The physics of debris flows

Recent advances in theory and experimen-tation motivate a thorough reassessment of the physicsof debris flows. Analyses of flows of dry, granular solidsand solid-fluid mixtures provide a foundation for a com-prehensive debris flow theory, and experiments providedata that reveal the strengths and limitations of theoret-ical models. Both debris flow materials and dry granularmaterials can sustain shear stresses while remaining stat-ic; both can deform in a slow, tranquil mode character-ized by enduring, frictional grain contacts; and both canflow in a more rapid, agitated mode characterized bybrief, inelastic grain collisions. In debris flows, however,pore fluid that is highly viscous and nearly incompress-ible, composed of water with suspended silt and clay, canstrongly mediate intergranular friction and collisions.Grain friction, grain collisions, and viscous fluid flowmay transfer significant momentum simultaneously.Both the vibrational kinetic energy of solid grains (mea-sured by a quantity termed the granular temperature)and the pressure of the intervening pore fluid facilitatemotion of grains past one another, thereby enhancingdebris flow mobility. Granular temperature arises fromconversion of flow translational energy to grain vibra-tional energy, a process that depends on shear rates,grain properties, boundary conditions, and the ambientfluid viscosity and pressure. Pore fluid pressures thatexceed static equilibrium pressures result from local orglobal debris contraction. Like larger, natural debrisflows, experimental debris flows of —10 m3 of poorly
sorted, water-saturated sediment invariably move as anunsteady surge or series of surges. Measurements at thebase of experimental flows show that coarse-grainedsurge fronts have little or no pore fluid pressure. Incontrast, finer-grained, thoroughly saturated debris be-hind surge fronts is nearly liquefied by high pore pres-sure, which persists owing to the great compressibilityand moderate permeability of the debris. Realistic mod-els of debris flows therefore require equations that sim-ulate inertial motion of surges in which high-resistancefronts dominated by solid forces impede the motion oflow-resistance tails more strongly influenced by fluidforces. Furthermore, because debris flows characteristi-cally originate as nearly rigid sediment masses, trans-form at least partly to liquefied flows, and then trans-form again to nearly rigid deposits, acceptable modelsmust simulate an evolution of material behavior withoutinvoking preternatural changes in material properties. Asimple model that satisfies most of these criteria usesdepth-averaged equations of motion patterned afterthose of the Savage-Hutter theory for gravity-driven flowof dry granular masses but generalized to include theeffects of viscous pore fluid with varying pressure. Theseequations can describe a spectrum of debris flow behav-iors intermediate between those of wet rock avalanche'sand sediment-laden water floods. With appropriate porepressure distributions the equations yield numerical so-lutions that successfully predict unsteady, nonuniformmotion of experimental debris flows.