Effective stress profiles and seepage flows beneath glaciers and ice sheets

The resistance to sliding and the extent of till deformation beneath soft-bedded glaciers depend on the spatially averaged level of effective stress (N) over bar, which is controlled by the distribution of water pressure at the bed. Major subglacial conduits that facilitate large-scale water transport are expected to be predominantly aligned with the direction of maximum hydraulic gradient, which is normally parallel to the slope of the glacier surface. When the basal heat flow promotes net melting or freezing, seepage transport can enable water exchange between these conduits and the rest of the basal surface area. For a simple glacier geometry with subglacial conduits that are aligned parallel to a uniform slope, the seepage transport is driven primarily by gradients in effective stress. Balance equations determine how (N) over bar varies with conduit spacing and the heat-flow regime. Considerations of thermodynamic equilibrium require that ice penetrates the pore space at high effective stress. Even when the glacier base experiences net melting, for a given heat-flow regime there are limits on the conduit spacing that can be attained before a finite till layer becomes partially frozen throughout. During net freezing, the resistance to flow through partially frozen sediments limits the steady-state conduit spacing. The partially frozen zone can actually be restricted to smaller thicknesses when the freezing rate is greater.