Recent advances in theory and experimen- tation 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 com- prehensive debris flow theory, and experiments provide data that reveal the strengths and limitations of theoret- ical models. Both debris flow materials and dry granular materials 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 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 incompress- ible, 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 (mea- sured 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 vibra- tional 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 be- hind surge fronts is nearly liquefied by high pore pres- sure, which persists owing to the great compressibility and moderate permeability of the debris. Realistic mod- els of debris flows therefore require equations that sim- ulate 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 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 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- iors intermediate between those of wet rock avalanches and sediment-laden water floods. With appropriate pore pressure distributions the equations yield numerical so- lutions that successfully predict unsteady, nonuniform motion of experimental debris flows.

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The physics of debris flows

The goal of this article is to revise several aspects of the well-known classification of landslides, developed by Varnes (1978). The primary recommendation is to modify the definition of landslide-forming materials, to provide compatibility with accepted geotechnical and geological terminology of rocks and soils. Other, less important modifications of the classification system are suggested, resulting from recent developments of the landslide science. The modified Varnes classification of landslides has 32 landslide types, each of which is backed by a formal definition. The definitions should facilitate backward compatibility of the system as well as possible translation to other languages. Complex landslides are not included as a separate category type, but composite types can be constructed by the user of the classification by combining two or more type names, if advantageous.

The Varnes classification of landslide types, an update

The complexity of flow and wide variety of depositional processes operating in subaqueous density flows, combined with post-depositional consolidation and soft-sediment deformation, often make it difficult to interpret the characteristics of the original flow from the sedimentary record. This has led to considerable confusion of nomenclature in the literature. This paper attempts to clarify this situation by presenting a simple classification of sedimentary density flows, based on physical flow properties and grain-support mechanisms, and briefly discusses the likely characteristics of the deposited sediments. Cohesive flows are commonly referred to as debris flows and mud flows and defined on the basis of sediment characteristics. The boundary between cohesive and non-cohesive density flows (frictional flows) is poorly constrained, but dimensionless numbers may be of use to define flow thresholds. Frictional flows include a continuous series from sediment slides to turbidity currents. Subdivision of these flows is made on the basis of the dominant particle-support mechanisms, which include matrix strength (in cohesive flows), buoyancy, pore pressure, grain-to-grain interaction (causing dispersive pressure), Reynolds stresses (turbulence) and bed support (particles moved on the stationary bed). The dominant particle-support mechanism depends upon flow conditions, particle concentration, grain-size distribution and particle type. In hyperconcentrated density flows, very high sediment concentrations (>25 volume%) make particle interactions of major importance. The difference between hyperconcentrated density flows and cohesive flows is that the former are friction dominated. With decreasing sediment concentration, vertical particle sorting can result from differential settling, and flows in which this can occur are termed concentrated density flows. The boundary between hyperconcentrated and concentrated density flows is defined by a change in particle behaviour, such that denser or larger grains are no longer fully supported by grain interaction, thus allowing coarse-grain tail (or dense-grain tail) normal grading. The concentration at which this change occurs depends on particle size, sorting, composition and relative density, so that a single threshold concentration cannot be defined. Concentrated density flows may be highly erosive and subsequently deposit complete or incomplete Lowe and Bouma sequences. Conversely, hydroplaning at the base of debris flows, and possibly also in some hyperconcentrated flows, may reduce the fluid drag, thus allowing high flow velocities while preventing large-scale erosion. Flows with concentrations <9% by volume are true turbidity flows (sensuBagnold, 1962), in which fluid turbulence is the main particle-support mechanism. Turbidity flows and concentrated density flows can be subdivided on the basis of flow duration into instantaneous surges, longer duration surge-like flows and quasi-steady currents. Flow duration is shown to control the nature of the resulting deposits. Surge-like turbidity currents tend to produce classical Bouma sequences, whose nature at any one site depends on factors such as flow size, sediment type and proximity to source. In contrast, quasi-steady turbidity currents, generated by hyperpycnal river effluent, can deposit coarsening-up units capped by fining-up units (because of waxing and waning conditions respectively) and may also include thick units of uniform character (resulting from prolonged periods of near-steady conditions). Any flow type may progressively change character along the transport path, with transformation primarily resulting from reductions in sediment concentration through progressive entrainment of surrounding fluid and/or sediment deposition. The rate of fluid entrainment, and consequently flow transformation, is dependent on factors including slope gradient, lateral confinement, bed roughness, flow thickness and water depth. Flows with high and low sediment concentrations may co-exist in one transport event because of downflow transformations, flow stratification or shear layer development of the mixing interface with the overlying water (mixing cloud formation). Deposits of an individual flow event at one site may therefore form from a succession of different flow types, and this introduces considerable complexity into classifying the flow event or component flow types from the deposits.

