evaluation of diatomaceous earth content in …
TRANSCRIPT
EVALUATION OF DIATOMACEOUS EARTH CONTENT
IN NATURAL SOILS
FOR POTENTIAL ENGINEERING APPLICATIONS
by
Jeongki Lee
A thesis submitted in partial fulfillment of
The requirements for the degree of
Master of Engineering
(Civil and Environmental Engineering)
at the
UNIVERSITY OF WISCONSIN−MADISON
2014
The thesis is approved by the following members of the Final Oral Committee:
Dante Fratta, Associate Professor, Geological Engineering
James M. Tinjum, Assistant Professor, Engineering Professional Development
William J. Likos, Associate Professor, Geological Engineering
Juan Vivanco, Research Associate, Mechanical Engineering
© Copyright by Jeongki Lee 2014
All Rights Reserved
i
CONTENTS
CONTENTS…………………………………………………………………………….... i
LIST OF FIGURES……………………………………………………………………… ii
LIST OF TABLES……………………………………………………………………….. vi
ABSTRACTIVE…………………………………………………………………………. vii
1. INTRODUCTION………..…………………………………………………………… 1
2. MATERIAL DESCRIPTION…………………………………………………………. 5
3. MATERIAL PROPERTIES WITH ELECTROMAGNETIC WAVES……………… 8
4. IMPEDANCE ANALYZER SURVEY…………………………………………….. 12
5. EXPERIMENTAL STUDY………………………………………………………… 16
6. RESULTS AND DISCUSSION……………………………………………………. 21
7. CONCLUSION……………………………………………………………………... 34
8. REFERENCES……………………………………………………………………… 36
APPENDIX A. FIGURES…………………………………………………………….. A1
APPENDIX B. TABLES……………………………………………………………… A55
ii
LIST OF FIGURES
Figure 1.1. Scanning Electron Micrographs (SEM) of (a) diatom (20 μm), (b) silica
flour (20 μm), and (c) kaolinite (1 μm) samples. (d) Image of the three
samples previous to testing…………………..………………………….
A1
Figure 2.1. Grain size distribution of the three tested soils. The tests were run using
the ASTM 152 H type hydrometer……………………...……………….
A2
Figure 2.2. Liquid limit and plastic limit different sample compositions……...…….
A3
Figure 3.1. Schematic response of soil and electrolyte mixture under an electrical
field……………………………..…………………………………….....
A4
Figure 3.2. Electrical resistivity of saturated soils and rocks (surface conduction
Θ = 1.4 × 10-9 S – Attia et al. 2008)……………………………………...
A5
Figure 3.3. Polarization mechanism. (a) Electronic Polarization, (b) Ionic
Polarization, and (c) Molecular Polarization (the direction of electric
field is from left to right) (Fam, 1995)………………………...…………
A6
Figure 3.4. (a) Real and imaginary permittivity with frequency and (b) Cole-Cole
plot from Debye (1929)……………………...…………………………..
A7
Figure 3.5. Temperature effects on deionized water saturated silica flour in
consolidation testing at 600 kPa………………………..……………….
A8
Figure 3.6. Affected Relative real permittivity according to the diatomaceous earth
concentration with deionized water……………………..………………
A9
Figure 4.1. The impedance Z consists of a real part R and an imaginary part X. The
θ is phase angle of impedance (After Agilent Technologies, 2009)……...
A10
Figure 4.2. The schema of open and short calibration (after Agilent, 2009)…………
A11
Figure 4.3. The impedance vs. frequency of oedometric cell with low impedance
shorting-bar after calibration at different zero set frequency, 100 kHz, 1
MHz, and 10 MHz……………………...………………………………..
A12
Figure 4.4. Capacitors. (a) Parallel-plate. (b) Electric field inside a capacitor. (After
Santamarina et al., 2001)…………………..……………………………
A13
Figure 4.5. Leaking the current because of fringing effect………………..………... A14
iii
Figure 4.6. Electrode polarization effect of saturated silica flour at 50 kPa in
compression testing……………………………………………..………
A15
Figure 5.1. The apparatus to measure electrical properties (d = 6.28 cm, h = 0.4 cm).
A16
Figure 5.2. The consolidation apparatus made by PVC plastic (up-left), the
consolidation testing picture (up-right), and the cross section of
apparatus (bottom)……………………..………………………………..
A17
Figure 6.1. Comparison between idealized permittivity data (line) and measured
data by HP 4192A (dot)……………………………..…………………..
A18
Figure 6.2. Define the fringing effect of electrodes with different thickness of
specimen (0.4 cm and 7 cm)………………………………………..…...
A19
Figure 6.3. Relative real and imaginary permittivity of deionized water and air
tested different frequency calibration from 5 Hz to 10 MHz…………….
A20
Figure 6.4. Conductivity of deionized water and air tested different frequency
calibration from 5 Hz to 10 MHz…………………………..……………
A21
Figure 6.5. Permittivity of pure samples mixed with air in different porosity (100
kHz)…………………......………………………………………………
A22
Figure 6.6. Permittivity of pure samples mixed with air in different frequency (a)
diatomaceous earth (n = 0.73), (b) silica flour (= 0.56), and (c) kaolinite
(n = 0.57)……………...…………………………………………………
A23
Figure 6.7. Conductivity of pure samples mixed with air in different frequency (a)
and with different porosity (b) (100 kHz)………………………………..
A24
Figure 6.8. Relative real permittivity of diatomaceous earth with changing
volumetric water content………………………………...………………
A25
Figure 6.9. Relative real permittivity of kaolinite with changing volumetric water
content…………………………….…………………………………….
A26
Figure 6.10. Relative real permittivity of silica flour with changing volumetric water
content…………………………….…………………………………….
A27
Figure 6.11. Relative imaginary permittivity of diatomaceous earth with changing
volumetric water content…………………………………...……………
A28
Figure 6.12. Relative imaginary permittivity of kaolinite with changing volumetric
water content………………………………..…………………………...
A29
iv
Figure 6.13. Relative imaginary permittivity of silica flour with changing volumetric
water content……………………………..……………………………...
A30
Figure 6.14. Conductivity of diatomaceous earth with changing volumetric water
content………………………….……………………………………….
A31
Figure 6.15. Conductivity of kaolinite with changing volumetric water content……...
A32
Figure 6.16. Conductivity of silica flour with changing volumetric water content……
A33
Figure 6.17. Increasing relative real permittivity with increasing volumetric water
content and determining soil characteristic factor β for (a) diatomaceous
earth and (b) kaolinite……………………………..…………………….
A34
Figure 6.18. Increasing relative real permittivity with increasing volumetric water
content and determining soil characteristic factor β for silica flour……...
A35
Figure 6.19. Changing relative imaginary permittivity with increasing volumetric
water content for (a) diatomaceous earth and (b) kaolinite………………
A36
Figure 6.20. Changing relative imaginary permittivity with increasing volumetric
water content for silica flour………………………………..…………...
A37
Figure 6.21. Changing conductivity with increasing volumetric water content for (a)
diatomaceous earth and (b) kaolinite…………………………...………..
A38
Figure 6.22. Changing conductivity with increasing volumetric water content for
silica flour……………………………..………………………………...
A39
Figure 6.23. Figuring out the saturated volumetric water content by using
conductivity of three samples……………………………...…………….
A40
Figure 6.24. Relative real permittivity of diatomaceous earth with changing vertical
compression load. The void ratio is posted in Table 6.4…………………
A41
Figure 6.25. Relative real and imaginary permittivity of diatomaceous and silica flour
saturated mixtures at 600 kPa…………………………………...……….
A42
Figure 6.26. Relative real and imaginary permittivity of diatomaceous and kaolinite
saturated mixtures at 600 kPa…………………………………...……….
A43
Figure 6.27. Relative real and imaginary permittivity of diatomaceous, kaolinite,
silica flour, and even mixed three samples at saturated condition with
600 kPa……………………………………..…………………………...
A44
v
Figure 6.28. Relative real and imaginary permittivity of diatomaceous, kaolinite,
silica flour, and even mixed three samples at saturated condition with
600 kPa…………………………………..……………………………...
A45
Figure 6.29. Relative real permittivity of diatomaceous slurry, mixed with deionized
water or 1 M NaCl solution while changing vertical load………………..
A46
Figure 6.30. Relative real permittivity of kaolinite slurry, mixed with deionized water
or 1 M NaCl solution while changing vertical load…………………...…
A47
Figure 6.31. Relative real permittivity of silica flour, mixed with deionized water or
1 M NaCl solution while changing vertical load………………………...
A48
Figure 6.32. Relative imaginary permittivity of saturated (a) diatomaceous earth and
(b) silica mixed with deionized water or 1 M NaCl solution while
changing vertical load…………………………………………..……….
A49
Figure 6.33. Relative imaginary permittivity of kaolinite slurry, mixed with
deionized water or 1 M NaCl solution while changing vertical
load……………………………………………………………………...
A50
Figure 6.34. 1 M NaCl solution saturated specimens’ responses volumetric water
content at 600 kPa………………………..……………………………...
A51
Figure 6.35. Relative real permittivity of diatom, silica flour, and kaolinite mixtures
with deionized water or 1 M NaCl solution with similar volumetric water
content. The volumetric water content or void ration is shown in table
6.6 and 6.7…………………………………………………………..
A52
Figure 6.36. Relative imaginary permittivity of diatom, silica flour, and kaolinite
mixtures with deionized water or 1 M NaCl solution with similar
volumetric water content. The volumetric water content or void ration is
shown in table 6.6 and 6.7……………………...………………………..
A53
Figure 6.37. Conductivity of diatom, silica flour, and kaolinite mixtures with
deionized water or 1 M NaCl solution with similar volumetric water
content. The volumetric water content or void ration is shown in table
6.6 and 6.7………………………………………..……………………...
A54
vi
LIST OF TABLES
Table 2.1. Basic properties of tested samples………………………………………..
A55
Table 2.2. Specimen Compositions for the Experimental Study…………………….
A56
Table 3.1. Maxwell’s equations……………………………………………………...
A57
Table 3.2. Typical electromagnetic properties of different materials……...………...
A58
Table 6.1. Relative real and imaginary permittivity and conductivity of deionized
water at different frequencies…………………………………………….
A59
Table 6.2. Relative real and imaginary permittivity and conductivity of air at
different frequency and different calibrated frequencies…………………
A60
Table 6.3. Relative real permittivity and characteristic factor of each soil………….
A61
Table 6.4. Volumetric water content with increasing loads for each tested
specimens………………………………………………………………....
A62
Table 6.5. Void ratio with increasing loads for each of the tested specimens……….
A63
Table 6.6. Relative real and imaginary permittivity and conductivity of diatom,
silica flour, and kaolinite specimens with deionized water………………
A64
Table 6.7. Relative real and imaginary permittivity and conductivity of diatom,
silica flour, and kaolinite specimen with 1 M NaCl solution…………….
A65
vii
ABSTRACT
Diatomaceous earth is formed by the deposition of biological matter and as such has a number of
unique engineering properties. Unique diatomaceous earth’s characteristics include high specific
surface area, low dry density, high water storage ability, high friction angle, high compressibility,
and unstable response under dynamic loads. These properties came from its biological origin and
structure. Due to these peculiar characteristics, diatomaceous earth could be detrimental in some
engineering application while it could find application in in the cover of landfills, hydraulic
barriers, ionic barriers, low-weight fills, and etc. However to assess potential beneficial properties,
engineers and researchers much first completely characterize the material. This characterization
must include an estimation of the percentage of diatomaceous earth in the soil and how the
diatomite content controls the physical behavior of soils. In this study, the pure diatomaceous earth
mixed with kaolinite and silica flour in several proportion was used to assess how parameters such
as Atterberg limits, compression tests, and electrical properties change with diatomaceous earth
content and how these changes may affect the sue use on diatomic soils in engineering applications.
