in the saturated water content Wsat resulted in the
make the mathematics trivial (Gilpin 1980, Holden
largest variation of the three, as listed in Table 1,
1983) or attempting to maintain the physics while
leading to a reasonable solution strategy (Black
with a relative error range of 8 to 8%. These re-
and Miller 1985). This later approach was success-
sults suggest that a 10% uncertainty in the magni-
fully employed in this paper.
tude of Wsat, Wd and (kw)sat should not have a
The differential equations of secondary frost
severe adverse effect on the predicted heave pres-
heave (Miller 1978) are numerically solved in fi-
sure.
nite difference form with the program RIGIDICE.
The largest relative errors result from a 10%
change in the Brooks and Corey constants φb and
By choosing the language C++ and its object ori-
β for the soil as shown in Figures 4d and 4f. Table
ented nature, the core program is easily attached
to the mathematical analysis program MathCad
1 lists the largest range of 43 to 25% relative er-
5.0+. The ease of analysis in this new format al-
ror in the calculated heave pressure for a 10%
change in β and a 10 to 8% error for φb. Clearly,
lows simulations to be conducted in any physi-
cally correct model that the end user requires.
this indicates that the hydrologic properties of the
A brief sensitivity analysis of several impor-
soil must be known if any accurate heave behav-
tant parameters shows that current practices of
ior is to be calculated. This is unfortunate since
ground freezing monitoring are flawed. Calculated
this information is rarely even collected. Figure
behavior for heave rate and pressure was found
4e and Table 1 shows a smaller response, similar
to the soil water properties, for a change in α.
to be largely insensitive to penetration rate and
temperature gradients. Likewise, unfrozen water
Surprisingly, a 10% change in the boundary
content uncertainty did not strongly influence the
conditions also gives a similar response in rela-
heave rate and pressure behavior. Hydraulic con-
tive error to heave pressure as the soil water prop-
ductivity, though, was found to have a dramatic
erties. Figures 4g and h show the response for a
influence.
change in penetration vb and the temperature gra-
dient in the unfrozen soil ∇θ. The heave rate vi
These results indicate that the effort expended
in making accurate temperature profiles in freez-
response to calculated heave pressure ui is obtained
ing ground is not necessary. It also indicates that
from any of the graphs as it is always the center
the great efforts required to monitor unfrozen wa-
reference line. Again, this is unfortunate since the
ter content changes in the field might also be un-
penetration rate and temperature gradient are eas-
necessary. The sensitivity study did demonstrate
ily obtained from temperature profiles. This means
the importance of the hydraulic conductivity. A
that more accurate temperature measurements will
wise use of research and development efforts
not necessarily result in better predictive capabil-
should therefore be to develop techniques to mea-
ity.
sure the hydraulic conductivity in the laboratory
The last group of graphs displays the response
and monitor it in the field.
to an uncertainty in thermal conductivities. Inspec-
The current model relies upon assumed stan-
tion of Figures 4i, j and k along with Table 1 re-
dard expressions for thermal, hydraulic and stress
veals that an uncertainty in this group of param-
behavior in soil. Other expressions need to be ex-
eters has the least influence of all parameters on
plored (i.e., van Genuchten's expression for hy-
the calculated heave pressure.
draulic properties) in order to generalize the ap-
plicability of this model. The OON approach em-
ployed will make this a reasonable task. Empiri-
CONCLUSIONS
cal testing of this model is currently under way
with a refrigerated centrifuge. This approach will
The past problem of all frost heave models was
test the scaling laws for freezing (Miller 1990) as
the trade-off between physical correctness and ease
well as the predictions of this model.
of use. Those models that are easy to calculate tend
to be based upon curve fitting heave experiments
(Blanchard and Fremond 1985) or incorrectly ap-
plying phase equilibrium (Harlan 1973). The mod-
LITERATURE CITED
els that are physically based are difficult to imple-
Black, P.B. and R.D. Miller (1985) A continuum
ment and require time-consuming computation
approach to modeling frost heaving. Freezing and
(O'Neill and Miller 1985). Past efforts to overcome
Thawing of SoilWater Systems, Technical Council on
this dilemma relied on modifying the original
Cold Regions Engineering Monograph (D.M. Ander-
equations of Miller by simplifying the physics to
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