielectric permittivity than those filled with high dielectric media (e.g., water), and this
influence is much greater for case of three-rod probes than two-rod probes.
Ferré et al. (1996) defined the sensitivity of a TDR probe as the change in the
measured response per unit change in the property of interest, which can be expressed using
equation (2-6).
𝑑𝑡
𝑠 = 𝑑𝜃
(2-6)
where
t = the measured response;
𝜃 = the measured property;
For example, when we are measuring soil moisture using TDR technique, t refers
to the apparent length or dielectric constant of soil, while 𝜃 refers to the water content of
the soil. Therefore, the optimal probe design needs to combine a large sensor response to
minimize the effects of absolute errors in travel time measurements, with a high sensitivity
to distinguish among soil water content with great precision (Ferré et al. 2000).
31
In terms of spatial sensitivity analysis of different probe designs, Knight (1992)
compared the spatial sensitivity distribution of coaxial and straight probes. For coaxial
probes with low ratio of inner cylinder radius to outer cylinder radius, most of the energy
(or measurement sensitivity) is concentrated around the inner cylinder in a “skin effect”,
while for the two-rod probe, the measurement sensitivity is closed to the probe leg itself
for the probe with a diameter smaller than the spacing. Ferré et al. (2000) and Nissen et al.
(2003) analyzed the sensitivity of the conventional straight probe and several new designs,
and found the conventional probes are much more sensitive to the change of water content
in the medium than other alternative designs, such as surface probes by Zegelin et al. (1989).
Ferré et al. (1996) also pointed out that coatings can increase probe sensitivity in regions
with lower water content and it can be increased with the decrease of coating thickness.
Since probe sensitivity is associated with the sampling area, defined as the region
that contributes to the total probe response (Ferré et al. 1998), it is often employed to
investigate sensitivity characteristics of different types of probes. Ferré et al. (1998)’s
research indicated that the sampling area of two- and three-rod probes is mainly controlled
by the rod separation, two rod probes have larger sample areas than three-rod probes, and
thin rod coatings could reduce the sampling area of the probe. The increase of the rod
diameter with a constant rod separation only causes a slight increase in the sample area,
but reduction of probe height or width could improve the distribution of sensitivity. Baker
and Lascano (1989) experimentally investigated a two-rod probe with 𝑑 = 3.175 𝑚𝑚 and
𝑠 = 5 𝑐𝑚, indicating that the sensitivity of TDR in water was within the quasi-rectangular
area of about 20 × 65cm2 surrounding the rods, with no significant variation in sensitivity
32
along the rod length. In air, however, TDR is sensitive only in the vicinity of rods with
areas of 20 cm in diameter.
2.7
Summary and Conclusions
In this chapter, the technical basis of TDR technique has been introduced in detail.
This includes the components and working principle of the TDR system, interpretation and
analysis method of output signals, mixing formula for dielectric constant and typical
dielectric properties of several materials.
For the TDR signals analysis, the determination of reflection point is of great
significance for the use of TDR technique. Two tangential line method is the most
commonly used in the current interpretation analysis, which is also utilized in this
dissertation. Mixing formula for dielectric constant is the basis for the determination of
soil-water interface in the subsequent chapters.
Additionally, a comprehensive review on the research of TDR has been presented
in this chapter. The existing TDR probes are summarized and categorized into three types:
coaxial cell probe, straight-leg probe and non-straight probe. All these three probes have
their own advantages and people can choose appropriate probes based on the specific
requirements. Besides, the review also includes such aspects as probe material and
installation, geometric optimization, probe design and its effect on the sensitivity
performance.
33
CHAPTER 3 DESIGN AND EVALUATION OF THE NEW SPIRAL TDR
SENSOR WITH HIGH SPATIAL RESOLUTION
3.1
Introduction
The previous contents in chapter 2 reveal that the resolution and sensitivity of
conventional straight and coaxial probes may be within centimeter range for interface
detections (Drnevich et al. 2001; Zhang et al. 2010). The serpentine design by Selker et al.
(1993) and coil probe (Bittelli et al. 2004; Katsura et al. 2008; Lungal and Si 2008; Nissen
et al. 1998) indicate that spiral waveguide configuration might be a potential solution to
improve the sensitivity and resolution of the TDR sensor.
In this chapter, the concept, design and fabrication of the new spiral TDR sensor is
introduced. The technical background to assist the optimal design of probe is firstly
presented, such as the effective sampling area of TDR probe. Based on this, a simplified
2-dimensional model is constructed and Finite Element Method (FEM) analysis is
conducted to analyze the influence of probe design parameters (i.e., interval spacing
between spiral wire waveguide and dimension of the spiral wire) on the effective sampling
area of the probe. According to the computational analysis for the optimization design and
manufacturability of the sensor, a pilot spiral TDR sensor is designed and fabricated. A
special coating treatment using a super-hydrophobic coating is applied to prevent the
intraption of water and the consequent hysteresis effects on the response of the new sensor.
The performance of the new TDR spiral probe is then assessed using a series of
34
experiments in the laboratory, including the comparison with the traditional 2-rod straight
probes.
3.2
The Concept of Spiral-shaped TDR Sensor
The primary concept of the proposed spiral probe is designing the traditional
straight waveguide into spiral shape to increase the effective propagation path of EM wave
in the measured medium per unit length along the direction of the sensor probe.
Fig. 3-1. Schematic illustration of working principle for the spiral TDR sensor
Fig. 3-1 illustrates the basic idea of the spiral-shaped TDR sensor, which consists
of one central rod and two electronic wires wrapped around the rod. The central rod can be
chosen as either a circular or rectangular shape based on the practical requirements, but
35
shown in Fig. 3-1 is a rectangular central rod type. Threads or grooves need to be designed
on the central rod to guarantee the equality of the spacing between two electronic wires.
Otherwise, the waveguide wires can be easy to move on the central rod, which maybe
influence the sensor performance.
3.3
Computer-aided Design of Spiral TDR Probe
From the review of existing designs of TDR probe in Chapter 2, the geometric
parameters will impact the performance of conventional straight probes. For the new sensor
design, factors determining the performance of the spiral TDR probe also include the
properties of the sensor wire (i.e., diameter) and the spatial arrangement (spiral angle and
wire spacing). Computational simulations are implemented to assist the optimization
design of the spiral TDR probe. The technical background of the computational simulations
for assisting sensor design is presented in the following section.
3.3.1
Electric Field Distribution around a TDR Probe
The dominant mode of EM wave in a TDR waveguide is the Transverse
Electromagnetic (TEM) wave mode (Benson and Bosscher 1999; Topp and Davis 1985).
In the cross section perpendicular to the direction of EM wave propagation, the electric
field of TDR probes can be treated as an electrostatic problem and the electrostatic potential
satisfies Poisson’s equation (Ferré et al. 1998; Knight et al. 1997; Yu and Yu 2009), i.e.,
equation (4).
∇ ∙ (𝜀∇𝑉) = −𝜌
(3-1)
36
where
𝜀 = the permittivity of the medium;
𝜌 = the space charge density;
V = the electrical potential.
The medium permittivity and charge density are both a function of space coordinate.
The charge density can be assumed as zero for typical dielectric material (Bin et al. 2010;
Yu and Yu 2009).
The Poisson’s equation can be solved with the finite element method due to high
nonlinearity. From the results, information such as the electrical potential field distribution
and the electrical energy density can be determined.
3.3.2
Effective Sampling and Sensing Area of TDR Probe
The electrical energy density distribution is used to determine the effective spatial
sampling area of the spiral TDR probe, which is associated with the spatial sensitivity of
TDR probes (Ferré et al. 1998; Ferré et al. 2000; Ferré et al. 1996; Knight 1992; Knight et
al. 1997; Nissen et al. 2003; Yu 2009).
The effective sampling area of the TDR probe in the plane perpendicular to the
TDR probe is defined as the region that contributes to the total probe response (Ferré et al.
1998). The influence of materials outside this area can be neglected without causing
significant errors. To determine the effective sampling area, spatial weighting function is
37
employed to consider the spatial contributions to the overall electrical field (Nissen et al.
2003).
Ferré et al. (1998) presented a numerical method to determine the effective
sampling area of the TDR probe based on the spatial weighting function. As shown in
equation (3-2), starting from the element with the highest weighting function value, the
product of the weighting function and the area of the element is summed until its
cumulative value equals to a certain fraction (e.g., 90%) of the integration value over the
whole domain.
𝑓=
100∙∑𝑤
𝑤ℎ𝑖 𝑤𝑖 𝐴𝑖
(3-2)
∬Ω 𝑤𝑖 𝑑𝐴
where
𝑤𝑖 = the spatial weighting function;
𝐴𝑖 = the element area;
𝑤ℎ𝑖 = the highest weighting function;
For the contribution to the electrical field, the weighting function, 𝑤𝑖 , is replaced
with the electric energy density, 𝑤𝑒𝑖 (Yu and Yu 2009). Therefore, the sampling area of
the TDR probe can be determined from equation (3-3).
𝑓=
100∙∑𝑤
𝑤ℎ𝑖 𝑤𝑒𝑖 𝐴𝑖
(3-3)
∬Ω 𝑤𝑒𝑖 𝑑𝐴
in which,
38
𝑤𝑒𝑖 = the electric energy density, which can be acquired from the solution of
equation (3-1);
𝑓 = the percent contribution to the total weighted average values. In this dissertation,
90% sampling areas is selected to demonstrate the numerical simulation results.
3.3.3
Implementation of Computational Simulations
Direct simulation of the electrostatic potential distribution of a spiral TDR probe
(Fig. 3-1) requires solving three-dimensional Maxwell’s equations. To simplify the
analyses while not causing too much error, a 2-D approximation is used to study the design
of spiral TDR wires (Ferré et al. 1998). A two dimensional model of the longitudinal
section of the spiral probe is constructed in this chapter (Fig. 3-2). Due to the symmetry of
the wire probe, half of the cross section is considered, where 𝐷 denotes the diameter of the
copper wire; 𝑑 denotes the interval space between adjacent wires; 𝐿 denotes the side length
of the central rod; and 𝑆 denotes the center distance of adjacent two pairs of electrodes
(center-center distance of two positive-negative electrodes).
Fig. 3-2. Schematic diagram of spiral probe for FEM analysis
39
A general FEM software, COMSOL Multiphysics®, is utilized to solve the
Possion’s equation (equation (3-1)) for the spiral probe. Fig. 3-3 shows the mesh grid of
the computation domain. The computational domain is selected to be sufficiently large so
that further increase in the size of the domain does not have significant influence on the
electrical field distribution. The rectangle represents the fiberglass rod where the TDR
waveguide wires are mounted. The circles represent the pair of copper wire that acts as
positive and negative electrodes, respectively. The copper wire is assumed to be covered
with one layer of insulation coating with a thickness of 0.5 mm. The dielectric constant is
set as 3.5 according to the properties of coating material. The sensor is assumed to be
inundated in water, whose dielectric constant is set as 81. The dielectric constant of
fiberglass is set as 5.0. The unit potential of +1 V and -1 V are set for the two electrodes.
The value of the potential only affects the magnitude of the electrical field and has no effect
on the distribution pattern of the electric field (Knight et al. 1997; Yu 2009).
Factors including the diameter of the wire, 𝐷, and space between two adjacent wires,
𝑑, are taken into account for the simulation analysis (Table 3-1).
Table 3-1. Configurations of simulation parameters
Distance, d (mm)
Diameter, D (mm)
0, 1, 2, 3, 4, 5
1, 2, 3, 4, 5
40
Fig. 3-3. Mesh grid of computation domain
3.3.4
Simulation Results Analysis
1) Electrostatic field distribution
Fig. 3-4 and Fig. 3-5 show an example of the electric potential and electric energy
density distribution respectively when the sensor is submerged under water (d=2 mm,
D=0.5 mm). In Fig. 3-4, the isolines of electrical potentials are circles centered at both
electrodes and symmetric. There is a knee point for each potential isoline at the interface
of the fiberglass rod and water due to contrast in dielectric constant. From Fig. 3-5, the
effective sampling area contributing 90% of the total electric field energy is determined to
be 5.5 × 106 𝐽⁄𝑚3 using the Eq. (3-3).
41
Fig. 3-4. Electric potential (contour and color) and electric field (red arrow) distribution
(filled in water)
Fig. 3-5. Electric energy density (color), effective sampling area with 90% level
(contour) and electric field (red arrow) distribution (filled in water)
42
The domain with higher values of dielectric constant (water) has larger energy
density than that with lower values of dielectric constant (fiberglass core rod), which is
consistent with observations in other studies (Knight et al. 1997; Yu 2009).
2) Effect of wire distance on sampling area
The influence of wire distance, 𝑑, on sampling area (90% of total electrical energy)
is illustrated in Fig. 3-6. There is a linear relationship between effective sampling area and
wire spacing. This is consistent with the characteristics of the conventional two/three rod
probe given by Ferré et al. (2001) and Nissen et al. (2003). Therefore, design with larger
wire spacing is able to improve effective sampling area of the sensor.
43
Fig. 3-6. Influence of wire distance on sample area
However, the larger wire spacing will reduce the resolution of the spiral probe
(Fagert et al. 2014). Also, it could cause a potential overlap of the sampling area in the
adjacent spiral wire pairs given too small wire spacing is provided. To improve and
optimize the sampling efficiency of the probe, equation (7) can be utilized as the criteria of
wire spacing, in which 𝐷, 𝑑 and 𝑆 have the same meaning as that illustrated in Fig. 3-2,
and 𝑙 is assumed to be the length of the long axis of 90% sampling area in Fig. 3-4.
