A methodology to determine soil moisture movement due tothermal gradients

S. Krishnaiah a, D.N. Singh b,*

a Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, Indiab Geotechnical Engineering Division, Department of Civil Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

Received 26 February 2002; received in revised form 15 September 2002; accepted 25 October 2002

Abstract

Moisture and heat migration through the soil mass is an important consideration for the safety of electrical gadgets buried in the

soil mass. Continuous passage of current through these gadgets increases their temperature, which may result in redistribution or

migration of the moisture in the surrounding soil mass. Excessive changes in the soil moisture may lead to its thermal instability,

which may also affect the current carrying capacity of the electrical gadgets. To avoid such a situation, estimation of moisture

movement under an imposed thermal gradient becomes essential. With this in view, an attempt has been made in this paper to study

the influence of thermal gradient on moisture migration through the soil mass. Usefulness of an insertion tensiometer has been

demonstrated, for this purpose, when the soil water characteristic curve, SWCC, for the soil is already established.

� 2003 Elsevier Science Inc. All rights reserved.

Keywords: Moisture migration; Thermal gradient; Suction; Soil water characteristic curve; Soils

1. Introduction

Generally, distribution of power is accomplished with

the help of underground cables. Due to the transmission

of power through these cables, the soil mass surround-

ing them gets heated up and this may cause migration of

moisture from the soil mass. At the same time, de-

pending upon the rise in temperature of the soil mass

and its resistivity, its thermal instability may also occur[1]. Thermal instability of the soil mass refers to the

changes occurring in its thermal properties which may

affect its proper functioning for the intended purpose.

The movement of the moisture from the soil mass due to

thermal gradients is mainly responsible for its thermal

instability [1,2]. Such a situation may also be detrimental

to the buried power cables and may result in its mal-

functioning or even its melting. As such, continuousmonitoring of the moisture migration from the soil mass

becomes mandatory.

In this direction, several researchers [3–10] have de-veloped mathematical and numerical models for study-

ing heat and moisture transfer through the soil mass.

Most of these studies deal with modeling and under-

standing the fundamental process involved with the

migration of moisture through the soil mass due to the

thermal gradients [11]. Similarly, conventional [12–15]

and accelerated experiments [16], using a geotechnical

centrifuge, have been conducted to study the moisturemigration in the soil mass due to the thermal gradients.

However, as the heat and moisture migration through

the soil mass is a complex phenomenon that depends on

several parameters related to the soil properties and the

properties of the heat source [11], it is quite difficult to

apply the findings of the mathematical models as well as

the results obtained from the experiments to the real life

situations. In such a situation, direct measurement of themoisture level of the soil mass and the amount of

moisture migrating from it due to the thermal gradients

seems to be the best possible solution.

With this in view, a simple methodology that deals

with the application of an insertion tensiometer to esti-

mate the moisture migration in the soil mass, due to the

thermal gradients, has been developed and its details are

* Corresponding author. Tel.: +91-22-5767340; fax: +91-22-

5767302/5723480.

E-mail address: dns@civil.iitb.ac.in (D.N. Singh).

Experimental Thermal and Fluid Science 27 (2003) 715–721

www.elsevier.com/locate/etfs

0894-1777/03/$ - see front matter � 2003 Elsevier Science Inc. All rights reserved.

doi:10.1016/S0894-1777(02)00306-0

presented in this paper. The methodology employs ap-

plication of the soil water characteristic curve, SWCC,

for a soil mass, which can be determined with the help of

insertion tensiometer [17–19]. It must be noted here that

the SWCC for a soil is the relationship between the

suction, w, exhibited by it and its volumetric water

content, hv. Though application of SWCC for estimat-

ing unsaturated soil hydraulic conductivity [20], shearstrength [21], swelling potential [22] and its compress-

ibility [23] is very well established, its application for

establishing moisture migration due to the thermal

gradients has not been explored yet. With this in view,

efforts have been made to demonstrate usefulness of the

insertion tensiometer for establishing moisture migra-

tion in the soil mass due to thermal gradients.

2. Experimental investigations

2.1. Material properties

Two soils, a locally available silty soil, SS, and

commercially available Kaolin (white clay, WC), were

chosen in the present study. The physical properties ofthese soils are presented in Table 1. Specific gravity and

the particle size characteristics of these soils have been

obtained as per the guidelines provided by ASTM-D 854

[24] and ASTM-D422 [25], respectively. The standard

Proctor compaction characteristics of these soils have

been obtained as per the guidelines provided by ASTM-

D 698 [26].