Experimental results show that diatomaceous earth have high liquid and plastic limits. The higher
fraction volume of diatomaceous earth allows higher water storage and that is represented on the
results of liquid limit and electrical property test results. The permittivity of diatomaceous earth,
kaolinite, and silica flour are governed by the availability of volume of free water in the soil
specimens. The higher volumetric water content determines the higher real and imaginary
permittivity. In compression tests, as pore fluid drains out with void ratio and volumetric fluid
viii
content decrease, the measured permittivity decreased as well. Unbroken microfossil diatom
particles with compression load allow higher permittivity than kaolinite and silica flour..
Overall, it is shown that the fraction of diatomaceous earth influenced to the physical, mechanical,
and electrical properties of soil mixtures. Diatomaceous earth shows different characteristic with
silica flour even has same chemical formula and also distinct behavior with clay. It can be told that
diatoms should be different classified material with silt and clay. The application of this unique
diatomaceous earth should show potential benefit in engineering sight.
A1
1. INTRODUCTION
As any porous media, soils consist of solid, gas and liquid phases. The proportions and
characteristics of solid and fluid phases are important parameters that control permeability,
compressibility, and strength of soils. However, the properties of the solid particles themselves are
very important in the overall behavior of porous media. Mineralogy, particle shape, particle size
distribution, and specific surface determine if the behavior of the soil mass is dominated by
mechanical, capillary or electrical forces and how the material will respond to hydrostatic or shear
stresses (Fam & Santamarina, 1995; Mitchell & Soga, 2005)
In this study, Atterberg limits, compression tests, and electromagnetic wave measurements are
used to assess the physical, mechanical and electromagnetic properties of diatomaceous soils with
the intent of determining the microfossil diatoms concentration and of characterizing the behavior
and relationships of how diatomaceous earth control the overall mechanical response of soils.
Diatoms and Diatomaceous Earth. Diatomaceous earth was discovered by Kasten (1836). The
natural diatomaceous earth consists more than 80% of amorphous silica with about 2% of alumina
and iron oxide (Antonides, 1997). The diatomaceous earth is easily fragile to white power
condition and has low density with high porosity likes diatoms. It is fossilized remains of rigid
part of diatom such as deposition of exoskeleton or unicellular algae or plankton (Hong et al.,
2006). These organisms are abundant in the oceans (Chester & Elderfield, 1968) and bodies of
fresh water (Conley, 1988) where the water is rich in dissolved silica that the unicellular algae and
plankton use build up their skeletons (Treguer et al., 1995; Antonides , 1997). Once the unicellular
2
algae or plankton die, the inorganic and organic compound of the dead biogenic silica settled on
the bottom of the water and deposit to form sediments, soils, and rocks (Conley, 1988).
Most diatomaceous earth and soils have fine grains formed by milky white siliceous powder
(Stokes & Varnes 1955; Terzaghi & Peck, 1967). The nanostructure structures of diatom look like
lattice with long donut shape as shown in Figure 1.1 (Noll et al., 2002). Diatom particles have
intra-aggregate and intra-skeletal structure yielding dual porosity (Burger & Shackelford 2001).
These particles are also fragile and may break during compression. As they break, they deform
yielding high compressibility (Day, 1995; Hong et al., 2006). This dual porosity also creates larger
void space than the void space in soils with the same number of particles. Due to this characteristic,
diatom particles can trap large amount of water (ω = 30-80%). In spite of this large amount to
water in the pore space, diatomaceous soils tend to form a stable structure that does not shrink
during drying (Palomino et al., 2011). Larger fractions of natural diatomite soils yield high liquid
limit, plasticity index, and void ratio (Tanaka & Tanaka, 2003; Diaz-Rodriguez, 1992).
Furthermore, the dual porosity creates a structure that has very low dry density and high specific
surface area (SS = 100 m2/g) (Collins & McGowan 1974; Tanaka & Locat 1999). In spite of the
large specific surface area, microfossil silica has low surface charge density compared with clays
and they are insensitive to chemical changes in the pore water. Finally, the hydraulic permeability
significantly increases with increasing diatom content due to the hollow skeleton of the diatoms
(Shiwakoti 2002).
An arrangement of microfossil diatom particles (i.e., biogenic silica - BSi) has high friction angles
because of their rough outer surface such as protrusions and indentations (Day et al., 1995 - Figure
3
1.1). It is common to finds soils with diatoms with high friction angle as high as 45⁰ (Diaz-
Rodriguez et al., 1992). The addition of diatom to soils tends to decreasing unconfined
compressive strength and increase shear strength (Tanak & Tanaka, 2003). However, the fragile
diatoms particles tend to break and lose shear strength and friction angle decreased when the
effective stress is higher than the yield stress of the diatom particles (Locat & Tanaka, 2001).
Particle breakage has other important consequences. Day (1995) and Hong et al. (2006) observed
that the diatomaceous fill compressed less than 1% with vertical stress 50 kPa, but the
compressibility dramatically increased caused by crushed microfossil diatom hollow structure with
vertical stress of 1600 kPa. These observations show that the presence of diatomaceous earth in
natural soils can play major role on improving and degrading engineering properties (Tanaka &
Tanaka, 2003). However, the critical concentration of diatoms is not well understood how to
address how to classify these soils is still not well defined (Locat & Tanaka, 2001).
For this characteristics, diatoms and diatomaceous earth are used in many applications including
as abrasive (Rood 2005), natural insecticide (Fields et al., 2002), insulation (Flynn 2005), DNA
filtration (Goren et al., 2002), etc. In geotechnical engineering, the diatoms have a higher potential
application in hydraulic and ionic barrier because of its high water content and their insensitivity
to changes in pore fluid chemistry. These properties make diatoms a premising material to be used
in landfill covers are they may not crack under dry conditions or during seepage of leachate
(Palomino et al., 2011).
4
However, the issue of characterizing diatomaceous soil and assessing the concentration of diatom
in soil is still elusive. Several methods have proposed to determine the fraction of bio-mineralized
silica in natural soils. These methods include techniques such as micro fossil counts (Pokras, 1968),
infrared absorption (Chester & Elderfield, 1968) X-ray diffraction (Calvert, 1966; Ellis & Moore,
1973; Eisma & Van Der Gaast, 1971), and alkali digestion (DeMaster, 1991; Krausse et al., 1983;
Ragueneau, 1994; Eggimann et al., 1980). All of them have are based on assumptions that either
have limited application or are too complex for characterization of diatomaceous soils for
engineering applications.
5
2. MATERIALS DESCRIPTION
For this experimental program three different type of soils were used either pure or by mixing
different proportions. The soils used were diatomaceous earth, silica flour, and kaolinite. These
soils were selected in this study include a material with dual porosity, small particle size, high
liquid limit, and silica based (diatomaceous earth), a material with single porosity, small particle
size, low liquid limit, and silica based (silica flour), and a material with small particle size, high
liquid limit, and non-silica based (kaolinite) (Table 2.1, Figure 2.1). These combinations of
materials provided a good spectrum of differential parameters to study the response of soils under
different percentage of diatom content.
The tested diatomaceous earth was obtained from fossilized deposits of microscopic shells created
by plankton or algae in fresh water.. The diatomaceous earth is sold commercially as “Fossil Shell
Flour” by PERMA-GUARD Company. The particles of microfossil diatom are amorphous silica
which does not have specific shape. Before testing, the diatomaceous earth was washed with
deionized water to remove ionic compounds and impurities.
The silica flour was purchased from the Glass Rock Operation in Glenford, OH and the untreated
kaolinite was purchased from the Old Hickory Clay Company in Hickory, KY. These samples
were also rinsed by deionized water to remove ionic compounds and impurities. The washed
samples were moved to evaporation dishes and placed in the oven for 24 hours to remove water
content. The dry samples were pulverized using the mortar with pestle and stored in sealed bags
to reduce the absorption of water.
6
Atterberg Limits Tests. The Atterberg limits are used to assess the water content in soil that
corresponds to specific shear strength (Michel & Soga, 2005). In the liquid limit test, the fall cone
(Humboldt, B056-10) method was used to determine the liquid limit in the soil tested in this study.
Wroth and Wood (1978) suggested the liquid limit from the Casagrande test corresponding with
1.7 kPa of undrained shear strength and the plastic limit is similar with 170 kPa. The fall cone
measures the penetration depth in to a soil specimen caused by a cone with a mass of 80 g (Houlsby,
1982). The shear strength of fall cone test determined by:
Tf = 0.85W
d2 (2. 1)
where Tf is the shear strength, W (=0.785 N for the 80 g mass of the cone cone) is weight of the
cone, and d is the depth of penetration. This test seems like much obvious test than the Casagrande
falling cap because the fall cone test includes less empirical judgment in part of the operator (Wroth
& Wood, 1978).
The particles in diatomaceous earth have various cylinder shapes with uneven outer surfaces as
shown in the Scanning Electron Micrographs (SEM) images (Figure 1.1-(a)). The dual porosity
observed in the SEM of the diatom particles correspond to the porosity both between particles and
intra-particles. Due this type of dual porosity, diatoms can absorb large amount of water and yield
a liquid limit LL = 133 and have a large specific surface Ss = 103 m2/g. These values are larger
than those find in silica flour and kaolinite (Table 2.1 - Shiwakoti et al., 2002; Tanaka and Locat,
7
1999). The specific gravity Gs = 2.02 of diatomaceous earth is smaller than that of silica flour
even same chemical formula because of polymorphism in diatoms.
In grain size distribution (using the ASTM H152 type hydrometer), the mean particle d50 of the
diatomaceous earth d50 = 3.7 μm, the silica flour is 13 μm, and the kaolinite d50 = 2.4 μm (Table
2.1, Figure 2.1). The silica flour shows sharp angular and bigger grains size without internal void
area (Figure 1.1-(b)). The particle structure of kaolinite looks like overlapped continuous plate
sheets which have thin thickness comparing with the width of it (Figure 1.1-(c)).
For the testing program, the diatomaceous earth, silica flour, and kaolinite samples were mixed in
specific proportions as shown in Table 2.2. For these specimens, the liquid and plastic limits
increase with increasing diatomaceous earth concentration (Figure 2.2). The increased in liquid
limit increasing diatomaceous earth concentration is due to the intra-skeletal porosity of diatom
which has great ability to store the water (Shiwakoti et al., 2002; Tanaka and Locat, 1999).
8
3. MATERIAL PROPERTIES WITH ELECTROMAGNETIC WAVES
The properties of fine grain soils, as a particulate media, are governed by the micro inter-particle
forces rather than macro mechanical forces (Fam, 1995) and by the interaction between different
phases (e.g., percolation – Attia et al. 2008). Columbian electrical forces can be excited by
electromagnetic wave propagation tests to assess properties such as dielectric permittivity and
electrical conductivity. The electromagnetic phenomenon has been studied since 19th century and
is defined by Maxwell’s equations (Table 3. 1).