𝑆≥
𝑙+𝑑
(3-4)
2
Fig. 3-7. Influence of wire diameter on sample area
44
3) Effect of wire diameter on sample area
Fig. 3-7 illustrates the influence of wire diameter on effective sampling area. The
sampling area increases linearly with the wire diameter. However, it is impossible to
manufacture a spiral TDR sensor with too large diameter due to practical limitations, even
though the effective sampling area increases significantly.
3.4
Design and Fabrication of Spiral Sensor
Appropriate spiral probe parameters (i.e., wire diameter, wire spacing, mounting
materials, etc) should be chosen by considering factors such as the effective sampling area,
manufacturability, and application requirements. Based on a comprehensive evaluation of
the design parameters, copper conductive wire with diameter of 0.5 mm is selected to make
spiral TDR sensor; the spacing between the wires is set as 2 mm; and the mounting rod is
chosen as a square fiberglass rod with 5 mm in side length and 250 mm in length. Photo of
the sensor is shown in Fig. 3-8. The inclination angle of the wire around center rod is about
22° , which guarantees the water flow away immediately. Fabrication grooves are created
along the fiberglass rod to facilitate the control of wire spacing. Noted that grooves are
only carved at the corner of the square rod to avoid the measurement influence similar to
Lungal and Si (2008). Two copper conductive wires are wrapped parallelly around the
fiberglass rod with predefined spacing. The copper wires are coated with polyurethane, a
widely used commercial insulation material.
45
Fig. 3-8. Photo of spiral-shaped TDR probe
In order to eliminate the lagging effects of the spiral sensor due to residual water
between two adjacent wires when water level retreats, a commercial superhydrophobic
coating is sprayed to completely cover the surface of the rod. The effects of this
superhydrophobic coating on the performance of the new spiral probe will be evaluated
and discussed in the subsequent section of this chapter. The spiral probe for the basic
evaluation in this chapter is 250 mm long, which will be adjusted to 400mm and 500 mm
for the following chapters. At the end of the spiral wire, a Bayonet Neill-Concelman (BNC)
adapter is used to connect the coaxial cable and TDR system.
3.5
Performance Evaluation of Spiral TDR Sensor
Laboratory experiments are conducted to evaluate the performance of the spiral
probe. As shown in Fig. 3-8, three TDR sensors with identical equivalent length are
prepared, including (1) conventional straight probe, (2) spiral probe without
superhydrophic coatings, and (3) spiral probe with coatings. The texture and fabrication of
the three sensors are identical. The traditional two rod probe (sensor 1) is used as a control
group. Sensor 3 is treated by spraying a layer of superhydrophobic coating.
46
3.5.1
Comparison with Traditional Two Rod TDR Probe
Straight and spiral probes (sensor 1 and sensor 3) are firstly tested in air and water.
Fig. 3-9 shows the output signals of two sensors in air and water. The reflection points of
EM wave at air-water interface and probe end for both cases are determined using
tangential line method described in Chapter 2 (black arrows in Fig. 3-9). The apparent
length for each case are also acquired by following the theory introduced in Chapter 2,
listed in Table 3-2.
47
Fig. 3-9. Comparison of traditional and spiral TDR probe (a- in the air; b- totally
submerged in the water)
From both Fig. 3-9 and Table 3-2, for the same probe length (identical equivalent
length), the apparent length of the spiral probe is much larger than that of the two-wire
straight probe, i.e., around 1.285⁄0.241 = 7.7 and 5.181⁄1.405 = 3.7 times of in air and
water, respectively. This indicates that the resolution of the TDR sensor can be significantly
improved by the spiral design. The extent of improvement, however, is associated with the
dielectric permittivity of the material around the probe.
Table 3-2. Comparison of two sensors in air and water
48
Sensor type
Straight probe
Starting point (m) Ending point (m) Scaled length (m)
7.189
7.430
Note
0.241
Air
Spiral probe
7.189
8.474
1.285
Straight probe
7.209
8.614
1.405
Water
Spiral probe
3.5.2
7.209
12.39
5.181
Effect of Superhydrophobic Coating
The spiral geometry might potentially allow water to be trapped between the
adjacent spiral wires. Thus, one type commercial superhydrophobic coating is applied to
prevent this phenomena. To evaluate the effect of superhydrophobic coating on the
performance of spiral the TDR probe, sensor 2 and sensor 3 are tested in a tank filled with
water.
The test procedures include the following steps: 1) two sensors are partially
submerged into a plastic tank with 30 cm of water column; a TDR signal is acquired and
named as “initial state”; 2) water is added into the tank to totally submerge the two TDR
sensors; 3) the depth of tap water is then decreased to the “initial state”, and a second TDR
signal is acquired and named as “final state”.
49
(a)
(b)
50
Fig. 3-10. Comparison of spiral TDR probe with and without superhydrophobic
coating (a- with coating; b- without coating)
Fig. 3-10 shows the output signals of the two sensors at the initial and final state.
As illustrated in Fig 3-10 (b), spiral probe without coating treatment shows hysteresis
behavior due to trapping of water along the wire probe. However, as shown in Fig. 3-10
(a), spiral probe with superhydrophobic coating shows excellent repeatability that is not
affected by cyclic water level variation or fluctuation. This implies that the
superhydrophobic coating is effective in preventing water to reside or retain between two
adjacent spiral wires.
3.5.3
Sensitivity of Spiral TDR Probe
Experiments are also conducted in a plastic tank with 25cm of water column to
assess the sensitivity of the spiral probe. A modified micrometer caliper is employed to
control and measure the depth of the sensor submerging in water with an accuracy of 0.01
mm. As shown in Fig. 3-11, TDR probes (sensor 1 and sensor 3) are fixed at the end of
micrometer and then gradually dipped into water each 0.025 inch (around 0.06 cm) by
adjusting micrometer.
Fig. 3-12 shows the acquired TDR signals at different water levels for both straight
and spiral probe (sensor 1 and sensor 3). The initial state is denoted as “25cm” and the
signal at arbitrary state is written as “25cm + x mm”, x means the additional depth of
sensors submerged into water. For example, “25cm+0.06 mm” means the sensor is dipped
into water by 0.06 mm more. This process is continued to the state of “25 cm + 1.5 cm”.
51
Fig. 3-12 (a) (b) illustrate the output signals of two sensors for water level variation by 0.06
cm, while Fig. 3-12 (c) (d) show that when water level varies every 0.5 cm.
Fig. 3-11. Photo of converted micrometer
From Fig. 3-12 (a) (b), no obvious change can be observed for the output signals of
traditional two-rod probe, however, the reflection point at the probe end offsets
significantly for the spiral probe. This indicates that the spiral TDR probe is sufficiently
sensitive to detect 0.06 cm water layer, compared to that of the straight probe in Fig. 3-12
52
(c) (0.5 cm). This means the resolution of the spiral sensor in this study is at least
0.5⁄0.06 = 8 times of two rod straight probe to detect thin water layer.
(a)
53
(b)
(c)
54
(d)
Fig. 3-12. Output signals of two-rod straight and spiral probe at different water levels
Fig. 3-12 (c) (d) show the output signals of two sensors when water level varies
every 0.5 cm. Both probes demonstrate an apparent offset at the reflection point of the
probe end. However, only the signal from the spiral probe has appreciable offsets at the
reflection point of the air-water interface. The signal of the straight probe does not respond
obviously. This implies that the spiral TDR probe can detect air layer as thin as 0.5 cm.
Note the difference can be only qualitatively observed from the zoomed-in view in Fig. 312 due to the scale issue, but the quantitative illustration is shown in Table 3-3.
55
Table 3-3. Measurement results of two probes with micrometer caliper
Water level
Probe
start (m)
Air-water
interface (m)
Probe end
(m)
Scaled length
(m)
25cm
7.209
7.329
8.052
0.723
25cm+0.5cm
7.209
7.329
8.092
0.763
Note
Straight
probe
25cm+1.0cm
7.209
7.329
8.133
0.804
25cm+1.5cm
7.209
7.329
8.173
0.844
25cm
7.209
7.771
9.538
1.767
25cm+0.06cm
7.209
7.771
9.578
1.807
25cm+0.13cm
7.209
7.771
9.598
1.827
25cm+0.19cm
7.209
7.771
9.618
1.847
Spiral
probe
25cm+0.25cm
7.209
7.771
9.659
1.888
25cm+0.5cm
7.209
7.731
9.699
1.968
25cm+1.0cm
7.209
7.691
9.739
2.048
25cm+1.5cm
7.209
7.651
9.819
2.168
Fig. 3-13 shows the relationship between scaled length and water levels measured
by straight and spiral TDR sensors. Based on the definition of sensitivity Ferré et al. (1996),
56
i.e., equation (2-6) in section 2.6.4, the sensitivity of both sensors to detect water layer
herein can be represented using the slope of two linear curve-fitting lines in Fig. 3-13,
which are 0.0808 and 0.2543, respectively. This means the spiral TDR probe is around 3
times more sensitive than a straight TDR probe. The spiral TDR probe shows slight nonlinear responses, which is possibly due to the fabrication issues and can be improved by
refining the design and fabrication procedures.
Fig. 3-13. Relationship between scaled length and water level (air-water interface) for
two sensors
57
3.6
Summary and Conclusions
This chapter presents the design and fabrication details of the innovative spiral TDR
sensor that improves the resolution and sensitivity in interface detection. Based on the
theory proposed by Knight et al. (1997) and Ferré et al. (1998), FEM simulations are
conducted to assist the optimization design of the new TDR sensor. The performance of
this new sensor is then evaluated using laboratory experiments. According to the FEM
simulation and laboratory experiments results, the following conductions on the new spiral
TDR sensor can be drawn:
1) The effective sampling area is chosen as an important indicator for the
optimization design of the new spiral TDR sensor, which increases with the
increment of wire diameter and spacing distance. Considering the
manufacturability and application requirements of the new sensor, copper wire
with diameter of 0.5 mm and spacing distance of 2 mm is selected to fabricate
the pilot new sensor.
2) The experimental results show that this new sensor achieves significant higher
spatial resolution for interface detection than the conventional TDR sensor. The
application of superhydrophobic coating is effective to prevent the influence of
entrapped water between two adjacent wires.
3) Compared traditional 2-rod straight probe, the spatial resolution in detecting
water layer for the new spiral TDR sensor can be at least 8 times higher than
that of the conventional straight probe.
58
4) The spiral TDR probe is about 3 times more sensitive than conventional 2-rod
straight probe to detect water layer.
59
CHAPTER 4 ASSESSMENT OF THE HIGH RESOLUTION SPIRAL TDR
SENSOR FOR SIMULATED BRIDGE SCOURING
4.1
Introduction
Bridge scour has been found to cause majority of bridge failures in the United States
over the past 40 years (Briaud et al. 2011; Briaud et al. 2005; Briaud et al. 2001;
Prendergast and Gavin 2014). The scour around bridge foundations compromise its
capability to support the superstructures and lead collapse in the extreme cases (e.g., flood).
Based on the National Cooperative Highway Research Program (NCHRP) report, almost
60% of the reported bridge failures are caused by bridge scour during 1966-2005 (Hunt
2009; Yu and Zabilansky 2006). The erosion of soil around the bridge foundations due to
scouring might leave the superstructures without sufficient support and eventually result in
complete collapse of the bridge.
The bridge failures induce millions of economic loss in United States every year
due to direct cost of restoring and repairing these bridges as well as indirect cost associated
with transportation system disruption (Yu et al. 2013). Around 26,000 bridges in the United
States are categorized as “scour critical” (Briaud et al. 2011). Therefore, deploying scour
countermeasures including monitoring scour is imperative to prevent the catastrophic
consequences due to scour induced bridge failures.
60
4.2
Review of Bridge Scour Monitoring Technology
Three options are generally applied to mitigate the bridge scour and associated
economic losses and casualties, i.e., structural, hydraulic, and monitoring countermeasures
(Briaud et al. 2011; Hunt 2009). Hydraulic countermeasures involve the prevention of rapid
flow expansion or contraction caused by suddenly induced changes in flow direction that
would occur due to blunt pier faces obstructing the flow. These sudden flow changes can
lead to the creation of the vortices that is the main reason of bridge scour. This can be
prevented by maintaining larger bridge openings at the design stage and also by
streamlining pier geometries. However, maintaining large bridge openings and streamlined
pier faces can often be a futile method as natural changes in channel deposition and erosion
upstream of a bridge can often change the angle of flow relative to the alignment of a bridge
and cause these hydraulic problems. Structural countermeasures can be implemented at the
design stage by ensuring spread footings that are located below the maximum design scour
depths, or as remediation by adding rock-armor and rip-rap to the base of piers and
abutments, but this is limited by the uncertainties in the prediction design of scour depth.
Monitoring or surveillance using sensing instruments, is considered to be the most effective
and viable method to mitigate the risk of bridge failure for bridge maintenance due to its
economic cost and real-time feature, especially for the existing bridges (Prendergast and
Gavin 2014). Therefore, several typical and primarily used monitoring technologies for
bridge scouring will be reviewed and summarized in the following section, including sonar,
magnetic sliding collars, float-out devices, tilt sensors, sounding rods, fiber bragg grating
(FBG) sensors, “smart rocks” technology and TDR (Briaud et al. 2011; Deng and Cai 2009;
Hunt 2009; Prendergast and Gavin 2014; Zheng 2013).
61
4.2.1
Sonars
The sonar instrumentation system for bridge scouring monitoring typically consists
of two sound sensors: transmitter and receiver. It works by sending a sonic pulse from the
transmitter, which propagates in the water until it reaches the soil-water interfaces
(streambed), and then it is reflected back and captured by the receiver. The time taken for
the signal to propagate from the emitter to the receiver in combination with signal
propagation speed in water gives an estimate of the distance from the emitter to the
streambed (De Falco and Mele 2002; Hayes and Drummond 1995; Mason and Sheppard
1994). The variation of this distance also indicates the process of bridge scouring or
refilling.
