generalized relationship for determining soil electrical resistivity from its thermal resistivity

Experimental Thermal and Fluid Science 29 (2005) 217–226

www.elsevier.com/locate/etfs

Generalized relationship for determining soil electrical resistivityfrom its thermal resistivity

S. Sreedeep, A.C. Reshma, D.N. Singh *

Department of Civil Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India

Received 15 May 2003; received in revised form 15 March 2004; accepted 5 April 2004

Abstract

The knowledge of soil electrical and thermal resistivity finds its application in many of the real life engineering projects like laying

of high voltage buried power cables, ground modification techniques etc. This necessitates determination of soil electrical resistivity

and thermal resistivity and development of a relationship between them. However, as these resistivities mainly depend on the type of

the soil (i.e. its physical composition) and its saturation, efforts have been made in this paper, to develop a generalized relationship to

relate them. Validation of the relationship has been conducted vis-a-vis the results obtained from the laboratory experiments and

those reported in literature.

2004 Elsevier Inc. All rights reserved.

Keywords: Soil; Thermal resistivity; Electrical resistivity; Laboratory investigations; Generalized relationship

1. Introduction

The knowledge of soil electrical resistivity has been

used to predict various soil parameters, phenomenonand mechanisms occurring in soils, such as for obtaining

the soil water content [1], degree of compaction [2] and

saturation [3], estimating liquefaction potential of the

soil [4], detecting and locating geomembrane failures [5],

to estimate corrosive effects of soil on buried steel [6], for

designing earthing resistance of the grounding systems

[7], to study the electro-osmosis phenomenon in soils [8],

investigating the effects of soil freezing [9] and for esti-mating the soil salinity for agricultural activities [10].

These studies highlight that determination of soil elec-

trical resistivity is quite cumbersome and depends on

several parameters such as frequency of the current

used, geometry and type of the electrodes used etc. [11].

On the contrary, it has been demonstrated by previ-

ous researchers that soil thermal resistivity can be

determined easily and rapidly using the transient heatmethod [12,13]. Based on this study, generalized rela-

*Corresponding author. Tel.: +91-22-2576-7340; fax: +91-22-2576-

7302.

E-mail address: [email protected] (D.N. Singh).

0894-1777/$ - see front matter 2004 Elsevier Inc. All rights reserved.

doi:10.1016/j.expthermflusci.2004.04.001

tionships for determining soil thermal resistivity were

developed [14,15]. It must be noted that determination

of thermal properties of geomaterials is important for

safe execution of various civil engineering projects suchas design and laying of high voltage buried power cables

[16], oil and gas pipe lines [17], nuclear waste disposal

facilities [18], ground modification techniques employing

heating and freezing [19] etc.

In such a situation, determination of soil electrical

resistivity by relating it to its thermal resistivity seems to

be an excellent and handy solution. Such a relationship

would also encompass the coupled electrical and ther-mal processes in soils. A generalized relationship to re-

late these resistivities has been developed and reported

in literature [20]. However, this relationship incorpo-

rates the effect of soil type only, and cannot take into

account the effect of saturation, which influences both

soil electrical and thermal resistivities [3,11,21].

With this in view, efforts were made to modify the

generalized relationship between soil thermal and elec-trical resistivities, reported in literature [20] by incor-

porating the influence of saturation of the soil. This

paper presents details of the methodology developed for

this purpose followed by the validation of the derived

relationship.

mail to: [email protected]

Nomenclature

A, B constant parametersa constant parameter

CR constant parameter

e void ratio

F percentage sum of the sand and gravel frac-

tions in the soil

G specific gravity of the soil

I current

LL liquid limitM molarity

PI plasticity index

R resistance of the soilRE electrical resistivity of the soil

REss electrical resistivity of the silty soil

REwc electrical resistivity of the white clay

RT thermal resistivity of the soil

Sr saturation

V voltage

w gravimetric water content

X , Y , Z constant parameterscd dry unit weight of the soil

cw unit weight of water

218 S. Sreedeep et al. / Experimental Thermal and Fluid Science 29 (2005) 217–226

2. Description of the test setup

As depicted in Fig. 1, a Perspex cubical box termed as

‘‘electrical resistivity box’’, which is 100 mm in dimen-

sion and 10 mm thick was fabricated and used for esti-

mating the electrical resistivity, RE, of the soil sample.

