ELEMENTS OF AN IMPROVED MODEL OF DEBRIS-FLOW MOTION

A new depth-averaged model of one-dimensional debris-flow motion seamlessly connects the quasi-static mechanics of initiation with the inertial dynamics of fully developed flow. Previous debris-flow models fail to make this connection because they employ initial conditions with unbalanced forces arbitrarily specified by the modeler. Natural debris flows, in contrast, commence when the balance of forces is tipped by an infinitesimal amount. Mechanical feedbacks involving coupled shear deformation, porosity change, and pore-pressure change can then cause dramatic evolution of the force balance in the course of a few seconds, enhancing or hindering subsequent motion and determining the potential for liquefaction and flow. To represent such feedbacks, our new model describes coupled evolution of the depth-averaged solid volume fraction, m, depth-averaged porosity, 1-m, depth-averaged flow velocity, v, flow depth, h, and the non-hydrostatic component of basal pore-fluid pressure, p_bed. This coupling can drive motion toward dynamic equilibrium (yielding a slow landslide) or runaway acceleration and liquefaction (yielding a debris flow), contingent on evolution of m. We derive an evolution equation for m by considering mass conservation during porosity change in conjunction with the effects of both classical soil consolidation (caused by changes in effective normal stress) and dilatancy (caused by shearing). The dilatancy is characterized by an angle, ψ, which expresses the depth-averaged ratio of the plastic volume strain rate and shear strain rate. The value of ψ is positive during dilative behavior and negative during contractive behavior, but it necessarily evolves toward 0 as m evolves toward a value that is equilibrated with the ambient state of stress and shear rate. Moreover, as m and ψ evolve, p_bed evolves in concert because fluid is drawn toward regions of dilation and expelled from regions of contraction. Analytical solutions of simplified versions of the model equations illustrate the basic physics and feedback mechanisms involved. Numerical solutions of the full set of coupled partial differential equations exhibit a wide variety of behaviors, consistent with the variety of behaviors observed in experiments and in the field.