Sonar can be manufactured in both portable and fixed forms. Fig. 4-1 illustrates the
idea of fixed sonar system to monitor bridge scour, in which the sonar sensors are mounted
onto the pier of the bridge. Fixed sonar sensors can provide continuous data record for the
soil erosion, so it can track both the scour and refill processes. Portable sonar, on the other
hand, is a useful bridge inspection tool and it cannot provide a continuous data record for
the soil erosion. Therefore, it usually applied to determine the final status of the scouring
or sedimentation surrounding a pier.
Though sonar has been successfully used to detect the profile of the bridge scour,
it also has some limitations in monitoring scour process (Briaud et al. 2011). First, it is only
accurate within given depth tolerances. Too shallow installation of a sonar unit or too short
resolution distance between sonar sensor and riverbed will result in useless data. Second,
sonar is generally accurate only within a narrow area if a fixed sonar system is employed,
62
and it is very expensive if more sonar installations are required. So if a sonar unit is not
mounted properly above the deepest point at which the scour hole is developing, it will
give a false sense of security information about the development of scour. Third, sonar is
a below waterline instrument. If the channel is subject to debris loading, the sonar will be
exposed to debris and can be easily destroyed. Finally, the interpretation of sonar signals
is challenging for unexperienced users or people without sufficient professional trainings.
Fig. 4-1. Schematic diagram of sonar scour monitoring system (Hunt 2009)
4.2.2
Magnetic Sliding Collar
A magnetic sliding collar (MSC) system includes a sliding collar and a stainless
steel pipe that is attached to the pier of the bridge and driven vertically into the streambed
(Yankielun and Zabilansky 1999). As shown in Fig. 4-2, a collar with magnetic sensors is
63
placed on the streambed around the rod. The collar slides down the rod into the scour hole
when the streambed erodes or the scour progresses. The location of the collar is determined
by sensing a magnetic field created by magnets attached to the collar. A sensor, consisting
of a magnetic switch attached to a battery and buzzer on a long cable, is fabricated. It is
lowered through the annulus of the support pipe and the buzzer is activated when the sensor
reaches the magnetic collar. Thus, the collar position can be determined from the reading
on the cable. This also indicates the current riverbed depth, which can also provide
information of present scour.
Fig. 4-2. Schematic diagram of a magnetic sliding collar monitoring system (Hunt 2009)
This device measures the maximum scour that occurs during a given flood event.
However, it cannot be employed for continuously monitoring the scouring process, since
64
if the scour refills, the collar will become buried. Thus, it might need to be reset after each
flood event, which is time consuming. Besides, the scour depths can only be detected in
the direct vicinity of the device so a number of devices may be required to capture the true
condition of scour.
4.2.3
Float-Out Devices
Float-out devices typically consists of a radio transmitter buried in the streambed
at a pre-determined depth. Fig. 4-3 shows the working principle of the float-out device.
When the scour reaches that particular depth, the float-out device will be floating to the
stream surface, in a horizontal position, which will activate the radio transmitter in the
float-out cylinder. This is an indication that the scour depth has reached a level at which
the instrument is buried and now the instrument is in float-out state. The internal radio
transmitter will send a value of 0 to the data acquisition system if the float-out device is
vertical and a value of 1 if the float-out device floats out (in horizontal position).
The float-out device is easy to operate and is self-contained, but still has some
disadvantages. The internal battery has a limited lifespan, even though it can stay in
standby mode for seven years. The float-out device can just give an estimation of the local
scour, showing the scour depth only at the location where the device is installed. It does
not provide any intermediate indication of the scour depth, neither the process of
sedimentation. The installation process in the field requires coring and drilling, which is
expensive and difficult in certain circumstances. Besides, the installation depth of the floatout device has to be determined in advance. This significantly limits the accuracy and
65
effectiveness of the float-out device, since the device will lose efficacy if the maximum
scour depth is overestimated or underestimated.
Fig. 4-3. Schematic diagram of a float-out device and float-out sensors (Hunt 2009)
4.2.4
Tilt Sensors
Tiltmeter, known as inclinometer or tilt sensor, is typically employed to measure
the change in the angle of the object it is attached to with respect to a level or an axis. When
it is used to measure the movement of the bridge scour, two tilt sensors are required. As
presented in Fig. 4-4, one (X) monitors bridge position parallel to the direction of the traffic
(longitudinal direction of the bridge), and the other (Y) monitors the position perpendicular
to traffic (parallel with the stream flow). One or both two tilt sensors will response if the
66
bridge is subjected to scour causing one of the support piers to settle. If the change detected
by the X, Y tilt sensor in bridge position exceed a programmable limit, the data system
would send out an alert status message.
Fig. 4-4. Schematic diagram of a float-out device and float-out sensors (Hunt 2009)
This is a very straightforward method to measure the bridge scouring process. It is
compact, lightweight, and is easy to integrate mechanically and the signals are also not
difficult to interpret. However, it is sometimes too “sensitive” to capture the bridge position
variations that normally occur due to the traffic, temperature, wind, hydraulic and
earthquake loads. It is difficult to set the critical magnitude of the tilting angle at which the
bridge is in danger. Therefore, this will impact negatively the correctness of the monitoring
67
results or increase the complexity and difficulty of setting critical value for the “alarm”
angle.
4.2.5
Sounding Rods-BRISCO Monitors
Sounding-rod or falling-rod instruments are manual or mechanical gravity-based
physical probes (Lefter 1993). As the streambed scours, the rod, with its foot resting on the
streambed, drops following the streambed with certain length to guarantee the soundingrod still resting on the riverbed. This dropping is then recorded by the system as the
scouring depth. Note that the foot should be large enough to prevent penetration of the
streambed caused by the weight of the rod and the vibration of the rod from flowing water.
Fig. 4-5 shows the schematic working diagram of the sounding-rod for bridge
scouring. The sounding-rod is sitting with its base plate on the streambed and the upper rod
penetrates through the supportive pipe to keep it vertical. The top of the sounding-rod is
then connected to a reel by a cable, from which scouring depth information can be captured.
This method is similar to the concept of the magnetic sliding collar and sonar sensor
technology, but it is much cheaper than these two approaches. However, this technique still
possesses the limitation that it can be only used to monitor the scouring process.
68
Fig. 4-5. Schematic diagram of a sounding-rod monitoring system (Haas et al. 1999)
4.2.6
Fiber Bragg Grating Sensors
Another relatively new piezo-electric based sensor, Fiber Bragg Grating (FBG)
sensors, works based on the concept of measuring strain along embedded cantilever rods
to generate electrical signals (Sohn et al. 2004). Fig. 4-6 presents the mechanism of two
types of fiber optic sensors for monitoring local bridge scouring (Lin et al. 2005; Lin et al.
2004).
In model I, three FBG sensors are mounted on the surface of a cantilevered beam
and arranged in series along one single fiber. In model II, several FBG sensors are arranged
along one single optical fiber, but are mounted on cantilevered plates installed at different
69
levels of a hollow chamber of a steel pile fixed to the pier or abutment. In both models,
when the scouring process reaches the level at which the embedded cantilevered beam
(a)
(b)
70
Fig. 4-6. The FBG scour monitoring system (a) model I (b) model II (Lin et al. 2004)
or plate becomes partially exposed to the flowing water, they will be subjected to
hydrodynamic forces from the flow of water and become deformed due to bending moment.
Strain will be generated and detected by FBG sensors. However, only the FBG sensors that
are exposed to the water flow will pick up the strain information; for those buried under
the river bed surface, no or very small strains will be generated because that part of the
cantilevered beam or plate is not bended. Therefore, the progression of scour can be
detected and monitored by knowing the exposure conditions of the FBG sensors.
This FBG sensor performs particularly well in monitoring the change in scour depth
with time at their installed location and is relatively cheap to fabricate. The resolution,
however, depends on the spacing of the sensor array along the rod and the number of FBG
sensors used in the systems, and theoretically it can be utilized to monitor both the scouring
and deposition process. Also the fragility of the optical fiber might be a potential challenge
for the application of this type of sensor in the field.
4.2.7
“Smart Rock” Technology
Even though the conventional approaches introduced above have played a
significant role in the monitoring of bridge scour, several advanced techniques are also
attempted and evaluated in the field，such as the wireless monitoring system, neutral
buoyancy “fish” and “smart rocks” developed by Zabilansky (1996), Radchenko et al.
71
(2013) and Chen et al. (2014). The “smart rocks” technology is selected as an example to
present in this section.
(a)
2.2”
4 √2 = 5.6
2.2”
4”
(a)
4”
4”
(c)
(d)
(a) Geometry of magnets and encasement (b) Prototype in spherical shape
Fig. 4-7. The “smart rocks” scour monitoring system (Chen et al. 2014) (a) (b) working
Design and prototype of magnets and passive smart rocks
principle of “smart rocks”; (c)(d) smart rocks;
Fig. 4-7 shows the working principle of the “smart rocks” system for monitoring
bridge scour, also including a sample of “smart rocks”. “Smart rocks” are natural rocks or
artificial concrete encasements embedded with sensors that can send data, including depth,
location and orientation of the rocks, to the main station wirelessly, from which the
scouring depth can be estimated. The idea of “Smart Rocks” is similar to the “Magnetic
Sliding Collar” introduced in the previous section, but it is much more intelligent and
automated, since many smart rocks can be simultaneously distributed in the vicinity of
bridge piers and the data can be collected from the main station at one time. This can
significantly increase the monitoring area around the bridge pier, not just one limited region
as the Magnetic Sliding Collar system.
72
In practice, smart rocks were first designed to be located at the surface of the
riverbed and will gradually roll into the bottom of the scour hole as the deposits beneath
and around the smart rocks begin to be eroded. This can be employed to measure the
maximum scour depth. “Smart rocks” can be categorized into three types: active, passive
or hybrid-type. The passive smart rock is equipped with magnets that can be read with a
remote magnetometer; the active version is outfitted with electronic devices, such as
pressure sensors, gyroscope, timer, and battery indicator; the hybrid, semiactive smart rock,
includes a free-to-remote magnet that can be controlled with electronic circuitry (Fig. 4-7).
The “smart rocks” technique is a very cost-effective technology, ranging from 5001000 dollars for each unit and easy to install and operate. But it still has limitations to
monitor the deposition or refill process of the riverbed, since it will be buried by the
refilling sediments even though it can still give the information of maximum scour depth
after it’s buried in the streambed.
4.2.8
Time Domain Reflectrometry
TDR is also used as an alternative approach for the surveillance of bridge scouring
(Yankielun and Zabilansky 1999; Yu 2009). The working principle will be presented in the
following section. Yu (2009) studied the feasibility of using traditional 3-rod stainless steel
TDR probe for scouring measurement in the laboratory and developed an algorithm for
signal analyses. The subsequent study by Yu and Yu (2010), Zhang et al. (2010) and Yu
and Yu (2010) developed a 3-strip TDR sensor to facilitate field installation. These
previous studies proved the capability of the TDR to reliably monitor the scour
development. In their laboratory experiments with a conventional straight TDR probe, the
73
sediment layer is designed to vary within centimeter range (2 cm or 10 cm). It will still lose
capability to detect scouring when the scouring depth is smaller than that range.
In summary, these approaches have inherent advantages and limitations in certain
aspects. For example, sonar technology is relatively easy to install and collect real time
condition of scouring, but the measuring signals are complex and difficult to analyze and
interpret and the measurement is highly influenced by the turbidity of stream (Yu et al.
2013). The magnetic sliding collars is easy to operate, but the effective measuring range
for one unit is still limited. The size, cost, sacrificial nature, and power supply demand
remains challenging for “fish” and “smart rocks” technology. Table 4-1 elucidates the
advantage as well as the might-be shortcomings for each technique in the previous context
(Chen et al. 2014; Deng and Cai 2009; Lu et al. 2008; Radchenko et al. 2013; Yu and Yu
2010; Zheng 2013).
Therefore, people can select proper method in terms of their specific requirements.
If a series of streambed elevations over time are of interest, sonar, magnetic sliding collars,
and sounding rod monitors can be used. If a bridge owner is interested only when a certain
streambed elevation is reached, float-outs can be employed. For specific information on a
pier or abutment, tilt sensors measure the movement of the structure.
74
Table 4-1. Comparison of existing instruments for monitoring bridge scour
Instrument
Advantages
Disadvantages or limitations
Relative cost
Easy to install; Accurate record of riverbed; Susceptible to the situation of flowing water;
Sonar
Medium
Monitor both scour and refill process in real-time; Difficult to analyze and interpret signals;
Excavation of riverbed required; Cannot
Magnetic sliding Easy to install and operate; Somewhat prevent the
collect data for refill process; Limited
collar
Medium
destruction from debris in the streambed;
monitor region;
Excavation of riverbed required; Only
Float-out device
Easy to install and operate and self-contained;
provide information if the scour has
Low
progressed past a critical value;
Cannot avoid the noisy influence caused by
Easy to install and operate; Signals are easy to
Tilt sensor
traffic, temperature, wind, hydraulic and
Low
analyze and interpret;
earthquake loads.
