Journal of Applied Geophysics 148 (2018) 265–271

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Journal of Applied Geophysics

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Evaluation on expansive performance of the expansive soil usingelectrical responses

Ya Chu a,b, Songyu Liu a,⁎, Bate Bate b,c, Lei Xu a

a Institute of Geotechnical Engineering, Southeast University, Nanjing 210096, Jiangsu, Chinab Department of Civil, Architectural and Environmental Engineering, Missouri University of Science and Technology, Rolla, MO 65409, United Statesc Institute of Geotechnical Engineering, College of Civil Engineering and Architecture, Zhejiang University, Hangzhou, China

⁎ Corresponding author.E-mail addresses: 101004004@seu.edu.cn (S. Liu), bat

https://doi.org/10.1016/j.jappgeo.2017.12.0010926-9851/© 2017 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 5 June 2017Received in revised form 29 November 2017Accepted 1 December 2017Available online 05 December 2017

Light structures, such as highways and railroads, built on expansive soils are prone to damages from the swellingof their underlain soil layers. Considerable amount of research has been conducted to characterize the swellingproperties of expansive soils. Current swell characterizationmodels, however, are limited by lack of standardizedtests. Electrical methods are non-destructive, and are faster and less expensive than the traditional geotechnicalmethods. Therefore, geo-electrical methods are attractive for defining soil characteristics, including the swellingbehavior. In this study, comprehensive laboratory experiments were undertaken to measure the free swellingand electrical resistivity of the mixtures of commercial kaolinite and bentonite. The electrical conductivity ofkaolinite-bentonite mixtures was measured by a self-developed four-electrode soil resistivity box. Increasingthe free swelling rate of the kaolinite-bentonitemixtures (0.72 to 1 of porosity of soils samples) led to a reductionin the electrical resistivity and an increase in conductivity. A unique relationship between free swelling rate andnormalized surface conductivity was constructed for expensive soils by eliminating influences of porosity andmexponent. Therefore, electrical response measurement can be used to characterize the free swelling rate ofexpensive soils.

© 2017 Elsevier B.V. All rights reserved.

Keywords:Electrical responseExpansive soilNormalized surface conductionPorosityFree swelling rateEstimation

1. Introduction

Light structures, such as highways and railroads, built on expansivesoils are prone to damages from the swelling of their underlain soillayers (Nelson and Miller, 1992; Pedarla et al., 2011). Hence, it isimportant to evaluate the total volume change (swelling or shrinkage)potentials of these soils. Both direct and indirect methods have beendeveloped for such purpose (Seed et al., 1962, Sridharan et al., 1986,Puppala et al., 2006). Direct method measures the swelling potentialof two grams of clay in deionized water (ASTM D5890-11, 2006),while indirect methods correlate soil classification designation orother soil properties (i.e. electric resistivity and conductivity) to swellpotential (Chen, 1983; Puppala et al., 2006). Thomas et al. (2000)suggested that swell behavior can best be predicted by examining acombination of physical and mineralogical properties. However,because the mineralogical and chemical properties are not easy to bemeasured, it is hard to apply them to grade swelling potential inengineering practice. Therefore, finding a new swelling potentialindex (electric resistivity and conductivity), which should be easilymeasured and strongly correlated with the mineralogical and physical

ebate@zju.edu.cn (B. Bate).

properties of expansive soils, is of attracted considerable concern to pro-fessionals and planners.

