full-scale behavior of ice is subject to interpiece
el must satisfy geometric, kinematic, and dynamic
freeze-bonding.
similitude criteria, which usually are stated as di-
Table 1 lists common ice processes treated by
mensionless parameters whose values should be
means of physical modeling and indicates the
the same at model and full scales. The model ice
important variables influencing them. Model
material is chosen in accordance with the simili-
veracity depends on the accuracy with which the
tude criteria.
model replicates those variables. Note that some
Geometric similarity relates full-scale, or proto-
modeling situations may involve a combination
type, linear dimensions Lp and model dimensions
Lm by a length scale λL; i.e.,
of processes. Consequently, the variables may be
grouped differently than in Table 1.
Lp
(1)
= λL.
Lm
SIMILITUDE CRITERIA
Similitude criteria prescribe the quantitative
Kinematic similarity requires constant propor-
relationships between model and full-scale val-
tionality of prototype and model periods and ve-
ues of variables. For complete similitude, a mod-
locities. In other words,
Table 1. Ice processes and important variables to be modeled.
Ice process to be modeled
Variables of importance
Hydraulic models
Stage increase due to ice
roughness of underside of cover
ice thickness
water velocity profile
Ice transport
ice thickness
ice concentration
water velocity
ice velocity
iceshore frictional resistance
Ice accumulation/jamming
water velocity
ice velocity
ice piece size
ice concentration
iceshore frictional resistance
angle of internal friction of ice material
coefficients of lateral pressure, passive pressure, friction
Ice-cover breakup
ice-cover strength
water velocity
ice-cover velocity
covershore attachment
river discharge hydrograph
Ice load models
Ice sheet deflection
ice-cover flexural strength
modulus of elasticity
loading rate
ice thickness
Ice ridging
velocity of ice sheet
ice thickness
iceice friction
ice cover strength (flexural, crushing, shear)
Icestructure interaction
structure stiffness
velocity of ice sheet
ice thickness
ice-cover strength (crushing, flexural, shear)
iceice and icestructure friction
mode of breaking (crushing, flexure, shear)
Icebreaker modeling
vessel speed
iceice and icehull friction
ice thickness
ice-cover strength (crushing, flexural, shear)
ice piece size
piece movement around hull and propeller
mode of breaking (crushing, flexure, shear)
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