Frost heave is estimated from the total amount
20 cm from 340 cm (11.2 ft) to 400 cm (13.1 ft).
of ice segregation in the frozen zone by:
The upper boundary pore water pressure was
chosen to be computer-generated, as follows.
(
)
θs = θi - θo - θn
(6)
When the profile is completely thawed and down-
ward vertical drainage occurs, the surface pore
where θs = volumetric segregated ice content (%)
water boundary condition is modeled by
θo = porosity (%)
θn = residual unfrozen water content (%).
h
=0
(7)
x
If θs is greater than 0, ice segregation has occurred
and the frost heave is computed by multiplying θs
which means that the velocity flux across this
by the zone thickness. The θn parameter estab-
boundary is zero. The upper-boundary condition
is set to 0 cm of water when the upper-boundary
lishes the pore water stress at the freezing front
temperature is above 0C and frozen regions re-
for the solution of the moisture transport equa-
tion. In this study, θn was obtained by assuming a
main in the column. When the surface tempera-
ture is below 0C, a specified constant upper-
moisture tension of 800 cm of water and solving
boundary pore pressure is used. To be consistent
eq 2. The use of the 800 cm of water condition
with previous studies, a value of 300 cm of water
stems from that being the highest tension mea-
was used.
sured in various field studies. Thaw settlement
The lower-boundary pore pressure condition of
from ice melting is the reverse process of that
FROST is set by specifying discrete pore water
described above for ice segregation.
pressures that relate to the water table elevation at
To conduct the calculations described above,
times when these conditions occur. At intermedi-
FROST requires the following input for each ma-
ate times, lower-boundary pore water pressures
terial: 1) Gardner's coefficients for soil moisture
are linearly interpolated. For all the Mn/DOT cases,
characteristics, 2) Gardner's coefficients for hy-
we set the lower boundary pore pressure to pro-
draulic conductivity characteristics, 3) porosity and
duce a constant water table depth throughout the
density of the soil, 4) thermal conductivity and
simulation. We simulated the water table in each
volumetric heat capacity of the dry soil, and 5) the
test section at the depth determined by field mea-
E-factor.
surements to be representative of the on-site con-
FROST also requires the following input for
ditions. Where the measured water table varied
initial and boundary conditions: 1) element lengths,
through a test section, we conducted two simula-
2) upper- and lower-boundary pore water pres-
tions using the deepest and shallowest values.
sures, 3) upper- and lower-boundary temperatures,
Input for the upper boundary temperature con-
4) initial temperature, pore pressure and ice con-
dition consists of a set of specified times and tem-
tent distributions with depth, 5) surcharge pres-
peratures that are implemented as step changes.
sure, 6) freezing point depression and 7) modifier
Values were input in 24-hr increments using the
of the upper node during thaw.
mean daily air temperature. Conditions at Buf-
In all cases, the pavement structure was simu-
falo, Minnesota, were simulated, since this is the
lated as a column with its upper boundary at the
nearest station to the Mn/ROAD facility (16 km;
pavement surface and extending down to 400 cm
10 mi) with a reasonably long record of meteoro-
(13.1 ft) using 99 elements. The length of ele-
logical data. The time period simulated was 1
ments within the expected zone of freezing
October 1959 to 14 November 1960. If the sever-
(down to 110 cm or 3.6 ft) was about 2 cm (0.8
ity of a winter is judged by its air freezing index,
in.). These lengths were adjusted for individual
the 19591960 winter is very near the average
cases to provide nodes positioned exactly at the
value for the 28-year period ending in 1987. The
depths where the interface between materials
distribution of freezing indices at Buffalo during
are located in the Mn/ROAD test sections. The
this time is shown in Figure 3. Starting the simu-
deeper soil was modeled with element lengths
lations on 1 October gave 30 days of computa-
of 4 cm between 110 and 230 cm (3.67.6 ft), 10
tions before the first freeze event, allowing the
cm between 230 and 340 cm (7.611.2 ft), and
4
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