Geoderma 209–210 (2013) 136–142

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Improved near surface soil characterizations using a multilayer soilresistivity model

T. Islam a,b,c,⁎, Z. Chik a

a Department of Civil and Structural Engineering, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysiab Department of Electrical and Electronics & System Engineering, Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysiac Department of Electrical and Electronics Engineering, Faculty of Computer Science and Engineering, PSTU, Bangladesh

⁎ Corresponding author at: Department of Civil and StEngineering & Built Environment, Universiti KebangsaanMMalaysia. Tel.: +60 1115551986; fax: +60 3 8921 6147.

E-mail address: staohidul@yahoo.com (T. Islam).

0016-7061/$ – see front matter © 2013 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.geoderma.2013.06.015

a b s t r a c t

a r t i c l e i n f o

Article history:Received 21 September 2012Received in revised form 5 June 2013Accepted 18 June 2013Available online 10 July 2013

Keywords:Multi-layer soil resistivityResistivity ratioStandard penetration testSoil characteristics

This paper presents a method for determining near surface soil characteristics using multi-layer soil resistivitymodel. Usual soil resistivity model has its limitations in obtaining accurate soil characteristics because of theinterrelationships between soil apparent electrical resistivity (ρ) and other soil physical or chemical properties.For most soils with varying layers, multi-layer resistivity profile is therefore more suitable to obtain near surfacesoil characteristics. The nobility of the research is to obtain soil characterizations using multi-layer resistivitymodel in near surface soil profile. In thismulti-layer soilmodel, soil resistivity and resistivity ratio in soilmediumat various depths are considered for soil field investigations. The results of multi-layer model are comparedwiththe data from standard penetration test (SPT) and the profile from Multi-channel Analysis of Surface Wave(MASW) method to show the feasibility and reliability of using this model in soil profile. This method is alsofar simpler to perform compared to SPT and other methods.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Near surface soil characterizations and soil strength determinationsare prerequisite in highway and road engineering, geotechnical engi-neering, and other divisions of civil engineering. Soil electrical resistivityhas been widely applied to many geotechnical and other engineeringinvestigations to obtain near surface soil profile (Chaplot et al., 2010;Zhu et al., 2007). In particular, direct current (DC) resistivity monitoringhas beenwidely used by correlating the changes of subsurface resistivitywith the soil properties (Samouelian et al., 2005; Son et al., 2010). Soilelectrical resistivity is a very important parameter which can be usedto determine the specific soil characteristics of a soil profile in the nearsurface such as soil type, dry density of soil compaction, salinity andporosity of soil (Yoon and Park, 2001).

The soil resistivity measurements are commonly used with afour-point probemethod such asWenner'smethod. The basic principleof the soil resistivity, ρ measurement system is that when a constantvoltage is applied across two probes placed in the soil, the currentthat flows between the probes is inversely proportional to the resis-tance of the soil (Herman, 2001).

As shown in Fig. 1, current, I is passed through two conductingprobes, at the surface of the earth. The potential difference, v betweentwo points at the surface of the earth is then taken as shown in Fig. 1.

ructural Engineering, Faculty ofalaysia, 43600 Bangi, Selangor,

rights reserved.

The electrical resistance, R is then obtained by dividing v by I accordingto the Ohm's law.

The passing of electric current using a four-point probe methodcreates electric field in near surface soil profile (Lu et al., 2002).The equation of the electric filed is a function of the gradient of scalarpotential (Dutta, 1997; Herman, 2001).

E ¼ −gradψ ð1Þ

Another basic equation is related to current density, J is that

div J ¼ 0: ð2Þ

The conductivity, σ(z) varies according to the depth, z. Hence, thepartial differential equation of electrical potentiality can be expressedas,

∂2ψ∂x2

þ ∂2ψ∂y2

þ ∂2ψ∂z2

þ 1σ

∂ψ∂x

∂σ∂x þ ∂ψ

∂y∂σ∂y þ ∂ψ

∂z∂σ∂z

� �¼ 0: ð3Þ

Using cylindrical coordinates (r,z), we obtain

∂2ψ∂r2

þ 1r∂ψ∂r þ ∂2ψ

∂z2þ ∂ψ

∂z1σ∂σ∂z ¼ 0 ð4Þ

where r ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2 þ y2

p.

Fig. 1. Soil resistivity measurements using a four-point probe method.

137T. Islam, Z. Chik / Geoderma 209–210 (2013) 136–142

Due to the azimuthal symmetry, we can separate Eq. (4) into twoequations as

d2R̂dr2

þ1rdR̂dr

þλ2R̂ ¼0 ð5Þ

where R̂ is the vector of cylindrical coordinates, and

d2Zdz2

þ 1σdσdz

dZdz

−λ2Z ¼ 0 ð6Þ

where λ is the separation constant.Thus, a general solution for electric potential can bewritten as Eq. (7).

