Geoscience Reference
In-Depth Information
Table 9.2
Basic soil constituent data to calculate the composite soil heat capacity
and thermal conductivity according to the method of De Vries (
1963
)
Constituent
Sand
Clay
Organic
Water
Air
Volumetric heat capacity
C
i
(J cm
-3
K
-1
)
2.128
2.385
2.496
4.180
1.212
Thermal conductivity
λ
i
(J cm
-1
d
-1
K
-1
)
7603
2523
216
492
Variable
Shape factor
g
i
(-)
0.144
0.00
0.50
0.144
Variable
Weight factor
k
i
(water continuous) (-)
0.2461
0.7317
1.2602
1.0000
Variable
Weight factor
k
i
(air continuous) (-)
0.0143
0.6695
0.4545
0.1812
1.0000
where
k
is a weighting factor and the subscripts denote the soil components: quartz (q),
clay mineral (c), organic matter (o), water (w) and air (a). The weighting factors depend
on the shape and orientation of the soil components and the ratio of the conductivities.
De Vries assumed the particles to be spheroids whose axes are randomly oriented in the
soil. In that case the weighting factor for soil component
i
can be calculated by:
−
1
1
3
3
λ
λ
∑
k
=
1
+ −
i
1
g
(9.16)
i
j
j
=
1
0
where the subscript zero refers to the continuous luid (air for dry soil, and water for
moist soil), and
g
j
represents the shape factor for the
i
th component with
g
1
+
g
2
+
g
3
= 1.
We may assume
g
1
and
g
2
to be equal. Therefore only one shape factor must be esti-
mated for each soil component and Eq. (
9.16
) can be written as:
066
.
033
.
k
=
+
(9.17)
i
λ
λ
λ
λ
+
( )
−
1
+
g
i
−
1
112
g
i
1
i
i
0
0
The shape factors should be calibrated and common values are given in
Table 9.2
. The
weighting factors based on these shape factors and calculated with Eq. (
9.17
) are also
listed in
Table 9.2
.
Question 9.7:
Derive the weight factor
k
i
for sand with water as continuous phase,
using Eq. (
9.17
) and the shape factors listed in
Table 9.2
.
For 'dry' soil (
θ
<
θ
dry
) air is considered as the continuous phase and the thermal con-
ductivity is determined as:
kf
λ
+
kf
+ + +
++++
λ
kf
λ θλ λ
θ
k
f
q
qq
cc c
o
oo
ww
aa
(9.18)
λ
=
125
.
s
kf
kf
kf
k
f
a
q
q
c
c
o
o
w
where all weighting factors
k
i
are deined with respect to air (
Table 9.2
).
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