Each face of the resistivity box is provided with three

brass electrodes, of length 12.5 mm and diameter 2.5mm, and spaced at 30 mm center-to-center interval, as

shown in the figure. Such an arrangement facilitates nine

pairs of electrodes viz. 1–10, 2–20, . . ., 9–90. Electrodesnumbered from 1 to 9 are depicted in Fig. 1 and elec-

trodes 10–90 are the mirror images of electrodes 1–9.

These electrodes can be screwed into the compacted soil

sample with embedment length being equal to 2.5 mm

[22].A known voltage, V , was applied between these nine

electrode pairs and the current, I , passing through the

soil sample was measured. Hence, the resistance, R, ofthe soil sample can be expressed as

R ¼ V =I : ð1ÞThe computed value of R can be correlated with

electrical resistivity, RE, using a parameter, a. This

Fig. 1. The electrical resistivity box.

parameter depends on the geometry of the box, as ex-

pressed by Eq. (2), and can be determined by measuring

resistance of the standard KCl and NaCl solutions of

known electrical resistivity [21,22]:

RE ¼ a R: ð2ÞAs nine sets of resistivity values can be obtained with

the help of the resistivity box, inhomogeneity, stratifi-

cation, and change in water content due to compaction

of the soil sample can be taken care of appropriately.

3. Experimental investigations

3.1. Calibration of the test setup

Standard solutions of NaCl and KCl, with different

molarity, were used for determining the parameter a, asdiscussed in the following. Electrical conductivity valuesof these solutions were measured with the help of a

water quality analyzer (Model PE-138, Elico Limited,

India). The obtained conductivity values were corrected

to 25 C after applying temperature correction. Further,

the conductivity values were converted to resistivity

values.

Using a constant voltage AC power supply, values of

current I corresponding to different voltages V wererecorded for different molarity solutions of NaCl and

KCl solutions. The power supply operates at 50 Hz and

yields a output voltage varying from 0 to 50 V, in step of

5 V. For the sake of brevity, only the response of 0.1 M

NaCl solution is being presented herein, as depicted in

Fig. 2. It was noted that I versus V response of all the

electrodes is a straight line and the coefficient of

regression is very close to unity. Another observationfrom this exercise is that the maximum difference be-

tween the measured values of I , corresponding to dif-

ferent voltages for the same electrode, is less than 10%.

Further, to demonstrate that the adjacent electrodes

have negligible influence on the performance of indi-

R3

R2

R1

3

2

1

3’

2’

1’R1

R2

R3

1

2

3

1’

2’

3’

Rm Rm

(a) (b)

Fig. 3. (a) The three resistance model and (b) individual resistance

model.

0 500 1000 1500 20000

2

4

6

8

10

a=0.57

R ( )

RE (

.m)

Solution NaCl KCl

Ω

ΩFig. 4. Variation of RE versus R for NaCl and KCl solutions.

0 5 10 15 20 25 30 35 400

50

100

150

200

250

300

350

400Electrode pair

1-1' 2-2' 3-3' 4-4' 5-5' 6-6' 7-7' 8-8' 9-9'

I (m

A)

V (V)

Fig. 2. Applied voltage versus measured current response for 0.1 M

NaCl solution.

S. Sreedeep et al. / Experimental Thermal and Fluid Science 29 (2005) 217–226 219

vidual electrodes, electrodes on each face were applied

with the same voltage, as depicted in Fig. 3(a). The

resistance offered by the solution Rm was determined.

This resistance is compared with the computed resis-

tance Rc (Eq. (3)), obtained by applying the same volt-

age to individual electrode system Ri, as depicted in Fig.