3.1 Electrical Conductivity
The electrical conductivity σ (S/m) is an ability to move electric charges in the presence of an
electric field:
J = σE (3. 1)
where J is the current density (A/m2) and E is the electric field (V/m). The electrical conductivity
property allows dividing two types of materials into conductor and dielectric materials. The
conductor likes metal has free electrons that can move freely inside of metal to conduct electrical
current. The amount and speeds of these free electrons control the electrical conductivity in metals.
The electrical conductivity of soils is controlled by the movement of hydrated ions. The overall
electrical conductivity depends on electrolyte content, salt concentration, porosity, degree of
saturation, tortuosity and surface of particle and double layer conductivity (Figure 3.1)
9
(Santamarina et al., 2001). The electrical resistivity ρ (= 1/σ) for porous media with coarse grained
soils may be estimated as (Attia et al., 2008)
ρf
=ρ
pore liquid
∅ ∙ Sr + (1 − ∅) ∙ Θ ∙γ
ming Ss ∙ ρ
pore gas
(3. 2)
where ρpore liquid
and ρpore gas
is the electrical resistivity of pore fluid and gas, ∅ is the porosity of
specimen, Sr is the degree of saturation, Θ is the surface conduction, γmin
is the mineral unit
weight, and Ss is the specific surface area of specimen. Figure 3.2 shows how the electrical
resistivity of rocks in saturated condition with different pore fluid, porosity, and specific surface
area. Typical conductivity values for geotechnical engineering materials are presented in table 3.2.
3.2 Dielectric Permittivity
The dielectric permittivity is the ability of a material to store charges under the presence of an
electric field:
D = εE (3. 3)
where D is the electric displacement vector (C/m2) and ε is the dielectric permittivity (F/m). The
electrical displacement vector D changes with the dielectric permittivity of the material specimen
under a constant electric field.
10
The dielectric permittivity in soils is affected by the characteristic of the soil particles (ionic
concentration and valence), volumetric water content, and the properties of the water. Typical
permittivity values are presented in table 3.2. Dielectric permittivity in materials occurs in three
mechanisms such as electronic polarization, ionic polarization, and molecular polarization (figure
3.3). In electronic polarization case, the center of positive nucleus and the negative electron cloud
physically deform after applied alternative electrical field. The ionic polarization in non-polar
molecules is caused when anions and cations are displaced relative to each other and induce a
dipole moment. The polar molecular polarization polarizes by rotating its dipoles direction
according to the oriented electrical field. These three kinds of polarization allow storing the charge
while alternating electrical field (Santamarina et al., 2001). The homogenous material permittivity
from polarization effect can be estimated by Debye’s equation (1929) as:
k∗ = k∞
′+
k0
′− k
∞
′
1 + jωτ (3. 4)
where k∗ is the complex permittivity, k0
′ is the relative real permittivity below than the relaxation
frequency, k∞
′ is the optical relative real permittivity, and ω (= 2πf) is the angular frequency, and
τ (= 1/ ωrel, ωrel is the relaxation frequency) is the relaxation time. This typical equation shows
single relaxation time (Figure 3.4-(a)) and appropriates for homogenous materials. The figure 3.4-
(b) shows the Cole-Cole diagram (Cole & Cole, 1941), the each X- and Y-axis represent the
relative real and imaginary permittivity. The parameters that affect the dielectric permittivity are
11
temperature (Scaife, 197; von Hippel, 1988) (Figure 3.5), pressure (Owen et al., 1961), and
concentration (Smyth, 1955; Hasted, 1973; Pottel, 1973) (Figure 3.6).
12
4. IMPEDANCE ANALYZER SURVEY
To measure the electrical properties of soil, the 4192A Low Frequency (LF) Impedance Analyzer
made by Hewlett Packard Company was used. As a high performance test instrument, the HP
4192A can measure from 5 Hz to 13 MHz with 1 mHz frequency resolution. The applied direct
current is 35 V with 10 mV increments. The phase range of this device is from - 180⁰ to 180⁰ and
the accuracy is ranging from 0.1⁰ to 0.2⁰. The measuring range of impedance is from 0.0001 Ω to
1.2999 MΩ with 100 µΩ resolution. (HP 4192A manual, 1986)
The HP 4192A impedance analyzer measures the impedance with alternating current at given
frequency. Measured data is important parameter used to frequency spectrum of electrical
properties of materials such as complex impedance |Z|, complex admittance |Y|, phase angle θ,
resistance R, reactance X, conductance G, and susceptance B. The screen of device shows complex
impedance and phase angle (Figure 4.1).
The imaginary part of the electrical impedance has two components. First, the inductance XL is
representative the ability of energy store in magnetic fields. Second, the capacitance XC measures
the difference potential energy between two electrodes applied equivalent current in electric field.
In this program, only the capacitance component is considered because the testing soils assumed
as non-ferromagnetic materials
Instrument Calibration. A zero offset calibration is required before testing to remove stray
impedance inherent in the device. Without this calibration, the measured impedance Zm represents
13
not only the impedance of tested material Zdut but it also incorporate the strain impedance ZS and
stray admittance Y0 caused by the instrument (Figure 4.2).
The instrument calibration is carried out with an empty oedometer cell that is used in the
experimental program. The low impedance shorting-bar assumes 0 Ω load is located between the
two electrodes. Then a series-circuit measurement is collected. Then, the bar is removed and the
measurement circuit is changed from series to parallel and a zero offset is conducted to remove
the residual current. The calibrated frequencies were performed at 100 kHz or 1 MHz. The 100
kHz calibration shows reasonable corrections for impedance measurements from 100 kHz to 1
MHz which has the largest valuable frequency range. The rational frequency range of calibration
at 1 MHz is 1 MHz to 10 MHz (HP 4192A manual, 1986). However, this higher frequency
accuracy has advantage for the testing with high conductivity materials where electrode
polarization effects control the impedance results (Santamrina and Fratta 2002). Figure 4.3 shows
the complex impedance results according to the changing impedance after calibration at different
frequencies. The impedance measured in the oedometer cell with low impedance shorting-bar to
check the quality of the HP 4192A measurement. The lower calibrated frequency, 100 kHz has
less error than other two calibrations up to 200 kHz and the error increases exponentially after 100
kHz. Each calibrated frequencies have the lowest error at whole range of frequency. Then, the 100
kHz and 1 MHz data were used for the calibration of frequencies at 100 kHz and 1 MHz to
represent the electrical properties of the specimen.
Two-electrode configuration. The two-terminal electrode measurement method used to test the
electrical properties of material in the low frequency. High current HC and high potential HP were
14
connected using coaxial cables; and low current LC and low potential LP were also connected with
another set of coaxial cables (Figure 4.2-(a)). The connected high current and voltage channels
where connected to the top electrode and the low current and voltage channels were connected.
The electrodes used in this testing program were made of lead, metal foil, brass, and silver. All of
which have high electrical conductivity. While applying constant current i from the high to the low
channels, the electrical properties of specimen are measured by measuring the difference in
electrical potential energy between top and bottom electrodes. Then the impedance can be
concerted in to resistivity and capacitance because of the uniform electrical field distribution in
the specimen (Figure 4.4) (Santamarina et al., 2001).
Fringe effects corrections. The electric field in real test shows current leaks along the boundaries
that are called fringing effects (Figure 4.5). The fringing effect increases with increasing distance
between the two electrodes and decreases with increasing the diameter of the electrodes. The
correction methods from current leaking suggested in ASTM D150-11 that use guard ring to block
the fringing effect or use correction equation:
Ce = (A − B ∙ ln t) ∙ P (4. 1)
where Ce (= pF) is the capacitance of the fringing effect, t is the thickness of the specimen and the
P (= π (diameter + height)) is the modified perimeter. A is 0.0087 (pF/mm) and B is 0.00252
(pF/mm2). Then, the true capacitance of capacitor is determined by deducting the capacitance of
fringing effect from measured specimen capacitance.
15
Electrode Polarization. Other potential error in this test procedure is electrode polarization effect.
This is the main source of the error in the measurements using capacitance electrodes. The
generated charges are accumulated at the interface of electrodes and specimen and makes
increasing the impedance and permittivity. To block the electrode polarization effect, frequency
must be increase(Figure 4.6). Oxidation-reduction (REDOX) and chemical reactions and the
condition of the contact between electrodes and specimen influence the measured data
(Santamarina et al, 2001)
16
5. EXPERIMENTAL STUDY
In an attempt to evaluate the potential of deferential testing methodologies to assess the presence
of microfossil diatoms in different soils, I developed an experimental program and tested
specimens prepared by mixing diatomaceous earth, silica flour, and kaolinite in the different
proportions. On those specimens, I measured the electrical properties and Atterberg limits on
specimens prepared with and without water content, with deionized water and salt solution and
under controlled void ratio conditions (i.e., tested in an oedometer cell).
5.1 Surveying the electrical behavior of the pure soils
The rinsed and dried specimens were placed in Plexiglas cylinder specimen holder (h = 0.4 cm, d
= 6.28 cm) (Figure 5.1). The mass of soil in the specimen was measured using an electronic scale
with 0.01 g resolution to calculate the porosity. The top electrode is connected to the current and
voltage channels and the bottom electrode is connect to the low current and voltage channels of
the impedance. To prevent noise in the measurements, the testing cell is placed as left far from
ferromagnetic materials as possible. The measured impedance and phase angle were used to
calculate the relative real permittivity as a function of the porosity of the material. The assumption
in the test is that the perfect dried pure material should not present electrode polarization effect
because the intensity of electromagnetic field is not enough to rearrange the molecular solid
particles direction. The electrical relative real permittivity can be defined by using the equation
5.1 (Sen et al., 1981):
km′ β
= (1 − n) ∙ kp′ β
+ n ∙ 𝑆𝑟 ∙ kw′ β
+ n ∙ (1 − 𝑆𝑟) ∙ ka′ β
(5.1)
17
where km′ , ka
′ , and kP′ are the relative real permittivity of mixture, air (= 1), and soil particles. β is
the characteristic mixing factor of each soil, n is the porosity, and 𝑆𝑟 is the saturation. The mixing
factor β is a function of the relative distribution of the different phases in the material.
5.2 Electrical properties of soils with different water content
The treated samples were mixed with deionized water with volumetric of water content ranging
from 0 to 100% in a sealed plastic bag. The mixtures were left to rest for 24 hours to allow for
proper hydration. After one day, the prepared specimens were placed in the measuring cell for
testing (Figure 5.1) and their masses of each specimen were measured. Then the impedance
spectrum was measured with the HP4192A impedance analyzer. After completing the testing, the
specimens were oven dried in to determine the water content, porosity, and degree of saturation.
The measured impedance values in the soil specimens represent the combination of the properties
of the three phases: air, water, and soil and how they interact with each other.
The impedance analyzer yield impedance amplitude |Z| and phase angle θ or the resistance R and
reactance X as defined in figure 4.1. From the real part of impedance, the resistivity is obtained,
R = ρL
A (5.2)
where ρ is the resistivity (Ω·m), L is the height of specimen (= 0.4 cm), and A is the cross section
area of specimen (m2). The conductivity σ (S/m or Ω-1·m) can obtain as the reciprocal of the
resistivity.