Easy to install and operate; Straightforward to Excavation of riverbed required; Limitation
Sounding-rod
Low
analyze the monitoring data;
on monitoring the refill process;
75
Time consuming in operation; Specialized
Fiber bragg
Continuous monitoring of riverbed;
training required; Fiber is easy to be
High
grating sensor
destroyed;
Larger monitor region around the bridge pier;
Smart rock
Limitation on monitoring the refill process;
Low
Cost-effective technology;
Easy to install and operate; High resolution on Excavation of riverbed required; Limited
TDR
Medium
detecting scouring and refilling process;
monitoring region for each sensor;
76
On the basis of the evaluation of the new spiral TDR sensor in chapter 3, the
subsequent section in this chapter primarily presents its applicability and performance on
monitoring bridge scouring process. It is fabricated with two parallel copper wires
waveguide wrapped around a supporting rod and then calibrated using liquid with known
dielectric constant and soils with different moisture contents. Its performance was then
evaluated using simulated scour experiments and also compared with the conventional 2rod straight TDR sensor.
4.3
Principle of Bridge Scour Depth Estimation with TDR
Fig. 4-8 shows the schematic diagram of estimating bridge scour using TDR
technology. Water and saturated soil are prepared in a tank with increasing/decreasing
thickness of soil layer to simulate the sediment/scour process. TDR signals are acquired at
different stages to measure this process by locating the interface between water and soil
sediment.
From Chapter 2, mixing model of dielectric permittivity can be applied here for
estimating bridge scouring process, i.e., for the multi-layered system of water and sediment
in Fig. 4-8, equation 2-4 can be expressed as follows. Note that the straight TDR probe is
selected to illustrate the working principle of TDR-based bridge scour measurement.
𝐿1 √𝐾𝑎,𝑤 + 𝐿2 √𝐾𝑎,𝑏𝑠 = 𝐿√𝐾𝑎,𝑚
where
77
(4-1)
𝐾𝑎,𝑤 = the dielectric constant of water, which is commonly selected as 81 for pure
water from the introduction in Chapter 2;
𝐾𝑎,𝑏𝑠 = the dielectric constant of sand-water mixture in the sediment layer, in this
dissertation, the sand-water mixture is assumed to be fully saturated;
Fig. 4-8. Schematic diagram of bridge scouring measurement with TDR technique
𝐾𝑎,𝑚 = the measured bulk dielectric constant;
𝐿1 = the thickness of water layer;
78
𝐿2 = the thickness of sand layer;
𝐿 = the thickness of water layer and sand layer, in this experimental program, 𝐿 is
kept constant;
Assume the thickness of sand in Fig. 4-1 is x, then L1 = L − x. Substituting into
equation (4-1), the following equation (4-2) can be derived. If the total thickness, L, is a
constant, the thickness of sediment, x, is linearly proportional to the square root of
measured bulk dielectric constant. After mathematical operation, equation (4-1) is
transferred into equation (4-2):
𝑥=
√𝐾𝑎,𝑚 −√𝐾𝑎,𝑤
√𝐾𝑎,𝑏𝑠 −√𝐾𝑎,𝑤
𝐿
(4-2)
In the equation (4-2), 𝐾𝑎,𝑤 is known (set as around 81 for pure water) and L is
invariable by keeping the water level constant. The determination of the dielectric constant
of saturated sand layer, 𝐾𝑎,𝑏𝑠 , is dependent on the following equation (4-3), which is also
derived from mixing formula of dielectric constant for mixture and equation (2-4).
𝑛√𝐾𝑎,𝑤 + (1 − 𝑛)√𝐾𝑎,𝑠 = √𝐾𝑎,𝑏𝑠
(4-3)
in which,
𝑛 = the porosity of the saturated sand layer;
𝐾𝑎,𝑠 = the dielectric constant of solid sand particles, which is assumed as 3-7 for
dry sand particles (a value of 5 is used in this study);
79
Other parameters possess the same meanings as that in previous sections. The void
ratio can be measured and acquired by using such parameters as the weight and volume of
the saturated sand layer as well as the maximum and minimum relative density of this type
of dry sand. Hence, from equation (4-3), the value of 𝐾𝑎,𝑏𝑠 is easy to derive. Then equation
(4-2) indicates that the thickness of sediment is only correlated to the value of 𝐾𝑎,𝑚 , which
can be obtained directly from the output signals of TDR measurements using the theory
introduced in Chapter 2.
Therefore, the simulated scouring and sediment process can be monitored with the
TDR method. The scouring or sediment depth can be estimated and predicted from
measured dielectric constants using equation (4-2).
4.4
Design and Fabrication of Spiral-shaped Sensor
As illustrated in Chapter 3, Fig. 4-9 shows the design of a spiral TDR scour sensor.
It is made of a square fiberglass rod as the mechanical mount and two conductive copper
wires as the TDR waveguide. The fiberglass rod is 500 mm in longitudinal length and 5
mm in cross-section length. The copper wires are 0.5 mm in diameter and wrapped in spiral
around the central rod with wire spacing of 2 mm. The cross-section of the central rod is
selected as square shape so that fabrication grooves can be easily created along the
fiberglass rod to assist the control of wire spacing. The copper wires are coated by
polyurethane insulating material. The commercial super-hydrophobic coating is also
sprayed on the surface of the copper wire and the core rod to eliminate the effects of
residual water trapped between adjacent wires. The sensing component of the TDR probe
80
used for the monitoring of bridge scour in this chapter is around 400 mm in length. A BNC
adapter is used to connect the spiral sensor and TDR system.
Fig. 4-9. Comparison of straight TDR probe and spiral-shaped TDR probe
Also shown in Fig. 4-9 includes a conventional two-rod straight probe, which has
an identical equivalent length to the spiral probe. Two copper wires are fixed in parallel on
the supportive rod with spacing of 3 mm.
81
Fig. 4-10. Effects of coating on the dielectric constant (  is the dielectric constant of
coating)
4.5
Calibration of Spiral-shaped Sensor
The measured dielectric constant by the TDR probe can be affected by the coating
materials (Xiong 2003). Fig. 4-10 shows the influence of coatings on the dielectric
permittivity measurement by TDR. From the figure, coatings with lower dielectric constant
have much larger impact on the measurement results. In addition, the mounting fiberglass
rod may also affect the measured effective dielectric constant. Therefore, these factors can
be accounted for by calibration on materials with known dielectric constant. Some
82
commonly used standard liquid with known dielectric information and wet soil with known
water moisture are employed to calibrate the new sensor.
4.5.1
Calibration with Liquid
Four commonly used standard solvents and ethanol-deionized (DI) water mixtures
are employed to calibrate the spiral TDR probe. The standard solvents include deionized
water (with dielectric constant of 80.4), methanol (33.1), ethanol (24.3), and acetone (20.7)
(Lidström et al. 2001). Different amounts of DI water is mixed with ethanol shown in Fig.
4-4 (b).
((
a)
b)
83
Fig. 4-11. Output signals of spiral sensor in liquid (a- in standard solvent; b- in ethanolDI water mixture )
The spiral sensor is totally submerged in these liquids and the TDR signals in each
solution are acquired. The TDR signal in the air is also obtained as a control group. Fig.
4-11 illustrates the TDR signals of the spiral TDR sensor under different testing liquids,
showing very reasonable results. The black arrows shown in the figures represent the
reflection points at the start and end of the probe. The measured dielectric constant for each
solution is calculated by using equation (2-3). The dielectric constant of ethanol-DI water
mixture can be calculated using equation (2-4) with 𝛼 = 1.0 . Fig. 4-12 shows the
relationship between measured results using a spiral probe and actual dielectric constant
by equation (2-4). By fitting the data in this figure, the calibration equation can be given
84
by equation (7) with R2 = 0.99, in which 𝐾𝑎,𝑟 , 𝐾𝑎,𝑚 are the real dielectric constant of the
liquid and the measured dielectric constant by coated TDR probe, respectively.
3
2
𝐾𝑎,𝑟 = 0.7872𝐾𝑎,𝑚
− 22.143𝐾𝑎,𝑚
+ 215.78𝐾𝑎,𝑚 − 688.79
(4-4)
Fig. 4-12. Relationship between measured and real dielectric constant
4.5.2
Calibration using wet soil with known water moisture
The dielectric constant of soil is closely related to its moisture content, since water
has a much larger dielectric constant than that of soil particles or air (Drnevich et al. 2001;
Siddiqui and Drnevich 1995; Topp and Davis 1985; Yu and Drnevich 2004). Siddiqui and
Drnevich (1995) developed an empirical formula to explicitly correlate measured dielectric
85
constant by TDR to the gravimetric water content, see equation (4-5), which is extensively
adopted in geotechnical engineering.
Fig. 4-13. Calibration of spiral TDR probe with moisture sand
𝜌
√𝐾𝑎 𝜌𝑤 = 𝑎 + 𝑏𝜔
(4-5)
𝑑
where
𝜌𝑑 = the dry density of soil;
𝜌𝑤 = the density of water;
86
ω = the gravimetric water content;
𝐾𝑎 = the apparent dielectric constant;
a, b = soil dependent calibration coefficient;
Sand with different water content is prepared and compacted in a stainless cylinder.
The spiral probe is completely embedded in the moisture sand (Fig. 4-13). The density and
water content of the sand is measured. TDR signals are obtained as shown in Fig. 4-14.
With the increasing water content of soil, the travelling distance of EM wave in the soil
increases. This is because the increasing water content results in increases of the soil
dielectric constant. The dielectric constant of soil is computed using equation (2-4).
87
Fig. 4-14. Output signals of TDR with spiral probe in moisture sand
The relationship between dielectric constant, dry density and water content of soil
is plotted in the format of equation (4-5) and shown in Fig. 4-15. A highly linear
relationship (R2 = 0.95) is demonstrated between measured dielectric constant and soil
properties with a = 0.91 and b = 1.95, respectively. This high linearity also indicates that
the soil physical properties can be accurately determined from the TDR measured dielectric
constant.
Fig.4-15. Calibration of spiral probe with moisture sand
88
4.6
Simulated Scouring Experiment Using New Spiral TDR Probe
4.6.1
Experimental Program
TDR technology has been utilized for the bridge scour monitoring by Yankielun
and Zabilansky (1999) and (Yu 2009). Bin et al. (2010) and Yu et al. (2013) conducted
bridge scour experiments by traditional 3-rod and a distributed strip TDR sensor.
Considering the resolution and sensitivity limitation of the sensor, the incremental
thickness in the sedimentation layer during these previous studies were set around 4 cm
and 10 cm, respectively.
To evaluate the performance of the new sensor, simulated sedimentation/scour tests
are implemented in the laboratory. The tank was first filled with tap water with constant
water level (39.6 cm in this study). Both the spiral and straight TDR probe (Fig. 4-8) are
vertically installed in the tank. Dry soils are then gradually added into the tank to simulate
the sedimentation process. In this way, the sand layer can be guaranteed to be fully
saturated situation. TDR signals are acquired at each prescribed thickness of the sediment
layer. This process continues until the tank is totally filled with soils. Commercial
Campbell CS 605 3-rod probe is also employed in the tests only with tap water and soils,
which are used to calculate dielectric constant of tap water and saturated soils.
4.6.2
Experimental Materials
Two types of soils are prepared to simulate the sediments, i.e., coarse sand and fine
sand. The grain size distribution of the two soil samples is shown in Fig. 4-16.
89
Fig. 4-16. Grain size distribution of two types of testing materials
4.6.3
Experiment Results Analysis and Discussion
Fig. 4-17 shows TDR output signals of scouring test for fine and coarse soils,
including conventional straight and new spiral probe. The sediment layer is changed with
2 cm increment, which is one fifth of that Yu’s (2009) experiment using a strip probe. The
resultant TDR signals for the spiral TDR probe are shown in Fig. 4-17 (a) and (c). Those
for the straight TDR probe are shown in Fig. 4-17 (b) and (d). With the increasing soil
thickness, the dielectric constant of the overall system, 𝐾𝑎,𝑚 , decreases, giving rise to the
decrease of the apparent length. An obvious observation is that with the same change in
the sediment layer thickness, there are much more significant changes in the travel time of
the EM wave (reflection at the end of the TDR probe) for the spiral TDR probe than the
straight TDR probe.
90
(
a)
(a)
(
b)
(b)
91
(
c)
(c)
(
d)
(d)
92
Fig. 4-17. TDR output signals for fine and coarse soil (a – spiral probe in fine sand; b
– straight probe in fine sand; c – spiral probe in coarse sand; d – straight probe in
coarse sand)
The dielectric constant of the water-soil mixture is computed based on the theory
introduced in the previous context. 𝐾𝑎,𝑟 is then obtained using calibration equation (4-4).
Fig. 4-18 illustrates the measured dielectric constant of water-soil mixture versus sediment
layer thickness in the format of equation (4-2) for coarse and fine soils. The square root of
the dielectric constant of water-soil mixture changes linearly with the sediment layer
thickness for both fine and coarse sediments. This is consistent with the relationship
illustrated in equation (4-2). Therefore, the algorithm for the scour depth estimation based
on equation (4-2) can be used for the spiral TDR probe.
The dielectric constant of tap water and saturated soil used in this test program are
obtained using the commercial Campbell CS 605 3-rod probe, which is 69.9 and 20.77,
respectively. Substituting the value of K a,w , K a,bs , K a,m and L into equation (4-2), the
sediment layer thickness can be estimated from the dielectric constant measured by the
spiral TDR probe.
93
(a)
(b)
94
Fig. 4-18. Relationship between dielectric constant and sediment thickness (a - fine
soil; b – coarse soil)
(
a)
Fig. 4-19 compares the physically measured sediment layer thickness by a ruler
versus TDR predicted values for both fine and coarse grained sediments. The predicted
values using the new spiral TDR sensor closely matches those of ruler measurements. This
indicates that the new sensor can be employed to accurately estimate the scour depth or
sediment layer thickness. The accuracy of the new sensor in predicting the sediment layer
thickness falls within ±5%, which is satisfactory for practical applications. The accuracy
for fine sediment is significantly higher (generally within ±2%).