3(b). A summary of the results obtained from this

exercise is presented in Table 1:

Table 1

Comparison of three-resistance and individual resistance models using 0.1 M

Electrode pair Resistance (X) Rc (X)

Computed

1 1835.87 618.31

2 1877.58

3 1851.85

4 1783.80 594.81

5 1823.15

6 1747.95

7 1692.33 551.97

8 1698.66

9 1582.03

Rc ¼X3i¼1

R1i

!1

: ð3Þ

It can be noted from the data presented in Table 1

that adjacent electrodes have negligible effect on the

performance of individual electrodes. Hence, further

experiments were conducted using the configuration of

the electrodes depicted in Fig. 3(a).

From the applied voltage versus current relationshipsfor different molarity solutions, and employing Eq. (1),

the resistance, R, is estimated. Further, to obtain the

parameter a, RE has been plotted against R, as shown in

Fig. 4, for NaCl and KCl. It can be noticed from the

figure that for NaCl and KCl solutions, the slope of RE

versus R relationship is equal to 0.567 and 0.574,

respectively. Hence, the average value of the parameter

a, was adopted as 0.57.

NaCl solution

Percentage error (%)

Experimental

642.38 3.75

623.68 4.63

575.28 4.05

Table 2

Properties of the soils used in the study

Soil property SS WC BC

Specific gravity 2.62 2.65 2.58

Particle size characteristics

Sand:

Coarse (4.75–2.0 mm) 2 – 1

Medium (2.0–0.420 mm) 23 – 4

Fine (0.420–0.074 mm) 31 – 3

Silt size (0.074–0.002 mm) 33 39 32

Clay size (<0.002 mm) 11 61 60

F 56 0 8

Consistency limits

Liquid limit (%) 44 46 67

Plastic limit (%) 34 25 34

Plasticity index (%) 10 21 33

Soil classification (USCS) ML CL CL

Standard proctor compaction

Maximum dry unit weight (kN/m3) 16 14 14.4

Optimum moisture content (%) 21.4 20.8 28.0

Minerals present in the soil

(using Cu-Ka assembly)

Halloysite, muscovite,

illite

Anorthite, albite, illite,

montmorillonite, microcline

Halloysite, clintonite,

moganite, despujolsite, quartz

Table 4

Compaction state of the soils used for electrical resistivity measure-

ments

Soil w (%) cd (kN/m3) e Sr (%)

SS 26.2 10.0 1.62 42.4

17.8 12.6 1.08 43.3

22.2 12.2 1.15 50.7

21.6 12.4 1.11 51.0

27.1 11.2 1.34 53.1

23.0 12.3 1.13 53.4

23.7 12.4 1.11 55.8

22.5 12.8 1.05 56.3

22.7 12.8 1.05 56.8

26.3 12.4 1.11 62.0

21.6 13.8 0.90 63.1

25.9 12.7 1.06 63.8

27.7 12.4 1.11 65.3

26.8 12.8 1.05 67.2

26.8 12.8 1.05 67.2

23.7 13.8 0.90 69.3

27.3 13.0 1.02 70.4


4. Results and discussion

Locally available silty soil (SS) and commercially

available white clay (WC), with their properties listed in

Table 2, were used in this study. Properties of the Black

cotton soil (BC), which was used for developing the

generalized relationship between thermal resistivity (RT)and electrical resistivity (RE) are also presented in the

table [20]. Table 3 presents chemical composition of

these soils, which was obtained by using a Phillips 1410

X-ray Fluorescence setup and following the methodol-

ogy presented in the literature [23].