18
The relative real permittivity κ′ and the effective relative imaginary permittivity κeff′′ are
determined from equations (5.3) to (5.7) (Santamarina, 2001):
Y∗ =1
R+ jωC (5.3)
where C (= κ∗C0 = κ∗ε0A/d is the capacitance (F), where ε0 is the dielectric permittivity of free
space (8.85 × 10−12 F/m)), and ω is angular frequency (ω = 2πf, where f is the frequency). The
complex admittance Y* is:
Y∗ = ωε0
A
d[jκ′ + (κ′′ +
σ
ωε0)] (5.4)
where κ′′ is the relative imaginary permittivity. Then, the complex admittance is:
Y∗ = ωC0(jκ′ + κeff′′ ) (5.5)
where κeff′′ (= κ′′ + σ/ωε0) is the relative effective imaginary permittivity. Equation (5.5) shows
that the relative real and effective imaginary part of the permittivity can be calculated using the
following equations:
κ′ =Im(Ymeas
∗ )
ωε0 (5.6)
19
κeff′′ =
Re(Ymeas∗ )
ωε0 (5.7)
where Im(Ymeas∗ ) and Re(Ymeas
∗ ) are the imaginary and real components of the measured complex
admittance. In equations (5.6) and (5.7), the imaginary part of admittance determines the real part
of the relative permittivity and the real part of the admittance yields the imaginary part of relative
permittivity.
5.3 Measuring electrical properties during compression testing
The specimens were prepared by mixing certain proportions of diatomaceous earth, silica flour
and kaolinite (Table 2.2) after each component was washed with deionized water and then dried
in an oven. The prepared specimens mixed with deionized water or NaCl solution and vacuumed
to remove air bubble and saturate the specimens. The specimens under slurry condition were left
for 24 hours sealed to allow for hydration of the solid particles to occur. Then, the fully saturated
specimen were placed in an oedometer cell and the compression test began.
The PVC oedometric cell (h = 1.2 cm, d = 6.3 cm) was used to measure the electrical properties
while compression testing (Figure 5.2). The height of specimen (minimum 0.6 cm) was required
to measure the electrical properties of soils and a maximum height of 1 cm was maintained to
control fringing effect errors (Figure 4.5 - ASTM D 150).
The compression/consolidation test was carried out following the standard consolidation method
(ASTM D2435). However few modification was required. Two metal porous plates were used
20
instead of porous stones. These metal porous plates permitted the creation of double drainage
condition while they also acted as electrodes for impedance measurements.
The vertical displacements were obtained with a dial gauge with 0.0235 m resolution. The
displacement interval followed log of time scale. The tests were performed from 50 kPa to 600
kPa loads for each specimen. While the testing, the specimens maintained saturated condition by
maintaining a fluid bath. The collected data was then interpreted with Taylor’s square root of time
method to determine t90 (time of 90% of consolidation) and d90 (the displacement at 90%
consolidation) and assess the completion of consolidation.
The metal porous plates acting as electrodes had to remain parallel to each other and had to be in
physical contact with the specimen directly. The interpretation of the impedance data followed the
electrode (Santamarina et al, 2001) (Figure 5.2). The applied current and the potential difference
between the electrodes were measured in the impedance analyzer and saved into a computer though
the GPIB cable. The measured frequency swiped from 5 Hz to 10 MHz with log scale measurement
intervals. The impedance measurements were performed the data corresponding to the time at 90%
consolidation were used to analyze the electrical properties of the specimens.
21
6. RESULTS AND DISCUSSIONS
6.1 Evaluating the quality of the HP 4192A Impedance Analyzer Results
One of the biggest challenges in measuring impedances in soils at the low frequency range is
electrode polarization. Klein and Santamarina (1996) presented equations to determine the relative
real and imaginary permittivity of homogenous specimens, including the effect of electrode
polarization at the low frequency.
𝑘′ =(
σm
ε0 ∙ ω)
2
∙de
dm+ km
′
1 + (de
dm)
2
∙ (σm
ε0 ∙ ω)
2 (6.1)
𝑘′′ =
σm
ε0 ∙ ω
1 + (de
dm)
2
∙ (σm
ε0 ∙ ω)
2 (6.2)
where σm is the conductivity of the tested material, de and dm are the thickness of the electrode-
specimen gap and the height of the specimen, respectively. The gap de was assumed to be 10-9 m
for all materials, that dimension is the size of the water molecule (Klein & Santamarina, 1996).
The collected impedance data on specimens prepared with deionized water and NaCl aqueous
solutions along with the fitting equations 6.1 and 6.2 are presented in figure 6.1. In figure 6.1, the
idealized equation 6.1 and 6.2 are used to match the relative real and imaginary permittivity of the
measured data. The impedance measurement results for the specimens prepared with NaCl
aqueous show the effect of electrode polarization over the whole testing range. However, the
22
measured permittivities on the specimens with NaCl aqueous solutions tend to converge towards
the model as the frequency increases. Then, the testing results of impedance measurements using
the HP 4192A impedance analyzer seem to yield high quality capturing the proper electromagnetic
properties of soil specimens prepared with both deionized water and NaCl aqueous solutions.
The values of relative real permittivity calculated using the idealized equations show different
ranges of electrode polarization effect for different NaCl concentrations in the aqueous solution.
The higher concentration of NaCl in the solutions increases the conductivity and influences to the
electrodes polarization lasting frequency. However, different NaCl concentrations do not influence
the real relative permittivity results once the electrode polarization effect is remove at high
frequencies. This means that the relative real permittivity of material is directly influenced by the
conductivity of the specimen at low frequency.
The fringing effect caused by the relative separation to the diameter of electrodes can be observed
in figure 6.2. The real and imaginary parts of permittivity were calculated by equations 6.1 and 6.2
for a 0.04 M NaCl solution. The assumed thickness was 7 cm that is general used height to triaxial
test and the other one is 0.4 cm, prepared cell for this study (Figure 5.1). The thicker specimen, of
course, yields higher polarization electrodes effect at low frequency because of high fringing effect.
However, the relative real permittivity is not influenced by the specimen thickness. It seems like
that the results from the equations 6.1 and 6.2 would allow measuring the electromagnetic
properties of high conductivity specimen with thicker thicknesses.
23
Figures 6.3 and 6.4 show the relative real and imaginary permittivity, and conductivity of
deionized water for different frequencies (100 kHz, 1 MHz, and 5 MHz). The effect of electrode
polarization in the deionized water was detected in the relative real permittivity plots at the low
frequency. But at the high frequency range shows less electrode polarization influence. The
relative imaginary permittivity has higher loss factor at low calibration frequencies. The
conductivity measurements are also influenced by the electrode polarization at low frequencies.
However, the conductivity increases linearly in log scale after electrode polarization effects are
removed. The relative real and imaginary, and conductivity results for each frequency are shown
in table 6.1.
The electrical properties of air shown in figures 6.3 and 6.4 display no electrode polarization
effects; i.e., the relative real permittivity of air is frequency independent. The imaginary part yield
low values while the conductivity increases with increasing frequency. For the air test, the data do
not show in low frequency because the thickness of the specimen (=0.4 cm) is not thin enough and
the impedance are greater than the range of the instrument. The electrical properties of air attach
to the table 6.2.
6.2 Determining the Electrical Properties of Pure Soils
The testing was performed using the HP 4192A impedance analyzer calibrated at 100 kHz and
acquired the data from calibrated frequency. The measured electromagnetic properties of
diatomaceous earth, silica flour, and kaolinite were performed while changing the porosity. The
measured data were converted to permittivity and conductivity by using equations 5.2, 5.6, and 5.7
for analysis and presentation. The relative real permittivities in 100% specimens were modeled
24
with the mixture equations and calculated by trend line equation in EXCEL (Figure 6.5-(a)). The
Pearson’s correlation coefficient of the trend lines 0.95 for diatomaceous earth, 0.95 for kaolinite,
and 0.94 for silica flour. The permittivity of the solid particles of diatomaceous earth, silica flour,
and kaolinite are 8, 4, and 11, respectively (Table 6.3). The relative real and effective imaginary
permittivity decreased with increasing porosity due to the greater contribution of the air volume.
The decreases in relative effective imaginary permittivity of three samples are different from each
other. The silica flour shows nearby zero imaginary permittivity. However, the results of kaolinite
and diatomaceous earth specimens show decreasing loss factor (imaginary permittivity) at 100
kHz and it appears that electrode polarization electrodes still effects the measurements. Figure 6.6
shows that the changing effective imaginary permittivity changes with frequency. It seems like
that the larger imaginary permittivity yields the larger amount of decreasing real permittivity. On
the other hand, the silica flour (n = 0.56) (Figure 6.6-(b)) shows constant permittivity in both real
and imaginary parts.
Leluk et al. (2006) tested kaolinite specimens at different temperature (from 20 ⁰C to 450 ⁰C) and
the relative real permittivity of the kaolinite at 20 ⁰C is similar to the results in our studies (Figure
6.5). However, the relative real permittivity deceased with increasing temperature due to the
removed adsorbed water (Leluk et al., 2006). It can be expected that the kaolinite specimen used
in this test include some water content that may have yielded higher relative real permittivities
than expected at laboratory temperature. It is possible that the higher relative real permittivity of
diatomaceous earth is also caused by adsorbed water in the high specific surface area that
diatomaceous earth has as compared to silica flour.
25
The conductivities of three samples are presented in figure 6.7-(a): they increase with increasing
frequency. The diatomaceous earth and kaolinite increase the conductivities, while silica flour
decreases the conductivity with additional fraction volume of air (Figure 6.7-(b)). Figure 6.7-(b)
shows similar results of conductivity for diatomaceous earth (n = 0.73) and kaolinite (n = 0.57)
and smaller for silica flour (n = 0.56). The diatom has typically higher porosity distribution than
other two samples in this test because of internal porosity (Figure 6.7-(b)). This characteristic
allows storing more air proportion and decreases the electrical conductivity. However, kaolinite
seems like has low conductivity particle than silica flour because the kaolinite has lower
conductivity than silica flour in similar porosity.
6.3 The Electrical Properties with Water Volume Change
The air-water-soil phase specimens were tested with the HP 4192A impedance analyzer for
volumetric water content ranging from θ = 0-100 (these specimens were prepared with deionized
water). The 5 MHz frequency data were selected in the analysis to remove electrode polarization
effects and to take advantage of the high accuracy of the results in the 5 MHz calibrated range.
The measured impedance and phase angle data were converted to permittivity and conductivity
using equations (5.2), (5.6), and (5.7).
Figures 6.8, 6.9, and 6.10 show the relative real permittivity of the diatomaceous earth, kaolinite
and silica flour specimens. At the high frequencies in the tested range, the relative real permittivity
k’ values of all three samples, mixed with different volumetric water content, are between
permittivity of air (= 1) and water (= 80). The electrode polarization effect decreases with
increasing frequency until attach to the critical frequency. At the low frequency, the electrode
26
polarization effect in the diatomaceous earth specimens increases with increasing volumetric water
content until saturated condition (around 80% of volumetric content). Similar behavior is observed
in silica flour (θ = 50%) and kaolinite (θ = 50%). However, for those soils, the error at low
frequency decreases with volumetric water content after saturated condition is reached.
The electrode polarization affect increases with increasing the volumetric water content until
saturated condition; but decrease for even higher volumetric water contents. The reason for this
behavior is that the unsaturated specimen’s permittivity is controlled by the permittivity of particle,
water and air and the conductivity of water. The higher volume of water, the higher conductivity
is (Figure 6.22) for unsaturated condition and the increased conductivity renders larger electrode
polarization effect (Attia et al., 2008). The permittivities of the specimen over the saturated water
condition are dominated by the electromagnetic properties of water; that is the permittivities of
saturated soils are closer to the pure water permittivity.
