Creep closure of channels in deforming subglacial till

We examine theoretically the creep closure of subglacial tunnels cut into basal till, generalizing Nye's classical analysis of tunnel closure in glacier ice to rheologies in which the creep rate depends on effective pressure (the difference between total pressure and pore-water pressure). The solutions depend critically on a dimensionless permeability parameter. For the appealingly simple Boulton-Hindmarsh rheology in which strain rate depends on powers of applied stress and effective pressure, solutions to the closure problem may not exist; this is related to the existence of a 'failed' zone next to the channel, where piping occurs, and also to a non-physical degeneracy of the assumed rheology, whereby the viscosity is indeterminate at zero effective pressure. Consideration of the failed zone allows solutions to be obtained and shows that the closure characteristics of high permeability tills and low permeability tills are very different.