An adequate amount of oven-dried soil was mixed

with varying water content, and stored for 24 h in air-

tight bags, for its preconditioning and maturing. Thematured soil was compacted to achieve different com-

paction states of these soils, as listed in Table 4. The

Table 3

Chemical composition (by % weight) of various soils used in the study

Oxide SS WC BC

SiO2 34.2 43.46 47.56

Fe2O3 12.1 1.56 9.85

Al2O3 10.1 33.57 13.58

CaO 6.1 0.37 3.77

MgO 2.4 0.74 1.62

TiO2 1.9 3.33 1.24

Na2O 0.5 0.17 0.23

K2O 0.3 0.07 0.29

MnO 0.2 0.05 0.13

P2O5 0.01 0.03 0.04

SrO 0.01 0.00 0.02

25.2 13.9 0.88 74.9

31.4 13.0 1.02 81.0

28.0 13.8 0.90 81.7

29.6 13.9 0.88 87.6

31.8 13.9 0.88 94.2

WC 9.8 8.9 1.98 13.1

16.1 10.3 1.54 27.6

18.1 10.0 1.62 29.6

16.7 10.6 1.47 30.0

17.0 11.2 1.34 33.7

21.2 11.7 1.24 45.4

25.9 11.3 1.32 52.1

27.7 11.7 1.24 59.1

29.8 12.6 1.08 73.3

30.7 12.9 1.03 79.0

37.1 12.5 1.10 89.8

38.7 12.4 1.11 92.1


compaction of the soil sample was performed in three

layers, using the electrical resistivity box as the mold, by

giving sufficient number of blows with the help of a flat

bottom hand rammer that weighs 250 g. After measur-

ing the current, I , corresponding to a particular appliedvoltage, V , about 10 g soil samples were scooped from

the top, middle and bottom of the box for determining

the average gravimetric water content, w, of the soil

sample [24]. From this data, and using Eq. (4), the sat-

uration, Sr, of the soil sample can be obtained:

Sr ¼ w cwcd

1

G

1

; ð4Þ

where cw is the unit weight of water, cd is the dry unit

weight of the soil and G is the specific gravity of the soil.

RE corresponding to different compaction states ofthe silty soil and the white clay were computed using Eq.

(2), and were plotted against Sr as depicted in Fig. 5.

From the figure, it can be noted that, in general, RE

decreases exponentially with increase in saturation

(Sr 6 40%) for both the soils, followed by a transition

zone (406 Sr ð%Þ6 60) and beyond which RE remains

almost constant. However, at very low saturations

(Sr < 15%) the current passed through the soil samplescould not be measured using the present setup. Based on

the trends observed, the following relationships can be

proposed:

REss ¼ 630 eððSr13:4Þ=14:5Þ; ð5Þ

REwc ¼ 150 eððSr20Þ=25Þ; ð6Þ

0 20 40 60 80 1

0

200

400

600

800Silty soil

S

R E (.m

)

Experimental data b

Ω

Fig. 5. RE versus Sr relationship and its valida

where REss and REwc correspond to the electrical resis-

tivity of the silty soil and white clay, respectively (in

Xm), and Sr is the degree of saturation (in %).

For validating Eqs. (5) and (6), data available in the

literature [11], for soils with similar particle size char-acteristics and USCS classification, was superimposed in

Fig. 5. It can be noted that the resistivity of the soils

reported in the literature matches very well with the

trends depicted by these equations. Further, using these

equations, a generalized relationship between RE, Sr andtype of the soil has been developed. To achieve this, a

parameter F (defined as the percentage sum of the sand

and gravel fractions in the soil) has been used. With thehelp of linear interpolation, variation of electrical

resistivity, RE, with Sr for different values of F (¼ 0, 20,

40, 60, 80 and 100) is obtained and the same has been

plotted as depicted in Fig. 6.

Based on the trends presented in Fig. 6, the following

generalized equation can be proposed:

RE ¼ A eððSr5Þ=BÞ; ð7Þwhere A and B are constants and can be expressed as

A ¼ 490þ 13:5 F ; ð8Þ

B ¼ 15þ 1:5 eðF =33:5Þ: ð9Þ

4.1. Relationship between soil electrical resistivity and

thermal resistivity

The soil electrical resistivity, RE, and its thermal

resistivity, RT, can be related as

00

r

0 20 40 60 80 100

est fit Abu-Hassanein [11]

White clay

tion for the silty soil and the white clay.

0 20 40 60 80 100

0

200

400

600

800

1000

1200

1400

1600

1800

Sr

R E (.m

)Ω

F 0 20 40 60 80 100

Fig. 6. Variation of RE with Sr and F .