Figure 6.10 shows that the θ = 19% silica flour specimen has two static relative real permittivity
frequencies. This is because air, water, and silica flour have different static permittivity. This
heterogeneous behavior is also detected in the diatomaceous earth and kaolinite specimens
especially for lower volumetric water content specimens. In addition, the diatom and kaolinite
particles seem to have higher static relative real permittivity frequency than the silica flour and
deionized water.
The relative imaginary permittivity of samples with increasing volumetric water contents are
presented in figures 6.11, 6.12, and 6.13. In general, the relative imaginary permittivity k”
27
increases with increasing volumetric water content until saturated condition is reached. The
relative imaginary permittivity at saturation has the highest permittivity in whole testing frequency.
The lowest loss correspond to the the specimen without the water content (i.e., low electrical
conductivity).
Figures 6.14, 6.15, and 6.16 show the conductivity of three samples change with water content.
The conductivity at low frequency dramatically increases with increase volumetric water content
until the saturated condition is reached. Kaolinite and silica flour specimens show higher amount
of conductivity increase than the diatomaceous earth because the high void ratio inside the particles.
In this case, the conductivity of diatom is lower than those of silica flour and kaolinite at
unsaturated condition. The conductivity for saturated condition shows similar values for diatom,
silica, and kaolinite specimens. The higher water contents than the saturated condition have
decreasing conductivity at same frequency. The reason for this observation is that the conductivity
is controlled by the mobility of hydrated ions, electrolyte conductivity, and surface conductance.
The presence of water permits the formation of the double layer which creates better paths for the
movement of anions and cations. The mobility of hydrated electrolyte and the surface conductance
create conditions for higher conductivity. However, the conductivity decrease with more fraction
of water amount than the saturated condition because of the inherent low conductivity of deionized
water. Therefore, the conductivity of soil and water mixture is governed by the water amount rather
than the conductivities of particles.
Figures 6.14, 6.15, and 6.16 show the conductivity increases with frequency. At the end of the
testing range, the larger conductivity specimen has higher water content. The reason of the
28
increased conductivity seems due to the high intensity of the frequency. The water shows high
sensitivity conductivity with alternative frequency than particles because of high permittivity of
water (Figure 6.22).
The relative real permittivity of specimens at 5 MHz frequency are presented in figures 6.17 and
6.18 to compare the changing of electromagnetic properties with increasing volumetric water
content and air at certain frequencies. From those figures, the k’ increases with volumetric water
content and decreases with increasing air volume. The particle characteristic β (see equation 5.1)
is estimated the using the electromagnetic properties of the specimens over the whole frequency
range and different water contents. The coefficient β is determined using the same values between
the two laboratory studies, one is prepared without water content and the other is mixed with air
and water content. The coefficient β ranges from 0.3 to 0.6 for most soils (Sen et al, 1981). The
results of kaolinite are 0.5-0.53 and for the silica flour is 0.32. Those values are the typical behavior
for common soils. However, the obtained value of β for the diatomaceous earth specimens (Figure
6.17-(a)) is much greater than the suggested range. This appears to show the special properties of
diatom.
Figures 6.19 and 6.20 show the relative imaginary permittivity for increasing volumetric water
content at 1 MHz and 5 MHz. The relative imaginary permittivity k” decreases from 1 MHz to 5
MHz because of the reduction of electrode polarization effect. As the volumetric water content
increases beyond saturation, the higher proportion of air and water decrease the loss part of
permittivity. This phenomenon assumes that the imaginary permittivity soil, air, water mixture is
dominated by the air phase when the soil is unsaturated and by the water phase when saturated.
29
The imaginary permittivity increases dramatically between when the soil is reaching saturation.
This transition can be used the water content point at the phase changing from 3 to 2 (from
unsaturated to saturated condition). The diatom mixture (Figure 6.19-(a)) has the highest
imaginary permittivity than other two specimens for the same volumetric water content at saturated
condition. The silica flour mixture (Figure 6.20) shows the lowest imaginary permittivity for all
volumetric water contents because of the small electrode polarization effect.
The conductivity of diatomaceous earth, kaolinite, and silica flour specimens mixed with air and
water at two different frequencies (1 MHz and 5 MHz) are presented in figures 6.21 and 6.22. The
conductivity data for 1 MHz reveal large changes between unsaturated and saturated conditions,
just like the imaginary permittivity. This phenomenon can be observed clearly in figure 6.23. When
the conductivity is dramatically increasing, at the point of volumetric water content represents the
saturated condition from unsaturated soil and the water content is equivalent with the water
content with exponentially increasing relative imaginary permittivity. In addition, the saturated
water point is influence to the specific surface and liquid limit of the samples. However, the
conductivity changes with increasing frequency: as frequency increases so is the conductivity.
Conductivity also increases with increasing volumetric water content.
6.4 Measuring Electrical Properties during Compression Testing
Compression tests were performed from 50 kPa to 600 kPa while the electrical impedance was
measured using the HP4192A impedance analyzer.
30
Table 6.4 summarizes the compression test results. In these tests, the diatomaceous earth had
highest initial void ratio and maintained the highest void ratio through the end of test (600 kPa).
In spite to the high void ratio, the particles of diatomaceous earth can support the applied loads
and while showing high ability to trap water content in the intra-skeletal space (Day, 1995; Hong
2006). From these reasons, the higher volume of diatomaceous earth specimen show higher
volumetric water content and void ratio at all applied loading.
The kaolinite contains as much as water as the diatomaceous earth in saturated condition without
load (Table 6.4) because it develops thicker double layer due to the larger surface charge density
compare with diatomaceous earth and silica flour. However, the double layer is compressed with
increasing applied loading. The amount of drained water volume in kaolinite is the highest of the
three samples (Table 6.4). The silica flour specimen has lowest initial water content because of
low charge density, porosity, and low specific surface area. The decrease in volumetric water
content from initial to 600 kPa vertical pressure is not large.
The higher fraction of diatom volume in the specimens renders higher pore fluid storage ability
and greater void ratio in any vertical pressure than kaolinite and silica flour. The kaolinite shows
the highest sensitivity of volumetric water content according to the increasing applied pressure.
(Figure 6.34)
The relative real permittivity of pore fluid saturated diatomaceous earth determined by the amount
of volumetric pore fluid content. The relative real permittivity k’ decreases with increasing load
31
because drained pore fluid between electrodes (Figure 6.24). The highest applied load showed the
lowest relative real permittivity for all tested specimens.
The saturated diatomaceous earth and silica flour specimen prepared with deionized water
decrease its volumetric water content, void ratio, and relative real and imaginary permittivities
with increasing vertical stresses (Figure 6.25). The special structure of diatomaceous earth can
carry more water content than silica flour and the higher amount of water yield higher
permittivities. The electrode polarization effect in diatomaceous earth is higher than in silica flour
specimens. Kaolinite specimen also shows the similar relationship than for diatomaceous earth
with respect to higher conductivity (Figure 6.26). However, the kaolinite specimen has higher
permittivity than silica flour (Figure 6.27). It seems that because of slightly lower volumetric water
content of silica flour specimen, it yields smaller electrode polarization effect and lower relative
real permittivity.
Figure 6.28 shows the conductivity of each of the specimen with increasing frequency. The
conductivities pure diatomaceous earth, kaolinite, and silica flour were explained in figure 6.7.
The conductivity of saturated diatomaceous earth with high vertical pressure defines higher than
kaolinite and silica flour. That is the reason why the diatomaceous earth has higher volumetric
water content at that pressure (600 kPa).
Figures 6.29 to 6.30 compare the relative real permittivity of specimens prepared with deionized
water and electrolyte. The deionized water and 1 M NaCl solution saturated specimens are
compared to each other. In low the frequency range, the electrode polarizations of 1 M NaCl
32
solution mixed specimens are higher than the specimen with the deionized water because of larger
conductivity figure 6.1. At the high frequency range, the k’ of deionized water and 1 M NaCl
solution are expected similar value in table 3.2 which are about 80 and the test results shows similar
permittivity at the end of frequency. However, the imaginary permittivity yield higher loss for
higher concentration of NaCl (Figure 6.1)
The double layer is affected by the pore fluid properties as shown in the results presented in figures
6.29, 6.30, and 6.31. Specially, the kaolinite shows decreased volumetric water content for the 1
M NaCl solution. The changes in volumetric water content between deionized water and 1 M NaCl
solution is caused by the changes in the thickness of double layer. However, the permittivity results
are not influenced by the similar volumetric water content in different pore fluid. The
diatomaceous earth specimen does not show significant changes in the volumetric water content
between two different pore fluids at 600 kPa. This mean that the diatomaceous earth has really low
surface charge that renders a little of thin double layer which not affected by pore fluid.
To compare the electrical properties, similar volumetric water content of each specimen (Table 6.6
and 6.7) were selected in the compression testing with deionized water or 1 M NaCl solution at
100 kHz and 1 MHz. Figure 6.35 shows the relative real permittivity in different particle
characteristics. The higher volume fraction of diatom yields higher relative real permittivity for
similar volumetric water contents. Although, the diatomaceous earth particle relative real
permittivity is lower than that of kaolinite, the slurry condition of diatom k’ is higher than the
kaolinite. The higher proportion of silica flour influences to decreasing relative real permittivity
of the specimens because of its low relative real permittivity of particles. The relative real
33
permittivity of specimens mixed with deionized water or 1 M NaCl solution yields similar values.
However, the relative imaginary permittivity is higher in the mixture with 1M NaCl solution pore
fluid (Figure 6.36). The 1 M NaCl solution mixture shows higher conductivity than the deionized
water. The reason is that high concentration of hydrated ions enhanced the ability of charges to
move and conduct electricity in the specimen.
34
7. CONCLUSIONS
The electrical properties and mechanical properties of three soils were measured at different
volumetric water content, porosity, and pore fluid. Each of soils shows different characteristics
for the applied electric field.
The diatomaceous earth has high liquid limit and specific surface with low surface charge and
density. The increased fraction of diatomaceous earth yields increasing liquid and plastic limit.
The relative real permittivity of diatom particles is 8, kaolinite particles is 11, and the silica
flour particles is 4. The conductivity of silica flour is the highest between three samples and
the kaolinite and diatom shows similar value of it. These results acquired from no water content
pure specimen to minimize the electrode polarization effect.
The relative real permittivity affected by the volumetric water content because of its high
permittivity. However, at the low frequency range, the highest relative real permittivity is the
specimen when the water content reaches the saturated condition because of the large electrode
polarization effect at that water content.
The ability to move the charge is enhanced with increasing frequency, volumetric water
content, and characteristic pore fluid. The conductivity increases until the water content
reaches the liquid limit and the decreases for greater water content in the low frequency range.
The higher concentration of NaCl solution yield higher conductivity.
The saturated conditions of specimens are observed by dramatically increased imaginary
permittivity and conductivity at the low frequency range.
Due to compression, the relative real permittivity of diatom, silica flour, and kaolinite
specimens decreased respect with increasing loading as the water drains from the specimens.
35
Even changes in pore fluid from deionized water to 1M NaCl solution the relative real
permittivity is similar. But the 1 M NaCl solution mixture specimen shows stronger electrode
polarization effect at low frequency. The imaginary permittivity also decreased with increasing
loading and increased with high concentration of pore fluid. However, the diatom and kaolinite
specimens still had electrode polarization effect until the end of testing frequency range (5 Hz
to 10 MHz). To get the relative real permittivity, the higher frequency ranges need to be tested.
Diatom and kaolinite specimens had higher relative permittivity than silica flour specimens.
