Environmental Engineering Reference
In-Depth Information
between thermal conductivity and other volume-mass soil
properties such as water content and dry density. The empir-
ical relationships were developed for both unfrozen and
frozen soil conditions. Soil fabric was found to have an
important influence on thermal conductivity giving rise to
different equations for coarse- and fine-grained materials.
The empirical thermal conductivity equations proposed by
Kersten (1949) for sandy soils were converted to SI units by
Andersland and Anderson (1978). The proposed empirical
equation for unfrozen sandy soils is as follows:
unfrozen and frozen soils. The normalized thermal conduc-
tivity equation for unfrozen sandy soils is as follows:
λ ru =
0 . 7log (S u )
+
1
(10.50)
where:
λ ru =
normalized thermal conductivity of the unfrozen soil,
W/m/K, and
S u =
degree of saturation of the unfrozen soil.
0 . 1442 0 . 7log ( w )
0 . 4 ×
The normalized thermal conductivity equation for frozen
sandy soils was written as follows:
10 0 . 6243 ρ d
λ u =
(10.46)
where:
λ rf
=
S u
(10.51)
λ u =
thermal conductivity of the unfrozen soil, W/m/K,
where:
w
=
gravimetric water content, %, and
dry density, g/cm 3 .
ρ d
=
λ rf =
normalized thermal conductivity of the frozen soil,
W/m/K, and
The above equation shows that the water content and the
dry density of the soil are the dominant factors influencing
thermal conductivity.
The proposed empirical equation for frozen sandy soils is
S u =
degree of saturation in decimal form.
The
normalized
thermal
conductivity
equation
for
unfrozen fine-grained soils was written as follows:
10 0 . 8116 ρ d
10 0 . 9115 ρ d
(10.47)
λ f
=
0 . 001096
×
+
0 . 00461 w
×
λ ru =
log (S u )
+
1
(10.52)
where:
The normalized thermal conductivity equation for frozen
fine-grained soils was written as follows:
λ f
=
thermal conductivity of the frozen soil, W/m/K.
λ rf
=
S u
(10.53)
Kersten (1949) proposed the following empirical equation
for unfrozen fine-grained soils:
The normalized thermal conductivity, λ r , equation with
respect to saturated and fully dried conditions is as follows:
0 . 1442 0 . 9log ( w )
0 . 2 ×
10 0 . 6243 ρ d
λ u =
(10.48)
λ
λ dry
λ r =
(10.54)
Another empirical equation was proposed for frozen fine-
grained soils:
λ s
λ dry
where:
10 0 . 4994 ρ d
(10.49)
Cote and Konrad (2005) applied the Kersten (1949) model
to a variety of coarse-grained materials and found the model
generally predicted thermal conductivities that were higher
than the measured values. The closest predicted thermal con-
ductivity values were for crushed sandstone and quartzite.
It should be noted that the Kersten (1949) model does not
include the influence of the thermal conductivity of the solid
particles which can have a significant influence on the over-
all thermal conductivity.
10 1 . 373 ρ d
λ f
=
0 . 001442
×
+
0 . 01226 w
×
λ r
=
normalized thermal conductivity of the soil at a
particular water content, W/m/ C,
λ s
=
thermal
conductivity
of
the
saturated
soil,
W/m/ C, and
thermal conductivity of the dry soil, W/m/ C.
λ dry =
Johansen (1975) normalized thermal conductivity with
respect to the amount of water in the soil (i.e., normalized
water content or degree of saturation, S ). This infers that
the following limiting condition must be observed:
10.6.1.2 Johansen Model
Johansen (1975) used the concept of a normalized (or relative)
thermal conductivity and reanalyzed the database generated
by Kersten (1949). The mineralogy of the soil was taken
into consideration as well as the degree of saturation. A nor-
malized thermal conductivity equation was developed for
S
=
0
;
λ
=
λ dry
or
λ r =
0
(10.55)
S
=
1 . 0
;
λ
=
λ s
or
λ r =
1
(10.56)
It should be noted that the equations proposed by Johansen
(1975) do not satisfy the equation for the unfrozen soil when
the degree of saturation goes to zero.
 
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