Measurement and Estimation of State Variables - Unsaturated Soil Mechanics in Engineering Practice - page 140

than 5 months prior to flooding the test track. The results
demonstrated that the thermal conductivity suction sensors
can provide stable measurements of matric suction over rel-
atively long time periods.
Matric suction variations in the field can be related to
environmental changes. Several AGWA-II sensors have been
installed at various depths in the subgrade of roads and rail-
roads. Matric suctions in the soil were monitored at various
times of the year. The results clearly indicate seasonal varia-
tions of matric suctions in the field with the greatest variation
occurring near ground surface.

particularly in the low temperatures near freezing and
the high temperatures near the boiling point. The thermal
conductivity of water versus temperature can be best fit with
the following linear equation:

λ =

0 . 0014 T

+

0 . 5743 (4.7)

where:

thermal conductivity of water, W/m ◦ C, and λ =

temperature, ◦ C. T =

Campbell et al., (1994) proposed the following parabolic
equation for the thermal conductivity of water:

4.2.9.5 Influence of Ambient Temperature
The thermal conductivity suction sensor measurement is
dependent upon the thermal conductivity of the individual
components of the sensor, namely, the ceramic, the water,
the air, and the internal electrical and epoxy components.
Several research studies have been undertaken to assess the
effect of ambient temperature on the calibration curve.
The thermal conductivity λ of the ceramic portion is about
1.7 W/m ◦ C. Published thermal conductivities have shown
the thermal conductivity of the ceramic to be essentially
independent of the ambient temperature. The thermal con-
ductivity of air is about 0.025 W/m ◦ C. Published values
show that the thermal conductivity of air has a slight depen-
dence on temperature.
The thermal conductivity of water is known to change
with temperature. Table 4.7 provides a list of thermal con-
ductivities for water, λ over the range from the freezing
point to the boiling point of water.
Shuai et al. (2002) graphically presented results of the
thermal conductivity of water versus temperature (Fig. 4.50).
The results show some nonlinearity in the relationship
between the thermal conductivity of water and temperature,

− ( 0 . 000000026 ) T 2 λ = 0 . 024 + ( 0 . 0000773 ) T (4.8)

Figure 4.51 provides a comparison of the thermal con-
ductivities of the ceramic, air, and water over a range of
temperatures. The water phase appears to show the greatest
dependency on ambient temperature. A number of studies
have been undertaken to assess the influence of temperature
on the measurements of soil suction when using thermal
conductivity suction sensors. The effect of ambient temper-
ature on thermal conductivity suction sensor readings has
been observed since the 1970s (Phene et al., 1971; Wong
et al., 1988). Concern over the effect of ambient tempera-
ture changes has been expressed when using both the GCTS
thermal conductivity suction sensor and the Campbell Sci-
entific CS229 thermal conductivity suction sensors.
In 2002, Shuai et al. conducted a series of tests in an
attempt to quantify the effect of ambient temperature on the
measurement of soil suction when using the GCTS type of
thermal conductivity sensors. (These tests were performed
on suction sensors manufactured at the University of
Saskatchewan but are of the same design as used by GCTS.)
Figure 4.52 shows the effect of temperature change on the
observed readings from the GCTS-type suction sensors.
A thermometer was placed next to the GCTS thermal
conductivity suction sensor embedded in a soil sample that
was wrapped in tin foil to maintain a constant suction value.
The results showed that when the ambient temperature
increased, the measured suction (i.e., obtained from the
23 ◦ C calibration curve) decreased. When the temperature
decreased, the opposite behavior was observed.
It was suggested that the inter relationship between
temperature and the thermal conductivity suction measure-
ment might be due to the change in thermal conductivity
of the water in the soil. The dependency of the thermal
conductivity of water on temperature led Shuai et al., (2002)
to propose a correction equation that could be applied to
the observed measurement, taking ambient temperature into
consideration. The proposed temperature correction took
the form of Eq. 4.5. It should be noted that the temperature
variation was only about 3 ◦ C and the sensor reading change

Table 4.7 Thermal conductivity of Water at Various
Temperatures

Temperature, ◦ C Thermal Conductivity, λ ,W/m ◦ C

0.01 0.5610

10 0.5800

20 0.5984

30 0.6155

40 0.6306

50 0.6436

60 0.6543

70 0.6631

80 0.6700

90 0.6753

100 0.6791

Source : Cooper and Dooley, 2008.