The document provides details from a final report submitted by Arjun Narayanan for an Indian Academy of Sciences summer fellowship. Tests were conducted on creek sand to determine its thermal properties and their relationship to soil characteristics. Particle size analysis showed the sand was poorly graded. Chemical analysis and XRF found high iron and titanium content. Electrical impedance spectroscopy and crushing strength tests were also performed. The results will help understand how soil parameters like particle size, moisture, density affect thermal conductivity.

1. INDIAN ACADEMY OF SCIENCES
SUMMER FELLOWSHIP
FINAL REPORT
Project completed under the guidance of
Professor DN Singh
Department of Civil Engineering,
Indian Institute of Technology, Bombay
Submitted by,
Arjun Narayanan
IAS Application No: ENGS 266

2. 1. Introduction
Thermal properties of soil are an important set of parameters that are to be obtained in order to be able
to estimate the heat flow through soil under the influence of a temperature gradient. This is particularly
important for underground power cables, foundation design of chemical plants or power plants, and
nuclear waste repositories.
The important thermal properties of a material are:-
a) Thermal Resistivity: The ease with which heat can flow through a material of given dimension
under a given temperature gradient.
b) Thermal Heat Capacity: The heat required to raise a unit mass of a substance by a unit Kelvin.
c) Thermal Diffusivity: It is a measure of the lag in heat transfer through a material, often
described as ‘thermal inertia’. It is obtained by dividing the thermal conductivity of a material by
its density and thermal capacity.
The thermal properties are strong functions of numerous soil parameters like:-
1) Particle Size
Soils composed smaller granules show a lower thermal resistivity than soils composed of larger
granules (Singh and Devid, 2000). Also, well graded soils show lower thermal resistivity as
compared to poorly graded or uniformly graded soils (Campbell and Bristow, 2009). The main
factor at play here is the presence of air voids, which have a thermal resistivity of 4000 o
C-cm/W
as compared to soil solids which show a resistivity of 4 o
C-cm/W (Erzin, Rao and Singh, 2007).
2) Moisture Content
Soils with higher moisture content show a lower thermal resistivity than dry soils (Rao and
Singh, 1999; Mason and Kurtz, 1952). This is because water tends to occupy the voids by
removing air, and the thermal resistivity of water is around 170 o
C-cm/W which is lower than
that of air.
3) Density
Thermal conductivity is dependent on the state of compaction of a material (Singh and Devid,
2000; Becker, Misra and Fricke, 1992). The more closely packed a material, the lesser is the
presence of air voids. This facilitates easy transport of heat through a material.
There exist other factors as well, such as the mineralogy and the organic content of the soil, but such
parameters are difficult to control, and hence are not considered as important as the three factors
mentioned above.

3. The following tests were performed on a sand which was sourced from the creek areas of Bombay:-
1) Particle Size Distribution
2) Specific Gravity
3) Organic Content
4) Chemical Analysis
5) X-Ray Fluorescence Spectroscopy
6) Electrical Impedance Spectroscopy
7) Crushing Strength
8) Thermal Tests
a) Thermal Resistivity
b) Thermal Expansion Test
The tests were performed in order to understand the effect of soil characteristics on the thermal
conductivity of soils.
NOTE: The sample designation CS shall be used henceforth in the report when referring to the creek
sand.
1. Particle Size Distribution
The particle size distribution was obtained by performing sieve analysis on an oven-dry specimen in
accordance with ASTM D6913. The data obtained is displayed below:
0.1 0.2 0.3 0.4 0.5
0
10
20
30
40
50
60
70
80
90
100
110
120
PercentageFiner(%)
Sieve Size (mm)
Fig. 1 Particle Size Distribution Curve for CS