Electric response is a non-invasivemethod that can provide useful in-formation about moisture condition, structural characteristics, salinityand contamination of subsoil (Fukue et al., 1999; Yoon and Park, 2001;Ya et al., 2015). The use of electrical conductivity in subsurface investiga-tion has become very popular among geotechnical engineers (Kibriaet al., 2014; Abu-Hassanein et al., 1996;Mitchell and Soga, 2005; Lesmesand Friedman, 2005). Furthermore, the most influential property of anexpansive soil on volume change is its mineralogical properties (suchas montmorillonite content MC, clay content CC and specific surfaceSSA) (Zheng et al., 2008; Li et al., 2014), which electrical response isalso sensitive to (Abdul et al., 1990; Liu et al., 2004; Keller andFrischknecht, 1966; Delaney et al., 2001; Fukue et al., 1999; Demondand Roberts, 1993; Mitchell and Soga, 2005; Santamarina et al., 2001).Based on the response on physical and mineralogical properties of sub-soil, Electric response ground surveys can be used to correlate to swellparameters (i.e. free swelling rate) of expansive soils (Lesmes andFriedman, 2005). To date, however, the relationships between electricresistivity (conductivity) and free swelling rate of expansive soils havenot beenwell documented in the literature. Consequently, it is importantto develop reliable swell methods for better volume change predictions.

The goal of this study is to establish a newmodel relating free swell-ing rate of expansive soils to their electrical resistivity. Laboratory tests

Table 1Index properties of kaolinite and bentonite.

Parameter Bentonite Kaolinite

wopt (%) 7.10 12.95wL (%) 281.2 65.8wp (%) 39.4 34.5Clay content (%) 40.26 22.19Gs 2.67 2.70

266 Y. Chu et al. / Journal of Applied Geophysics 148 (2018) 265–271

are carried out onmixtures of bentonite and kaolinite at different ratiosto simulate wide range of free swell rates of expansive soils. Thequantitative relationships between either the swelling deformation orstructural parameter (porosity) and resistivity will be obtained with aself-developed improved four-electrode soil resistivity box (Chu et al.,2016). On the basis of the test results, theoretically based models,which capture the intrinsic connections between the normalizedsurface conductivity (σs/σw) and free swelling rate and is simple enoughto be applied in the field, are established.

2. Background

In fact, it is important to note that resistivity (ρ) collapses to thereciprocal of conductivity (σ) σ = 1/ρ (de Lima and Sharma, 1990).So, the conductivity was used to analyze the function of conductivity(σ), porosity (φ) and free swelling rate (δ).

Based on the experimental results of a sedimentary rock under fullysaturated conditions, Archie (1942) suggested a widely-used empiricalequation, which is suitable for characterizing the electrical conductivityof both coarse-grained soils and marine sediments (i.e. fine-grainedsoils in high-salinity environments) (Choo et al., 2016b; Salem andChilingarian, 1999; Mitchell and Soga, 2005). Archie's equation relatesthe electrical resistivity of saturated soils (ρmix) to the resistivity ofpore water (ρw) and porosity (φ):

ρmix ¼ φ−m � ρw;σmix ¼ φm � σw ð1Þ

where σmix is electrical conductivity of mixed soils, σw is conductivity ofpore fluid, φ is porosity, m is a fitting parameter. Archie's equation(Eq. (1)), however, may not be applicable to fine-grained soils, whosesurface conduction contributes significantly to the electrical conductiv-ity (Choo et al., 2016a; Santamarina et al., 2001). Therefore, electricalconduction (Gmix) of fine-grained soils, such as the montmorillonite-rich expansive soils in this study, should be expressed as the sum ofthe pore fluid conduction (Gw) and the surface conduction (Gs) asshown in Eq. (2) (Bussian, 1983; Choo and Burns, 2014; Glover, 2010;Glover et al., 2000; Klein and Santamarina, 2003; Mitchell and Soga,2005; Pfannkuch, 1972).

Gmix ¼ Gw þ Gs ð2Þ

Among the formulas of previous studies (Bussian, 1983; Feng andSen, 1985; Choo et al., 2016b; Niwas et al., 2007), the work of Glover(2010) and Bussian (1983) (i.e. a theoretically derived electrical con-ductivity formula based on the Hanai-Bruggeman equation) is suitable

Table 2Index properties of natural expansive soils. S1: sample one of Hanzhong expansive soils, S2: sa

