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

Capillary Pressure and Electrical Resistivity Measurements.” Oil & Gas Science and

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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