4. SIEVE
SIZE
(mm)
PERCENTAGE
GRANULES
RETAINED
(%)
Cu Cc
0.300 0.75
1.6983 1.0861
0.250 2.80
0.212 11.39
0.180 33.18
0.150 21.99
0.106 21.64
0.075 7.10
PAN 0.55
The table above shows the percentage granules retained on a particular sieve for a range of sieve
dimensions which was relevant to the sample.
According to ASTM D2487, the sand samples can be classified as SP (poorly graded sand).
It was further observed that the fraction retained on the no. 140 (106 μm) sieve was of a distinctly
darker colour, while the fines are of the same colour as the bulk of the sample. It is believed that these
dark particles are possibly iron particles.
2. Specific Gravity
The specific gravity was ascertained by means of a Helium Ultrapycnometer, (Quantachrome, USA)
which uses helium gas as the displacing fluid, in accordance with ASTM D5550. The results over three
trials are displayed below.
SPECIFIC GRAVITY OF HPCL SAND
SPECIMEN
NO.
WEIGHT
OF
SAMPLE(g)
Specific Gravity
TRIAL 1 TRIAL 2 TRIAL 3 AVERAGE
DENSITY
1) 6.0898 3.2995 3.3353 3.3527 3.3290
2) 7.2635 3.2913 3.3041 3.3312 3.3088
3) 8.5908 3.2719 3.2785 3.2825 3.2776

5. The average specific gravity is 3.3, which is abnormally high for sand, and may be attributed to the
presence of heavy minerals like oxides of iron.
3. Organic Content
The organic content of the soil was determined by CHN (carbon, hydrogen, nitrogen) analysis as well as
by furnace heating in accordance with ASTM D2974-07a.
In the furnace method, an oven dry specimen of the sand was gradually heated up to 440 o
C. The sample
was weighed at frequent intervals until the weight of the sample remained constant with the progress
of time. This weight loss, reported as a percentage, was deemed the organic content of the sample.
The organic content by furnace method was 3.08%.
The results of CHN analysis are tabulated below.
COMPONENT PERCENTAGE (%)
Nitrogen 0.044
Carbon 0.067
Hydrogen 0.015
TOTAL 0.126
The total organic content by CHN analysis is significantly lesser than the organic content as reported by
furnace method. This can be attributed to any latent moisture or other volatile chemicals that may be
present in the sand.
4. Chemical Analysis
Chemical analysis was performed using standard chemical kits and by maintaining a liquid/solid ratio of
10 and 20 using distilled water as the dispersant. The chart below contains the results of the tests.
CHEMICAL ANALYSIS OF CREEK SOIL (HPCL)
SAMPLE
(liquid/solid
ratio)
CHLORIDE
CONTENT
(ppm)
ALKALINITY
(ppm)
CALCIUM
HARDNESS
(ppm)
TOTAL
HARDNESS
(ppm)
pH
ELECTRICAL
CONDUCTIVITY
(μS)
TOTAL
DISSOLVED
SOLIDS (ppm)
CS (10) 90 50 6 10 8.1000 689.2 310.5
CS (20) 40 20 4 8 8.0780 334.0 152.7
The abnormally high value of electrical conductivity and pH is to be noted.

6. 5. X-Ray Fluorescence Spectroscopy
In order to obtain a better picture of the elemental composition of the material, the samples were
subjected to X-Ray fluorescence spectroscopy. The sample was prepared in the form of pellets by mixing
1 gram finely ground sample with 4 grams of cellulose (cellulose is used because of its binding
properties). Isopropyl alcohol was added and the three components were thoroughly mixed. The
mixture was placed under an infrared lamp for drying. An aluminium dish was filled with 2/3rd
cellulose
and 1/3rd
cellulose-sample mixture, and the set-up was compressed under a loading of 15 tons for
approximately 1 minute to produce a pellet.
The results shown below describe the elemental composition of the sand.
X-Ray Fluorescence
Spectroscopy Results
ELEMENT
PERCENTAGE
(%)
Al 15.57
Si 46.73
Ca 6.39
Ti 5.85
Fe 24.30
An interesting observation is the high percentage of iron and titanium. It was observed that a magnet,
when brought near the sample, is able to attract a large number of black particles from the sand. These
particles are most probably iron or the magnetic oxide of iron.
6. Electrical Impedance Spectroscopy
Electrical Impedance Spectroscopy is a study of the electrical response of a system when subjected to a
time-varying voltage signal.
It has been mentioned in the literature (K Arulanandan, 2002) that the dielectric dispersion of the soil
can be used to study the composition of the soil. Keeping this in view, Electrical Impedance
Spectroscopy was performed on the supernatant of the samples (liquid/solid ratio 20) and Nyquist and
Bode plots were developed for the data, the results of which are displayed below.
It can be seen from the Bode phase plot that the material shows high capacitive tendencies at very low
and very high frequencies.