(
a)
(a)
95
(
b)
(b)
Fig. 4-19. Measured and predicted sediment layer thickness (a - fine sediment; b –
coarse sediment)
The possible sources of experimental errors include: 1) the small diameter of the
copper waveguide implies a smaller effective sensing area, which might cause inaccuracy
for sediments with larger grain as seen in Figure 4-19; 2) inaccurate measurement of sand
layer thickness due to the difficulty to achieve a complete even surface; 3) errors in the
determination of reflection points from TDR signals; 4) the dielectric constant of water
maybe not be exactly equal to that of tap water acquired by CS 605 sensor due to the
turbidity of water layer, as discussed by Yu (2009).
96
4.6.4
Comparison with Straight TDR Scour Probe
As presented in Chapter 2, the sensitivity of a sensor is defined as the ratio of the
magnitude of its response to the magnitude of measured quantity or equation (2-6) (Radatz
1997). To compare the sensitivity of the new spiral TDR probe versus that of a conventional
straight TDR probe, Fig. 4-20 plots out the effects of sediment layer thickness on the
measured apparent length by the spiral and straight probes.
(
b)
97
Fig. 4-20. Relationship between sediment layer thickness and apparent length (a –
straight probe; b – spiral probe)
The apparent length is highly linear with sediment layer thickness. There are,
however, significant differences in the slope of the sensitivity curves by two different TDR
probes. The slope of the sensitivity curve by the new spiral TDR sensor is about 4 times
that of a regular straight TDR sensor probe. This implies that the spiral TDR probe is about
4 times more sensitive than the straight TDR probe in scour depth determination. The
sensitivity can be further improved by refining the spiral geometry design, which will be
introduced in detail in the following Chapters.
98
4.7
Summary and Conclusions
This chapter presents the development of an innovative spiral TDR scour sensor in
terms of the introductions in previous chapters. This new spiral sensor features higher
sensitivity and resolution than traditional probes due to the longer traveling distance of the
EM wave per unit length along the direction of the mounting rod. A laboratory
experimental program is conducted to evaluate this new sensor for bridge scouring
applications. Based on the experiment results, some conclusions and findings can be
summarized as follows:
1) The algorithm for estimating the bridge scouring process has been derived and
developed from the mixing model of the dielectric constant presented in chapter
2, which is the basis of the entire experiment program.
2) The fabricated new spiral TDR sensor is calibrated using some common
standard liquid solvent with known dielectric constant and soils with different
moisture contents due to the impact of the center rod and coatings. This results
in an empirical equation to correlated measured dielectric properties and real
dielectric constant of the materials.
3) Simulated scour experiments are conducted in the laboratory to evaluate the
performance of the spiral TDR probe in monitoring the scour process. The
results show that the spiral TDR scour sensor easily detect the change of
sediment layer thickness of less than 2cm, which indicates the resolution of
detecting scouring process using the new spiral TDR sensor is much higher than
the previous studies.
99
4) The square root of measured dielectric constant by the spiral TDR changes
linearly with the measured sediment layer thickness. This is consistent with the
theoretical predications, which again indicates the feasibility of monitoring the
bridge scouring process with the new spiral sensor. In addition, the predicted
sediment layer thickness from the spiral TDR sensor agrees very well with the
thickness of the sediment layer by direct ruler measurement.
5) Compared with a straight TDR scour probe, this new spiral sensor is about 4
times more sensitive in detecting the scour thickness. And the sensitivity can be
further improved by refining the spiral design.
100
CHAPTER 5 DETERMINATION OF THIN WATER FILM DUE TO VOID
REDISTRIBUTION USING SPIRAL TDR SENSOR
5.1
Introduction
The United States is facing severe threats from earthquakes, especially in the west
coast area (Petersen et al. 2014), including State of California and Alaska. Soil liquefaction
is a major contributor to these seismic-induced failures and risks. Soil liquefaction
describes a phenomenon whereby a soil substantially loses strength and stiffness in
response to cyclic loading, such as seismic earthquake loadings.
During the course of liquefaction, the accumulation of excess pore water pressure
will induce the decrease of effective stress between soil particles and the loss of soil
stiffness and strength, especially shear strength. This could result in devastating failure of
structure foundations, levee, embankment and other infrastructures, such as 1964 Niigata
earthquake (Hamada and O'Rourke 1992; Kishida 1966; Mogi 1989; Seed and Idriss 1967),
1989 Loma-Prieta earthquake (Dietz and Ellsworth 1990; Kasai and Maison 1997; NolenHoeksema and Morrow 1991), 1995 Kobe earthquake (Yoshida et al. 1996), 2008
Wenchuan earthquake (Chigira et al. 2010; Huang et al. 2009; Yin et al. 2009) and 2011
Christchurch earthquake (Bradley and Cubrinovski 2011; Cubrinovski et al. 2011; Smyrou
et al. 2011), etc.
People have extensively investigated this topic over the last 50 years using both
experimental and numerical simulation aspects (Castro 1975; Ishihara 1993; Martin et al.
1975; Seed and Idriss 1967; Seed and Lee 1966), especially after 1964 Niigata earthquake.
101
But they primarily focus on the liquefaction in uniform soils. In fact, most laboratory
experiments results might not be applicable to stratified soil conditions, since water film or
shear band will be formed in the stratified soil profile due to void redistribution, which will
significantly reduce the soil liquefaction resistance compared with a uniform soil layer.
Therefore, design based on the liquefaction resistance of uniform soil could lead to unsafe
design of geo-structures.
Water film due to void redistribution has been observed in a number of laboratory
experiments and field studies (Boulanger and Truman 1996; Fiegel and Kutter 1994; Fiegel
and Kutter 1994; Kokusho 1999; Kokusho and Kojima 2002; Kulasingam et al. 2004;
Malvick et al. 2008; Malvick et al. 2006; Seed and Lee 1966). It was found that the
redistribution of water content, especially in the dilation zone (shear band) where the
accumulation of water at the interface area between the liquefied soil and soil layer of low
permeability, can cause significant loss of shear strength in slopes and embankments during
and after earthquakes. And this is strongly dependent on the extent of void redistribution
or thickness of water film. Therefore, the estimation and predication of the thickness of
water film is of great significance to clearly understand the liquefaction in stratified soils.
5.2
Review of Water Film Due to Void Redistribution
5.2.1
Water Film due to Void Redistribution
Fig. 5-1 shows the schematic diagram of the liquefaction phenomenon in multi-
layered soil profile caused by void redistribution, which illustrates an idealized submerged
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mild slope with an incline angle of 𝜃. The slope comprises a liquefiable sand layer overlain
by a low-permeability clay or silt layer and underlain by an impermeable base.
Fig. 5-1. Sketch of void redistribution in submerged layered infinite slope (Malvick et
al. 2006)
Fiegel and Kutter (1994), Kulasingam et al. (2004) and Malvick et al. (2006)
explained the mechanism of void redistribution in stratified soil profile. When soil is
subjected to cyclic loading, such as seismic loading, the solid particles will deposit due to
its higher density than pore water, which cause much higher excess pore water pressure in
the bottom than that in the upper. The pore water will migrate upward because of excess
pore water pressure gradient (equal to 𝛾𝑏 ⁄𝛾𝑤 , 𝛾𝑏 - effective unit weight; 𝛾𝑤 - unit weight of
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water (Fiegel and Kutter 1994)). However, the overlying low-permeability layer will
preclude the drainage of pore water upward. This consequently results in the accumulation
of water film in the region between A and B, which is also regarded as shear band by some
researchers (Kulasingam et al. 2004; Malvick et al. 2008; Malvick et al. 2006).
The thickness of water film (shear band or dilation zone, 𝐻𝑑 ) is a significant factor
to influence the stability of mild slope, i.e., whether or not the current dilation zone could
induce lateral spreading. It is proved that some parameters of the liquefiable soil layer could
influence the thickness of the water film or dilating zone, including initial relative density,
𝐷𝑅 , total thickness, 𝐻𝑏 , permeability, burying depth, 𝐻𝑡 , as well as the intensity and
duration of shaking, etc.
5.2.2
Previous Investigations on Water Film
The earliest works on water film stem from investigations with regard to the
mechanism of sand boils. Housner (1958) considered the “reservoir” for sand boils as a
region of water and loose soil due to the settlement of the sand particles in the liquefied
soil layer. Scott and Zuckerman (1964) explained how the sand in this reservoir was ejected
to the surface and proposed that the low permeable soil layer might be the essential
condition for sand boils. The “water interlayer” or “water film” was clearly observed in the
shaking table tests (Kokusho 1999; Kokusho and Kojima 2002; Liu and Qiao 1984), and
centrifuge model tests (Boulanger and Truman 1996; Fiegel and Kutter 1994; Fiegel and
Kutter 1994; Kulasingam et al. 2004; Malvick et al. 2008; Malvick et al. 2006). Horizontal
soil columns and mildly sloping ground (inclining angle less than 15 degrees) are typically
configured in the laboratory model tests to explain the development mechanism of water
104
film, influence factors as well as its significance of causing lateral spreading or flow failure
after liquefaction.
In 1-D column shaking tests, the development of the water film is captured with the
installation of several pore water transducers at different depths. This suggests the
existence of low permeable silt seam precludes the dissipation of excess pore water
pressure in the liquefied sand layer or significantly extend its dissipation time even after
the liquefaction (Kokusho 1999). But if the soil layer is configured with a slight inclined
angle, the water film can serve as the sliding surface and shear stress isolator for lateral
flow failure, limiting the shear stress transmitted into upper sand layer, and this often
occurs in loose sand with relative density no less than 40% from the results of shaking table
tests (Kokusho 1999; Kokusho and Kabasawa 2005; Kokusho and Kojima 2002).
Kokusho (1998) presented 1-g shaking table tests of a slope model consisting of
loose sands layer with embedded silt seams (Fig. 5-2), in which the strength loss, slope
deformations and flow failure can be clearly observed after shaking has ceased. The four
images represent (a) the geometry before the start of shaking, (b) the geometry immediately
after shaking has ceased and pore water seepage from the sand below the silt seams is just
starting to break up through the silt seams, (c) the geometry as the lower silt seam and
overlying sand are weakened by the upward pore water flow and begin to flow both
laterally and down the adjacent slope, and (d) the final state of model deformation and
geometry after flow failure. The testing results indicate that the high gradient of the excess
pore water pressure and subsequently formed water film beneath the silt seam is the major
factor to induce the lateral flow failure of the slope model. The third image also shows the
105
lower white silt seam initially spreads laterally over the adjacent muddy water, which
accelerates the flow deformations of the submerged slopes (Boulanger et al. 2014).
Fig. 5-2. Photos of shaking table tests on layered slope with embedded silt layer
(Boulanger et al. 2014; Kokusho 1998)
Fiegel and Kutter (1994) explained the onset and developing process of water film
in layered soil deposits, as well as the mechanism of sand boils. From the centrifuge model
testing results, the author confirms that the low permeable silt interlayer is of importance
to sand boils and water film, which acts as an isolator to preclude the propagation of
acceleration, stress and strain to the upper soil layer. The centrifuge tests results also
indicate that the nonuniformity of the low permeable layer determines the failure of sand
boils. The thicker and heavier portions of overlying layer fall through the interfacial zone
106
causing water to flow laterally, which in turn forces thinner and lighter portions of the
overlying layer to bulge and fail. The images of shaking table tests by Butterfield and
Bolton (2003) also provide convincing evidence and support for this explanation.
Brennan and Madabhushi (2005) illustrated in detail the dissipation pattern of
excess pore water pressure and the development and vanishing of water film in layered
soils during liquefaction. As shown in Fig. 5-3 (a), the sand layer is completely liquefied
after shaking. Dissipation begins at the base, and due to the low permeable silt layer, the
volume of the sand layer maintains constant in a short term. The excess pore water pressure
profile now resemble Fig. 5-3 (b), i.e., the soil immediately below the silt layer experiences
a value of excess pore pressure greater than initial vertical effective stress. If the water is
at an excess pore pressure greater than initial vertical effective stress, then a force
imbalance exists and the silt layer should be forced upward, which leads to an increase in
volume of the underlying soil, a reduction of the pore water pressure and subsequently the
formation of water film (Fig. 5-3 (c)). As the sand layer continue to settle, three phases can
be identified shown in Fig. 5-3 (d). Phase I begins at the onset of a water film and contains
the sand resettlement beneath, until the excess pore pressure throughout the sand equals
that in the film; phase II, the pressure is maintained in the sand while the fluid in the film
dissipates through the silt layer; phase III begins the moment water film vanishes. However,
based on the consolidation theory, Wang et al. (2013) simply considered this process as the
phase transformation between two phase for the liquefiable sand layer, i.e. solidification
phase and liquefaction phase. The liquefaction occurs from the top soil layer, which just
contradicts to the solidification process. The boundary between the upper liquefied region
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and lower solidified region is defined as the solidification front. Therefore, during this
process, the solidification front propagates from the base to the top soil layer.
Fig. 5-3. Excess pore water pressure redistribution pattern during liquefaction in layered
soils (Brennan and Madabhushi 2005)
Boulanger and Truman (1996) and (Malvick et al. 2003) proposed that void
redistribution in layered soils contributed to the formation of water film. They utilized
infinite idealized slope model to illustrate the influence of dilating shear zone due to void
redistribution on the instability of the mild slope. They defined the dilation capacity as the
amount of water that the dilating zone can absorb before the undrained strength reduces to
the driving static shear stress. After the dilation zone reaches its dilation capacity,
additional influx of water causes instability. They also indicate that the potential for
strength loss due to void redistribution is strongly dependent on the thickness and initial
relative density of the liquefiable sand layer because the effect of increasing relative density
will reduce the volume of water expelled from the contracting zones and increase the
capacity of the dilating zone to absorb water inflow. In addition, the slope angle and the
thickness of water film or shear band are another two significant factors for the stability of
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slope, which is confirmed by Malvick et al. (2006) with more detailed explanation.
