(C-days) (F-days)
3000
1600
1200
2000
800
1000
400
Buffalo, MN
0
0
1960
1970
1980
1990
Figure 3. Distribution of seasonal freezing index with time at Buffalo,
Minnesota.
model to stabilize and gradational moisture and
intermediate water table depths (3.6, 5.6 and 6.1
temperature conditions to develop.
m; 12, 18, and 20 ft), the initial tension was set to
FROST adjusts the air temperature values to
200 cm water (an estimate of optimum condi-
represent the soil surface temperatures using a
tions) from the surface to the depth beneath which
procedure similar to the Corps of Engineers n-
the tension from the theoretical gradient would
factor approach for seasonal freezing indices (U.S.
increase positively. In simulations with the deep-
Army 1966). An n-factor is defined as the ratio of
est in-situ water tables (13.7 and 15.2 m or 45 and
the surface index to the air index, separately cal-
50 ft), we set a minimum bottom tension of 300
culated for the full freeze and thaw season. In this
cm, with tensions decreasing from the bottom to 2
study, 0.5 was used for the freezing n-factor (i.e.,
m (6.5 ft), and a constant tension of 200 cm
on days when the air temperature was ≤ 0C), and
water from 2 m (6.5 ft) to the surface. Initial volu-
1.8 was used for the thawing n-factor.
metric ice content was set at 0.0% for all ele-
Bottom boundary temperature conditions consist
ments, since the simulations began prior to the
of a set of times and temperatures that are linearly
start of the freeze season.
interpolated at intermediate times. Three points
Surcharge (overburden) pressure is a constant
were set during the simulations using estimated
value to simulate the pressure acting on the top
values of a reasonable ground temperature. The start
node of the modeled column. In a case where only
and end temperatures are estimated to be 9.59C
soil beneath a pavement surface is being modeled,
(49.3F), which is 3C (5F) higher than the mean
this overburden should simulate the pressure of
annual air temperature 6.83C (44.3F). The third
the pavement on the soil. For the Mn/ROAD test
point was set so that a minimum value of 6.0C
section simulations, the pavement properties were
(42.8F) would occur at the end of the freeze season.
included in the modeled column, so the overbur-
Initial conditions required to be set for the
den pressure was set at zero.
FROST program are temperature, moisture stress,
The freezing point depression is a constant value
and ice content. The initial temperature of all ele-
that represents the temperature at which in-situ soil
ments was estimated to be 5F higher than the
water freezes. This was set in all cases to be 0C.
mean annual air temperature. For cases with wa-
A modifier is included that adjusts the overbur-
ter table depths less than 3 m (10 ft), the initial
den pressure acting on the upper node during thaw
moisture tension/pressure was set at a gradient to
periods. This value can be set between 0.0, to
produce a water table (i.e., pressure = 0) at the
represent old, cracked pavements, and 1.0, to rep-
specified depth, increasing positively downwards
resent brand new pavements. We used 1.0 for the
at 1 cm water/1 cm depth. For simulations with
Mn/ROAD cases.
5
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