20 40 60 80 1001.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0F

0 20 40 60 80 100

C R

Sr

Fig. 7. Variation of CR with Sr and F .


logðREÞ ¼ CR logðRTÞ; ð10Þwhere CR is a constant, and its values can be obtained

from Eq. (11) [20]:

CR ¼ 1:34þ 0:0085 F ; ð11Þwhere F is the percentage sum of the gravel and sand

size fractions in the soil.

Table 5

CR values for the soils compacted at different saturations

Sr F (%)

56 8 0 20

5 1.95 1.81 1.78 1.84

10 1.91 1.74 1.71 1.78

15 1.87 1.68 1.65 1.73

20 1.83 1.62 1.59 1.67

25 1.79 1.57 1.53 1.63

30 1.76 1.52 1.48 1.58

35 1.73 1.48 1.43 1.54

40 1.71 1.44 1.39 1.50

45 1.68 1.40 1.35 1.47

50 1.66 1.37 1.32 1.44

55 1.64 1.34 1.29 1.41

60 1.63 1.31 1.26 1.39

65 1.61 1.29 1.24 1.37

70 1.60 1.28 1.22 1.36

75 1.59 1.26 1.21 1.35

80 1.59 1.25 1.20 1.34

85 1.59 1.25 1.19 1.33

90 1.59 1.25 1.19 1.33

95 1.59 1.25 1.19 1.34

100 1.60 1.26 1.20 1.34

However, trends depicted in Fig. 5, and results re-

ported in literature [11,20] demonstrate that both RE and

RT strongly depend on the saturation, Sr, of the soil.

Hence, Eq. (10) must be modified to incorporate the

influence of Sr on CR. With this in view, data reported inliterature for the same silty soil (for which F ¼ 56)

[14,20] and a black cotton soil [20] (for which F ¼ 8)

were used for establishing variation of CR with Sr, fordifferent soils (i.e. with different F values), as presented

40 60 80 100

1.90 1.96 2.03 2.09

1.85 1.92 1.99 2.06

1.81 1.88 1.96 2.04

1.76 1.85 1.93 2.02

1.72 1.81 1.91 2.00

1.68 1.78 1.88 1.98

1.65 1.75 1.86 1.97

1.62 1.73 1.84 1.95

1.59 1.70 1.82 1.94

1.56 1.68 1.81 1.93

1.54 1.67 1.79 1.92

1.52 1.65 1.78 1.91

1.51 1.64 1.77 1.91

1.49 1.63 1.77 1.90

1.48 1.62 1.76 1.90

1.48 1.62 1.76 1.90

1.47 1.62 1.76 1.90

1.47 1.62 1.76 1.90

1.48 1.62 1.76 1.91

1.48 1.63 1.77 1.91

Table 6

Properties of the soils used by Abu Hassanein [11]

Soil G LL (%) PI (%) Gravel fraction (%) Sand fraction (%) Fines fraction (%) Clay fraction (%) F