Soils w/% r/kN/m3 Gs pH LL/% PL/%

S1 28.41 2.34 2.72 7.2 119.80 46.1S2 31.23 2.24 2.70 8.6 115.27 35.8S3 25.33 2.08 2.73 7.5 123.28 36.9BC / / 2.74 7.6 187.18 37.7

for the interpretation of electrical conductivity of clayey soils. Bothresearchers suggested a modified equation under the assumption thattwo different conductions as follows:

σmix ¼ σwφm þ σ s � 1−φmð Þ ð3Þ

where σs is matrix surface conductivity in clayey soils, m is the cemen-tation factor, and strongly reflects the depolarization factor of dispersedparticle (i.e. the path for pore water conduction) (Bussian, 1983; Fengand Sen, 1985; Niwas et al., 2007). The surface conductivity, which isrelate to the mineralogical properties (i.e. free swelling rate), can becalculated by Eq. (3).

3. Materials and experimental methods

3.1. Materials

Expansive soils used in the test were prepared by mixing thecommercial kaolin (Suzhou Kaolinite, Nanjing, China), primarily com-posed of kaolinite and bentonite (Sunan Bentonite, Zhenjiang, China),primarily composed of sodium montmorillonite. Index properties ofKA and BE are listed in Table 1. Distilled water (electrical conductivityranging from 2.44 to 2.74 μs/cm at temperature 22.0 ± 0.5 °C) wasused as the control samples.

Two natural expansive soils (Hanzhong expansive soils and BlackCotton soils BC) were used as references. Both soils were excavated,wrapped with plastic bags, transported to the laboratory, and thenstored in a moisture room until used. Both soils were classified as highplasticity clay (CH) according to the unified soil classification system(ASTM D422-63), and their index properties was shown in Table 2. Ascanning electron microscopy (SEM) test (SEM S-3400N, Hitachi,Tokyo, Japan) was performed on mixed soils (Fig. 1). SEM imagingsuggested that larger face-to-face (FF) aggregations have induced withthe additional of bentonite fraction (BF). And the structure of particlesurface or micro-porosity in the clay interior is also changed.

3.2. Experimental method

Free swelling rate and free swelling index experiments wereperformed on kaolinite-bentonite mixtures and natural expansivesoil samples according to ASTM D5890-11 standard and Chinese JTGE40-2007 standard. The volume level was recorded after the minimum16-h hydration period from the last increment addition until rate ofexpansion is b0.0002 in/h.

The conductivity experiments were performed by a self-developedfour electrodes soil resistivity testing cylinder (5 cm × 15 cm, diameter× length) (Fig. 2) at 22 °C in accordance with ASTM D G57-06 (1995).The cylinder is constructed with polyvinyl chloride (PVC), which is anelectrical insulator (electrical resistivity about 1016 Ω cm). Alternatingcurrent (AC) (16 V and 50 Hz) was used to avoid electrophoreticphenomena, which could alter water content, soil structure, and pore-fluid chemistry (Hamed et al., 1990). The frequency of 50 Hz wasselected for two reasons: (1) It is the frequency of the householdpower supply in China, and (2) it is sufficiently low to avoid electrodepolarization at higher frequency (N500 Hz) (Arulanandan and Smith,

mple two, S3: sample three.

PI δ% Particle concentration %

b0.005 0.005–0.075 N0.075

8 73.63 92.8 30.06 62.40 7.547 79.40 106 46.06 47.40 6.542 86.35 118.5 46.72 47.64 5.647 149.41 225 / / /

%07=FB %03=FB %0=FB

Fig. 1.Micrographs of mixed soils with different bentonite fraction (BF = weight of bentonite/total weight).

Fig. 2. Four electrodes soil resistivity testing cylinder: (a) electrical circuit illustration, and (b) laboratory set-up.

267Y. Chu et al. / Journal of Applied Geophysics 148 (2018) 265–271

1973; Mitchell and Arulanandan, 1968). Using Ohm's law, electricalresistance and electrical resistivity are obtained by Eqs. (4) and (5),separately:

R ¼ ΔV=I ð4Þ

σ ¼ 1=ρ ¼ L= RAð Þ ¼ IL= ΔVAð Þ ð5Þ

where R is resistance, σ is conductivity, ρ is electrical resistivity, ΔV ispotential difference, A is a cross-sectional area, I is electric current, L isthe distance between the electrodes.

