Figure 7. Comparison of simulated jam profiles and the analytical solution

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for the zero bank friction case.

The simulated result and analytical solution are

In this study, the constitutive law is modified for a small

compared in Figure 8. The simulated profile for t ≥ 4

strain rate condition to avoid these problems.

In the simulation, critical values of σij and P for

hours and the analytical solution are different because

the ice momentum was neglected in the analytical

each ice parcel were determined as the following

solution. Figure 9 presents two-dimensional plots

conditions are all satisfied: 1) ice parcel velocity is

showing the development of the ice thickness

smaller than a small critical value of 0.001 m/s, 2) ice

distribution upstream of the boom.

parcel velocity is smaller than the value in the previous

time step, and 3) δ =| ε1 - ε2 | is smaller than a very

Theoretically, the viscousplastic constitutive law

small value δc = 1 104s1. When these critical

cannot simulate static conditions correctly. For very

small strain rates, the viscosity becomes very large. In

conditions are reached, the following approximation is

numerical computations, a limiting value for is often

introduced to calculate ice stresses for the particular

used. This approximation changes the constitutive

ice parcel:

relationship to a linear viscous law and the shear stress

σij = σijc

approaches zero when the strain rate approaches zero.

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