was the temperature at the soil surface, to inves-
infinite in lateral extent (Fig. 1d). It is covered by
tigate the sensitivity of the results to these two
a horizontally infinite soil layer of the same
factors, other influences on heat flow being un-
thickness and underlain by another soil layer
changed.
that is infinite in depth and in lateral extent. A
Heat capacity and thermal conductivity, both
piecewise linear finite element mesh of 75
for the frozen and unfrozen state, and latent heat
unequally spaced nodes is used for the one-
are specific input parameters of the program.
dimensional simulations, with node 1 at the sur-
The dry densities of the sand and soil are calcu-
face (0 cm) and node 75 at a depth of 20.52 m.
lated from their mineral content per volume by
Node spacings (and element sizes) range from
assuming a mineral density of 2.65 g/cm3. The
2.5 cm (one-dimensional simulations) or 5 cm
(two-dimensional simulations) within and above
mineral contents used are 0.6 (sand) and 0.55
the sand inclusion to some meters in size in dis-
(soil) based on assumed porosities of 0.4 and
tant regions.
0.45, respectively. The resultant dry density of
A simulation proceeds in hourly time steps.
the sand, 1.59, is within the range reported by
The output is soil or sand temperature at select-
Miller et al. (1992) for uniform sand that is loose,
ed nodes. Locations of freezing and thaw fronts
1.45, to dense, 1.75.
are linearly interpolated from the temperature
The moisture content (weight percent) of the
data.
sand, 3%, is that of a concrete sand buried in
sandy loam soil at the CRREL field site, known
as SOROIDS, in Vermont. The moisture content
Properties of the soil and inclusion
For simulations the silty soil and inclusion are
of the SOROIDS sand was determined from the
assigned the properties listed in Table 1. The
reduction in sample weight upon drying. The in-
physical and thermal conditions of the inclusion
termediate soil moisture content, 17%, is that of
(sand or sandy soil) and surrounding silty soil
the medium-grained soil at SOROIDS in Novem-
were selected as being representative of situa-
ber/December, prior to freezing; 10% and 25%
tions relevant to installations of electromagnetic
moisture contents are representative of dryer
sensor systems, and intentionally did not dupli-
Mesh
cate conditions at the field site in Vermont. The
0
moisture content of the silty soil was varied, as
20
40
)
60
80
100
0
20
40
60
80
100
X (cm)
.
Soil Surface
c.
Silty Soil
15 cm
Sand or Sandy Soil
30
d.
Figure 1 (cont'd).
3
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