ψ ¼ ∫∞0 F λð ÞR̂ λ; rð ÞZ λ; zð Þdλ ð7Þ

Fig. 2. Multi-layer resistivity pro

In addition, because the electric potential varies according to depth,it is also a function of z. For two-layer resistivity model, the potentialityis given by Seedher and Arora (1992).

ψ1 ¼ Iρ1

2π∫∞0 A λð Þe−λz þ B λð Þeλzh i

J0 λrð Þdλ ð8Þ

Lower layer is considered as half space in two-layer model wherez → ∞ is seen. So, the factor eλz cannot appear. Now,

ψ2 ¼ Iρ1

2π∫∞0C λð Þe−λzJ0 λrð Þdλ: ð9Þ

The apparent resistivity is obtained through this model which isconverted to true resistivity to get near surface profile. There is thelack of accuracy for empirical relationship between soil apparent elec-trical resistivity and several soil physical or chemical properties(Herman, 2001; Samouelian et al., 2005). Therefore, some researchersconcentrate for optimization in inversion analysis to get soil true re-sistivity corresponding to depth (Kleefeld and Reibel, 2011).

Some researchers also include multi-layer soil structure to opti-mize soil apparent resistivity profile (Takahashi and Kawase, 1990).There is another theoretical approach of using multi-layer structurefrom kernel function to get optimization of soil apparent resistivityprofile (Kang et al., 2010; Zhang et al., 2006). The apparent resistivitycurves in multi-layer soil structure, different parameters are calculat-ed again and again to fit the measurement data (Zhang et al., 2005,2006). It is also difficult to obtain the derivatives of the optimized ex-pression. Two stage algorithms are presented to invert the parameterof horizontal multi-layer soil (Zou et al., 2004). There is inclusion oferror factor at conversion of apparent resistivity to true resistivity instraight forward inversion (SIS) algorithm (Gupta et al., 1997). Kanget al. (2010) show another algorithm for optimization of apparent re-sistivity data based on kernel function through multi-layer earthstructure. This optimization also includes complex on nonlinear mul-tivariable equation for matching of apparent resistivity data.

Moreover, electric resistivity tomography (ERT) is obtained basedon soil apparent resistivity data by Loke (2007). This ERT is used inhydrological applications (Cousin et al., 2009) and agricultural appli-cations (Michot et al., 2003). For ERT, soil apparent resistivity isconverted to true resistivity through inversion analysis for soil char-acterizations (Sudha et al., 2009).

file in soil characterizations.

Fig. 3. 3-D profile of soil electric potential in near surface soil.

138 T. Islam, Z. Chik / Geoderma 209–210 (2013) 136–142

In practice, two-layer soil model is still used for non-homogeneoussoil characterizations using soil apparent resistivity (Lacerda et al.,2007). Though several optimization techniques are practiced to getsoil resistivity profile from measurement of apparent resistivity, thisresult can be misinterpreted for including only soil resistivity data inempirical relationships. Since soil resistivity is influenced by moisturecontents (Ozcep et al., 2010), consideration of only resistivity canchange the results of soil characterizations.

In this paper, a multi-layer resistivity model of earth structureis developed incorporating true resistivity profile with soil apparentresistivity profile to get better performance in resistivity profile. Thetrue resistivity profile is important for the accuracy in near surfacesoil characterizations. And, the apparent resistivity is able to showdeeper soil profile based on the probe distances in resistivitymeasurements. This paper also describes the implementation ofmulti-layer model with soil electric resistivity ratio for reliablenear surface soil characterizations. Data from SPT is used in thisstudy to assess the accuracy of multi-layer model for near surfacesoil characterizations. Moreover, seismic signal analysis is used asa non-destructive method in obtaining near surface soil properties.Multi-channel Analysis of Surface Wave (MASW) method is one ofthe improved methods in seismic signal analysis (Park et al.,1999a, 1999b). Near surface soil profile from multi-layer resistivitymodel is also verified with the soil profile from MASW method infield investigations.

Table 1Electric properties in true resistivity profile.

Depth (m) Current (mA) Voltage (V) Resistance (Ω) Resistivity

0.2 138 2.39 17.32 108.760.4 210 3.12 14.86 93.300.6 267 3.75 14.04 88.200.8 289 3.91 13.53 84.961 260 3.42 13.15 82.611.2 256 3.28 12.81 80.461.4 247 3.02 12.22 76.781.6 240 2.76 11.5 72.221.8 233 2.32 9.96 62.532 235 2.2 9.36 58.79

2. Methodology

Theoretical derivation on multi-layer soil characterizations usingnumerical analysis has been described in our previous study (Islamand Chik, 2011). In this study, a four-point probe method is used toestimate electric properties in soil. The parameters of soil resistivity,potential differences and thickness of each layer are used in themulti-layer earth model as shown in Fig. 2. When current is injectedin the soil, electric field is generated in the near surface soil. The elec-tric potential and electric field strength vary according to variation ofthe parameters with depth in the soil.

