Grant: Frozen-Ground Waste Containment
4
References
Alter, A.J., Water supply in cold regions, Cold Reg.
Notation
Res. Eng. Lab. Monograph, III-C5a, 1969.
Andersland, O.B., and B. Ladanyi, An introduction
to frozen ground engineering, New York, Chap-
ar
distance, relative to R, over which the soil
man and Hall, 1994.
was cooled by the freeze pipe, dimension 1
cvf volumetric heat capacity of a frozen soil,
Grant, S.A., G.E. Boitnott, A. Tice, Effect of dis-
MJ◦C-1m-3
solved NaCl on the freezing curves of kaolinite,
cvu volumetric heat capacity of an unfrozen soil,
montmorillonite, and sand pastes, Cold Reg. Res.
MJ◦C-1m-3
Eng. Lab. Spec. Rep., 99-2, 1999.
cvw volumetric heat capacity of liquid water,
Sanger, F.J., and F.H. Sayles, Thermally and rheo-
MJ◦C-1m-3
logical computations for artificially frozen ground
L fu∆Hvw , m3m-3
construction, Eng. Geol., 13, 311-337, 1979.
fu volumetric fraction of liquid water in the
Steven A. Grant, U.S. Army Engineering Research
soil, m3m-3
and Development Center, Cold Regions Research &
fw volumetric fraction of liquid water and ice
Engineering Laboratory, 72 Lyme Road, Hanover
in the soil, m3m-3
NH 03755. +1-603-646-4446, +1-603-646-4561 fax,
k thermal conductivity, W◦C-1m-1
steven.a.grant@usace.army.mil
kdry thermal conductivity of a dry soil,
W◦C-1m-1
W◦C-1m-1
This preprint was prepared with AGU's L TEX macros v4,
A
with the extension package `AGU++' by P. W. Daly, version
1.5g from 1998/09/14.
ksat thermal conductivity of a saturated soil,
W◦C-1m-1
W◦C-1m-1
Ke Kersten number, dimension 1
n porosity, m3m-3
R one-half the interval between freeze pipes,
m
r0 radius of the freeze pipe, m
n porosity, m3m-3
Q energy extracted by freeze pipes, MJm-1
Sr degree of saturation, m3m-3
t time required to freeze, s
Tf p freeze pipe temperature, ◦C
Tmp melting point temperature, ◦C
Ts soil temperature, ◦C
∆Hvw volumetric enthalpy of fusion for water,
MJm-3
ρd bulk density of the soil, Mgm-3
ρw density of liquid water, Mgm-3
ν0 Ts - Tmp, ◦C
νw Tmp - Tf p, ◦C
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