The three phases plots at 600 kPa show that diatom specimen have greater water content than
silica flour and kaolinite specimens. This means that the diatom specimens could store more
water at high vertical stresses and yield higher permittivity.
The volumetric water content for different pore fluid is observed in kaolinite specimen due to
the shrinkage of the diffuse double layer. However, the diatomaceous earth does not yield
significant changing between two pore fluids. This means that the diatom has really low surface
charges to from the double layer.
Diatomaceous earth shows different physical, mechanical, and electrical characteristic than
silica flour and kaolinite indicating the potential for more meaning description of geochemical
materials.
36
8. REFERENCES
Antonides, L. E. (1997). “Diatomite” U.S. Geological Survey Mineral Commodity
Summaries 1998, 56-57.
Attia, A. M., Fratta, D., and Bassionui, Z. (2008). “Irreducible Water Saturation from
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A1
APPENDIX A. FIGURES
(a) (b)
(c) (d)
Figure 3.1. Scanning Electron Micrographs (SEM) of (a) diatom (20 μm), (b) silica flour
(20 μm), and (c) kaolinite (1 μm) samples. (d) Image of the three samples previous to
testing.
Diatom
Kaolinite Silica flour
A2
Figure 2.1. Grain size distribution of the three tested soils. The tests were run using the
ASTM 152 H type hydrometer.
0
10
20
30
40
50
60
70
80
90
100
0.0010.010.1
Per
cen
t of
Fin
er (
%)
Grain Size, D (mm)
Diatom
Silica Flour
Kaolinite
Even Mixed of Three Samples
A3
Figure 2.2. Liquid limit and plastic limit different sample compositions.
0
20
40
60
80
100
120
140
160
Diatom 100% Silica Flour 100%
Wate
r C
on
ten
t (%
)
Sample Compositions
LL
PL
0
20
40
60
80
100
120
140
160
Diatom 100% Kaolinite 100%
Wate
r C
on
ten
t (%
)
Sample Compositions
0
20
40
60
80
100
120
140
160
Silica Flour 100% Kaolinite 100%
Wate
r C
on
ten
t (%
)
Sample Compositions
A4
Figure 3.1. Schematic response of soil and electrolyte mixture under an electrical field.
A5
Figure 3.2. Electrical resistivity of saturated soils and rocks (surface conduction Θ = 1.4
× 10-9 S – Attia et al. 2008).
A6
Figure 3.3. Polarization mechanism. (a) Electronic Polarization, (b) Ionic Polarization,
and (c) Molecular Polarization (the direction of electric field is from left to right) (Fam,
1995).
(a)
(b)
(c)
A7
(a)
(b)
Figure 3.4. (a) Real and imaginary permittivity with frequency and (b) Cole-Cole plot
from Debye (1929).
Rel
ati
ve
Per
mit
tivit
y
Log(ω) →
Real Permittivity
Imaginary Permittivity
Imagin
ary
Rel
ati
ve
Per
mit
tivit
y
Real Relative permittivity
A8
Figure 3.5. Temperature effects on deionized water saturated silica flour in consolidation
testing at 600 kPa.
400
500
600
700
800
900
1000
1100
1200
0 2000 4000 6000 8000 10000
Imp
edan
ce (
oh
m)
Time (min)
0.1 kHz 1 kHz 10 kHz 100 kHz 1 MHz
1 day 1 day 1 day
A9
Figure 3.6. Affected Relative real permittivity according to the diatomaceous earth
concentration with deionized water.
0
10
20
30
40
50
60
70
80
0.0 0.2 0.4 0.6 0.8 1.0
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Volumetric Water Content
A10
Figure 4.1. The impedance Z consists of a real part R and an imaginary part X. The θ is
phase angle of impedance (After Agilent Technologies, 2009).
A11
Figure 4.2. The schema of open and short calibration (after Agilent, 2009).
A12
Figure 4.3. The impedance vs. frequency of oedometric cell with low impedance shorting-
bar after calibration at different zero set frequency, 100 kHz, 1 MHz, and 10 MHz.
0.001
0.01
0.1
1
10
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Com
ple
x I
mp
edan
ce,
lZl
(Ω)
Frequency (Hz)
100 kHz
1 MHz
10 MHz
A13
Figure 4.4. Capacitors. (a) Parallel-plate. (b) Electric field inside a capacitor. (After
Santamarina et al., 2001).
A14
Figure 4.5. Leaking the current because of fringing effect.
A15
Figure 4.6. Electrode polarization effect of saturated silica flour at 50 kPa in compression
testing.
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
Electrode Polarization EffectNo Electrode
Polarization Effect
A16
Figure 5.1. The apparatus to measure electrical properties (d = 6.28 cm, h = 0.4 cm).
A17
Figure 5.4. The consolidation apparatus made by PVC plastic (up-left), the consolidation
testing picture (up-right), and the cross section of apparatus (bottom).
A18
Figure 6.1. Comparison between idealized permittivity data (line) and measured data by
HP 4192A (dot).
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10
Rel
ati
ve
Imagin
ary
Per
mit
tivit
y
Frequency (Hz)
Deionized Water 0.04 M NaCl Solution
0.1 M NaCl Solution 0.4 M NaCl Solution
1 M NaCl Solution 4 M NaCl Solution
Measured Deionized Water Data Measured 0.1 M NaCl Solution Data
Measured 0.4 M NaCl Solution Data
A19
Figure 6.2. Define the fringing effect of electrodes with different thickness of specimen
(0.4 cm and 7 cm).
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
7 cm Thickness of Specimen with 0.04 M NaCl
0.4 cm Thickness of Specimen with 0.04 M NaC
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10
Rel
ati
ve
Imagin
ary
Per
mit
tivit
y
Frequency (Hz)
A20
Figure 6.3. Relative real and imaginary permittivity of deionized water and air tested
different frequency calibration from 5 Hz to 10 MHz.
1.E-03
1.E-01
1.E+01
1.E+03
1.E+05
1.E+07
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Rea
l P
erm
nit
tivit
y
Frequency (Hz)
Water (100 kHz calibrated)
Water (1 MHz calibrated)
Water (5 MHz calibrated)
Air (100 kHz calibrated)
Air (1 MHz calibrated)
Air (5 MHz calibrated)
1.E-03
1.E-01
1.E+01
1.E+03
1.E+05
1.E+07
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Iam
gin
ary
Per
mn
itti
vit
y
Frequency (Hz)
A21
Figure 6.4. Conductivity of deionized water and air tested different frequency
calibration from 5 Hz to 10 MHz.
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Con
du
ctiv
ity (
S/m
)
Frequency (Hz)
Water (100 kHz calibrated)
Water (1 MHz calibrated)
Water (5 MHz calibrated)
Air (100 kHz calibrated)
Air (1 MHz calibrated)
Air (5 MHz calibrated)
A22
Figure 6.5. Permittivity of pure samples mixed with air in different porosity (100 kHz).
y = -6.9524x + 8.0019
R² = 0.9031
y = -2.5316x + 3.8339
R² = 0.8779
y = -11.521x + 10.663
R² = 0.9082
0
1
2
3
4
5
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Porosity
Diatomaceous Earth Silica Flour Kaolinite
0.0
0.2
0.4
0.6
0.8
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
Rel
ati
ve
Imagin
ary
Per
mit
tivit
y
Porosity
A23
(a)
(b)
(c)
Figure 6.6. Permittivity of pure samples mixed with air in different frequency (a)
diatomaceous earth (n = 0.73), (b) silica flour (= 0.56), and (c) kaolinite (n = 0.57).
0.001
0.01
0.1
1
1
10
1.00E+04 1.00E+05 1.00E+06
Rel
ati
ve
Per
mit
tiv
ity
Frequency (Hz)
Relative Real Permittivity
Relative Imaginary Permittivity
0.001
0.01
0.1
1
1
10
1.00E+04 1.00E+05 1.00E+06
Rel
ati
ve
Per
mit
tivit
y
Frequency (Hz)
0.001
0.01
0.1
1
1
10
1.00E+04 1.00E+05 1.00E+06
Rel
ati
ve
Per
mit
tivit
y
Frequency (Hz)
A24
(a)
(b)
Figure 6.7. Conductivity of pure samples mixed with air in different frequency (a) and
with different porosity (b) (100 kHz).
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.00E+04 1.00E+05 1.00E+06
Con
du
ctiv
ity (
S/m
)
Frequency (Hz)
Diatomaceous Earth (n = 0.73)
Silica Flour (n = 0.56)
Kaolinite (n = 0.57)
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85
Con
du
ctiv
ity (
S/m
)
Porosity
Diatomaceous Earth
Silica Flour
Kaolinite
A25
Figure 6.8. Relative real permittivity of diatomaceous earth with changing volumetric
water content.
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Rea
l P
erm
itti
vty
Frequency (Hz)
θ = 0 % θ = 13 %
θ = 22 % θ = 25 %
θ = 32 % θ = 36 %
θ = 42 % θ = 52 %
θ = 61 % θ = 71 %
θ = 80 % θ = 90 %
θ = 100 %
A26
Figure 6.9. Relative real permittivity of kaolinite with changing volumetric water content.
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Rea
l P
erm
itti
vty
Frequency (Hz)
θ = 0 % θ = 12 %
θ = 21 % θ = 30 %
θ = 41 % θ = 51 %
θ = 61 % θ = 70 %
θ = 80 % θ = 90 %
θ = 100 %
A27
Figure 6.10. Relative real permittivity of silica flour with changing volumetric water
content.
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Rea
l P
erm
itti
vty
Frequency
θ = 0 % θ = 09 %
θ = 19 % θ = 30 %
θ = 39 % θ = 49 %
θ = 59 % θ = 72 %
θ = 79 % θ = 89 %
θ = 100 %
A28
Figure 6.11. Relative imaginary permittivity of diatomaceous earth with changing
volumetric water content.
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Imagin
ary
Per
mit
tivty
Frequency (Hz)
θ = 0 % θ = 13 %
θ = 22 % θ = 25 %
θ = 32 % θ = 36 %
θ = 42 % θ = 52 %
θ = 61 % θ = 71 %
θ = 80 % θ = 90 %
θ = 100 %
A29
Figure 6.12. Relative imaginary permittivity of kaolinite with changing volumetric water
content.
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Imagin
ary
Per
mit
tivty
Frequency (Hz)
θ = 0 % θ = 12 %
θ = 21 % θ = 30 %
θ = 41 % θ = 51 %
θ = 61 % θ = 70 %
θ = 80 % θ = 90 %
θ = 100 %
A30
Figure 6.13. Relative imaginary permittivity of silica flour with changing volumetric
water content.
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Imagin
aey
Per
mit
tivty
Frequency
θ = 0 % θ = 09 %
θ = 19 % θ = 30 %
θ = 39 % θ = 49 %
θ = 59 % θ = 72 %
θ = 79 % θ = 89 %
θ = 100 %
A31
Figure 6.14. Conductivity of diatomaceous earth with changing volumetric water content.
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Con
du
ctiv
ity (
S/m
)
Frequency (Hz)
θ = 0 % θ = 13 % θ = 22 %
θ = 25 % θ = 32 % θ = 36 %
θ = 42 % θ = 52 % θ = 61 %
θ = 71 % θ = 80 % θ = 90 %
θ = 100 %
A32
Figure 6.15. Conductivity of kaolinite with changing volumetric water content.