The n potential functions can be written as n layer model fornormal surface in multi-layer earth structure. The electric potentialof ith layer model is given by Eq. (10).

ψi ¼ρiI2π

∫∞

0

Ai mð ÞJ0 mrð Þe−mzdmþ ∫∞

0

B0 mð ÞJ0 mrð Þemzdm

" #ð10Þ

Fig. 4. Electric resistivity measurements at site in UKM.

Fig. 5. Multi-layer soil resistivity ratio profile at site A in UKM.Fig. 7. Multi-layer resistivity ratio profile at site B in UKM.

139T. Islam, Z. Chik / Geoderma 209–210 (2013) 136–142

Moreover, the potential of nth layer is written as

ψn ¼ ρiI2π

∫∞

0

An mð ÞJ0 mrð Þe−mzdm

" #: ð11Þ

The reflection coefficient for the multi-layer soil structure is foundas

K1 ¼ ρnþ1−ρn

ρnþ1 þ ρn: ð12Þ

With summation and subtraction of the resistivity, the reflectioncoefficient can be represented as

K ′1 ¼ ρnþ1

ρn: ð13Þ

The resistivity ratio between two adjacent layers would be used inmulti-layer true resistivity model. This resistivity ratio is used to ob-tain reliable soil characteristics rather than criteria of using only soilapparent resistivity profile.

Simulations are carried out for proposed multi-layer earth modelwith different soil electric parameters. Soil resistivity and soil electricpotential are obtained through the creation of soil electric field innear surface soil. The study of the soil electric properties for differentlayers of soil is needed to obtain reliable information on the soil char-acteristics. Fig. 3 shows the simulation results for multi-layer soilelectric potential in near surface soil profile. The resistivity ratio forthe adjacent two layers is used in this multi-layer model for soil char-acterizations where resistivity ratio is obtained incorporating data oftrue resistivity with data of soil apparent resistivity. True resistivityis estimated based on the changes of electric resistance according tothe depth in soil as shown in Table 1. Moreover, apparent resistivity

Fig. 6. SPT data at site A in UKM.

is estimated based on the probe distances as Wenner's four-pointprobe method.

MASW method is performed to verify the resistivity ratio profileobtained from multi-layer resistivity model. The software, SurfSeisdeveloped at the Kansas Geological Survey is used to process seismicdata using the MASW method.

3. Result and discussion

To evaluate the proposed method, a test was carried out near theFaculty of Engineering and Built Environment, UKM for obtainingmulti-layer electrical properties. Data of SPT is also obtained at thesame site in UKM to verify the results obtained from multi-layermodel for soil characterizations.

SPT is carried out at two sites A and B according to the BritishStandard (B.S.) 1377 for the determinations of the penetration resis-tance in the soil. The value of standard penetration number resis-tance, N is obtained at different sites. Site A is located near theFaculty of Engineering and Built Environment in UKM. Field settingsof electric resistivity measurements are shown in Fig. 4.

Profiles of the soil electrical resistivity and resistivity ratio areshown in Fig. 5. The range of soil resistivity ratio is 0.6 at a depth of1.0 m. This is a soft soil with sand and clay at a depth of 1.0 asshown in the multi-layer soil resistivity profile. There is a layer ofhard soil consisting of sand and gravel after a depth of 7.0 m accord-ing to the observations of data of resistivity ratio in soil.

In the SPT at the same site, the number of blows is compared withsoil resistivity data obtained. Fig. 6 shows the number of blows forSPT at site A in UKM. According to Fig. 6, the number of blows is great-er than 50 after a depth of 7.0 m in soil. The number of blows, N is

Fig. 8. SPT data from site B in UKM.

Fig. 9. Soil Vs profile through MASW method.

140 T. Islam, Z. Chik / Geoderma 209–210 (2013) 136–142

very high after a depth of 1.5 m which indicates the presence of hardsoil in soil profile.

Site B is also selected near the Faculty of Engineering and BuiltEnvironment in UKM. Fig. 7 shows the multi-layer profile of soil resis-tivity ratio for this site. According to this profile, the resistivity ratio islower than 0.8 within 4.0 m from the surface. This resistivity profileresult shows that the site generally has very soft soil with has moresilt and clay. The resistivity ratio varies from 0.9 to 1.0 at a depth of4.0 m to 5.5 m which shows the presence of sandy material.

