Heat Flow Analysis for Unsaturated Soils - Unsaturated Soil Mechanics in Engineering Practice - page 504

specific heat of the soil. The specific heat of the soil, C p ,
is computed using the following equilibrium equation:

Stirrer

Thermal jacket

T w
T cf

C w M wa
M s

M wc C w + C cal

C p = − (10.35)

M s

where:
M s =

mass of soil used in the experiment.

Calorimetric
bucket

It may be necessary to correct the change in temperature,
T cf , for thermal losses and to compensate for energy added
by the stirrer. A detailed test procedure can be found in
Taylor and Jackson (1986).

Thermometer

Sample

10.5.3 Measurement of Unfrozen Water Content
A calorimeter can also be used to measure the unfrozen
water content of frozen soils. The test procedure is similar to
that used for the measurement of the specific heat capacity of
a soil. The test procedure requires that a soil specimen frozen
to a particular temperature below 0 ◦ C be placed inside the
calorimeter. The calorimeter is generally filled with water.
The calorimeter consists of an inner and outer jacket and an
internal stirrer, as shown in Fig. 10.20.
The temperature is recorded when a new equilibrium tem-
perature is achieved after the partly frozen soil has been
placed in the calorimeter. Radiation losses may need to be
taken into account when measuring the unfrozen water con-
tent. An equation satisfying thermal equilibrium can be used
to calculate unfrozen water content. It is necessary to know
the specific heat of each component of the soil mixture in
order to compute the unfrozen water content.
Thermal equilibrium can be written for each component of
the soil mixture. A soil specimen is prepared at a temperature
slightly below 0 ◦ C for testing purposes. A portion of the water
in the soil is frozen and a portion is unfrozen (i.e., a partly
frozen soil). The objective of the experiment is to determine
the percentage of the water that was unfrozen at the initial
temperature at which the soil specimen was prepared.
Several soil specimens can be prepared at slightly differ-
ent temperatures below 0 ◦ C and the unfrozen water content
corresponding to each initial temperature is computed based
on the calorimeter measurements. The results from several
measurements give rise to an unfrozen water content function.
The heat associated with each component of the soil mix-
ture can be quantified. The initial quantity of heat associated
with the soil solids, H is , can be written as the mass of the
solids times the specific heat of the solids and the absolute
temperature in Kelvin:

Figure 10.20 General layout of laboratory calorimeter.

Specific heat and volumetric heat capacity can be measured
using a commercially available calorimeter. Figure 10.20
shows the general layout of a calorimeter. The important
features of the calorimeter are the insulated walls, top, and
bottom along with a thermometer capable of measuring
temperature to within 0.01 ◦ C.
The heat capacity of the calorimeter should be measured
prior to its usage for measuring the heat capacity of a mate-
rial. This is done by adding a known amount of water at
a slightly higher temperature than the temperature of the
water already in the calorimeter. The heat capacity of the
calorimeter, C cal , is calculated using the following equation:

T w
T cf

C cal = M wc C w − M wa C w (10.34)

where:

M wc = mass of water initially in the calorimeter, g,

M wa = mass of water added to the calorimeter, g,

C w = specific heat of water at the mean temperature

when

determining the calorimeter calibration

(i.e., 4184 J kg − 1 at 15 ◦ C),

K − 1

T w = temperature change of the water in degrees Cel-

cius between its temperature before and after
being added to the calorimeter,

T cf = temperature change for the water already in the

calorimeter, and

C cal = mean specific heat or the calorimeter constant in

Jkg − 1

H is = M s C p T Ki (10.36)

K − 1 .

where:
M s

The specific heat capacity of the calorimeter is measured
once the mixture has come to a new equilibrium temper-
ature. It is then possible to place a mass of soil into the
calorimeter for the measurement and calculation of the

= mass of the soil solids, kg,

kg − 1 K − 1 , and C p = specific heat of the soil solids, J

T Ki = initial sample temperature, K.