the disruption in heat flow becomes more signif-
This is the most complex boundary condition
icant until eventually, at the vertical center plane
considered in that the temperature of the soil sur-
face transitions through 0C many times over the
of the inclusion, frost penetration is indistin-
guishable from that of an infinitely wide inclu-
winter. Figure 8 shows the predicted soil temper-
sion even though the inclusion itself is of finite
atures at three depths in response to the changes
width. Accordingly, the computationally sim-
in temperature at the soil surface. At shallow
pler one-dimensional simulations have been
depth (7.5 cm), the soil varies in temperature with
done to investigate the effects of soil moisture
the same frequency as the soil surface but with
content and soil surface temperature history on
lower magnitude. After its initial freezeup to at
frost penetration for a wide inclusion.
least 7.5 cm depth, the soil does not remain fro-
zen. It transitions from frozen to unfrozen, and
the reverse, several times. It also thaws to ∼0C
One-dimensional simulations
The first simulation is that of the freezing and
occasionally in midwinter. This simulation shows
thawing of a 17% moisture content silty soil (no
that shallow soil of this type is quite active ther-
sand inclusion present) under BC1 conditions.
mally during such a winter. The consequence for
a buried electromagnetic sensor system would be
1.5
a variation in detection capability throughout the
winter as the unfrozen moisture content of the
t = 140 days
1.0
soil above the sensor cable changes.
Deeper soil (22.5, 37.5 cm) experiences more
0.5
moderate temperature changes; a depth-depen-
dent thermal lag is evident during both cooling
Inclusion
x ~ 4.4 m
Centerline
and warming periods. At a depth of 22.5 cm, the
0
burial depth of an electromagnetic sensor cable,
the soil freezes eight days after the onset of sus-
Inclusion
0.5
Edge
tained low temperature at 7.5-cm depth. There is
a five-day delay between the times when the
1.0
c.
shallow soil and soil at cable depth warm to
above 0C for the first time in the spring. This
points out how misleading it can be during tran-
1.5
0
10
20
30
40
50
60
70
sitional periods (early and late winter) to assume
Depth (cm)
that the soil condition at the surface indicates the
2.0
110
0
t = 140 days
1.5
5
1.0
00
-5
0.5
0 cm
Inclusion
10
10
x ~ 4.4 m
Centerline
7.5 cm
0
22.5 cm
15
37.5 cm
Inclusion
20
20
0.5
0
40
80
120
160
Edge
0
40
Day (28 Oct is day 1)20
80
1
160
1.0
d.
27 Oct
6 Dec
15 Jan
24 Feb
5 April
1.5
0
10
20
30
40
50
60
70
Depth (cm)
Figure 7 (cont'd).
Figure 8. Temperature profiles for soil depths of 7.5, 22.5
and 37.5 cm, obtained from one-dimensional numerical
simulations of heat flow in a silty soil (17% moisture con-
tent) with no inclusion, under BC1 conditions. The im-
posed temperature history of the soil surface is also shown.
9
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