3.3. Sample preparation

In order to prepare Bentonite-Kaolinite mixed soils with varyingbentonite fractions, the bentonite was added to the kaolinite at abentonite fraction by weight (BF = weight of bentonite/total weight)of 0%, 10%, 20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, and 100%. Then, themixed soils were submerged into de-ionized water with a solid-to-water ratio of 0.1 (±0.02). The resulting mixtures was then manuallystirred for 30 min and then left to stand for a minimum of 24 h to com-plete the hydration process. After hydration process, soil samples weresealed with food wrap, placed in a ziploc bag, and stored in a moistureroomwith 95% relative humidity at 22 °C until use. Before testing, sam-ples were transferred into the resistivity cylinder with double drainageconditions (Sheeran and Krizek, 1971; Kang andBate, 2016). Then staticpressure was applied to compress the samples to varying prescribed

Table 3The expansive characteristics of bentonite-kaolinite mixtures.

Bentonite fraction BF 0% 10% 20% 30%

Free swelling rate (%) 27 31 55 68Free swelling index (2 g/mL) 1.62 1.73 2.13 2.36

porosities (all samples were saturated and porosities were controlledby the volume of samples using φ = (V-Ms/Gs)/V, V is the volume ofsamples, Ms is the weight of dry soils and Gs is the specific gravity ofsoils). After finishing sample preparation, the resistivity cylinder wasconnected with a power supply and current/voltage meter (Fig. 2).Then the resistivity of samples were calculated by Eqs. (1) and (2)using the reading value of current (I) and voltage (ΔV) meter.

4. Results and discussion

4.1. Free swelling test results

The free swelling test results are presented in Table 3. Free swellingrate and free swelling index of artificial expansion soil are presented inFig. 3.

It was observed that increase in the bentonite content of the claymixtures yielded increases in the free swelling rate and free swellingindex. And there is a power function relation between the free swellingrate and the bentonite content. There is 2900% increase in its swellingpotential with the addition of 100% bentonite to the original samplewhich shows that soil has earn much of its expensively by the additionof bentonite (Kolay and Ramesh, 2016; Cokca, 2001). There is 790% in-crease in its free swelling index with the addition of 100% bentonite tothe original sample. According to Table 3, the artificial expansion soilhas a free swelling rate above 800% and a free swelling index above12.86 2 g/mL. The free swelling rate of black cotton soil is 225%. Sincethe free swelling rate of artificial expansion soil came out to be 288%

40% 50% 60% 70% 80% 90% 100%

85 142 180 288 430 577 8002.65 3.54 4.17 5.72 7.79 9.8 12.86

0.0 0.2 0.4 0.6 0.8 1.0

0

200

400

600

800

Free swelling rate Free swelling index

Percentages mixture of bentonite

Free

sw

ellin

g ra

te δ

(%

)

Free swelling rate of regur soil is 225%

Percentages mixture of bentonite<70%

0

3

6

9

12

Free

sw

elli

ng in

dex

(2g·

mL

-1)

Fig. 3. Free swelling rate and free swelling index of bentonite-kaolinite mixtures.

268 Y. Chu et al. / Journal of Applied Geophysics 148 (2018) 265–271

with the addition of 70% bentonite, so the 70% bentonite of artificial ex-pansion soil is chosen as the upper limit. Eight kinds of artificial expan-sion soil samples were used to analyze the relationship betweenresistivity and free swelling rate. The percentages mixture of bentonitewith kaolinite clay were 0%, 10%, 20%, 30%, 40%, 50%, 60% and 70% byweight.

4.2. Electrical conductivity versus BF and porosity

The typical measured electrical conductivities of mixed expansivesoils with varying BF are compared at ten different porosities asshown in Fig. 4. Fig. 4 clearly indicates that the measured mixed soilsconductivity σmix increases considerably with an increase in BF.Moreover, the relationship between σmix and BF was fitted by a linearequation, with a regression coefficient ranging from 0.90 to 0.95.

