The Froude criterion leads to the same result for
In comparatively simple situations, the
scaling stress or pressure (force divided by con-
strength and deformation behavior of accumulat-
tact area) when the density scale is unity.
ed ice pieces can be described in terms of accu-
mulation thickness η, porosity p, and angle of in-
For ice sheet flexure, values of E are estimated
ternal resistance φ. In its simplest state, an ice ac-
typically (e.g., see ITTC 1990) by means of the
plate-deflection method, whereby a local load is
cumulation can be treated as a floating particu-
applied to the ice sheet and the commensurate
late medium, analogous to a sand, a gravel, or a
deflection is measured over an elastic response
pile of rocks. The geomechanical relationships for
range. An alternate method is to measure the de-
the strength behavior of a particulate medium are
flection of ice beams under flexure. From estimat-
applicable to the ice accumulation. Most analyses
ed E, together with an assumed Poisson ratio of
of ice accumulation behavior adopt this ap-
0.3 for ice, modelers calculate a representative
proach.
characteristic length for the ice sheet in flexure.
In nature and in the laboratory, however, the
The sheet is treated as an elastic plate, or some-
strength behavior of ice accumulations varies as
times a beam, on an elastic foundation. The char-
widely as for any particulate material. Individual
acteristic length relates plate or beam stiffness to
particles in a particulate continuum are subject to
gravity and to electromagnetic force developed
foundation (usually water) stiffness in terms of a
between neighboring particles. When the parti-
load-influence length.
cles are sufficiently large, gravity dominates their
Because ice sheets do not always deform elasti-
movement within the continuum, and the contin-
cally, there is considerable uncertainty as to the
significance of Cauchy number constancy as a
uum behaves as if it were cohesionless. When the
particles are small, the electromagnetic forces be-
similitude criterion. Its use is an active subject of
tween particles dominates, the continuum be-
debate. Ice may behave as a visco-elastic material
haves cohesively, and the character of the indi-
whose deformation and failure depend on strain
vidual particle is insignificant. The classic exam-
rate. At very low strain rates, creep deformation
may occur, whereas brittle elastic failure may oc-
ple in this regard is the behavior of alluvial parti-
cur at high rates. Therein lie several kernels of the
cles, which range from cohesive clays to noncohe-
debate: thin ice sheets do not deform exactly as
sive boulders. An analogous range of behavior
thick ice sheets do, and deformation processes
occurs for ice pieces, though delineation of piece
may progress at different time scales than a time
size at which cohesive and noncohesive behav-
scale based on the Froude number criterion. Diffi-
iors dominate is not as well defined for ice pieces.
culties with model materials are not unique to ice
The iceberg or large ice mass lies at one end of the
modeling. They also occur when scale-modeling
ice-piece size range. At the other end lies the
most other two-phase processes, including trans-
snowflake. Modeling ice mass drift in water, or
port of alluvial sediment and air bubbles. The
snow drift in air, entails simulation of ice-piece
paramount concern is that the model ice sheet
motion, but at vastly different scales and with
deform and fragment in accordance with the
strikingly different model ice materials.
criterion for geometrical similarity while replicat-
The variable strength behavior of an ice-piece
ing the scaled dominant strength. Ideally, the
accumulation, and thereby of their angle of inter-
model ice should produce the same ratio of fail-
nal resistance, can be described in terms of a si-
ure-mode strengths (e.g., compressive to flexural
militude criterion expressing a balance of molec-
strength) as exists for the full-scale ice.
ular and gravitational forces. The criterion can be
stated as a ratio of molecular or interparticle bond
force and ice-piece buoyancy; i.e.,
Accumulations of ice pieces
The strength and deformation behavior of an
accumulation of ice pieces, such as forming an ice
P
Bo =
(19)
1
jam or an ice ridge, are determined by geometric
π(ρ - ρi )gd3
6
and material factors. Depending on the combina-
tion of these factors, the strength and deforma-
in which P is the sum of interparticle bond forces
tion behavior can be relatively simple, or very
holding the particle to its neighbors. The denomi-
complicated, to formulate and simulate. Thermo-
nator is the buoyancy force acting through a par-
dynamic factors, such as freeze-bonding, and ma-
ticle assumed to be spherical. Accurate estimate
terial nonhomogeneities, such as local variations
of P is difficult. Thus Bo remains, for the moment,
of piece size, are difficult to model at small scale.
5
Previous Page