2.2. Details of the heat source

As depicted in Fig. 1, a thermal probe made of a hollow

copper tube has been used for heating the soil mass i.e.

applying the thermal gradient. The probe, which acts as a

line heat source [27] is 9.5 cm long and 6 mm in externaldiameter, and consists of a nichrome wire (exhibiting

0.044 X/cm) as a heating element. A T-type (copper–

constantan) thermocouple has been fixed on the inner

surface of middle of the probe to monitor its temperature

as a function of time. The space between the heating ele-

ment and the copper tube has been filled with a thermal

epoxy, which provides excellent thermal conduction and

acts as an electrically insulating material.

2.3. Details of the insertion tensiometer

To measure the soil suction a Jib-P Tensiometer,as depicted in Fig. 2 and with its details presented in

Nomenclature

cd dry unit weight of the soilcd max maximum dry unit weight of the soil

hs volumetric water content at saturation

hv volumetric water content

cw unit weight of water

e void ratio

hr soil suction corresponding to the residual

water content

nf , mf soil parameters

OMC optimum moisture contentr radial distance from central line of probe

w soil suction

T temperature of the soil mass

t time

w gravimetric water content

w0 initial gravimetric water content

USCS unified soil classification system

Table 1

Physical properties of the soils used in the present study

Soil property SS WC

Specific gravity 2.50 2.65

Sand size:

Coarse (4.75–2.0 mm) (%) 5 –

Medium (2.0–0.42 mm) (%) 16 –

Fine (0.420–0.074 mm) (%) 25 –

Silt size (0.074–0.002) (%) 47 39

Clay size (<0.002 mm) (%) 7 61

Consistency limits:

Liquid limit (%) 44 46

Plastic limit (%) 34 25

Plasticity index (%) 10 21

USCS classification ML CL

Standard Proctor compaction:

cd max (g/cc) 1.59 1.39

OMC (%) 20.8 21.4

} Thermocouple leads Power supply leads {

Nichrome wire

95m

m

Copper tube

Thermocouple

6mm

Fig. 1. Details of the thermal probe.

716 S. Krishnaiah, D.N. Singh / Experimental Thermal and Fluid Science 27 (2003) 715–721

Table 2, attached to a �E-sensor� has been used. The ob-

servations from the �E-sensor� are data-logged over a

period of time, in terms of mA. Later, the logged data

can be converted into the soil suction, w, values using

the following calibration equation [17]:

w ðin kPaÞ ¼ ½�22:22 þ 5:61

� Output current ðin mAÞ�: ð1Þ

2.4. Sample preparation

The oven-dried silty soil, SS, and the white clay, WC,

were mixed thoroughly with 30.55% and 37.25% distilled

water, respectively, and these soils were stored for ma-

turing in airtight polythene bags for two days. This

water content corresponds to the initial gravimetric

water content, w0, of the soil mass. Later, silty soil andthe white clay were compacted in a 12 cm high Perspex

mold (with 12 cm inner diameter) to achieve a dry unit

weight, cd, of 1.3 and 1.1 g/cc, respectively, by com-

pacting these soils in three layers, and imparting 25

blows to each layer, with the help of a hand rammer that

weighs 250 g.

Using Eq. (2), the gravimetric water content, w, can

be converted into the volumetric water content, hv:

Table 2

Details of the Jib-P insertion type tensiometer

Parameter Value

Tensiometer tube:

Material Glass

Length (mm) 130

Viewing window height 44

Diameter (mm) 16.5

Thimble (cone):

Material Ceramic

Diameter (mm) 6.5

Length of the cone (mm) 30

Insertion depth (mm) 35

Suction measurement range 0–90 kPa

Fig. 3. The experimental setup.

Fig. 2. (a) Insertion tensiometer (tube and thimble), (b) E-sensor.

S. Krishnaiah, D.N. Singh / Experimental Thermal and Fluid Science 27 (2003) 715–721 717

hv ¼ wðcd=cwÞ; ð2Þwhere cd and cw are the dry unit weights of the soil and

water, respectively. Using Eq. (2), the initial hv for the

silty soil and the white clay are found to be 39.72% and40.97%, respectively.

