Exact Solutions for Nonlocal Steady Fully Developed Debris Flows Down Inclines

Abstract

Exact solutions for steady fully developed dry granular and saturated granular–liquid mixture flows down rough inclined planes are presented with an emphasis on nonlocal effects. The particle rheology of both dry granular and saturated granular–liquid mixtures is described by a recently developed nonlocal granular fluidity (NGF) model. The fluid rheology of a saturated granular–liquid mixture is represented by the eddy viscosity, and the contacting forces between the fluid and grains are drag and buoyancy forces. The problems are then reduced to solving the resulting partial differential equations (PDEs). Closed-form solutions for the critical stopping layer height of dry granular and saturated granular–liquid mixtures are derived by analytically solving the linearized equations of the NGF model. Moreover, exact solutions for velocity profiles are acquired by solving the coupled equations with a PDE solver.