VH = -kH (uW , uI ) ∇θ
(B28)
but subjected to different body forces, eq B18, B10
and B24 show how they must relate. Using the
in which kH (W/mK) is the thermal conductiv-
convention of calling the laboratory reference
ity. This conductivity is also a material property
experiment the prototype p and the experiment
that is assumed to be constant in the continuum
subjected to the different body force m for model,
sense for a given state of water and ice contents.
the reduced body force FW must be equal for both:
The reduced thermal conductivity is then
ζp λ p
ζλ
ηθo
KH (U W , UI ) ≡
kH (uW , uI ) .
fp = m m fm .
(B32)
(B29)
γ IA
γ IA
γ 2A
I
The most important characteristic of the Rigidice
If we say that fm = 100 fp, as might be expected in
model that sets it apart from others is the concept
a centrifuge, and we use the same soil in both
of thermally induced regelation. This results in the
experiments, then the total lengths of the two ex-
periments are related by ζm = 0.01 ζp. Since the
inclusion of an extra mass flux resulting from the
bulk movement of ice in the frozen fringe. The ve-
reduced temperatures Θ must be equal at corre-
locity of ice movement in the fringe is the heave
sponding locations, the actual temperatures θ will
velocity vR (m/s) relative to the stationary grains
therefore be the same in both the prototype and
of the porous media below the fringe. The volu-
the model. This leads to the most important ex-
metric flux of ice vI (m3/m2s) resulting from this
perimental consequence of centrifuge modeling.
regelation is
Since the reduced times T must be equal, the ac-
tual times are related by tm = tp/1002. Scaled ex-
vI = I (uW , uI ) vR .
(B30)
periments are finished in a very timely manner
compared to similar laboratory experiments.
From eq B22 we know how volumetric fluxes scale,
A final note is on the meaning of the micro-
so the reduced regelation velocity is therefore
scopic length λ. If the porous medium consisted
of identical pores, then this length would just be
ζη
VR ≡
.
(B31)
the pore size. But in real porous media there is a
λγ IA
distribution of sizes and geometries of pores. The
microscopic length in these cases represents some
This completes the scaling of the more impor-
averaged value of the pores. It is more like the
tant variables and parameters involved in ground
size of the smallest representative elementary
freezing. A list of all scaled variables applicable
volume (REV) that begins to describe the porous
to ground freezing, as well as all water phases,
media as a continuum of uniform material prop-
was presented by Miller (1990).
erties. The difficulty is in actually measuring this
An example of how heaving experiments should
be interpreted by reduced variables seems in or-
parameter without completely destroying the
der. Given two experiments using the same soil
original material.
17
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