Therefore, it is of importance to determine the thickness of the dilation zone at the top of
the liquefied sand layer during liquefaction.
The thickness of a dilating shear zone is significantly dependent on the thickness
of the consolidating zone (Kulasingam et al. 2004; Malvick et al. 2003). It has been
estimated or postulated empirically by many researchers but without quantitative
determination. For example, the simplistic approximation that the thickness of the dilating
zone is on the order of 10D50 (Roscoe 1970). Consider an infinite slope with a 1 m thick
layer of sand confined between overlying and underlying clay layers. If the sand has a D50
of 1 mm and undergoes 1% compressive volumetric strain during an earthquake, the
consolidating layer would expel 10 mm of water (1% of 1 m), which could cause a 100%
volumetric expansion of the 10 mm thick dilating zone (10D50 =10 mm). However, this
simple argument, along with the observation that many layered slopes do remain stable
during earthquakes, suggests that there might be some mechanisms besides the particle size
that controls the thickness of the dilating shear zone (Boulanger and Truman 1996), such
as the roughness of the interface between the sand and overlying less permeable soil. In
addition, Malvick et al. (2006) proposed an semi-empirical model to predict the thickness
of dilation zone, which is described in equation (5-1). The author included an example of
mild slope in this paper to demonstrate the method of computing the thickness of dilation
zone. But there still exists some difficulties in estimating the value of some parameters,
′
′
such as 𝜑𝑐𝑣
and 𝜑𝑝𝑘
.
109
𝑡𝑎𝑛𝜃
𝑡𝑎𝑛𝜑′𝑝𝑘
𝑡𝑎𝑛𝜃
1−
𝑡𝑎𝑛𝜑′𝑐𝑣
1−
ℎ𝑑 = (
− 1) 𝐻𝑡
(5-1)
where
ℎ𝑑 = thickness of dilation zone or water film;
𝐻𝑡 = thickness of soil overlying confined liquefiable bottom layer;
𝜃= slope angle;
′
𝜑𝑝𝑘
= peak friction angle;
′
𝜑𝑐𝑣
= critical state friction angle;
In addition, Malvick et al. (2003) and Kulasingam et al. (2004) demonstrated the
potential importance of other factors, such as shaking intensity and duration, permeability
contrasts, on the formation of dilation zone due to void redistribution.
Kulasingam et al. (2004) employed a series of centrifuge model tests to investigate
the potential void redistribution of several sand slopes with and without silt interlayers and
the effects of several model parameters, such as initial relative density, slope geometry (silt
layer shape, sand layer thickness), shaking duration, shaking amplitude, and shaking
history on the instability of these slope models. For instance, Fig. 5-4 shows the testing
results for the slope models with different thickness of liquefiable sand layer, including a
thin silt interlayer embedded for both slope models. Compared with the model in Fig. 5-4
(a), showing significant lateral spreading, no obvious lateral deformation can be observed
for the model in Fig. 5-4 (b). The author attributed it to the different thickness of the
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liquefiable sand layer, which affects the amount of pore water migrated toward the bottom
of the silt interlayer. The centrifuge testing results with different combination of affecting
factors also indicated that slope models with less initial relative density or larger amplitude
of shaking input are much more susceptible to induce strength or shear localization and
form water film.
Fig. 5-4. Post-shaking photos of centrifuge models having identical initial relative
density but different underlying sand layer thicknesses; (Kulasingam et al. 2004)
On the other hand, few publications using numerical simulations can be found to
study the void redistribution in layered soil due to its complexity and limitations of current
numerical computation (Boulanger et al. 2014). Although some finite element based
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modellings have been proposed for the liquefaction behavior of layered soil deposits, but
they are still compromising the capability of capturing the strength or strain localization
and consequent formation of water film (Seid-Karbasi and Byrne 2007; Yang and Elgamal
2002; Yoshida and Finn 2000).
The proposed PM4Sand model by Boulanger is tentatively employed to simulate
void redistribution in layered soil slopes (Boulanger and Ziotopoulou 2012; Boulanger and
Ziotopoulou 2013; Kamai and Boulanger 2012). This model follows the basic framework
of the stress-ratio controlled, critical state compatible, bounding-surface plasticity model
for sand presented by Dafalias and Manzari (2004), includes some modifications and
additions (Boulanger and Ziotopoulou 2013) and is implemented as a user-defined module
with the commercial program FLAC (Boulanger and Ziotopoulou 2012).
(c)
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Fig. 5-5. Two examples of void redistribution simulation for slopes with low permeable
silt interlayer using PM4Sand model; a) post-shaking slope with sand permeability of
0.012 m/s, b) post-shaking slope with sand permeability of 0.06 m/s, c) slope geometry
before shaking event (Kamai and Boulanger 2012)
Fig. 5-5 shows an example of simulation with PM4Sand model, which simulates
centrifuge test of a slope with embedded silt arc and two horizontal silt layer. The void
redistribution pattern is consistent with that from centrifuge experiment, indicating there is
approximately 1.0-3.0 m (prototype scale) thick zone of sand immediately beneath the silt
arc that loosens as a consequence of a net inflow of pore water and that the greatest degree
of loosening occurs in a thin zone immediately beneath the silt arc (Boulanger et al. 2014).
However, this model still has no capability of reproducing the water film formed beneath
the silt layer.
El Shamy et al. (2010) attempted to simulate the void redistribution and lateral
deformation of soil deposits using the Discrete Element Method (DEM) technique. The
appealing aspects of this method lies in its capability to capture and reproduce the gradient
distribution of excess pore water pressure during and after shaking event. Fig. 5-6
illustrates the excess pore water pressure at different depths during shaking table test,
showing that the liquefaction begins from the top soil layer and gradually propagate from
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the top to the bottom layer, i.e. an apparent time difference can be observed from Fig. 5-6.
This is, however, still facing challenges and difficulties if FEM/FDM based method are
chosen for the simulation work (Dashti and Bray 2012).
Fig. 5-6. Excess pore water pressure ratio time history at different depth using DEM
(Zeghal and El Shamy 2008)
In summary, physical modelling tests, such as shaking table test and centrifuge test,
are typical choices to investigate the shear location, void redistribution and consequent
water film in layered soil deposits, since there is not an effective computational technique
114
available so far to quantitatively capture and reproduce this phenomenon. For laboratory
physical model test, highly instrumented models with horizontal soil layers or slopes with
slight inclined angles are constructed, but it is still located at the stage of qualitative
measurement and analysis. The thickness variation of dilation zone or water film is
measured with the aid of a measuring ruler (direct reading method), for example, in the
shaking table test (Kokusho 1999; Kokusho and Kabasawa 2005; Kokusho and Kojima
2002), and centrifuge tests (Kulasingam et al. 2004; Malvick et al. 2003; Malvick et al.
2006). But it can be only measured from the side of the model, and the information in the
middle of the model still remains unknown.
Based on the introduction and performance evaluation of the new spiral TDR sensor
in previous chapters, a spiral sensor with a much finer spacing design is developed, which
features higher sensitivity and resolution. The static and dynamic tests are designed to
reproduce the phenomena of water film, in which the new spiral sensor is utilized to capture
and measure the thickness variation of water film.
5.3
Sensor Configuration and Calibration
The development of the spiral TDR sensor used in this chapter is generally identical
with that described in previous chapters. But in order to further improve the resolution of
the new sensor, some modifications have been implemented, i.e., the central rod with a
square cross section is replaced by the 3-D printed circular rod with much finer or denser
threaded grooves.
115
connect to TDR
(a)
(b)
(c)
Fig. 5-7. Configuration of new spiral TDR sensor
Fig. 5-7 illustrates the configuration of this new spiral TDR sensor. The sensor is
500 mm in longitudinal length and 5 mm in diameter. The circular central supportive rod
is double threaded with 1 mm spacing between two adjacent grooves. This means the
spacing interval between two adjacent electronic wires (electrode) is also only around 1
mm, which is half of the spacing distance in chapter 3 and chapter 4. As shown in Fig. 5-7
(c), the groove should be designed with appropriate dimension to guarantee the waveguide
wires are partly embedded in the central rod. The depth of the grooves can’t be too large
or too small, as too large depth design will significantly decrease the sampling area of the
sensor, impacting the sensor performance and too small depth will affect the fixity of the
electronic wires. In this chapter, the depth of the groove is selected 0.1 mm, which is one
fifth of the wire diameter and one tenth of the spacing distance.
116
Fig. 5-8. Output waveforms of the new spiral TDR sensor with standard solvent
With the same calibration method in section 4.5.1, several standard liquids are
utilized to correlate the measured and real dielectric constant. The output TDR waveforms
are shown in Fig. 5-8. The relationship between two parameters can be approximated with
the fitting equation (5-2) with 𝑅 2 = 0.996 (Fig. 5-9). 𝐾𝑎,𝑟 and 𝐾𝑎,𝑚 are the real dielectric
constant of the solvent and the measured dielectric constant by new TDR probe,
respectively.
3
2
𝐾𝑎,𝑟 = 0.0151𝐾𝑎,𝑚
− 0.6692𝐾𝑎,𝑚
+ 12.062𝐾𝑎,𝑚 − 48
117
(5-2)
Fig. 5-9. Relationship between measured and real dielectric constant
5.4
Water Film Detection in Static Experiments
5.4.1
Deployment of Experiment Apparatus
In order to verify and validate the feasibility of detecting thin water film using this
new spiral sensor, a series of static experiments are conducted in the laboratory. In the
static testing program, a special testing unit is designed, shown in Fig. 5-10.
118
connect to TDR
(a)
(b)
Fig. 5-10. Testing setup for static experiment (a- sketch diagram; b- photo of test
device)
This testing unit consists of two transparent plastic cylinders to contain two layers
of saturated sands, with the external diameter (100 mm) of the inner cylinder equaling to
the inner diameter of the outer cylinder. The bottom of the inner cylinder is sealed with a
micro-meter scale sieve filter, through which water is able to permeate but soil particles
are inhibited to drop down from the upper soil layer. An aperture with the diameter equaling
to the sensor rod is designed at the center of the sieve, from which the TDR sensor can be
inserted to the bottom soil layer. Two slim tubes with diameters of 5 mm are attached at
the internal surface of the inner cylinder, denoted as #6 in Fig. 5-10 (a), which is applied
to inject water in the space between two soil layers. One or two microcallipers are fixed to
the external surface of the outer container to manually control the elevation of the internal
119
container. When the elevation of the internal container rises with the aid of the
microcalliper, an air gap will be generated between two layers of soil. Water is then injected
from the tube on one side, and air is extruded from the other tube on opposite side. Using
this approach the gap can be fully filled with water, and a thin water interlayer with
different thickness can be manually embedded between saturated soil layers.
5.4.2
Testing Materials
The soil sample used in this experiment is standard sand. The particle size
distribution is shown in Fig. 5-11. 𝐷50 = 0.23 𝑚𝑚 , 𝐶𝑢 = 2.17 , 𝐶𝑠 = 0.9 , 𝜌𝑚𝑎𝑥 =
1.84 𝑔⁄𝑐𝑚3, 𝜌𝑚𝑖𝑛 = 1.60 𝑔⁄𝑐𝑚3, 𝑒𝑚𝑎𝑥 = 0.66, 𝑒𝑚𝑖𝑛 = 0.44. The relative density of the
bottom and upper saturated sand layer is 𝐷𝑅 = 42% and 𝐷𝑅 = 48%, respectively.
100
90
Percent finer (%)
80
70
60
50
40
30
20
10
Sand
0
1
0.1
Particle size (mm)
120
0.01
Fig. 5-11. Particle size distribution of testing soil
5.4.3
Experiment Procedure
Fig. 5-12 illustrates the procedures of the experiment, which can be summarized in
details as follows:
i.
Measure physical parameters or dimensions of the testing device, such as the
weight of empty container and diameter, weight of dry sand, etc.
ii.
Prepare certain amount of water in the outside container, and pour dry sands
into the container to the desired depth (e.g. 100 mm). Keep the depth of water
higher than soil to guarantee the fully saturation condition of the soil (Fig. 512 (a) (b)). Measure the weight of container and saturated soil and calculate
the density of the bottom layer of soil.
iii.
Lay down the inner container to the surface of the bottom soil and insert the
spiral TDR sensor to the desired depth (60 mm); keep the probe straight and
pour some dry sand to the inner container, and measure the total weight and
calculate the density of the upper layer of soil (Fig. 5-12 (c)).
iv.
Obtain the initial TDR signal with PCTDR software package from Campbell
Scientific Inc., and adjust the microcalliper to change the thickness of the gap
between soil layers.
v.
Slowly infuse water from one of the water injection tube (Fig. 5-12) to fully
fill the embedded air gap and obtain TDR signal (Fig. 5-12 (d)). Note that the
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(a)
(b)
water interlayer
(c)
(c)
Fig. 5-12. Procedures of static testing to measure water film
122
water level should be kept at the same level, so that the soil in the internal
tube can be guaranteed at the same water content (fully saturation).
vi.
5.4.4
Repeat procedure (4) (5) and capture a series of TDR signals.
