Flow law for polycrystalline ice in glaciers: Comparison of theoretical predictions, laboratory data, and field measurements

Abstract

Theoretical considerations, laboratory experiments, and limited field data support a value of 3 for the exponent n in the commonly used empirical flow law ϵ = (τ/B)n relating stress and strain rate in polycrystalline ice. If this value is accepted, the viscosity parameter B can be determined for a wide variety of experiments. In a plot of log B against reciprocal temperature, points scatter about a line defined by an empirical equation of the form B = B0 exp {(T0/T) ‐ [C/(Tr ‐ T)k]}, where T is the temperature in kelvins and B0, C, T0, Tr, and k are empirically determined constants. For laboratory data the scatter is equivalent to approximately a factor of 5 variation in strain rate for a given stress and temperature. The cause of this variation is unclear, but because results from any single laboratory are generally internally consistent, sample preparation procedures should be studied. Field experiments yield values of B that are systematically higher than laboratory results. Thus natural ice appears stronger than laboratory ice, despite the coarser texture and the presence of anisotropic fabrics in the natural ice, both of which should tend to soften it. In addition, natural ice in glaciers appears stronger than natural ice deformed in the laboratory. These observations suggest either that the stress is systematically overestimated in field studies or that a flow law based on the von Mises yield criterion (or the second invariant of the stress deviator tensor) does not provide an adequate description of the deformation of ice in multiaxial stress fields.