σmix ¼ a� BF þ b ð6Þ

where a and b are the fitting parameters. Furthermore, an increase ofbentonite fraction yields changes in the expansive soils structure,whichmay change the special surface and surface boundwater, includ-ingmineral composition of clay clods, elimination of inter-cloud micro-voids and the microscale, reorientation of clay particles (Fig. 1)(Santamarina et al., 2001; Kolay and Ramesh, 2016; Wang et al., 2013;Erzin and Gunes, 2013). According to the above theory, the additionalof BF cause an increase in special surface and surface bound water,

0 20 40 60 80 100

0

500

1000

1500

2000

Porosity ↑

σmix

=55+4.6×BF

σmix

=400+16.4×BF

Porosity (φ) = 0.730 0.844 0.890 0.915 0.931 0.942 0.950 0.956 0.960 0.964

Bentonite Fraction BF/%

Ele

ctri

cal c

ondu

ctiv

ity σ

mix/µ

s·cm

-1

Fig. 4. Reciprocal resistivity according to porosity and bentonite fraction.

which plays a significant role on the conductivity of soil. Additionally,it can be observed from Fig. 4 that the measured σmix increased with adecrease in volumetric fraction of pore fluid (in terms of porosity). Sim-ilar resultswere also reported by Choo et al. (2016a, 2016b). From Fig. 3,it is clearly shows that the free swelling rate has a high coefficient func-tion with BF. Thus, the fitting results suggest that electric resistivity canbe used to correlate to the free swelling rate of expansive soils.

The results of the previous studies (Bussian, 1983; Choo and Burns,2014; Glover, 2010; Klein and Santamarina, 2003) clearly indicatedthat the mixture conductivity σmix of clay soils can be expressed as afunction of pore water conductivity σw and surface conductivity σs

(Eq. (3)). It should be noted that surface conductivity σs, which has asensitive on the change of special surface and surface bound water(Klein and Santamarina, 2003; Kolay and Ramesh, 2016; Niwas et al.,2007), is the major part of mixture conductivity related to the swellingpotential of expansive soils.

However, variations ofσmix and free swelling rate δ are debatable ac-cording to the values of pore water conductivity, which is changedwiththe observations presented in previous studies (Choo and Burns, 2014;Klein and Santamarina, 2003; Li et al., 2014; Erzin and Gunes, 2013). Inorder to highlight this contrasting behavior of the measured σmix withthe tested pore water conductivity, the normalized conductivity,which is defined as the ratio of the measured conductivity (σmix) tothe pore water conductivity (σw), is plotted as a function of porosity φin Fig. 5. The normalized conductivity (σmix/σw) can be expressed as fol-lows based on Eq. (8), and it is a reciprocal of Archie's formation factor(F = ρmix/ρw) (Archie, 1942):

σmix=σw ¼ 1−σ s=σwð Þφm þ σ s=σw ð8Þ

Fig. 5 clearly indicates that the measured values of σmix/σw remark-ably decrease with the increase in porosity φ. Because of the effect ofsurface conductivity σs, the measured σmix is higher than σw at low σw

(σw = 0.00025S/m) (Choo et al., 2016b). As anticipated in Eq. (3) andFig. 5, at highwater fraction (φ ranging from 0.9 to 1.0) a linear approx-imation is sufficient in relating pore water resistivity to mixed soilsconductivity. That is, the pore water conduction is dominant over thesurface conduction. Therefore, an increase in σmix/σw with a decreasein φ demonstrates that a reduction in pore water conduction with a de-crease in φ is overcompensated by the increased surface conduction(Bate and Burns, 2014; Choo and Burns, 2014; Klein and Santamarina,2003). Additionally, it should be observed from the past researches(Kolay and Ramesh, 2016; Cokca, 2001; Santamarina et al., 2001) thatvarying the value of σw may change the mineral structure, which

0.4 0.5 0.6 0.7 0.8 0.9 1.0

0

200

400

600

800

1000

Free swelling rate:

σmix

/σw=

(1-400)×φ1.97+400

Nor

mai

lized

con

duct

ivity

σm

ix/σ

w

Porosity φ

288% 180% 142% 85% 68% 55% 31% 27.5%

Free swelling rate δ↑Special surface S

a↑

Low σw

High σs

σmix

/σw=

(1-880)×φ3.69+880

Fig. 5. Normalized conductivity variation of the tested soil mixtures according to porosityand free swelling rate.

