Introductory Geotechnical Engineering An Environmental Perspective by Hsai-Yang Fang

162 Thermal and electrical properties of soils

While these assumptions are not met explicitly, testing conditions often approximate
them sufficiently. Typical thermal resistivity, ЊC-cm/watt results are ice ϭ 44.6,
water ϭ 165, mica ϭ 170, air ϭ 4000, moist clay ϭ 80–90, loose dry sand ϭ 175.

2 Graphical interpretation of thermal resistivity data: Figure 6.5 presents a three-
dimensional plot on a surface depicting thermal resistivity as a function of solid, air,
and water phases (Van Rooyen and Winterkorn, 1959). The density of soil is
expressed as the volume fraction of solids per unit volume of material on the X-axis,
the moisture as the volume fraction of water per unit volume of material on the
Y-axis, and the thermal resistivity along the Z-axis. The intersection c of the solids
and moisture axes corresponds to 100% air. In Figure 6.5 the maximum point a on

Z

Resistivity c9
of dry air

Resistivity Chernozem
of saturated air 1000
Thermal sand
Crushed quartz

Resistivity
(log scale)

100

b9 c a9

Moisture a
(by volume) X

Solids
(by volume)

Saturation line Temperature = ±20oC
(0 air)

b
Y

Figure 6.5 Three-dimensional surface depicting thermal resistivity as a function of solid, air, and water
phases.

Source: Van Rooyen, M. and Winterkorn, H. F. Structural and textural influences on the thermal conductivity of
soils. In Proceedings of the 38th Annual Meeting, Highway Research Board. National Research Council,Washington
DC, 1959, pp. 576–621. Reproduced with permission of The Transportation Research Board.

Thermal and electrical properties of soils 163

the X-axis represents 100% solid; aa’ is then the thermal resistivity of the solids alone.
The point b on the Y-axis represents 100% water and bb’ the thermal resistivity of
water. The length ccЈ along the Z-axis constitutes the thermal resistivity of air.

For different soils, the only limiting value in the figure that will show a considerable
change will be the effective thermal resistivity of a solid alone, which is represented by
the value aaЈ. The value of bbЈ may be altered by the amount and type of pollutant
in solution, temperature, or presence of other liquids. Similarly, ccЈ the thermal resis-
tivity of air may be changed by changes in its composition and temperature. Curve ab
represents the variation in thermal resistivity for saturated systems in which the solid
content varies from 0% to 100%. As an illustration of this variation, the dotted
curves were drawn, which are representative of a clay system with lower thermal
resistivity in the dry state and somewhat higher resistivities in the saturated state.

Three types of materials are presented in the Figure 6.5 include chernozem soil,
thermal sand, and crushed quartz. Chernozem soil is a zonal group of soil (Sec. 2.6)
having a deep, dark-colored to near black surface horizon, rich in organic matter,
which grades below into lighter-colored soil and finally into a layer of lime accumula-
tion; developed under tall and mixed grasses in a temperate to cool subhumid climate.

6.4.3.1 Comments on equations for calculating the soil thermal resistivity

With all these complex independent, and interdependent variables present, it is
evident that the problem of soil thermal resistivity is a complicated one; and that the
development of an equation for this quantity is a formidable task. A number of inves-
tigators have, however, developed such equations; and a summary of the available
results is given below. In general, equations may be classified under two groups:
(a) empirical equations based on data obtained by measurement and analyses by
graphical or numerical methods; and (b) theoretical equations which are based on
imaginary models in which the actual soil structure is simplified in such a way as to
permit a mathematical analysis. For dry soils, equations have been presented by
several investigators. The major difference between these equations lies in the
difference in the models on which they are based.

From the geotechnical engineer’s perspective, the equations for dry soils are largely
of academic interest. Dry soil is rarely encountered outside of the laboratory, since all
soils have a considerable water affinity and have a strong tendency to absorb water
from the atmosphere, at least to the extent of their hygroscopic requirements.
Frequently, some capillary water diffuses in the soil from groundwater level. In
considering the formulas for moist soils, it should be noted that some formulas are
theoretical and some are empirical.

EXAMPLE 6.2 Thermal conductivity and resistivity

Insulated soil

T = 25°C

T = 0°C

A = 0.5 m2

x=1m

164 Thermal and electrical properties of soils

For the above figure, calculate the thermal conductivity of the soil contained in the
tube if the heat per unit area Q ϭ 21.3 watts. Recall Equation (6.1), rearranged in
terms of thermal conductivity, K:

SOLUTION

K ϭ dQ · ddTx · A1 ϭ 21.3 watts · (25ЊC1 m 0ЊC) · 1 ϭ 1.7 watts
dt Ϫ 0.5 m2 mЊC

The above figure is a conceptual design for experimentally determining the thermal
conductivity. This is a useful property, particularly when assessing the extent to which
frost or thaw penetration (Sec. 6.7.3) may affect foundation footings, pavements or
landfill covers.

6.4.4 Thermal diffusivity

The diffusivity is the quotient of the thermal conductivity and the heat capacity per
unit volume. It is used in calculations where non-steady state conditions prevail,
unlike Example 6.2, which assumed steady state conditions, that is, the temperature
gradient from 25oC to 0oC had existed long enough for a constant flow of heat to
occur. An example of unsteady state conditions is the calculation of the time it takes
to freeze soil that is initially unfrozen. The diffusivity value may be determined by cal-
culation if the thermal conductivity, specific heat and density of a soil are known. Its
unit in the SI system is cm2/s.

6.5 Effect of heat on engineering properties of soils

Heating soils can lead to changes in the chemical structure of the constituent miner-
als. An extreme example is the manufacture of bricks or pottery from clay. While the
temperature effect is quite straight forward in relatively pure clay-water systems
within a limit range of temperature, it may cause marked dispersion or flocculation
effects depending on clay mineral and type of exchange ion. A comprehensive
study on temperature and heat effects on soil is given by Chandrasekharan et al.
(1969) and some of these results are summarized as follows:

6.5.1 Effect of temperature on soil constants

1 Moisture content of soil: The moisture content has a strong influence on the engi-
neering behavior of soil. Of course, to determine the moisture content in a reasonable
amount of time it is generally necessary to heat the soil. There are three basic proce-
dures for determination of moisture content namely (a) oven dry (ASTM D2216), (b)
air-dry at room temperature, and (c) microwave oven dry. The air-dry method is time
consuming and does not remove all soil moisture. As such, conventional and
microwave ovens are typically used. Different oven temperatures yield different dry
weights for the soil, particularly for organic soils. Increasing the oven temperature for
some organic soils causes organic matter to burn. This results in a lower dry weight