was conducted by Miller and Miller (1956). They
The use of prototype soils in centrifuge mod-
presented a set of scaled relationships describ-
els is an accepted practice and is an attempt to
ing the isothermal flow of liquids in the unsatur-
achieve structural response similarity of the model
and prototype by ensuring that the constitutive
ated soil, and they concluded from length, stress
response of the model will be as close as possible
and time scale factors that a centrifuge experi-
to the prototype material response. Langhaar
ment would be appropriate for small-scale mod-
(1951) and Schmidt and Holsapple (1980) have
eling of this flow (Miller and Miller 1955). Miller 's
suggested that when a model is made of the ma-
1990 scaling analysis of the Rigidice equations
terial of the prototype, when there are no time
was an extension of these earlier investigations
scale conflicts, and when the material response
of scaling laws for unsaturated porous flow. An
is independent of model size, prototypes with
expansion of this analysis is presented in Ap-
general constitutive behavior such as nonlinear
pendix B.
elasticity, plasticity and fracture can be modeled
Like the previous scaling investigations,
by following the scaling relations of Table 1. The
Miller 's Rigidice analysis was based on scaling
use of prototype soils within typical scale mod-
the effects of surface tension and viscous flow,
els (e.g., 1/25 to 1/100 scale) does not generally
but it also incorporated heat transfer, phase change
result in scale effects unless soils with particles
of the pore water, and ice lens initiation and
larger than sands are tested. It is common in cen-
growth. The analysis yielded reduced equations
trifuge testing to ensure that the parts of models
that are consistent with the techniques of con-
are much larger than the soil particle sizes so that
ventional centrifuge modeling and the scale fac-
particle size does not result in adverse scale ef-
tors in Table 1. It provided a complete theoreti-
fects. It is also common to test different scale
cal basis for small-scale frost heave modeling in
models of the same prototype to ensure that scale
a geotechnical centrifuge. Miller (1990) empha-
effects are insignificant.
sized that the ratio of model time to prototype
To correctly model heat transfer processes in
time for the freezing process in a centrifuge model
would be 1/N2, and he cited Pokrovsky and
saturated ground, the model and prototype must
be thermally similar, in addition to being geometri-
Fyodorov (1969) as the first to suggest the use of
cally, kinematically and dynamically similar. Ther-
a geotechnical centrifuge for modeling frozen and
mal similarity includes the similarity of internal
freezing ground structures. On the basis of Miller's
energy and energy density, as evidenced by similar
earlier unpublished discussions on model laws
temperature changes and differences at homolo-
for soil freezing, Black (1985) presented a set of
gous points. For centrifuge modeling, Savidou
scaling relationships for frost heave centrifuge
modeling, recommended a simple model study
(1988) has shown that the scale factor for tem-
of frost penetration and heave, and demonstrated
perature change is 1 and that the time scale fac-
that a great time savings would be obtained over
tor for conductive and convective heat transfer
through a soil body is 1/N2, which is the same as
a full-scale experiment.
the time scale factor for seepage processes.
EXPERIMENTAL TECHNIQUE
FROST HEAVE MODELING
Our preliminary soil freezing experiments were
conducted on an International Equipment Com-
When the differential equations of a particu-
pany Model PR-2 centrifuge. The device is a small
lar mechanical problem or physical process are
refrigerated centrifuge manufactured for appli-
known to the modeler, a scaling analysis can be
cations in biology, bacteriology, physiology and
performed to determine techniques for appropri-
biochemistry. It has a nominal operating radius
ate small-scale modeling of the problem. Scaling
is a method of dissolving passive physical pa-
of 0.2 m for the rotor and cups used in our test
configuration. During the experiments the centri-
rameters into active variables in a differential
fuge was located in a coldroom with an ambient
equation (Miller 1980a). Any solution to the scaled
temperature of approximately 4.5C.
equation is also a solution to any other distinct
Two insulated sample containers were made
physical system that can obtain the same scaled
to allow simultaneous testing of saturated soil
variables and scaled boundary conditions from
samples. In each container a Plexiglas cylinder
its distinct physical parameters. The earliest scaling
analysis of soils containing water and its vapor
enclosed the soil sample. The cylinder was mount-
3
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