7. 0.1 1 10 100 1000 10000 100000 1000000 1E7
-60
-30
0
Phase(degrees)
Frequency (Hz)
Bode phase plot for creek sand at l/s ratio of 20
0.1 1 10 100 1000 10000 100000 1000000 1E7
0
5000
10000
Impedance(Ω)
Frequency (Hz)
Bode magnitude (impedance) plot at l/s ratio of 20
The Bode magnitude plot of impedance vs. frequency displays a near constant value for the middle
frequency range. This frequency range corresponds to the region with least capacitive effect (as per the

8. phase plot). The real part of the impedance in this range, then, will correspond to the resistance of the
solution and is approximately equal to 775 Ω.
0 200 400 600 800 1000 1200 1400
0
200
400
600
800
1000
1200
1400-Zs"(Ω)
Zs' (Ω)
Nyquist plot at l/s ratio of 20
The nyquist plot is developed by plotting the negative of the imaginary component of impedance (-Zs”)
vs. the real part of the impedance (Zs’), both impedances taken as series components.
The point at which the nyquist plot meets the x-axis is the frequency at which the imaginary component
of impedance vanishes to zero. Therefore, this value of the real part of the impedance is truly the
resistance of the material. This value is also obtained as 775 Ω.
Direction of increasing frequency

9. 7. Crushing Strength
The crushing strength of the sand was obtained by developing stress vs. deformation plots (Bartake and
Singh, 2007). The material was packed in a mould of 33 mm inner diameter and 110 mm length at a
density corresponding to 90% of the maximum dry density. Sufficient material was taken to maintain a
length/diameter ratio of unity. The material was subjected to gradual loading, at a rate of 1.25 mm/min,
on a compression testing machine of 5 ton capacity (AIMIL, India), and the deformation was obtained
from a dial gauge of 0.01 mm least count.
The method of determining the crushing strength of the material involves plotting the applied load vs.
the deformation developed with the load taken on a log-scale. Tangents are drawn at the initial linear
portion and the final linear portion. The load corresponding to the point of intersection of these two
tangents (point of maximum curvature) is reported as the crushing load, and the corresponding stress is
reported as the crushing stress.
The crushing strength obtained was 4.34 MPa. Shown below is the log (deflection) vs. load plot.
-1000 0 1000 2000 3000 4000 5000 6000
10
100
Deflection(10
-2
mm)
Load (Kg)
Log (deflection) vs. load plot for creek sand: Crushing Strength

10. 8. Thermal Tests
Apart from physical characterization of the sand, it is also imperative that the thermal properties such as
thermal resistivity, thermal diffusivity, and specific heat capacity and co-efficient of thermal expansion,
are studied.
A heat probe modeled along the principle of an infinitely long heat source (ASTM D5334-08) was used to
determine the thermal resistivity, thermal diffusivity, and specific heat capacity of the materials. A
dilatometer was utilized to obtain the co-efficient of thermal expansion.
8.1 Thermal Probe
The concept of the infinitely long heat source has been used in the past (Blackwell, 1954; De Vries
and Peck, 1958; Rao and Singh, 1999; Singh and Devid, 2000). A heat probe of length 6 cm and
radius of 3.5 mm was used to model an infinitely long heat source. The probe possesses a nichrome
wire of known resistance which is used for heating, and a T-type (copper-constantan)
thermocouple which is used to measure changes in temperature. The probe is connected to a
regulated DC power supply source and the temperature of the thermocouple is data logged on a
personal computer as a function of time.
The fundamental differential heat flow equation for this model is given below and was solved by
Carslaw and Jaeger, 1958.
𝜕𝑇
𝜕𝑡
= 𝛼
𝜕! 𝑇
𝜕𝑟!
+
1
𝑟
𝜕𝑇
𝜕𝑟
Here T is the temperature of the probe, t is the time at which measurement was made, α is the
thermal diffusivity of the medium and r is the radius from the axis of the probe at which the
temperature is measured.
The complete derivation is available in numerous papers including the documents cited and, for the
sake of brevity, has not been included in this report.
The working equation of the probe method of determining thermal properties is:-
𝑅! = 𝑠
4𝜋
𝑄
Here RT is the thermal resistivity of the medium, Q is the heat generated by the probe per unit
length, and s is the slope of the temperature vs. loge(time) curve for the probe.