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Con
du
ctiv
ity (
S/m
)
Frequency (Hz)
θ = 0 % θ = 12 %
θ = 21 % θ = 30 %
θ = 41 % θ = 51 %
θ = 61 % θ = 70 %
θ = 80 % θ = 90 %
θ = 100 %
A33
Figure 6.16. Conductivity of silica flour with changing volumetric water content.
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Con
du
ctiv
ity (
S/m
)
Frequency
θ = 09 % θ = 19 %
θ = 30 % θ = 39 %
θ = 49 % θ = 59 %
θ = 72 % θ = 79 %
θ = 89 % θ = 100 %
A34
(a)
(b)
Figure 6.17. Increasing relative real permittivity with increasing volumetric water
content and determining soil characteristic factor β for (a) diatomaceous earth and (b)
kaolinite.
0
10
20
30
40
50
60
70
80
0.0 0.2 0.4 0.6 0.8 1.0
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Volumetric Water Content
Measuredβ=0.82 (different water content)β=1.02 (without water)
0
10
20
30
40
50
60
70
80
0.0 0.2 0.4 0.6 0.8 1.0
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Volumetric Water Content
Measured
β=0.53 (different water content)
β=0.50 (without water)
A35
Figure 6.18. Increasing relative real permittivity with increasing volumetric water
content and determining soil characteristic factor β for silica flour.
0
10
20
30
40
50
60
70
80
0.0 0.2 0.4 0.6 0.8 1.0
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Volumetric Water Content
Measured
β=0.32 (different water content)
A36
(a)
(b)
Figure 6.19. Changing relative imaginary permittivity with increasing volumetric water
content for (a) diatomaceous earth and (b) kaolinite.
0
50
100
150
200
250
300
350
0.0 0.2 0.4 0.6 0.8 1.0
Rel
ati
ve
Imagin
ary
Per
mit
tivit
y
Volumetric Water Content
5 MHz 1 MHz
0
50
100
150
200
250
300
350
0.0 0.2 0.4 0.6 0.8 1.0
Rel
ati
ve
Imagin
ary
Per
mit
tivit
y
Volumetric Water Content
5 MHz 1 MHz
A37
Figure 6.20. Changing relative imaginary permittivity with increasing volumetric water
content for silica flour.
0
50
100
150
200
250
300
350
0.0 0.2 0.4 0.6 0.8 1.0
Rel
ati
ve
Imagin
ary
Per
mit
tivit
y
Volumetric Water Content
5 MHz 1 MHz
A38
(a)
(b)
Figure 6.21. Changing conductivity with increasing volumetric water content for (a)
diatomaceous earth and (b) kaolinite.
0.E+00
1.E-02
2.E-02
3.E-02
4.E-02
5.E-02
6.E-02
7.E-02
0.0 0.2 0.4 0.6 0.8 1.0
Con
du
ctiv
ity (
S/m
)
Volumetric Water Content
5 MHz 1 MHz
0.E+00
1.E-02
2.E-02
3.E-02
4.E-02
5.E-02
6.E-02
7.E-02
0.0 0.2 0.4 0.6 0.8 1.0
Con
du
ctiv
ity (
S/m
)
Volumetric Water Content
5 MHz 1 MHz
A39
Figure 6.22. Changing conductivity with increasing volumetric water content for silica
flour.
0.E+00
1.E-02
2.E-02
3.E-02
4.E-02
5.E-02
6.E-02
7.E-02
0.0 0.2 0.4 0.6 0.8 1.0
Con
du
ctiv
ity (
S/m
)
Volumetric Water Content
5 MHz 1 MHz
A40
Figure 6.23. Figuring out the saturated volumetric water content by using conductivity
of three samples.
0.0E+00
5.0E-03
1.0E-02
1.5E-02
2.0E-02
0.0 0.2 0.4 0.6 0.8 1.0
Con
du
ctiv
ity (
S/m
)
Volumetric Water Content
Diatomaceous Earth (1 MHz) Silica Flour (100 kHz) Kaolinite (1 MHz)
Three-Phase Two-Phase
A41
Figure 6.24. Relative real permittivity of diatomaceous earth with changing vertical
compression load. The void ratio is posted in Table 6.4.
300
350
400
450
500
1.00E+05 1.25E+05 1.50E+05 1.75E+05 2.00E+05
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
50 kPa 100 kPa
200 kPa 400 kPa
600 kPa
A42
600 kPa Volumetric Water Content Void Ratio
Diatom 0.66 1.90
2/3 Diatom + 1/3 Silica Flour 0.63 1.71
1/3 Diatom + 2/3 Silica Flour 0.52 1.06
Silica Flour 0.45 0.83
Figure 6.25. Relative real and imaginary permittivity of diatomaceous and silica flour
saturated mixtures at 600 kPa.
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
Diatom
2/3 Diatom + 1/3 Silica Flour
1/3 Diatom + 2/3 Silica Flour
Silica Flour
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
im
agin
ary
Per
mit
tivit
y
Frequency (Hz)
A43
600 kPa Volumetric Water Content Void Ratio
Diatom 0.66 1.90
2/3 Diatom + 1/3 Kaolinite 0.57 1.30
1/3 Diatom + 2/3 Kaolinite 0.48 0.93
Kaolinite 0.47 0.90
Figure 6.26. Relative real and imaginary permittivity of diatomaceous and kaolinite
saturated mixtures at 600 kPa
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
Diatom
2/3 Diatom + 1/3 Kaoliniter
1/3 Diatom + 2/3 Kaolinite
Kaolinite
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
im
agin
ary
Per
mit
tivit
y
Frequency (Hz)
A44
600 kPa Volumetric Water Content Void Ratio
Diatom 0.66 1.90
Silica Flour 0.45 0.83
Kaolinite 0.47 0.93
1/3 Diatom + 1/3 Silica Flour
+ 1/3 Kaolinite 0.51 1.05
Figure 6.27. Relative real and imaginary permittivity of diatomaceous, kaolinite, silica
flour, and even mixed three samples at saturated condition with 600 kPa.
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
Diatom
Kaolinite
Silica Flour
1/3 Dia + 1/3 Sili + 1/3 Kao
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
imagin
ary
Per
mit
tivit
y
Frequency (Hz)
A45
600 kPa Volumetric Water Content Void Ratio
Diatom 0.66 1.90
Silica Flour 0.45 0.83
Kaolinite 0.47 0.93
1/3 Diatom + 1/3 Silica Flour
+ 1/3 Kaolinite 0.51 1.05
Figure 6.28. Relative real and imaginary permittivity of diatomaceous, kaolinite, silica
flour, and even mixed three samples at saturated condition with 600 kPa
0
0.02
0.04
0.06
0.08
0.1
1.E+04 1.E+05 1.E+06 1.E+07
Con
du
ctiv
ity (
S/m
)
Frequency (Hz)
DiatomSilicaKaolinite1/3 Diatom + 1/3 Silica + 1/3 Kaolinite
A46
Pore Fluid
Load (kPa)
100 200 300 400 500 600
Volumetric Water Content
Deionized Water 0.71 0.69 - 0.67 - 0.66
1 M NaCl Solution 0.74 0.72 0.70 0.69 0.68 0.66
Figure 6.29. Relative real permittivity of diatomaceous slurry, mixed with deionized
water or 1 M NaCl solution while changing vertical load.
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
100
1.E+05 1.E+06
Rel
atu
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
Deionized Water-50 kPaDeionized Water-100 kPaDeionized Water-200 kPaDeionized Water-400 kPaDeionized Water-600 kPa1 M NaCl-100 kPa1 M NaCl-200 kPa1 M NaCl-300 kPa1 M NaCl-400 kPa1 M NaCl-500 kPa1 M NaCl-600 kPa
A47
Pore Fluid
Load (kPa)
100 200 300 400 500 600
Volumetric Water Content
Deionized Water 0.60 0.56 - 0.51 - 0.48
1 M NaCl Solution 0.52 0.46 0.43 0.41 0.39 0.36
Figure 6.30. Relative real permittivity of kaolinite slurry, mixed with deionized water or
1 M NaCl solution while changing vertical load.
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
veR
eal
Per
mit
tivit
y
Frequency (Hz)
70
1.E+05 1.E+06
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
Deionized Water-50 kPaDeionized Water-100 kPaDeionized Water-200 kPaDeionized Water-400 kPaDeionized Water-600 kPa1 M NaCl-100 kPa1 M NaCl-200 kPa1 M NaCl-300 kPa1 M NaCl-400 kPa1 M NaCl-500 kPa1 M NaCl-600 kPa
A48
Pore Fluid
Load (kPa)
100 200 300 400 500 600
Volumetric Water Content
Deionized Water 0.48 0.47 - 0.46 - 0.45
1 M NaCl Solution 0.51 0.48 0.45 0.43 0.41 0.39
Figure 6.31. Relative real permittivity of silica flour, mixed with deionized water or 1 M
NaCl solution while changing vertical load.
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
20
1.E+05 1.E+06
Rel
ati
ve
Rea
l P
erm
itti
vit
y
Frequency (Hz)
Deionized Water-50 kPa
Deionized Water-100 kPa
Deionized Water-200 kPa
Deionized Water-400 kPa
Deionized Water-600 kPa
1 M NaCl-100 kPa
1 M NaCl-200 kPa
1 M NaCl-300 kPa
1 M NaCl-400 kPa
1 M NaCl-500 kPa
1 M NaCl-600 kPa
A49
(a)
(b)
Figure 6.32. Relative imaginary permittivity of saturated (a) diatomaceous earth and (b)
silica mixed with deionized water or 1 M NaCl solution while changing vertical load.
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Eff
ecti
ve
Imagin
ary
Per
mit
tivit
y
Frequency (Hz)
Deionized Water-50 kPaDeionized Water-100 kPaDeionized Water-200 kPaDeionized Water-400 kPaDeionized Water-600 kPa1 M NaCl-100 kPa1 M NaCl-200 kPa1 M NaCl-300 kPa1 M NaCl-400 kPa1 M NaCl-500 kPa1 M NaCl-600 kPa
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Eff
ecti
ve
Imagin
ary
Per
mit
tivit
y
Frequency (Hz)
Deionized Water-50 kPaDeionized Water-100 kPaDeionized Water-200 kPaDeionized Water-400 kPaDeionized Water-600 kPa1 M NaCl-100 kPa1 M NaCl-200 kPa1 M NaCl-300 kPa1 M NaCl-400 kPa1 M NaCl-500 kPa1 M NaCl-600 kPa
A50
Figure 6.33. Relative imaginary permittivity of kaolinite slurry, mixed with deionized
water or 1 M NaCl solution while changing vertical load.
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07
Eff
ecti
ve
Imagin
ary
Per
mit
tivit
y
Frequency (Hz)
Deionized Water-50 kPaDeionized Water-100 kPaDeionized Water-200 kPaDeionized Water-400 kPaDeionized Water-600 kPa1 M NaCl-100 kPa1 M NaCl-200 kPa1 M NaCl-300 kPa1 M NaCl-400 kPa1 M NaCl-500 kPa1 M NaCl-600 kPa
A51
Figure 6.34. 1 M NaCl solution saturated specimens’ responses volumetric water content
at 600 kPa.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Soils Water
A52
]
Figure 6.35. Relative real permittivity of diatom, silica flour, and kaolinite mixtures with
deionized water or 1 M NaCl solution with similar volumetric water content. The
volumetric water content or void ration is shown in table 6.6 and 6.7.