The SPT data for site B as shown in Fig. 8 can be used to evaluatethe accuracy of results obtained from the multi-layer soil resistivityprofile. According to the SPT data, the number of blows N is lessthan 16 within a depth of 4.0 m. The value of N varies from 40 to 60at a depth 4.0 m to 5.5 m which indicates the presence of the sandysoil.

Shear wave velocity, Vs profile is obtained through MASWmethodusing analysis of SurfSeis software. Fig. 9 shows the 2-D Vs profileincluding a depth of 20 m where surface location is shown as 512 to

Fig. 10. Soil resistivity ratio profile from multi-lay

516 at near surface soil. Results of SPT are included at surface locationof 514 for a depth of 6 m as shown in Fig. 9. According to the resultsthrough SurfSeis software, there is very soft soil (Vs = 200 m/s to250 m/s) at a depth of 2 m for the position of 514 as shown in Fig. 9.

Soil resistivity ratio profile with a depth of 6 m is shown in Fig. 10.The resistivity ratio is seen within the range of 0.6 to 0.8 at a depth of2 m as shown in Fig. 10. This range of resistivity ratio indicates thepresence of soft soil through multi-layer resistivity model. The resis-tivity ratio profile with a depth of 6 m obtained from multi-layer re-sistivity model is falling close with the soil Vs profile from MASWmethod. Similarity of variations of both profiles shows the feasibilityof using resistivity ratio in obtaining near surface soil propertieswith non-destructive nature. SPT results show the accuracy of using2-D tomography of soil resistivity ratio profile. The outcomes of soilresistivity model are also free from near field effects and other noisyeffects as seen in the MASW methods.

Usually, the spacing between two adjacent probes is increasedsuccessively along a linear survey line to get multiple records in

er model at the same site of MASW method.

Fig. 11. Soil characterizations using a conventional four-point probe method.

141T. Islam, Z. Chik / Geoderma 209–210 (2013) 136–142

conventional soil resistivity model as shown in Fig. 11. Acquired datarecords are processed to produce a 1-D soil resistivity profile in soilcharacterizations. The empirical equations for the relationship be-tween the depth and soil resistivity profile in conventional resistivitymodel shows inaccuracy in the near surface soil characterizations(Herman, 2001) because the properties of soil vary according to hor-izontal distance and other parameters like particle size distributions,water contents of soil and chemical properties in field investigations(Laver and Griffiths, 2001; Son et al., 2010). As an example, soil resis-tivity profile is also changed when field tests are carried out beforerain and after rain in surface soil investigations.

However, Takahashi and Kawase (1990) use analysis of apparentresistivity in a multi-layer earth structure to match ρ–a curves. Thatstudy includes measuring gauge conception of geology to obtain theapparent resistivity data. Soil profile is shown by comparing thecurve measured in field with the gauge. There are limitations ofthose criteria to cover all the situations by the gauges. So the soil pa-rameters determined are only approximate ones.

Moreover, soil resistivity data in conventional model can influencedecision on site location for best type of earthing electrode system tobe installed. For example, it needs to drive rods to a greater depth orto increase the surface area according to apparent resistivity data. Ifthe results gained from the soil resistivity survey are unclear thensoil modeling can be started again.

Therefore, multi-layer resistivity model is considered in this studywhere resistivity ratio of adjacent two layers is considered to getaccurate results in soil characterizations. Accuracy of the model isverified with the comparison of SPT data and MASW profile in field.From the comparison made between this multi-layer soil resistivityprofile and SPT data, it is evident that this model can give accuratesoil characterization profile. Moreover, this model is easy to set upin field as there is no need for excavation of hole in surface soilwhich is tedious and time consuming. This model is potentially usedas a non-destructive method to estimate soil compaction performancefor highway embankments, earth dams and many other applicationsof civil engineering. It is expected with further technical refinement, itcould also be used for detecting porosity of soil (Samouelian et al.,2005), detection of anomalous materials in soil (Frohlich et al., 2008)and estimating the depths of bedrock surface.

4. Conclusion

Multi-layer resistivity model is described to obtain soil resistivityand resistivity ratio for near surface soil characterizations. The accuracyof this model for soil investigation has been tested by comparing withSPT data at different sites. This method is much simpler to set up com-pared to SPT. This multi-layer soil electric model could also be furtherdeveloped to obtain bulk density, detecting type of soil and rocks,detecting hazardous materials in soils and estimating depth of bedrocksurface in geotechnical engineering.

Acknowledgments

This research is sponsored by Research Project of Science Fund no.01-01-02-SF0681 fromMinistry of Science, Technology and Innovationof Malaysia.

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