Over the years, a great variety of semi-empirical and theoretical models for ice and frozen soils have been established. More recently, fundamentally different types of stress-strain-time constitutive relationships based upon thermo-mechanics and visco-plastic flow theories, coupled with numerical analysis, have been pursued. These models, however simple (or complex) contain empirical parameters measured from laboratory or from in-situ experiments and the paper highlights some of the methods used to determine parameters such as the exponents of the power law in the case of ice. Of particular interest, it was found that for polycrystalline ice, the time exponent for Hult's primary creep law has a constant value of around 2/3 regardless of the magnitude of stresses or the temperature variation. On the other hand, the paper shows that the secondary creep behaviour of such a material can be predicted using results measured from the primary creep phase. This is of significance since for polycrystalline ice, secondary creep, when it occurs, is usually reduced to an inflection point on the strain-time curve heralding the beginning of tertiary creep and hence failure. The paper also discusses the validity of Fish's viscoplastic flow model in conjunction with results measured from different types of laboratory tests (uniaxial and pressuremeter tests) carried out on polycrystalline ice.
A large number of mathematical models have been published to model the non-linear behaviour of ice. These models vary from simple power laws to more complex ones based upon thermo-mechanics and computing methods. They all however, depend on parameters and mechanical properties that have to be determined experimentally, then fed through in order to make the models work. If we consider the early mathematical equations for creep modelling, then the expression suggested by Hult [6] is widely accepted for the description of the primary creep of ice and frozen soils. (Equations shown in the paper)
