Grant: Frozen-Ground Waste Containment
2
Table 1. Selected thermal properties of system components.
Material
Heat capacity
Thermal conductivity
Density
kJ◦C-1kg-1
W◦C-1m-1
Mgm-3
1.59a
Clay
0.92
0.9
Water
4.2177
0.56
1.0
Ice
2.09
2.21
0.9
a
Bulk density
Source: Alter [1969].
Thermal conductivity
All of the pipe would be installed in unsaturated
soil.
The thermal conductivities of the unfrozen and frozen
soils were estimated with the protocols presented in
Revised design
Andersland and Ladanyi [1994, p. 53-54] The ther-
mal conductivities of the soils were calculated via:
The revised design would require 30 15.32-m-long, 4
k = (ksat - kdry)Ke + kdry.
(3)
13.72-m-long, 4 11.76-m-long, 4 9.80-m-long, 4 7.84-
m-long, 4 5.88-m-long, 4 3.92-m-long and 4 1.96-m-
For the unfrozen soils the Kersten number was cal-
long pipes. The total length of pipe would be 679.72
culated via:
m, slightly more than six times the length required
Ke = log Sr + 1.0.
(4)
in the original design. All except the shortest freeze
pipes would be installed in both water-saturated and
This yielded values of 0.7 for the unsaturated soil
unsaturated soil. The various total lengths of pipe
and 1.0 for the saturated soil. The Kersten number
that would be installed in unsaturated or unsatu-
was also 1.0 for the saturated and unsaturated frozen
rated soil are presented in Table 2.
soil. The thermal conductivity of the dry soil was
calculated via:
0.137ρd + 0.0647
Calculation of thermal properties
kdry =
(5)
2.7 - 0.947ρd
Heat capacity
which yielded a value 0.2366 W◦C-1m-1. The
The heat capacities of unfrozen soils were calculated
thermal conductivity of saturated unfrozen soils was
via:
ρd
calculated via:
(0.17 + 1.0fw ) cvw .
(1)
cvu =
ρw
ksat = ks-nkw
1
n
(6)
The heat capacities of frozen soils were calculated
via:
yielding a value of 0.7444 W◦C-1m-1. The ther-
mal conductivity of saturated unfrozen soils was cal-
ρd
[0.17 + 1.0fu + 0.5 (fw - fu)] cvw
cvf =
(2)
culated via:
ρw
ksat = ks-nkwu ki -fu
n
1
f
(7)
[Andersland and Ladanyi, 1994, p. 57]. The calcu-
lated heat capacities are presented in Table 3.
yielding a value of 1.2629 W◦C-1m-1. The calcu-
lated thermal conductivities are presented in Table
3.
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