To monitor temperature of the soil mass, a 5 cm long

T-type thermocouple, its outer diameter being 1 mm and

which is grounded at its bottom end, has been installed

at a radial distance, r, of 1.5 cm from the axis of the

thermal probe, as depicted in Fig. 3. To measure the soil

suction, at the same radial distance, an insertion tensi-

ometer is also inserted into the soil mass, as depicted inFig. 3. A data-logger has been used to record the tem-

perature, T , in �C, and soil suction, w, in terms of mA,

of the soil mass. A 20 V constant power supply has been

used for the E-sensor. A 4 A constant current supply is

used for the thermal probe, which yields an input power

of 71 W/m.

3. Results and discussion

The variation of T and w of the soil mass with time thas been recorded as depicted in Figs. 4 and 5, respec-

tively. It can be observed from these figures that as time

increases the temperature as well as the suction of the

soil mass increases. The increase in soil suction, as a

function of time indicates depletion in moisture of thesoil mass, which can be attributed to the migration of

moisture. After a certain time the suction of the soil, w,

attains a constant value. From Figs. 4 and 5, it can also

be noted that for a certain time t the w for the white clay,

WC, is higher than the silty soil, SS. This may be at-

tributed to the fact that for fine-grained soils (i.e. WC)

suction would be higher as compared to the coarse-

grained soils (i.e. SS) [28,29]. The maximum w values of78 and 70.3 kPa for the white clay, WC, and silty soil,

SS, are noticed to occur corresponding to 39.35 and

40.16 h, respectively.

The SWCCs for the silty soil SS and the white clay

WC are depicted in Fig. 6 [17,19]. As insertion tensio-

meter cannot be used to measure soil suction higher than

90 kPa, the best-fit represented by the following equation[18] has been used to define the SWCC of the two soils.

hv

hs

� �¼ 1

24 �

ln 1 þ whr

h i

ln 1 þ 106

hr

h i35

� 1

ln expð1Þ þ waf

nfh ih imf

264

375 ð3Þ

where hv is the volumetric water content at any suction

w, hs is the volumetric water content at saturation, af is

the soil parameter which is a function of air entry value

and is equal to 32.96 and 73.78 kPa for the silty soil SS

0 500 1000 1500 2000 2500 30002830323436384042444648505254

WC

SS

t (min)

Fig. 4. Variation of the soil mass temperature with time.

0 500 1000 1500 2000 2500 30000

10

20

30

40

50

60

70

80

90

100

SS

WC78

70.3

2361 2410

ψ(k

Pa)

t (min)

Fig. 5. Variation of the soil suction with time.

Fig. 6. The soil water characteristic curve, SWCC, for the two soils.

718 S. Krishnaiah, D.N. Singh / Experimental Thermal and Fluid Science 27 (2003) 715–721

and the white clay WC, respectively, nf is the soil pa-

rameter which is a function of rate of extraction of water

from the soil beyond the air entry value and is equal to

1.29 and 13.89 for soils SS and WC, respectively, mf is

the soil parameter which is a function of the residualmoisture content and is equal to 0.67 and 0.78 for SS

and WC respectively, hr is the suction corresponding to

the residual moisture content and is equal to 699005.8

and 165613.8 kPa for SS and WC, respectively [17,19].

It can be noted from Fig. 6 that w increases as hv

decreases. As such, these curves can be employed for

establishing migration of moisture due to the thermal

gradient as discussed in the following.

From Figs. 4 and 5, the temperature T and suction w of

the two soils for a given time is known. Hence, knowing

the w as a function of time t and knowing the SWCC

of the soil, its hv can be obtained. It must be noted that

the variation of hv with time t would indicate migration ofthe moisture from the soil mass. Table 3 depicts details

of the temperature T , suction w, volumetric water content

hv and gravimetric water content w as a function of time t.It can be noted from the data presented in the table that

an increase in T causes increase in w of the soil and a de-

crease in its hv and hence w. Using the data presented in

the table, variation of normalized water content, w=w0,

as a function of time has been developed, as depicted in

Table 3

Summary of the test results

Time (h) Temperature (�C) w (kPa) hv (%) W (%)

