Deforming beds: Viscous and plastic scales of deformation

Abstract

Small scale field and laboratory observations of sub-glacial sediment deformation suggest that failure is the predominant method of sediment deformation, while large scale modelling studies using a viscous model of till deformation have been reasonably successful in predicting the geological consequences of ice sheet action. This suggests that the cross-over scale between viscous and plastic deformation occurs at a much larger scale than the grain-grain interaction scale previously thought to be appropriate to deforming till. Sediment deformation and the drainage of sub-glacial areas are considered at different scales, and how these interact to produce failure and viscous behaviour is discussed. A fluctuation length scale is proposed, whose horizontal dimensions are of the order of the depth of the base of deformation (1–10 m). On this length scale, the glacier/deforming bed system is highly variable in time as well as in space. Till deformation occurring at this length scale is plastic, happening though failure events. Three other specific scales are proposed, whose different properties depend on the relative spatial variability of static and seepage pressures and topography. The key theoretical problem which has yet to be solved is how multiple small scale failure events combine into a viscous type flow. This is discussed in the context of self-organised criticality. It is argued that the length scales appropriate for some drainage features are not appreciably larger than the scale for plastic failure events, implying that modelling sub-glacial drainage channels by balancing erosion rates against viscous closure of the channel is misconceived. The outlines of an alternative model involving percolation theory are presented. Certain key questions which can only be settled through observations by glaciologists and glacial geologists are discussed. It is suggested that the difference between lodgement tills and deformation tills reflects the rate of motion of till by deformation, and that lodgement from the ice is unimportant.