Diffusive mixing between shearing granular layers: constraints on bed deformation from till contacts

Shearing of subglacial till has bem invoked widely as a mechanism of glacier motion and sediment transport, but standard indicators for determining shear strain from the geologic record are not adequate for estimating the very high strains required of the bed-deformation model. Here we describe a laboratory study of mixing between shearing granular layers that allows an upper limit to be placed on bed shear strain in the vicinity of till contacts. Owing to random vertical motions of particles induced by shearing, mixing can be modeled as a linearly diffusive process, and so can be characterized with a single mixing coefficient, D. Ring-shear experiments with equigranular beads and lithologically distinct tills provide the value of D, although in experiments with till D decreases systematically with strain to a minimum value of 0.0045 mm(2). Kinetic gas theory provides an estimate of the dimensionless mixing coefficient which is within an order of magnitude of laboratory values. Knowing the minimum value of D, the distribution of index lithologies measured across till contacts in the geologic record can be used to estimate the maximum shear strain that has occurred across till contacts. Application of this technique to the contact between the Des Moines and Superior Lobe tills in east-central Minnesota, U.S.A., indicates that shear strain did not exceed 15 000 at the depth of the contact.