Abstract. Recent advances in theory and experimentation motivate a thorough reassessment of the physics of debris flows. Analyses of flows of dry, granular solids and solid-fluid mixtures provide a foundation for a comprehensive debris flow theory, and experiments provide data that reveal the strengths and limitations of theoretical models. Both debris flow materials and dry granular materials can sustain shear stresses while remaining static; both can deform in a slow, tranquil mode characterized by enduring, frictional grain contacts; and both can flow in a more rapid, agitated mode characterized by brief, inelastic grain collisions. In debris flows, however, pore fluid that is highly viscous and nearly incompressible, composed of water with suspended silt and clay, can strongly mediate intergranular friction and collisions. Grain friction, grain collisions, and viscous fluid flow may transfer significant momentum simultaneously. Both the vibrational kinetic energy of solid grains (measured by a quantity termed the granular temperature) and the pressure of the intervening pore fluid facilitate motion of grains past one another, thereby enhancing debris flow mobility. Granular temperature arises from conversion of flow translational energy to grain vibrational energy, a process that depends on shear rates, grain properties, boundary conditions, and the ambient fluid viscosity and pressure. Pore fluid pressures that exceed static equilibrium pressures result from local or global debris contraction. Like larger, natural debris flows, experimental debris flows of --•10 m 3 of poorly sorted, water-saturated sediment invariably move as an unsteady surge or series of surges. Measurements at the base of experimental flows show that coarse-grained surge fronts have little or no pore fluid pressure. In contrast, finer-grained, thoroughly saturated debris behind surge fronts is nearly liquefied by high pore pressure, which persists owing to the great compressibility and moderate permeability of the debris. Realistic models of debris flows therefore require equations that simulate inertial motion of surges in which high-resistance fronts dominated by solid forces impede the motion of low-resistance tails more strongly influenced by fluid forces. Furthermore, because debris flows characteristically originate as nearly rigid sediment masses, transform at least partly to liquefied flows, and then transform again to nearly rigid deposits, acceptable models must simulate an evolution of material behavior without invoking preternatural changes in material properties. A simple model that satisfies most of these criteria uses depth-averaged equations of motion patterned after those of the Savage-Hutter theory for gravity-driven flow of dry granular masses but generalized to include the effects of viscous pore fluid with varying pressure. These equations can describe a spectrum of debris flow behav-

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Rock avalanches, debris flows, and related phenomena consist of grain-fluid mixtures that move across three-dimensional terrain. In all these phenomena the same basic forces govern motion, but differing mixture compositions, initial conditions, and boundary conditions yield varied dynamics and deposits. To predict motion of diverse grain-fluid masses from initiation to deposition, we develop a depth-averaged, threedimensional mathematical model that accounts explicitly for solid-and fluid-phase forces and interactions. Model input consists of initial conditions, path topography, basal and internal friction angles of solid grains, viscosity of pore fluid, mixture density, and a mixture diffusivity that controls pore pressure dissipation. Because these properties are constrained by independent measurements, the model requires little or no calibration and yields readily testable predictions. In the limit of vanishing Coulomb friction due to persistent high fluid pressure the model equations describe motion of viscous floods, and in the limit of vanishing fluid stress they describe one-phase granular avalanches. Analysis of intermediate phenomena such as debris flows and pyroclastic flows requires use of the full mixture equations, which can simulate interaction of high-friction surge fronts with more-fluid debris that follows. Special numerical methods (described in the companion paper) are necessary to solve the full equations, but exact analytical solutions of simplified equations provide critical insight. An analytical solution for translational motion of a Coulomb mixture accelerating from rest and descending a uniform slope demonstrates that steady flow can occur only asymptotically. A solution for the asymptotic limit of steady flow in a rectangular channel explains why shear may be concentrated in narrow marginal bands that border a plug of translating debris. Solutions for static equilibrium of source areas describe conditions of incipient slope instability, and other static solutions show that nonuniform distributions of pore fluid pressure produce bluntly tapered vertical profiles at the margins of deposits. Simplified equations and solutions may apply in additional situations identified by a scaling analysis. Assessment of dimensionless scaling parameters also reveals that miniature laboratory experiments poorly simulate the dynamics of full-scale flows in which fluid effects are significant. Therefore large geophysical flows can exhibit dynamics not evident at laboratory scales. tigators have modeled these events mathematically by specifying rheological rules that govern flow behavior. In general, however, specified rheologies are neither well-constrained nor sufficient to explain flow dynamics, because steady, uniform, rheometric flows of grain-fluid mixtures do not occur in nature.Here we investigate a simpler hypothesis, which holds that most gravity-driven, grain-fluid flows obey no particular stressstrain rate relation. Instead, intergranular stresses satisfy the familiar Coulomb rule, and variation...

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[1] Aggregation of data collected in 28 controlled experiments reveals reproducible debris-flow behavior that provides a clear target for model tests. In each experiment ∼10 m 3 of unsorted, water-saturated sediment composed mostly of sand and gravel discharged from behind a gate, descended a steep, 95-m flume, and formed a deposit on a nearly horizontal runout surface. Experiment subsets were distinguished by differing basal boundary conditions (1 versus 16 mm roughness heights) and sediment mud contents (1 versus 7 percent dry weight). Sensor measurements of evolving flow thicknesses, basal normal stresses, and basal pore fluid pressures demonstrate that debris flows in all subsets developed dilated, coarse-grained, high-friction snouts, followed by bodies of nearly liquefied, finer-grained debris. Mud enhanced flow mobility by maintaining high pore pressures in flow bodies, and bed roughness reduced flow speeds but not distances of flow runout. Roughness had these effects because it promoted debris agitation and grain-size segregation, and thereby aided growth of lateral levees that channelized flow. Grain-size segregation also contributed to development of ubiquitous roll waves, which had diverse amplitudes exhibiting fractal number-size distributions. Despite the influence of these waves and other sources of dispersion, the aggregated data have well-defined patterns that help constrain individual terms in a depth-averaged debris-flow model. The patterns imply that local flow resistance evolved together with global flow dynamics, contradicting the hypothesis that any consistent rheology applied. We infer that new evolution equations, not new rheologies, are needed to explain how characteristic debris-flow behavior emerges from the interactions of debris constituents.