A 2.75 27 15 2 22 76 28 26

B 2.80 67 46 0 6 94 53 6

C 2.69 61 35 9 38 53 40 47

D 2.80 24 11 3 35 62 20 35

E 2.70 49 26 0 6 94 40 6

F 2.80 70 38 0 6 94 65 6

G 2.78 37 20 0 19 81 25 19

H 2.68 29 16 0 48 52 16 48

K 2.68 58 15 0 36 64 23 36

L 2.67 23 5 0 46 54 7 46

M 2.90 53 41 0 12 88 36 12

Table 7

Validation of CR values

Soil Sr (%) RE (Xm) RT (Cm/W) CR (Eq. (10)) CR (Eq. (12)) % Difference

A 41 44.77 10.60 1.61 1.62 )0.8046 43.83 10.17 1.63 1.60 2.09

54 27.87 8.00 1.60 1.56 2.61

63 25.53 7.30 1.63 1.52 6.56

64 18.19 6.42 1.56 1.52 2.59

78 22.63 6.70 1.64 1.48 9.89

79 23.17 6.49 1.68 1.48 12.19

87 16.58 5.66 1.62 1.46 10.07

90 15.21 5.42 1.61 1.45 9.89

90 13.36 5.16 1.58 1.45 8.18

91 15.02 5.38 1.61 1.45 10.01

93 13.83 5.16 1.60 1.45 9.68

94 17.21 5.55 1.66 1.44 13.06

96 14.62 5.24 1.62 1.44 11.13

97 15.15 5.25 1.64 1.44 12.32

B 38 28.94 10.02 1.46 1.54 )5.5939 22.67 8.87 1.43 1.53 )7.2647 11.71 6.27 1.34 1.48 )10.1953 8.99 5.28 1.32 1.44 )9.0560 9.17 5.23 1.34 1.40 )4.6066 10.73 5.32 1.42 1.37 3.28

71 7.51 4.50 1.34 1.35 )0.9271 7.64 4.51 1.35 1.35 )0.1787 6.36 3.98 1.34 1.30 3.14

87 5.25 3.51 1.32 1.30 1.67

92 5.8 3.71 1.34 1.28 4.15

95 5.25 3.45 1.34 1.28 4.71

97 4.94 3.26 1.35 1.27 5.77

99 4.45 3.13 1.31 1.27 3.24

106 5.29 3.34 1.38 1.25 9.20

C 41 82.28 13.18 1.71 1.73 )1.2446 66.99 11.69 1.71 1.71 )0.1855 52.93 10.05 1.72 1.69 2.02

59 47.72 9.85 1.69 1.67 0.90

71 34.03 8.16 1.68 1.65 1.87

75 30.64 7.67 1.68 1.64 2.30

78 31.5 7.89 1.67 1.64 2.01

80 33.06 8.33 1.65 1.63 1.01

89 29.22 7.28 1.70 1.62 4.64

91 24.92 6.78 1.68 1.62 3.65

92 31.27 7.58 1.70 1.62 4.85

94 31.29 7.49 1.71 1.62 5.54

95 30.41 7.54 1.69 1.61 4.48

(continued on next page)


Table 7 (continued)


99 26.91 7.02 1.69 1.61 4.72

D 32 70.27 13.37 1.64 1.72 )4.7737 53.81 11.53 1.63 1.69 )3.6750 34.66 8.36 1.67 1.63 2.45

56 46.91 9.49 1.71 1.61 6.05

58 28.78 7.39 1.68 1.60 4.78

67 53.81 10.43 1.70 1.57 7.51

86 28.78 6.82 1.75 1.53 12.58

87 21.99 5.91 1.74 1.53 12.18

92 20.09 5.61 1.74 1.52 12.65

93 20.56 5.63 1.75 1.52 13.24

94 19.2 5.46 1.74 1.52 12.83

95 18.9 5.47 1.73 1.52 12.41

96 21.55 5.67 1.77 1.51 14.47

100 24.42 5.96 1.79 1.51 15.73

E 34 16.65 8.16 1.34 1.57 )17.5136 18.82 8.52 1.37 1.56 )13.7143 12.72 6.67 1.34 1.50 )12.2450 10.65 5.84 1.34 1.46 )8.7754 9.23 5.25 1.34 1.43 )7.0062 8.26 4.83 1.34 1.39 )3.8764 7.21 4.47 1.32 1.38 )4.7372 7.54 4.47 1.35 1.35 0.12