1.E+01
1.E+02
1.E+03
1.E+04R
elati
ve
Rea
l P
erm
itti
vit
yDeionized Water - 100 kHz
Deionized Water - 1 MHz
1 M NaCl Solution - 100 kHz
1 M NaCl Solution - 1 MHz
A53
Figure 6.36. Relative imaginary permittivity of diatom, silica flour, and kaolinite
mixtures with deionized water or 1 M NaCl solution with similar volumetric water
content. The volumetric water content or void ration is shown in table 6.6 and 6.7.
1.E+01
1.E+02
1.E+03
1.E+04
Rel
ati
ve
Eff
ecti
ve
Imagin
art
Per
mit
tivit
y
Deionized Water - 100 kHz
Deionized Water - 1 MHz
1 M NaCl Solution - 100 kHz
1 M NaCl Solution - 1 MHz
A54
Figure 6.37. Conductivity of diatom, silica flour, and kaolinite mixtures with deionized
water or 1 M NaCl solution with similar volumetric water content. The volumetric water
content or void ration is shown in table 6.6 and 6.7.
0.00
0.01
0.02
0.03
0.04
0.05
0.06C
on
du
ctiv
ity (
S/m
)Deionized Water - 100 kHz
Deionized Water - 1 MHz
1 M NaCl Solution - 100 kHz
1 M NaCl Solution - 1 MHz
A55
APPENDIX B. TABLES
Table 2.2. Basic properties of tested samples.
Physical Property Silica Flour Kaolinite Diatomaceous
Earth
Color White Light Cream Light Cream
Specific Gravity,
Gs 2.61 2.57 2.03
Specific Surface,
S (m2/g)a 1.5 26.5 102.5
Particle Size,
d50 (μm)b 13 2.4 3.7
Liquid Limit (%)c 29.75 52.65 133.7
Plastic Limit (%)d NP 30.7 NP
ph Value
(10% solids) e 8.2 5.46 7.47
a EGEM results were obtained using aluminum tares with 48 mm diameter (Cerato &
Lutenegger, 2002) b Grain size distribution test with ASTM 152 H type hydrometer c Fall cone testing with Humboldt penetrometer d Casagrande method, ASTM D4318 e Measured by using Thermo Scientific, Orion 5 Star.
A56
Table 2.2. Specimen Compositions for the Experimental Study.
Diatom (%) Silica Four (%) Kaolinite (%)
Sample 1 100 0 0
Sample 2 66.6 33.3 0
Sample 3 33.3 66.6 0
Sample 4 0 100 0
Sample 5 0 66.6 33.3
Sample 6 0 33.3 66.6
Sample 7 0 0 100
Sample 8 33.3 0 66.6
Sample 9 66.6 0 33.3
Sample 10 33.3 33.3 33.3
A57
Table 3.1. Maxwell’s equations.
Faraday-Lenz’ Law ∇ ∙ E = −∂B
∂t
Ampere-Maxwell’s Law ∇ ∙ H =∂D
∂t+ I
Gauss’s Law of electricity ∇ ∙ D = ∇ ∙ (ε ∙ E) = qc
Gauss’s Law of magnetism ∇ ∙ B = 0
where E is the electric field (V/m), H is the magnetic field (A/m), B is the magnetic flux
density (W/m2), D is the electric displacement (C/m2), I is current density (A/m2), and
qc is the charge density (C/m3)
A58
Table 3.2. Typical electromagnetic properties of different materials.
Material Conductivity
(mS/m)
Relative
Permittivity
Air 0 1
Fresh Water 0.5 80
Salt Water 3000 81~88
Dry Sand 0.01 3~10
Wet Sand 0.1~1 20~30
Limestone 0.5~2 4~8
Shale 1~100 5~15
Clay 2~1000 5~40
Granite 0.01~1 4~6
Ice 0.01 3~4
Concrete 0.01~10 6
Sources: Schultz (2002), Milsom (2003), Davis and Annan (1989), and Conyers (2004).
A59
Table 6.1. Relative real and imaginary permittivity and conductivity of deionized
water at different frequencies.
Relative
Real Permittivity
Frequency (Hz)
100 kHz 1 MHz 5 MHz
Defined
Frequency
(Hz)
100 kHz 91.42 93.28 92.67
1 MHz 80.51 80.60 80.57
5 MHz 79.36 81.54 80.55
Relative
Imaginary Permittivity
Frequency (Hz)
100 kHz 1 MHz 5 MHz
Defined
Frequency
(Hz)
100 kHz 8.70.E+01 7.69.E+01 5.99.E+01
1 MHz 1.19.E+01 1.11.E+01 9.59.E+00
5 MHz 3.52.E+00 3.36.E+00 3.50.E+00
Conductivity
(S/m)
Frequency (Hz)
100 kHz 1 MHz 5 MHz
Defined
Frequency
(Hz)
100 kHz 9.58.E-04 9.94.E-04 1.06.E-03
1 MHz 2.61.E-02 2.80.E-02 3.22.E-02
5 MHz 4.11.E-01 4.54.E-01 4.25.E-01
A60
Table 6.2. Relative real and imaginary permittivity and conductivity of air at different
frequency and different calibrated frequencies.
Relative
Real Permittivity
Calibrated Frequency (Hz)
100 kHz 1 MHz 5 MHz
Defined
Frequency
(Hz)
100 kHz 1.48 1.47 1.47
1 MHz 1.46 1.45 1.46
5 MHz 1.47 1.46 1.46
Relative
Imaginary Permittivity
Calibrated Frequency (Hz)
100 kHz 1 MHz 5 MHz
Defined
Frequency
(Hz)
100 kHz 7.74.E-03 1.02.E-02 7.68.E-03
1 MHz 7.92.E-03 7.87.E-03 7.89.E-03
5 MHz 7.43.E-03 7.12.E-03 7.14.E-03
Conductivity
(S/m)
Calibrated Frequency (Hz)
100 kHz 1 MHz 5 MHz
Defined
Frequency
(Hz)
100 kHz 1.48.E-03 1.10.E-03 1.47.E-03
1 MHz 1.27.E-02 1.26.E-02 1.26.E-02
5 MHz 6.64.E-02 6.83.E-02 6.85.E-02
A61
Table 6.3. Relative real permittivity and characteristic factor of each soil
Diatom Kaolinite Silica flour
Relative Real Permittivity 8 11 4
Pearson correlation coefficient 0.95 0.95 0.94
Factor β
Without
Water Content 1.02 0.50 -
Changing
Water Content 0.82 0.53 0.32
A62
Table 6.4. Volumetric water content with increasing loads for each tested specimens
Specimen Load (kPa)
Initial 50 100 200 400 600
Diatom 0.747 0.718 0.708 0.691 0.670 0.655
2/3 Diatom
+ 1/3 Silica Flour 0.686 0.680 0.659 0.658 0.644 0.631
1/3 Diatom
+ 2/3 Silica Flour 0.598 0.570 0.560 0.546 0.528 0.516
Silica Flour 0.504 0.492 0.483 0.471 0.460 0.452
2/3 Silica Flour
+ 1/3 kaolinite 0.615 0.602 0.558 0.520 0.479 0.452
1/3 Silica Flour
+ 2/3 kaolinite 0.665 0.505 0.475 0.432 0.384 0.357
Kaolinite 0.723 0.631 0.600 0.556 0.506 0.475
1/3 Diatom
+ 2/3 Kaolinite 0.712 0.595 0.571 0.536 0.504 0.482
2/3 Diatom
+ 1/3 Kaolinite 0.697 0.687 0.663 0.628 0.591 0.566
1/3 Diatom
+ 1/3 Kaolinite
+ 1/3 Silica Flour
0.701 0.621 0.599 0.568 0.534 0.512
A63
Table 6.5. Void ratio with increasing loads for each of the tested specimens
Specimen Load (kPa)
Initial 50 100 200 400 600
Diatom - 2.543 2.420 2.234 2.034 1.899
2/3 Diatom
+ 1/3 Silica Flour - 2.129 1.930 1.920 1.805 1.709
1/3 Diatom
+ 2/3 Silica Flour - 1.324 1.273 1.200 1.121 1.065
Silica Flour - 0.967 0.933 0.890 0.852 0.826
2/3 Silica Flour
+ 1/3 kaolinite - 1.514 1.262 1.084 0.919 0.823
1/3 Silica Flour
+ 2/3 kaolinite - 1.020 0.906 0.761 0.625 0.555
Kaolinite - 1.713 1.503 1.251 1.023 0.904
1/3 Diatom
+ 2/3 Kaolinite - 1.469 1.329 1.156 1.015 0.930
2/3 Diatom
+ 1/3 Kaolinite - 2.194 1.967 1.691 1.443 1.302
1/3 Diatom
+ 1/3 Kaolinite
+ 1/3 Silica Flour
- 1.640 1.491 1.317 1.144 1.051
A64
Table 6.6. Relative real and imaginary permittivity and conductivity of diatom, silica
flour, and kaolinite specimens with deionized water.
Specimen θ e
Deionized Water
k' k" σ (S/m)
100
kHz
1
MHz
100
kHz
1
MHz
100
kHz
1
MHz
Diatom 0.66 1.90 438 118 4549 563 0.028 0.032
2/3 Diatom
+ 1/3 Silica Flour 0.66 1.92 299 98 3048 374 0.019 0.022
1/3 Diatom
+ 2/3 Silica Flour 0.57 1.32 175 64 2255 270 0.014 0.016
Silica Flour 0.49 0.97 46 33 1565 177 0.010 0.010
2/3 Silica Flour
+ 1/3 kaolinite 0.60 1.51 109 53 1494 178 0.009 0.011
1/3 Silica Flour
+ 2/3 kaolinite 0.51 1.02 212 74 2360 291 0.015 0.017
Kaolinite 0.63 1.71 278 94 2542 325 0.016 0.019
1/3 Diatom
+ 2/3 Kaolinite 0.60 1.47 261 95 2337 294 0.014 0.018
2/3 Diatom
+ 1/3 Kaolinite 0.66 1.97 301 103 3181 387 0.020 0.023
1/3 Dia +
1/3 Sili + 1/3 Kao 0.62 1.64 225 85 2416 294 0.015 0.018
A65
Table 6.7. Relative real and imaginary permittivity and conductivity of diatom, silica
flour, and kaolinite specimen with 1 M NaCl solution.
Specimen θ e
1 M NaCl Solution
k' k" σ (S/m)
100
kHz
1
MHz
100
kHz
1
MHz
100
kHz
1
MHz
Diatom 0.66 1.98 486 103 7926 924 0.046 0.048
2/3 Diatom
+ 1/3 Silica Flour 0.69 2.22 192 57 3217 376 0.018 0.020
1/3 Diatom
+ 2/3 Silica Flour 0.69 2.18 222 76 4242 487 0.024 0.026
Silica Flour 0.51 1.05 58 37 1744 196 0.010 0.010
2/3 Silica Flour
+ 1/3 kaolinite 0.53 1.11 150 53 2525 298 0.015 0.016
1/3 Silica Flour
+ 2/3 kaolinite 0.51 1.03 229 69 2831 347 0.016 0.018
Kaolinite 0.52 1.08 283 99 2802 352 0.016 0.019
1/3 Diatom
+ 2/3 Kaolinite 0.64 1.77 357 104 4024 490 0.023 0.026
2/3 Diatom
+ 1/3 Kaolinite 0.66 1.94 414 112 4931 593 0.028 0.031
1/3 Dia
+ 1/3 Sili + 1/3 Kao 0.63 1.74 258 83 3249 388 0.019 0.021