Table 4m exponents and specific surface values for typical clays.

Type m exponent Specific surface (m2/g)

Kaolinite 1.9–2.2 10–20Illite 2.2–2.4 65–100Smectite 2.4–2.7 650–800Montmorillonite 2.7–3.3 700–840

269Y. Chu et al. / Journal of Applied Geophysics 148 (2018) 265–271

could alter some parameters (eg. swelling potential), of soils. However,only low σw, which could representmajor sites of nature, was discussedand other influences were neglect in this study.

Several general observations were made from Fig. 5 that: (1) themeasured σmix was found to increase with an increase in free swellingrate δ, which suggests the increase in special surface (because of the ad-ditional BF) cause an increase in conductivity σs (Wang et al., 2013;Erzin and Gunes, 2013); (2) the surface conductivity σs is one by onecorrespondence with the free swelling rate δ and (3) the measuredσmix shows clear dependency on porosity φ, because the magnitudesof the pore water conduction and surface conduction are determinedfrom the volume fractions of pore space and soil particles, respectively,according to the research of Glover et al. (2000), Klein and Santamarina(2003), Mitchell and Soga (2005) and Choo et al. (2016b).

Varying the structure of particle surface or micro-porosity in the clayinterior (i.e. the additional of BF) impacted the special surface and thick-ness of the absorbed water layer (or diffuse double layer DDL) (Bate andBurns, 2014; Kolay and Ramesh, 2016; Cokca, 2001). The decrease inthe thickness of DDL causes increased the mobility of ions in DDL, whichresulted in an increase in surface conduction. Increasing the special sur-face increased the amount of surface bound water, which also causes anincrease surface conductance. (Santamarina et al., 2001; Bate, 2011).These changes in the structure of particle surface and thickness of theabsorbed water layer were reflected in the surface conductivity (σs),which tended to increase the value σmix/σw with a decrease in porosityor an increase in free swelling rate δ (Fig. 5), indicating that the normal-ized surface conductivity (σs/σw) can be utilized as a estimation factor offree swelling rate of expansive soils. Therefore, as anticipated in Eq. (3),the normalized surface conduction (σs/σw) can be calculated using thevalues of σmix, σw and porosity φ (Sadek, 1993; Choo and Burns, 2014;Glover, 2010; Choo and Burns, 2014; Klein and Santamarina, 2003).

4.3. Calculation of normalized surface conduction

Based on Eqs. (1) and (3), the normalized surface conductivity(σs/σw) of tested soils, which is defined as the ratio of the surfaceconductivity (σs) to the pore water conductivity (σw), can be deter-mined as:

σ s=σw ¼ σmix=σw−φmð Þ= 1−φmð Þ ð7Þ

To calculate the normalized surface conductivity (σs/σw) of the testedsoils using Eq. (7) the cementation factorm at a given bentonite fraction(free swelling rate) should be fitted with porosity as shown in Fig. 5.Fig. 6 shows the variation of Archie's m exponent of the tested material

0 20 40 60 80 100

2

3

4

mBF=0%

=1.97

Free swelling rate= 85% 142% 180% 288%

27.5% 31% 55% 68%

Cem

entio

n fa

ctor

m

Bentonite fraction BF/%

mBF=70%

=3.69

Fig. 6. Variation ofm exponent according to bentonite fraction.