73 6.52 4.09 1.33 1.34 )1.0982 6.11 3.90 1.33 1.31 1.27

88 6.02 3.74 1.36 1.30 4.77

90 5.99 3.69 1.37 1.29 5.87

94 5.56 3.56 1.35 1.28 5.24

96 4.97 3.31 1.34 1.27 4.89

F 58 28.56 8.69 1.55 1.41 8.91

74 14.52 6.10 1.48 1.34 9.41

90 9.85 5.18 1.39 1.29 7.22

92 8.66 4.73 1.39 1.28 7.60

95 9.97 4.94 1.44 1.28 11.33

G 42 13.67 6.48 1.40 1.58 )12.8962 8.94 4.73 1.41 1.48 )4.9589 7.95 4.06 1.48 1.40 5.62

91 7.8 4.01 1.48 1.39 5.92

92 8.37 4.20 1.48 1.39 6.07

H 36 54.57 11.29 1.65 1.76 )6.4559 35.21 7.93 1.72 1.68 2.25

86 41.88 7.37 1.87 1.63 12.68

87 25.56 6.31 1.76 1.63 7.29

100 22.86 5.74 1.79 1.61 10.11

K 41.6 377.82 18.60 2.03 1.67 17.66

63 243.76 14.41 2.06 1.59 22.79

91.1 168.45 12.05 2.06 1.53 25.76

93.5 162.85 13.09 1.98 1.53 22.95

93.7 141.43 12.19 1.98 1.53 22.96

L 24 90.71 16.73 1.60 1.81 )13.0436 62.88 11.43 1.70 1.75 )2.7682 40.67 7.25 1.87 1.62 13.23

87 27.94 6.56 1.77 1.62 8.72

90 31.23 6.69 1.81 1.61 10.95

M 36 19.65 8.27 1.41 1.59 )12.5344 10.02 5.58 1.34 1.53 )14.1880 6.5 3.81 1.40 1.37 2.45

83 7.04 3.91 1.43 1.36 5.12

86 7.02 3.87 1.44 1.35 6.35


Table 7 (continued)


WC 13.1 329.42 39.22 1.58 1.79 )12.9527.6 111.96 19.81 1.58 1.61 )2.1029.6 119.79 20.68 1.58 1.59 )0.6530.0 106.39 18.83 1.59 1.59 0.21

33.7 86.58 18.12 1.54 1.55 )0.5745.4 62.9 13.75 1.58 1.46 7.59

52.1 56.04 13.89 1.53 1.41 7.72

59.1 47.19 12.62 1.52 1.37 9.66

73.3 25.39 8.52 1.51 1.30 13.95

79.0 17.91 7.31 1.45 1.28 11.76

89.8 26.96 8.38 1.55 1.24 19.71

92.1 55.14 12.45 1.59 1.24 22.27


in Table 5. For this purpose, generalized relationships

for estimating soil thermal resistivity, RT, reported in

literature [14] have been used. This data when plotted, as

depicted in Fig. 7, yields the following generalized

expression:

CR ¼ X þ Y eðSrZÞ; ð12Þwhere X , Y and Z are constant parameters and mainly

depend on the type of the soil. These parameters can be

represented as

X ¼ ½1:1þ 0:01 F ; ð13Þ

Y ¼ ½0:9 0:01 F ; ð14Þ

Z ¼ ½0:02þ 0:0006 eðF =25Þ: ð15ÞResults of the white clay (WC) and different soils

reported in literature [11], with their properties listed in

Tables 2 and 6, respectively were used for validating Eq.

(12), as presented in Table 7. It can be observed from the

data presented in the table that for most of the soil

samples, the percentage difference between the two CR

values ranges from 0.1% to 18% except for Soil K for

which the percentage difference ranges from 17% to25.7%. However, the percentage difference between the

two CR values for white clay ranges from 0.2% to 14%

except for some values of Sr, for which this difference is

as high as 19–22%. Hence, the efficiency and generality

of Eq. (12), in relating RE and RT of soils, gets estab-

lished.

5. Conclusions

A generalized relationship to estimate electrical

resistivity of soils corresponding to different saturations,

easily and quickly, has been developed. To achieve this,

laboratory experiments have been conducted using a

electrical resistivity box, on different soil samples com-

pacted to different saturations. Using the generalizedrelationships for estimating soil thermal resistivity,

which has been developed by previous researchers, a

relationship between the soil electrical resistivity and its

thermal resistivity has been derived to incorporate the

effect of saturation. With the help of data available in

the literature and the results of experimental investiga-

tions, efficiency of this relationship has been demon-

strated.

References

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generalized relationship for determining soil electrical resistivity from its thermal resistivity

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