11. The probe was calibrated with glycerol which has a known thermal resistivity of 342.46 o
C-cm/W
(ASTM D5334), and was found to generate acceptable results when operated at 0.3V and 1.81A.
Hence, the factor Q can be calculated as
𝑄 =
𝐼! 𝑅
𝐿
Where I is the current flowing in the nichrome wire, R is the electrical resistance of the nichrome
wire and L is the length of the probe (6 cm).
It is also possible to obtain the thermal diffusivity (α) of the materials. The derivation of this
formula is not included and is available in the referred texts.
𝛼 =
𝑟!
!
2.246 X 𝑡!
Here, rp is the radius of the probe (3.5 mm) and t0 is the intercept of the tangent drawn to the
temperature vs. loge(time) curve, the intercept is taken at the initial temperature of the material.
Once RT and α are known, the thermal capacity Cp may be calculated as
𝐶! =
1
𝜌 𝑅! 𝛼
Here ρ is the density of the material.
Shown below is a chart which contains the thermal properties of the sand:

12. SAMPLE
STATE
BULK
DENSITY
(g/cc)
THERMAL
RESISTIVITY RT (
o
C-cm/W)
= s (Q/4π)
-1
THERMAL
DIFFUSIVITY α
(m
2
/s)
= rp
2
/(2.246 X t0)
THERMAL
CAPACITY Cp (J/
o
C-g) =
(RT.ρ.α)
-1
Oven dry 1.6 369.16 1.56E-06 0.11
Oven dry 1.75 334.04 1.82E-06 0.09
Oven dry 1.9 318.45 2.12E-06 0.08
NMC* 1.186 318.60 1.85E-06 0.14
NMC 1.3 275.26 2.72E-06 0.10
NMC 1.45 297.78 2.18E-06 0.11
NMC 1.6 272.13 2.58E-06 0.09
NMC 1.853 254.34 3.08E-06 0.07
*NMC = Natural Moisture Content and is equal to 3.94 %
A clear variation of thermal resistivity with density is observable, with the resistivity showing a
general decreasing trend with increasing density. The effect of moisture is also evident, with the
samples at natural moisture content (3.94 %) showing distinctly lower values of resistivity for the
same density.
An important observation to be made is that the density variation in the dry state is quite low as
compared to the density variation at the natural moisture content (NMC). Also, the presence of
moisture significantly reduces the thermal resistivity.
7.2 Thermal Expansion Test
The coefficient of thermal expansion was obtained using a dilatometer. The sample was prepared
in the form of a pellet by compressing it in a mould of diameter 10mm. Sufficient sample was taken
so as to obtain a pellet of length 13 ± 1 mm when compressed under a loading of 3 tons for 1
minute.
The sample was tested in a dilatometer, subjected to a gradual heating up to 600 o
C over a period
of 112 minutes. Variations in the length of the sample were recorded and were reported as a
Percentage Linear Change (PLC) of the original dimension.
A plot of PLC against temperature is shown below.