as a function of bentonite fraction BF (various free swelling rates). Addi-tionally, it can be observed that them exponent rapidly increaseswith anincrease in bentonite fraction BF. However, a rate of increase in them ex-ponent with BF decelerates with a further increase in BF. Note that themexponent determined as 3.69 is comparable to that of previous studiesfor typical bentonite, while m exponent determined as 1.97 at a low BF(high kaolinite fraction) is comparable to that of previous studies for typ-ical kaolinite (as shown in Table 4) (Choo et al., 2016a; Salem andChilingarian, 1999). However, both kaolinite and bentonite are all colloi-dal particles, whichhave a plate-like structure,may have the some depo-larization factor (Bussian, 1983; Feng and Sen, 1985; Niwas et al., 2007).But, due to the behaviors, including electrical conductivity, ofmixed soilswith two different constituent particles are determined by the volumefraction (not weight fraction) of the added particles (Mele et al., 2014;Tenchov, 1998; Choo et al., 2016a) the variation of the determinedm ex-ponents should change with the additional BF.

Previously observation (Glover et al., 2000; Choo et al., 2016a) canimplies that the relevance of Archie's equation for the electrical conduc-tivity of mixed soils can be reinforced with the significant porosity φbecause σmix at high porosity φ can be adequately captured by Eq. (1).As mentioned previously, Archie's m exponent (or cementation factor)can be calculated by the measured normalized conductivity (σmix/σw)at a given high porosity. Therefore, the approximate m exponent ofthe tested mixed soils can be expressed as at a high porosity (φ → 1):

mc ¼ log σmix=σwð Þ= logφ;φ→ 1 ð8Þ

wheremc is the approximate value ofm exponent. So, the approximatevalue of determinedmc exponents, which are calculated by Eq. (8), waschosen as the calculated factor in this article. Therefore, the normalizedsurface conduction (σs/σw) of tested soils can be expressed as:

σ s=σw ¼ σmix=σwð Þ−ϕmc� �

= 1−ϕmc� � ð9Þ

4.4. Estimation of free swelling rate of expansive soils using normalizedsurface conduction

Surface conductivity (σs) is the measure of the surface ions mobilityof soil components, and can be used as a good parameter to evaluate thespecial surface area and bound water content of soils (whichmeans theswell potential of soils) (Revil and Glover, 1997; Cokca, 2001; Berg,1995). Based on Eq. (3) surface conductivity (σs) is influenced by porewater conductivity. Therefore, the normalized surface conductivity(σs/σw), which was calculated by Eqs. (8) and (9), was used to analyzethe free swelling rate δ for the mixed soils, natural expansive soils andother research's values. The calculated normalized surface conductivity(σs/σw) is plotted with the free swelling rate of mixed soils in Fig. 7. Theobservation clearly demonstrates that an excellent linear relation can befound between log(σs/σw) and log(δ) as (R2 = 0.97):

logδ ¼ −5:38þ 2:63� log σ s=σwð Þ ð10Þ

Therefore, the free swelling rate δ of mixed soils (or other expansivesoils) can be estimated using Eq. (5) with knowledge of the σmix, σw, φ,and m exponents. Furthermore, m exponents of mixed soils canbe roughly estimated by determining the normalized conductivity(σmix/σw) of soil at given high porosity φ according to Eq. (8) because

400 600 800 1000

10

100

1000

Fre

e sw

ellin

g ra

te δ

/%

=Porosity (φ) 0.730 0.844 0.890 0.915 0.931 0.942 0.950 0.956 0.960 0.964

Nomarized surface conductivity σs/σ

w

BF↑Free swelling rate↑

logδ=-5.38+2.63×log(σs/σ

w)

Fig. 7. Variation of porosity-normalized surface conduction as a function of free swellingrate.

270 Y. Chu et al. / Journal of Applied Geophysics 148 (2018) 265–271

m values show typical values according to particle shape and structure(Choo et al., 2016a; Revil and Glover, 1997; Feng and Sen, 1985;Niwas et al., 2007). It is also note that the excellent linearity betweenlog(σs/σw) and log(δ) can be used to estimate the free swelling rate δ re-gardless of the values of porosity of soils.