SS WC SS WC SS WC SS WC

1 35.76 33.69 1.07 2.24 39.6 40.3 30.5 36.6

2 38.05 38.40 1.48 3.8 39.6 40.3 30.5 36.6

3 39.15 41.91 3.76 5.93 39.6 40.3 30.5 36.6

4 39.71 43.48 5.46 8.38 39.6 40.3 30.5 36.6

5 39.96 44.02 7.05 11.4 39.6 40.3 30.5 36.6

6 40.39 44.33 8.54 14.34 39.6 40.3 30.5 36.6

7 40.71 44.79 9.88 17.9 39.4 40.3 30.3 36.6

8 40.99 45.20 11.13 21.68 39.0 40.3 30.0 36.6

9 41.22 45.49 12.52 24.84 39.0 40.3 30.0 36.6

10 41.28 45.86 13.80 26.53 38.8 40.3 29.8 36.6

11 41.35 46.13 15.07 29.01 38.8 40.3 29.8 36.6

12 41.45 46.36 16.23 31.1 38.5 40.0 29.6 36.6

13 41.54 46.53 17.46 33.67 38.2 39.9 29.4 36.3

14 41.78 46.78 19.18 36.29 37.9 39.5 29.2 35.9

15 41.84 46.96 20.94 38.91 37.4 39.4 28.8 35.8

16 41.86 47.12 22.25 41.55 36.5 39.3 28.1 35.7

17 41.94 47.27 23.40 44.17 36.0 39.0 27.7 35.5

18 41.95 47.40 24.39 46.58 35.9 38.8 27.6 35.3

19 41.97 47.52 25.52 48.75 35.0 38.2 26.9 34.7

20 42.06 47.68 27.54 50.92 34.5 38.0 26.5 34.5

21 42.14 47.80 29.82 52.16 33.5 37.2 25.8 33.8

22 42.33 47.90 32.00 53.83 31.4 37.0 24.2 33.6

23 42.43 48.02 34.81 55.83 30.0 36.4 23.1 33.1

24 42.51 48.09 36.16 58.01 28.5 36.4 21.9 33.1

25 42.59 48.16 38.37 59.93 28.2 35.6 21.7 32.4

26 42.66 48.21 39.79 61.8 28.0 35.2 21.5 32

27 42.7 48.29 41.71 63.79 26.5 32.7 20.4 29.7

28 42.74 48.35 43.69 65.64 24.5 31.8 18.8 28.9

29 42.76 48.42 46.17 67.24 23.8 31.2 18.3 28.4

30 42.85 48.47 48.36 68.7 22.2 31.0 17.1 28.2

31 42.87 48.52 51.26 70.04 20.2 28.7 15.5 26.1

32 42.9 48.60 53.40 71.3 19.6 28.4 15.1 25.8

33 42.94 48.68 55.92 72.36 18.7 28.0 14.4 25.5

34 43 48.77 58.42 74.23 17.3 27.6 13.3 25.1

35 43.05 48.84 60.56 75.01 16.0 27.6 12.3 25.1

36 43.11 48.92 63.17 75.39 15.2 27.6 11.7 25.1

37 43.2 48.97 65.76 75.94 14.5 27.6 11.2 25.1

38 43.22 49.03 68.32 76.83 12.4 27.4 9.5 24.9

39 43.27 49.09 69.35 77.45 11.8 27.3 9.1 24.8

40 43.34 49.14 70.67 77.6 11.5 27.2 8.8 24.7

41 43.46 49.18 70.83 77.77 11.5 27.2 8.8 24.7

42 43.56 49.21 70.84 77.91 11.5 27.1 8.8 24.6

43 43.7 49.26 70.90 78.14 11.5 27.0 8.8 24.5

44 43.84 49.29 70.92 78.34 11.5 27.0 8.8 24.5

S. Krishnaiah, D.N. Singh / Experimental Thermal and Fluid Science 27 (2003) 715–721 719

Fig. 7. It can be noted from the figure that as time in-

creases, w=w0 for a soil decreases. From the figure it is

quite apparent that the drop in w=w0 as a function of time

is much more for the silty soil as compared to the whiteclay. This is consistent with the fact that water-holding

capacity of white clay (and hence its suction) is higher

than the silty soil. This indicates that due to the thermal

gradient the volumetric water content of the soil samples

decreases as a function of time. This demonstrates use-

fulness of the methodology discussed in the paper for

determining migration of the soil moisture due to the

thermal gradient.

4. Conclusions

The present study demonstrates the usefulness of in-

sertion tensiometer and the soil water characteristiccurve, SWCC, for establishing migration of moisture

due to thermal gradients quite easily. It has been ob-

served that the soil suction for the white clay is higher as

compared to the silty soil. As such, the moisture-holding

capacity of the white clay is higher than the silty soil. It

has been observed that with increase in temperature,

suction in the soil mass increases, which indicates de-

crease in its water content. Though the proposedmethodology is found to be working quite efficiently for

establishing migration of moisture due to thermal gra-

dient in the laboratory tests, its validity under in situ

conditions must be investigated.

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