13. -100 0 100 200 300 400 500 600 700
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
PLC(%)
Temp (
o
C)
α = 4.18x10
-4
(
o
C)
-1
Percentage Linear Change vs. Temperature, Creek Sand
It can be observed that there is a drastic drop in the length in the initial 100 o
C of heating. This can
be attributed to the shrinking effects produced by the loss in moisture in the sample, 100 o
C being
the boiling point of water. But beyond this temperature range, the sample shows a fairly consistent
increase in length.
The value of co-efficient of thermal expansion is reported as 4.18X10-4
o
C-1
, and is calculated as the
slope of the linear portion of the PLC vs. temperature plot.
8. Conclusions
On analysis of the results generated, it can be seen that the sand tested has shown typical trends in its
thermal properties. The material shows typical reduction in the thermal resistivity with an increase in
moisture content or density. The poorly graded nature of the soil further implies that the packing of the
granules will not be efficient, which means that the soil will display a higher ratio of voids as compared
to a well graded soil.
Further, it is important to develop error correction techniques in the methods employed to test the
thermal properties. The assumptions that are made in the single probe method are not very good
approximations of field conditions. Corrections for the finite radius of the probe, as well as the non-zero
thermal capacity of the probe will ensure that the results are descriptive of the true nature of the
material tested.

14. ACKNOWLEDGEMENTS
I would like to place on record my sincere thanks and immense gratitude to Prof. DN Singh for opening
the doors of his laboratory to me. The sheer amount of knowledge that I have gained in my short
association with this laboratory is invaluable. I would further like to thank the research scholars of the
Environmental Geotechnology Laboratory, IIT-Bombay, for taking time off in order to explain the most
trivial of doubts. I would like to thank Mrs. Ritu Singh and Ms. Yashi Singh for their warm hospitality.
I would like to thank Prof. CP Rao, Prof. Murugavel and Prof. Anindya Datta, IIT-Bombay for handling the
accommodation with panache despite the many problems that they inevitably faced.
And lastly, I would like to thank the Indian Academy of Sciences for providing me this unique
opportunity. I believe that this program has gone a long way in opening eyes to the world of research. I
hope that the program continues successfully in the years to come, as it will be of great benefit to the
student community at large.
REFERENCES
1) DN Singh, K Devid
Generalized relationships for estimating soil thermal resistivity,
Experimental Thermal and Fluid Science (pg. 133-143), 2000
2) GS Campbell, KL Bristow
The effect of soil thermal resistivity on underground power cable installations,
Application Note, Decagon Devices, 2009
3) Yusuf Erzin, BH Rao, DN Singh
Artificial neural network models for predicting soil thermal resistivity,

15. International Journal of Thermal Sciences, 2007
4) VV Mason, M Kurtz
Rapid measurement of the thermal resistivity of soil,
Power Apparatus and Systems, IEEE, 1952
5) MVBB Gangadhara Rao, DN Singh
A generalized relationship to estimate thermal resistivity of soils,
Canadian Geotechnical Journal, 1999
6) Bryan R Becker, Anil Misra, Brian A Fricke
Development of correlations for soil thermal conductivity,
International Communications in Heat and Mass Transfer (pg. 59 - 68), 1992
7) ASTM D6913-04 (2009)
Standard test methods for particle-size distribution (gradation) of soils using sieve analysis
8) ASTM D2487-11
Standard practice for classification of soils for engineering purposes (Unified Soil Classification System
9) ASTM D5550-06
Standard test method for specific gravity of soil solids by gas pycnometer
10) ASTM D2974-07a
Standard test methods for moisture, ash and organic matter of peat and other organic soils
11) K Arulanandan
Soil Structure: In-situ Properties and Behaviour
12) Prasad P Bartake, DN Singh
A generalized methodology for determination of crushing strength of granular materials,
Geotechnical and Geological Engineering, 2007
13) ASTM D5334-08
Standard test method for determination of thermal conductivity of soil and soft rock by thermal needle
probe procedure
14) JH Blackwell
A transient flow method for determination of thermal constants of insulating materials in bulk
Part I and II,
Journal of Applied Physics, 1954
15) DA De Vries, AJ Peck
On the cylindrical probe method of measuring thermal conductivity with special reference to soils,
Australian Journal of Physics, 1958