Hydraulic theory for a debris flow supported on a collisional shear layer

We consider a heap of grains driven by gravity down an incline. We assume that the heap is supported at its base on a relatively thin carpet of intensely sheared, highly agitated grains that interact through collisions. We adopt the balance laws, constitutive relations, and boundary conditions of a kinetic theory for dense granular flows and determine the relationship between the shear stress, normal stress, and relative velocity of the boundaries in the shear layer in an analysis of a steady shearing flow between identical bumpy boundaries. This relationship permits us to close the hydraulic equations governing the evolution of the shape of the heap and the velocity distribution at its base. We integrate the resulting equations numerically for typical values of the parameters for glass spheres. (c) 1999 American Institute of Physics.