Environmental Engineering Reference
In-Depth Information
The following equation by C ote and Konrad (2005) can
be used to estimate the thermal conductivity of dry soil:
4.5
4.0
Slusarchuk and Watson (1975)
Côté and Konrad (2005)
Smith and Byers (1938)
Johansen (1975)
Kerslen (1949)
Smith (1942)
(κ
2
P
λ
p
−
λ
f
)(
1
−
n)
+
λ
f
λ
dry
=
(10.70)
3.5
1
+
(κ
2
P
−
1
)(
1
−
n)
3.0
where:
2.5
κ
2P
=
from Eq. 10.69 with
β
=
0
.
81 for natural soils and
0.54 for crushed rock.
2.0
When the pore fluid in a soil is water, the ratio
λ
f
/λ
p
is
generally larger than
15
and there are no structural effects.
Consequently, the
β
factor can be set equal to 0.46 for
all particle types. The results are essentially the same as
those obtained by Johansen (1975) using the geometric mean
procedure.
The relative or generalized thermal conductivity model by
Cote and Konrad (2005) can be written as follows:
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
λ
(measured) (W/m/
°
C)
Figure 10.22
Comparison of measured and predicted thermal
conductivity of unfrozen gravelly materials using Cote and Konrad
(2005) model.
κ
(u,f )
S
(u,f )
λ
r(u,f)
=
(10.71)
1
+
(κ
(u,f )
−
1
)S
(u,f )
where:
4.5
S
(u,f )
=
degree of saturation, unfrozen or frozen,
Côté and Konrad (2005)
Kerslen (1949)
λ
r(u,f)
=
thermal
conductivity
of
either
unfrozen
or
4.0
frozen
soils,
u
designating
unfrozen
and
f
designating frozen soils, and
3.5
κ
(u,f )
=
an empirical factor that depends on the type of
soil, (Table 10.8)
3.0
2.5
A comparison of the predicted and measured values of ther-
mal conductivity for an unfrozen gravelly material when using
the Cote and Konrad (2005) model are shown in Fig. 10.22.
A comparison of the predicted and measured thermal conduc-
tivities for a frozen gravelly material is shown in Fig. 10.23.
There has been a gradual evolution of the equations used
for the estimation of thermal conductivity of both frozen and
unfrozen soils. The estimated saturated and unsaturated ther-
mal properties are adequate for solving most geotechnical
engineering problems.
2.0
1.5
1.0
0.5
0.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
λ
(measured) (W/m/
°
C)
Figure 10.23
Comparison of measured and predicted thermal
conductivity of frozen gravelly materials using C ote and Konrad
(2005) model.
Table 10.8 Empirical Factors
κ
(u,f )
for Unfrozen and
Frozen Soils
Material
κ
(u)
Unfrozen
κ
(u)
Frozen
10.6.1.4 Degree of Saturation versus Matric Suction
The equations proposed for the estimation of the thermal
conductivity of a soil show the importance of the degree
of saturation. The degree of saturation of a soil is also
related to soil suction, and therefore the thermal conductiv-
ity functions can also be written in terms of soil suction (see
Fig. 10.2). The relationship between soil suction and thermal
Gravel and coarse sand
4.6
1.7
Medium and fine sand
3.55
0.95
Silts and clays
1.9
0.85
Peat
0.3
0.25
Source
:Cote and Konrad (2005).
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