Interpretation of Testing Signals
Several typical TDR output signals for the soil profile with and without embedded
water interlayer are compared in Fig. 5-13. Also shown includes the spiral TDR sensor
used in this experiment program, in which the electronic wire waveguide is partially
wrapped around the central rod and the remaining is kept as straight, i.e., the waveguide
before E is straight and after E is spiral in Fig. 5-13 (a). This is to reduce the influence of
signal attenuation along the waveguide on the testing results. Some important reflection
points are also marked in the output signals and TDR sensor.
In Fig. 5-13 (b), the signal between A and B corresponds the wave guide embedded
in soil layer of the internal cylinder, and the signal from B to D is for the probe in the
bottom soil layer in the external cylinder. The upward bulge B (in the soil of inner cylinder)
is due to the tapes with low dielectric constant at Fig. 5-13 (a). Even though the signals
from point A to point B should be perfectly matched as the soil layer in the inner cylinder
is theoretically kept as fully saturated (identical water content), small difference still can
be observed from the output signals due to the experiment errors.
123
A
(a)
E
Air
B
C
D
Water
Soil
Soil
A
B
C
A
D
B
C
D
(b)
(c)
Fig. 5-13. Comparison of TDR output signal with and without water interlayer
In addition, compared with the output signal for soil profile without water interlayer,
the scaled length from the top surface of the soil profile to the probe end (from A to D) for
soil profile with water interlayer increases significantly. This is due to the fact that the
dielectric constant of water is much larger than saturated soil (water + soil particle) and the
additive water interlayer increases the dielectric constant of the whole saturated soil-water
system, which subsequently results in the increment of apparent length, 𝐿𝑎 , in terms of
equation (2-3) as the probe length, 𝐿𝑝 , is a constant. Besides, the existence of the water
124
interlayer can be clearly observed and identified from the output signal, corresponding to
Point B to Point C. That means the scaled length between point B and Point C stands for
the water interlayer, from which the thickness of the water interlayer can be determined.
5.4.5 Measurement of Water Interlayer Thickness
To theoretically determine the thickness of water interlayer, the mixing formula
illustrated in Chapter 2 is employed herein. Fig. 5-14 shows the schematic diagram of the
measuring principle. The apparent dielectric constant of the soil-water mixture at arbitrary
time can be illustrated using equation (5-3).
Fig. 5-14. Schematic diagram of test for water interlayer thickness measurement
𝐿1 √𝐾𝑎,𝑏𝑠 + 𝑥√𝐾𝑎,𝑤 + 𝐿2 √𝐾𝑎,𝑏𝑠 = 𝐿√𝐾𝑎,𝑚
125
(5-3)
where
𝐿1 = the thickness of upper soil layer, which is a constant during testing;
𝐿2 = the thickness of bottom soil layer. Note that 𝐿2 does not represent the whole
thickness of the bottom soil layer in the external cylinder, but just the thickness of bottom
soil layer with embedded TDR probe. Therefore, The value of 𝐿2 decreases with the rise
of the internal cylinder during the course of the experiment. In addition, no water interlayer
exists at the initial state, and the thickness of the water interlayer and bottom soil layer with
TDR probe should be equivalent with the initial value of 𝐿2 , i.e., 𝐿20 = 𝐿2𝑡 + 𝑥, 𝐿20 , 𝐿2𝑡
represents the value of 𝐿2 at initial and arbitrary time t, respectively.
𝑥 = the thickness of water interlayer;
𝐿 = the thickness of whole soil profile with embedded TDR probe, which can be
calculated from the TDR signal for soil profile without water interlayer;
𝐾𝑎,𝑤 = the dielectric constant of water, which is commonly selected as 69.9 for tap
water in this dissertation from the Chapter 4;
𝐾𝑎,𝑏𝑠 = the dielectric constant of sand-water mixture in the sediment layer, which
can be calculated using equation (4-3). In this dissertation, the sand-water mixture is
assumed to be fully saturated;
𝐾𝑎,𝑚 = the measured bulk dielectric constant;
In the above equation (5-3), the three terms on the left represent the contribution to
the dielectric constant of the whole soil profile from three parts, respectively, i.e., upper
126
soil layer, water interlayer and bottom soil layer. If no water film exists between two soil
layers, the dielectric constant of the soil mixture is only dependent on that of two separate
saturated soil layers, otherwise the dielectric information of the water interlayer should be
taken into account to estimate the dielectric constant of the whole soil profile.
If 𝐿 = 𝐿1 + 𝐿20 = 𝐿1 + 𝐿2𝑡 + 𝑥 is employed to substitute 𝐿 in equation (5-3), the
thickness of water interlayer can be represented as
𝑥=
√𝐾𝑎,𝑚 −√𝐾𝑎,𝑏𝑠
√𝐾𝑎,𝑤 −√𝐾𝑎,𝑏𝑠
𝐿
(5-4)
If the spiral TDR probe is used to replace the probe in Fig. 5-14. The value of x, L
should be transferred into actual length of spiral waveguide. The thickness of water
interlayer is then determined with the knowledge of equivalent spiral waveguide length per
unit vertical length, which can be obtained from the sensor fabrication process.
In addition, the reflection point at the interface of the upper soil layer-water
interlayer and water interlayer-bottom soil layer can be determined in Fig. 5-13 (b), which
correspond to top and bottom of the water interlayer. Therefore, the thickness of water
interlayer can also be directly determined using equation (2-3) with known value of 𝐾𝑎,𝑤 .
Fig. 5-15 shows the TDR output signals for the soil profile with different thickness of water
interlayer.
127
Fig. 5-15. Output signals of TDR with different thickness of water interlayer
An apparent increment of scaled length from B to D (scaled length in the bottom
soil layer) can be observed from Fig. 5-15. The water-soil interface evolves in a reasonable
manner, i.e., with the increase of water interlayer thickness, the scaled length increases
significantly. This is attributed to the higher dielectric constant of water than saturated soil
and EM wave requires a much longer time to propagate for the same distance. Also the
measuring results in Fig. 5-15 implies that this innovative spiral TDR sensor is able to
detect water interlayer as thin as 1 mm.
128
Fig. 5-16. Comparison of measured and actual water interlayer thickness
With the similar calibration process introduced in chapter 4, the actual dielectric
constant of the whole soil column, 𝐾𝑎,𝑚 in equation (5-4), can be determined. Then the
thickness of water interlayer thickness is computed using equation (5-4) (Method 1) and
(2-3) (Method 2), which is compared with the actual water interlayer thickness (measured
by ruler). The comparison in Fig. 5-16 indicates that the measurements using this spiral
TDR sensor are very reliable, agreeing relatively well with the actual value of water
interlayer thickness, even though some errors (within 10%) can be observed.
129
5.5
Water Film Measurement in Dynamic Shaking Table Test
The aforementioned contents of static testing indicate the viability of measuring
water interlayer or water film using this innovative spiral TDR sensor. In this section, a
shaking table test is implemented in the laboratory to dynamically monitor the development
and elapse of water interlayer beneath the low permeable layer.
5.5.1
Experimental Program
Fig. 5-17 illustrates the experimental configuration of dynamic shaking table test.
A transparent plastic cylinder is fixed on the shaking table, with two saturated sand layers
and one clay interlayer inside. The particle size distribution of two types of soil sample is
shown in Fig. 5-18. The property of sand is identical with that described in section 5.4.2,
whereas the clay interlayer is kaolin, which owns tenth to hundredth of particle size of sand.
Therefore, the permeability of the kaolin interlayer is much smaller than the saturated sand
layer (Shepherd 1989). The new spiral TDR sensor is installed at the center of the cylinder,
which is connected to the signal impulse generator, TDR 100, produced by Campbell
Scientific, Inc., and data logger. The marker C (Fig. 5-17) which can induce the upward
bulge (point B in Fig. 5-13) due to its lower dielectric property than water, is located on
the surface of the bottom sand layer in the test. A camcorder is employed to record the
whole process of testing. A vertical excitation is inputted from the base shaking table to
simulate the seismic earthquake event. Note that this vertical excitation is only applied to
produce vibration at the base of the cylinder, so that the water film can be formed during
excitation (Kokusho 1999). If the mechanical behavior of the soil is required to investigated,
some standard, such as sine wave or recorded earthquake loading, should be inputted.
130
Fig. 5-17. Schematic experimental setup for dynamic shaking table test
The TDR measuring and data acquisition system is designed and developed, which
characterizes the ability of collecting TDR signals in specific time intervals automatically.
The time interval of collecting data can be set as an arbitrary value between 1s and 10s in
light of the practical requirements.
131
Fig. 5-18. Particle size distribution of soil sample for dynamic experiments
5.5.2
Fundamentals of Estimation Water Film during Shaking Events
Estimation of water film thickness during the shaking process for multiple-layered
soil profile is much more difficult and complex than that in section 5.4. This is because the
dielectric constant of the upper and bottom sand layer is not invariant during the squeezing
out of the pore water from the sand layer, which makes it extremely challenging to
recognize reflection points on the TDR output waveforms.
1) Dielectric constant of soil layer after squeezing pore water
Prior to study the scenario of a multiple-layered soil profile with low permeable
clay layer, a simple case, only one saturated sand layer, is firstly taken into consideration.
As shown in Fig. 5-19, when one saturated sand layer is subjected to base shaking loading,
132
a layer of water film will form on the soil surface, since pore water in the void space
between sand particles will be squeezed out from the saturated soil layer. The following
section will first focus on deriving the dielectric constant variation of the soil column
during this process. Note that the TDR probe is inserted to the bottom of the container,
which means it measures the dielectric constant of the whole soil column.
(b)
(a)
Fig. 5-19. Schematic diagram of water film measurement in one soil layer system using
TDR sensor (a- the initial state; b- at any given time during shaking process)
For the initial state of one saturated sand layer shown in Fig. 5-19 (a), the mixing
formula for dielectric constant, equation (2-4) in Chapter 2, is applied. The dielectric
constant of the saturated soil layer can be expressed with equation (5-5), which is just
equation (4-3).
√𝐾𝑎,𝑚 = 𝑛0 √𝐾𝑎,𝑤 + (1 − 𝑛0 )√𝐾𝑎,𝑠
133
(5-5)
where
𝑛0 = the initial porosity of the saturated sand layer; other parameters possess the
same meaning with that in previous contexts.
For the state at any given time during shaking, the equation (2-4) can be described
as equation (5-6).
√𝐾𝑎,𝑚 =
𝐿𝑤
𝐿
√𝐾𝑎,𝑤 +
𝐿−𝐿𝑤
𝐿
√𝐾𝑎,b𝑠
(5-6)
Substitute equation (4-3) into equation (5-6), it becomes
√𝐾𝑎,𝑚 =
[𝐿𝑤 +(𝐿−𝐿𝑤 )𝑛𝑡 ]
𝐿
√𝐾𝑎,𝑤 +
(𝐿−𝐿𝑤 )(1−𝑛𝑡 )
𝐿
√𝐾𝑎,𝑠
(5-7)
where
𝐿𝑤 = the length of waveguide in the water film;
𝐿 = the length of waveguide in the whole soil layer;
𝑛𝑡 = the porosity of soil layer at any given time, t, which can be derived from mass
conservation of water during shaking process;
𝑛𝑡 =
𝑛0 𝐿−𝐿𝑤
𝐿−𝐿𝑤
(5-8)
Other parameters own the same meaning as the previous contexts. When equation
(5-8) is substituted into equation (5-7), equation (5-7) will exactly yield to equation (5-5).
This implies that for the saturated soil layer to be measured, the dielectric constant of the
whole soil column will keep invariant during the process of extruding pore water from the
134
soil layer or the formation of the water film on the soil surface, which subsequently means
the apparent length, 𝐿𝑎 , in equation (2-3), from TDR output signals is constant.
2) Water film measurement in layered soil
Fig. 5-20 shows the schematic diagram for the development and elapse of water
interlayer for three-layer soil column during shaking events, including three different
stages: (a) initial status of three soil layers; (b) three soil layers and two water interlayers
during transition stage; (c) final status after shaking events.
(a)
(b)
(c)
Fig. 5-20. Schematic illustration for the onset and elapse of water interlayer during
shaking event
Mixing model, equation (2-4), is again utilized to describe the dielectric properties
of the multiple soil layer system under these conditions. To estimate the thickness of water
interlayer at arbitrary time, i.e., for the general case in figure (b), equation (2-4) becomes:
135
𝐿𝑤,𝑢 √𝐾𝑎,𝑤 + 𝐿1 √𝐾𝑎,𝑏𝑠𝑠 + 𝐿𝑐 √𝐾𝑎,𝑏𝑠𝑐 + 𝐿𝑤,𝑚 √𝐾𝑎,𝑤 + 𝐿2 √𝐾𝑎,𝑏𝑠𝑠 = 𝐿√𝐾𝑎,𝑚 (5-9)
where
𝐿1 = the thickness of the upper sand layer;
𝐿2 = the thickness of the bottom sand layer with TDR probe;
𝐿𝑐 = the thickness of the clay layer;
𝐿𝑤,𝑢 = the thickness of the upper water layer;
𝐿𝑤,𝑚 = the thickness of the middle water interlayer;
𝐿 = the total thickness of the whole soil column. Similarly, if the spiral TDR probe
is used to replace the straight probe in Fig. 5-20. The value of 𝐿1 , 𝐿2 , 𝐿𝑐 , 𝐿𝑤,𝑢 , 𝐿𝑤,𝑚 and L
should be transferred into actual length of spiral waveguide.
𝐾𝑎,𝑏𝑠𝑐 = dielectric constant of embedded clay layer (clay and water mixture), in this
study, this value will be assumed to be constant during the course of testing for
simplification;
𝐾𝑎,𝑏𝑠𝑠 = dielectric constant of sand layer (sand and water mixture), which will
change during the shaking process due to variations of the soil porosity. But for saturated
soil, it can still be calculated via equation (4-3) with assumed value of 𝐾𝑎,𝑠 and 𝐾𝑎,𝑤 , and
the porosity at any given time, t, is correlated to the initial porosity and water film extruded
from this sand layer using equation (5-8).
