Environmental Engineering Reference
In-Depth Information
40
Maximum
Mean
Minimum
30
20
10
0
−
10
−
20
−
30
−
40
Figure 10.13
Minimum, maximum, and average air temperature readings at a site in northern
Canada in 2007.
closed-form equation that can be used for the estimation of
the soil temperature when the air temperature above the soil
is measured:
A mathematical function describing a boundary condition
that is intermediate between the Dirichlet- and Neumann-
type conditions can also be used when solving problems.
1
C
f
ηf (u)
(Q
n
−
T
s
=
T
a
+
AE
)
(10.30)
10.5 DIRECT MEASUREMENT OF
THERMAL PROPERTIES
where:
The following section presents information on the measure-
ment of the thermal properties of soils. Quite often the
thermal properties are computed using estimation proce-
dures, and as a result the thermal properties may not be
measured for geotechnical engineering purposes. However,
it is important to understand the principles involved with the
measurement of thermal properties for saturated and unsat-
urated soils.
soil temperature,
◦
C,
T
s
=
air temperature,
◦
C,
T
a
=
C
f
=
conversion factor (i.e., 1 kPa
=
0
.
0075 mHg),
psychrometric constant, 0.06733 kPa/
◦
C,
η
=
f(u)
=
wind
+
0
.
146
W
w
), where
W
w
is the wind speed in km/hr],
speed
function
[i.e.,
f(u)
=
0
.
35
(
1
.
Q
n
=
net radiation, mm/day, and
AE
=
actual evaporation, mm/day.
10.5.1 Measurement of Thermal Conductivity
Thermal conductivity is the most important soil property asso-
ciated with the analysis of conductive heat flow. It is possible
to estimate the thermal conductivity of a soil mixture, but
sometimes it is preferable to undertake measurements in the
laboratory. The principles behind the laboratory measurement
of thermal conductivity are similar to those associated with
the measurement of hydraulic conductivity. However, in this
case, a thermal gradient is applied across a soil specimen
rather than a hydraulic head gradient. Also, the sides of the
soil specimen must be thermally insulated rather than being
impervious, as in the case of permeability measurements.
Further information on the above equation is presented
in Chapter 6, where consideration is given to coupled heat
and moisture flow analysis for the assessment of actual
evaporation.
Thermal boundary conditions can also be applied inter-
nal to the overall geometry. As an example, consider the
case of a pipeline installed underground. The pipeline may
operate at a temperature different from the temperature of
the surrounding soil. Therefore, heat may be extracted from
the surrounding soil to the pipeline or vice versa. If heat is
extracted from the pipeline to the soil, the pipeline operates
as a source. If the reverse is true, the pipeline operates as a
sink. If the pipeline passes through a permafrost area and is
operated at a temperature above water-freezing conditions,
there will be a gradual thawing of the surrounding soil.
It is also possible to have Neumann-type boundary condi-
tions that are based on a computed heat flux from the system.
10.5.1.1 Laboratory Thermal Conductivity Apparatus
Numerous researchers have measured the thermal conduc-
tivity of dry soils as well as soils with varying water contents
(Smith, 1942; Kersten, 1949; van Rooyen and Winterkorn,
1959; Johansen, 1975). The apparatus recently developed
Search WWH ::
Custom Search