Fig. 8 shows the comparison of the measured and estimated freeswelling rate δusing electrical response (normalized surface conductionσs/σw). It clearly note that data of natural expansive soils (Hanzhong ex-pansive soils and Black Cotton soils BC) and previous studies (Gonget al., 2011; Ju, 2011) is also included in Fig. 8, and a good agreement be-tween the data of this study and that of natural expansive soils and pre-vious studies can be found, which may reveal the robustness of thisestimation equation and the reliability of the calculated free swellingrate δ values. Additionally, it may reveal that the results of this studyfor mixed soils (bentonite and kaolinite) can be used in the interpreta-tion of other expansive soils (i.e. black cotton soil). In summary, it can beconcluded that these empirically derived functions can be theoreticallyrelated to the statistics of the resistivity and the structure parameters ofthe soil sample. It is possibility that electrical resistivity measurementscould eventually be used to predict the free swelling rate for at leastsome types of expansive materials (ie. at low pore water conductivitycondition). Therefore, it would be aworthy effort to use the electrical re-sistivity, a non-destructive tool which can be economical aswell as timesaving, correlate free swelling rate of expensive soils.

0 50 100 150 200 250 300

0

50

100

150

200

250

300

Cal

cula

ted

free

sw

ellin

g ra

te δ

c %

Measured free swelling rate δm %

This study Natural soils Previous studies

Best-fit line

R2=0.98

Fig. 8. Comparison of experimental results with the predicted results.

5. Conclusions

New relationships to predict the swellingpotential in expansive soilswasproposed by the electrical resistivity technique in the present study.The electrical response (normalized surface conduction) is found to bedirectly correlated to free swelling rate. These experimental findingswill helpful to interpret the swelling potential observed in expansivesoils, and improve our understanding on the associated resistivity andfree swelling rate. The following lists a few of themajor conclusions ob-tained from the present experimental program:

1) The expansion of artificial expansion soil is closely related to thecontent of BE clay. Swelling potential related free swelling rate andfree swelling index experiments have yielded test results show thatthe 70% bentonite of artificial expansion soil can be chosen as theupper limit.

2) These changes in the structure of particle surface and thickness ofthe absorbedwater layerwere reflected in the surface conductivity (σs),which tended to increase the value σmix/σw with a decrease in porosityor an increase in bentonite fraction BF indicating that the normalizedsurface conduction (σs/σw) can be utilized as a estimation factor offree swelling rate of expansive soils.

3) As mentioned previously, Archie's m exponent (or cementationfactor) can be calculated by the measured normalized conductivity(σmix/σw) at a given high porosity. Therefore, the approximate mexponent of the testedmixed soils can be expressed as at a high porosity(φ → 1):

mc ¼ log σmix=σwð Þ= logϕ; ϕ→ 1

Therefore, the normalized surface conductivity (σs/σw) of testedsoils can be expressed as:

σ s=σw ¼ σmix=σwð Þ−ϕmc� �

= 1−ϕmc� �

4) An excellent linear relation can be found between log (σs/σw) andlog(δ) as

logδ ¼ −3:1þ 1:85� log σ s=σwð Þ

Therefore, the free swelling rate δ of mixed soils (or other expansivesoils) can be estimated with knowledge of the σmix, σw, φ, andm expo-nents. Furthermore,m exponents ofmixed soils can be roughly estimat-ed by determining the normalized conductivity (σmix/σw) of soil atgiven high porosity φ because m values show typical values accordingto particle shape and structure.

5) The electrical response measurements could eventually be usedto estimate the free swelling rate for at least some types of expansivematerials. It can be concluded that the electrical response can be usedto correlate free swelling rate of expensive soils being a non-destructive tool which can be economical as well as time saving.

Acknowledgment

Majority of the work presented in this paper was funded by the KeyProject of Natural Science Foundation of China (Grant No. 41330641),the Research Innovation Project of Ordinary University GraduateStudent of Jiangsu Province (Grant No. KYLX15_0140), and the post-graduate program of high-level University of National Construction(201606090143).

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