𝐾𝑎,𝑚 = measured bulk dielectric constant of the whole soil mixture, which can be
obtained from TDR signals at any time.
The above contents indicate that there are just two unknowns, 𝐿𝑤,𝑢 and 𝐿𝑤,𝑚 , in the
equation (5-8). The value of 𝐿𝑤,𝑢 can be acquired from the TDR signals directly (Fig. 5-
136
21). Therefore, the thickness of water film interlayer can thus be calculated from equation
(5-9).
5.5.3
Experiment results analysis
Fig. 5-21 shows the output signals from the new spiral TDR sensor at 11 given
moment, in which A, B, C and D are corresponding to the reflection at 4 points in Fig. 520(b), respectively, i.e., air-top water layer interface, top water layer-sand layer interface,
kaolin clay layer-middle water interlayer interface (the end of marker C in Fig. 5-17) and
probe end. The increasing trend of the apparent length for the entire soil column can be
clearly discerned from the testing results. The red arrow indicates the increase of water
layer thickness on the surface of soil column.
137
Fig. 5-21. Output signals of the new spiral TDR for shaking test
Fig. 5-22. Variation of apparent length and dielectric constant
Fig. 5-22 illustrates the variation of apparent length and dielectric constant for the
entire soil column and top sand and clay layer. Both the apparent length and dielectric
constant of the entire soil column (symbolized in triangle) show a slight increase trend
during the shaking process, which is due to the extruding of pore water from the soil
column (soil layer depth spanning from point B to point D in Fig. 5-17) or the formation
of the top and middle water film. This seems to contradict with the statement in section
5.5.2 (illustration for Fig. 5-19), which has been proven that the dielectric constant of the
saturated soil will remain invariant when the pore water is squeezed out from the soil layer.
138
But there are some differences for the case here. Since the spiral TDR sensor is not inserted
to the bottom of the testing cylinder, it does not measure the dielectric constant of the whole
soil column, but just measures the soil column from point B to D in Fig. 5-17. Therefore,
for the saturated soil system ranging from the depth of B to D, the involving of the pore
water from the soil layer under point D into the soil column from point B to D results in
the increment of the apparent and dielectric constant.
t=0s
t = 30s
t = 60s
t = 90s
139
t = 120s
t = 150s
t = 180s
t = 190s
t = 200s
t = 220s
140
t = 240s
Fig. 5-23. Screen shots from testing video capturing the development process of water
film interlayer
For the upper sand and clay layer (point B to C in Fig. 5-17), the apparent length
and dielectric constant (symbolized as square) remain constant at the initial stage (before
t=180s, red line), and then increase significantly after t=180s. This is because during the
initial stage (before t=180s), the water from the bottom sand layer has not penetrated to the
top sand layer due to the existence of the low permeable clay interlayer, which prevents
the penetration of pore water to the upper sand layer. This is consistent with the theoretical
prediction described in section 5.5.2 (Fig. 5-19). After around t=180s, due to the failure of
the middle clay layer (Fig. 5-25), the water film in the middle starts to permeate to the top
sand layer, and eventually vanishes. This process can also be clearly observed from the
screen shots of the testing video in Fig. 5-23.
141
Fig. 5-24. Comparison of the water interlayer measurement from the spiral TDR sensor
and testing videos
Fig. 5-24 illustrates the time history of the top and middle water film thickness with
spiral TDR sensor, also shown includes the measurements using a ruler attached on the
surface of the testing tank (Fig. 5-23). The blue arrow denotes the time of clay layer failure.
The thickness of middle water film increases initially due to the consolidation of the bottom
sand layer and then decreases because of the failure of the clay interlayer, while the
thickness of the top water film keeps the trend of increase, especially rises sharply on
account of the supplement of the middle water film at around t=180s.
142
Fig. 5-25. Photo of failure for clay layer during shaking test
In addition, the measuring results with the new spiral TDR sensor agrees very well
with the measurements with the ruler, indicating this new sensor is capable to capture the
development of the water film during the shaking events. But there still exist some
differences or errors between the two methods. The reason for this difference or errors is
complicated. For example, the thickness of water film varies at each measuring spot
probably due to the different consolidation speed of the bottom sand layer; the water with
sand or clay possesses different dielectric constant, which would also lead to calculation
errors in equation (5-9).
143
5.6
Summary and Conclusions
In this chapter, the previous efforts on the water film due to void redistribution in
multi-soil profile is reviewed, which includes experimental and computational studies. A
spiral TDR sensor is fabricated with much finer wire spacing to measure the thickness of
water film. Two experimental programs are designed to “manually” and “automatically”
produce the water film in multiple-layered soil profiles. The variation of the water film
under these two scenarios have been monitored with the new spiral sensor. Based on these
contents, some interesting findings and conclusions can be summarized as follows:
1)
Previous studies on water film due to void redistribution indicate that most
experimental works are implemented with shaking table and centrifuge model facilities,
and it is primarily measured indirectly with the pore water pressure transducers installed at
different depths of the model. On the other hand, the current computation techniques still
compromise the capability to fully reproduce this phenomenon, even though some
FEM/FDM-based model, such as PM4Sand proposed by Boulanger and Ziotopoulou
(2012), show potentials to capture the variation of porosity.
2)
The static experimental results suggest that the new spiral TDR sensor
possesses the capability to detect and measure thin water film within multiple-layered soil
profiles. The resolution of the new sensor can be up to 1 mm.
3)
The water film is reproduced beneath the low permeable soil layer in the
shaking column tests. The process for the onset and development of water film can be
clearly observed in the test.
4)
The algorithm for estimating water film thickness during the course of
shaking is developed, which is based on the mixing model for dielectric constant. The new
144
spiral TDR sensor is utilized to measure the development of the water film in the shaking
test. The development of water film can be clearly discerned from the output signals of the
new spiral TDR sensor. The thickness of the water film is calculated with the developed
algorithm, which shows that the new spiral TDR sensor might be an effective means for
the measurement of water film in layered soil.
145
CHAPTER 6 CONCLUSIONS AND FUTURE WORKS
6.1
Summary and Conclusions
TDR is a useful technique to detect and measure various types of discontinuities. It
has been proved to be effective and efficient for sensing interface such as air-water or soilwater, which can be utilized for large number of geotechnical applications, for example,
monitoring water level of reservoir and bridge scouring process, etc. The traditional
straight TDR probe gains its popularity due to its features of being cost-effective, easy to
install and stable in its sensing function.
However, owing to the limited resolution of the straight TDR probe, it will lose
capability and effectiveness to measure thin interfaces underlying many important
geotechnical processes, for instance, 1) the bridge scour process, where thickness of
erosion can occur within the range of millimeters, particularly under laboratory scaled
experimental conditions; 2) the water film thickness measurement due to void
redistribution in multi-soil profile. Especially for the second scenario, there isn’t an
effective approach currently available to quantify the thickness variation of water film, or
in other words, the extent of void redistribution, in the stratified soil profile. Quantifying
the water film formation, however, is essential to fully understand the mechanism of
liquefaction in layered soil conditions.
The design of the TDR probe into spiral shape might be a potential solution to detect
and measure the thin interfaces described above. In this dissertation study, the design and
development of the new spiral TDR sensor is elucidated in details. Its performance is
146
evaluated and validated via a series of experiments in the laboratory, including the
application for bridge scour and water film measurement, two scenarios where thin
interface has important engineering implications. Based on the organization of the
dissertation, it can be divided into the following three components.
6.1.1
Design and Evaluation of the New Spiral TDR Sensor with High Spatial
Resolution
The concept of the innovative spiral-shape TDR sensor is proposed, which features
much higher resolution and sensitivity in interface detection than the traditional straight
probe, i.e., with a spiral propagation path for EM wave, the effective travelling distance
per unit length along the direction of the sensor probe is significantly increased.
According to the theory of Knight et al. (1997) and Ferré et al. (1998), FEM analysis
are implemented to assist the optimization design of the new TDR sensor. The effective
sampling area is employed as an important indicator to assess the performance of design
with different geometric configurations (e.g., wire diameter and spacing). The simulation
results reveal that the effective sampling area increases proportionally with the augment of
wire diameter and spacing distance. A pilot spiral sensor is designed and fabricated with a
wire diameter of 0.5 mm and spacing distance of 2 mm. Its performance is then evaluated
with the conventional straight 2-rod probe via a series of laboratory experiments.
The experimental results indicate that this new sensor achieves significant higher
spatial resolution for interface detection than the conventional TDR sensor. The spatial
resolution the new sensor to detect water layer for can be at least 8 times higher than that
of the conventional 2-rod straight probe, while it is about 3 times more sensitive than the
147
conventional 2-rod straight probe to detect water layer. In addition, the application of
superhydrophobic coating is effective to prevent the influence of entrapped water between
two adjacent wires. This is especially useful for the application of measuring water film in
layered soil profile.
6.2.2
Assessment of the New Sensor for Bridge Scour
The algorithm for estimating bridge scouring process is developed with the
dielectric constant mixing model, which is only correlated to the scouring thickness and
the dielectric permittivity of the soil-water mixture.
Per the requirement for scouring testing, a new spiral TDR sensor is fabricated by
following the instruction described in section 6.2.1. It is then calibrated with some common
standard liquid, solvent with known dielectric constant and soils with different moisture
contents to eliminate the impact of center rod and coatings. This results in an empirical
equation to correlated measured and real dielectric properties of the materials.
A group of simulated bridge scour experiments are performed in the laboratory
using the calibrated spiral TDR sensor. The measured waveform at different scouring levels
from the new spiral sensor showed a clear systematic and reasonable pattern of change.
The square root of measured dielectric constant by the spiral TDR changes linearly with
the measured sediment layer thickness. This is consistent with the theoretical predications,
which again indicates the feasibility and correctness of the monitoring scouring process via
the new spiral sensor.
148
In addition, the estimation results from the spiral TDR sensor agree very well with
the thickness of sediment layer by direct ruler measurement. It could easily detect the
sediment thickness change of less than 2cm, which still has potential capability to sense
much thinner thickness of sediment layer. Compared with the 2-rod straight probe, this
new spiral sensor is around 4 times more sensitive in detecting the scouring thickness,
which can be further improved by refining the spiral design.
6.2.3
Determination of Water Film Thickness in Multi-Layered Soil Profile with the
New Sensor
The state-of-art on the water film formation due to void redistribution in layered
ground has been reviewed in this section, mainly incorporating different experimental and
computational studies. 1-g shaking table test and centrifuge model test are the primary
means to investigate this issue. The water film thickness is typically measured with a ruler
attached on the outside surface of the testing container, whereas this phenomenon has not
directly measured in the centrifuge model tests. Besides, the current numerical techniques
still does not possess capability to reproduce or capture the accumulation and elapse of
water film.
A spiral TDR sensor is fabricated to measure the thickness of water film in static
and dynamic scenarios. The design with much finer wire spacing than that in previous
chapters implies its higher resolution and sensitivity to detect thin water film. Static and
dynamic shaking table test are performed in the laboratory, in which the evolvement of the
water film has been monitored with the designed spiral TDR sensor.
In the static experimental program, a testing unit is designed to manually control
the thickness of the water film between two saturated sand layers. The measuring results
149
with the new spiral TDR sensor suggest its capability to detect and measure water film as
thin as 1 mm within multiple-layered soil profile.
In the dynamic shaking table test, the water film is reproduced and observed
beneath the low permeable clay layer, including the process of onset, development and
elapse. A solid algorithm based on the mixing model for dielectric constant is derived for
the estimation of water film thickness. According to the information from output
waveforms of the new sensor, the water film thickness can be computed using the
developed algorithm. The measuring results from the new sensor agree well with the
measurements from the standard ruler, despite some differences and errors still exist
between the two means, which implies that the new spiral TDR sensor might be an effective
approach for the measurement of water film in layered soil.
6.2
Recommendations for Future Work
Although significant amount of efforts have been made to conduct this innovative
dissertation work, there still remain plenty of areas which is worthwhile for the further
investigation. Recommendations for the future work in this research should include but is
not limited to:
1)
In this dissertation study, the performance of the new spiral TDR sensor is
only evaluated for the bridge scouring monitoring capability under the laboratory
conditions. The results show that it has very good performance, much more sensitive than
the traditional straight probes. No direct field demonstration is pursued during this work.
It is recommended to evaluate the feasibility of field deployment of this new TDR sensor
for bridge scour in the future research plan.
150
2)
There is no sensor currently available to capture and measure the formation
of thin water film in seismic centrifuge model testing. The void redistribution and
associated water film is typically inferred or estimated from the results of the pore water
pressure transducers located at different depth of the model. This new spiral sensor
provides a way to overcome the limitation of existing measurement methods. Its
performance can be further validated by the installation in centrifuge models. It is also
realized that there are additional technical issues that need to be addressed to fully utilize
the capability of this new sensor, for example, signal interpretation. These requires further
refinement and development in the future study.
3)
Exploring other potential applications of this new spiral TDR sensor in the
geotechnical community. For example, this sensor can be potentially applied to monitor or
detect the cracks in the concrete beam for infrastructures health monitoring. TDR
waveguide can be wrapped on the rebar of the concrete (e.g., concrete beam) to work as a
spiral TDR sensor. It will respond when the cracks, even very fine cracks, are generated
because of the much smaller dielectric property of air than concrete materials. The high
resolution of spiral TDR sensor will provide high sensitivity in crack detection.
151
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