Glen's Law++: Transition to a Rate-Weakening Flow Law As a New Framework for Damage Evolution
Friday, 19 December 2014
Continuum damage mechanics is gaining increasing acceptance as a framework for modeling flow enhancement caused by fractures in glaciers and ice shelves. To date, the temporal evolution of viscous damage has been handled using a transport equation with some kind of source term for damage. A number of empirical formulations for such a source term have been adopted, though no clear physical foundation exists for treating damage using flux terms. Furthermore, it remains to be demonstrated that the parameters of such a source term can be determined from observations. Here, we introduce a new framework for damage evolution that does not require specifying a damage source term and that results in a more intuitive physical interpretation of the coupled evolution of stress and damage. By postulating an explicit rate-weakening flow law above a threshold stress, damage can be calculated analytically from the results of a stress balance computation. A transport equation is still applied to advect damage, but the evolution of damage is explicitly linked to the evolving stress balance. This new damage formulation requires only two new parameters, both of which have clear physical interpretations and can be inferred from observations. Using the Ice Sheet System Model (ISSM), we determine values for both parameters by inverting for damage for the remnant Larsen B ice shelf using a time series of InSAR velocity data covering the years 2000-2010. The inferred patterns of damage and strain rate, in both space and time, are used to quantify the rate-weakening constitutive parameters using nonlinear regression. The resulting damage evolution framework is then applied in perturbation experiments to determine the conditions and timescales under which the remnant Larsen B ice shelf may collapse. We conclude by discussing advantages of this approach to damage evolution and applications to problems in iceberg calving, ice shelf stability, and buttressing at the grounding line.