Finite Element Modelling of Creep and Instability of Large Ice Masses

Abstract

<p>Detailed descriptions of finite element models for deformation, temperature and instability analyses of large ice masses are presented. Two non-Newtonian, creeping flow models are developed for steady-state creep situations; one enforces incompressibility, the other near incompressibility. The third creep model incorporates a large displacement formulation and an implicit time-marching scheme for transient creep analysis. To allow for basal sliding, a time-dependent sliding element is also developed. In addition to the creep models above, a transient heat transfer model is presented. By stepwise uncoupling of the stress and temperature dependent creep, it is possible to carry out transient thermal creep analysis for surging of the Barnes Ice Cap. An upwind scheme for triangular elements is given for thermal analysis where the influence of thermal advection is required.</p> <p>It is demonstrated that the three finite element creep models predict similar steady-state creep behaviour for simple ice masses with simple boundary conditions. For more complex problems, agreement of the computed velocities by the models is found to be very sensitive to the boundary conditions at the ice-bedrock interface. Results from the finite element simulations suggest that it may be premature to assume that the influence of elastic strains is negligible.</p> <p>The thermal regime of the Erebus Glacier Tongue is studied assuming steady-state conditions. It is shown that the temperature field is mainly influenced by the near horizontal thermal advection. Reasonable velocity fields for the thermal analysis could only be attained by assuming that the ice is not frozen to bedrock at the transition from a land-based glacier to a floating glacier.</p> <p>Finally, a basal instability model is presented. In this model, the basal shear resistance is reduced according to the excess sliding energy dissipated above some threshold value. The time for a surge to propagate is characterized by a lubrication factor incorporated in the basal instability model. It is confirmed that a geothermal flux approaching 1.9 HFU is required to bring most of the south-west ice-bed interface of the Barnes Ice Cap to pressure melting which would allow for basal sliding and instability. Furthermore, it is shown that the temperature changes during a surge are negligible. The numerical examples analyzed and presented indicate the appropriateness of the analytical modelling and versatility of the finite element method for incorporating complex material properties and boundary conditions.</p>