The physical character of subaqueous sedimentary density flows and their deposits

Landslides are generally associated with a trigger, such as an earthquake, a rapid snowmelt or a large storm. The landslide event can include a single landslide or many thousands. The frequency–area (or volume) distribution of a landslide event quantifies the number of landslides that occur at different sizes. We examine three well-documented landslide events, from Italy, Guatemala and the USA, each with a different triggering mechanism, and find that the landslide areas for all three are well approximated by the same three-parameter inverse-gamma distribution. For small landslide areas this distribution has an exponential ‘roll-over’ and for medium and large landslide areas decays as a power-law with exponent −2·40. One implication of this landslide distribution is that the mean area of landslides in the distribution is independent of the size of the event. We also introduce a landslide-event magnitude scale mL = log(NLT), with NLT the total number of landslides associated with a trigger. If a landslide-event inventory is incomplete (i.e. smaller landslides are not included), the partial inventory can be compared with our landslide probability distribution, and the corresponding landslide-event magnitude inferred. This technique can be applied to inventories of historical landslides, inferring the total number of landslides that occurred over geologic time, and how many of these have been erased by erosion, vegetation, and human activity. We have also considered three rockfall-dominated inventories, and find that the frequency–size distributions differ substantially from those associated with other landslide types. We suggest that our proposed frequency–size distribution for landslides (excluding rockfalls) will be useful in quantifying the severity of landslide events and the contribution of landslides to erosion. Copyright © 2004 John Wiley & Sons, Ltd.

Landslide inventories and their statistical properties

Foreword 1. Introduction 2. Runoff, erosion and delivery to the coastal ocean 3. Temporal variations 4. Human impacts Appendices. Global River Database: Appendix A: North and Central America Appendix B: South America Appendix C: Europe Appendix D: Africa Appendix E: Eurasia Appendix F: Asia Appendix G: Oceania References Index.

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River Discharge to the Coastal Ocean: A Global Synthesis

A rheologic classification of subaerial sediment-water flows

Nearly instantaneous melting of snow and ice by the March 19, 1982, eruption of Mount St. Helens released a 4 × 106 m3 flood of water from the crater that was converted to a lahar (volcanic debris flow) through erosion and incorporation of sediment by the time it reached the base of the volcano. Over the next 81 km that it traveled down the Toutle River, the flood wave was progressively diluted through several mechanisms. A transformation from debris flow to hyperconcentrated streamflow began to occur about 27 km downstream from the crater, when the total sediment concentration had decreased to about 78% by weight (57% by volume). The hyperconcentrated lahar-runout flood wave, transporting immense quantities of sand in suspension, continued to experience progressive downstream dilution. Although turbulence was significantly dampened by the extremely high suspended load, very large standing waves and antidune waves were observed. The hyperconcentrated lahar-runout flow deposited an unusual, faintly stratified, coarse sand which locally contained small, isolated gravel lenses. Very similar deposits in the Quaternary stratigraphy of Mount St. Helens and other Cascades volcanoes suggest that lahars may be more frequent than previously recognized.

Downstream dilution of a lahar : transition from debris flow to hyperconcentrated streamflow.

Perturbation and melting of snow and ice by the 13 November 1985 eruption of Nevado del Ruiz, Colombia, and consequent mobilization, flow and deposition of lahars

The rheology of slurries consisting of ≤2-mm sediment from a natural debris flow deposit was measured using a wide-gap concentric-cylinder viscometer. The influence of sediment concentration and size and distribution of grains on the bulk rheological behavior of the slurries was evaluated at concentrations ranging from 0.44 to 0.66. The slurries exhibit diverse rheological behavior. At shear rates above 5 s−1 the behavior approaches that of a Bingham material; below 5 s−1, sand exerts more influence and slurry behavior deviates from the Bingham idealization. Sand grain interactions dominate the mechanical behavior when sand concentration exceeds 0.2; transient fluctuations in measured torque, time-dependent decay of torque, and hysteresis effects are observed. Grain rubbing, interlocking, and collision cause changes in packing density, particle distribution, grain orientation, and formation and destruction of grain clusters, which may explain the observed behavior. Yield strength and plastic viscosity exhibit order-of-magnitude variation when sediment concentration changes as little as 2–4%. Owing to these complexities, it is unlikely that debris flows can be characterized by a single rheological model.

Debris Flow Rheology: Experimental Analysis of Fine-Grained Slurries

Two large, high-velocity lahars (volcanic debris flows) were triggered by a pyroclastic surge during the first few minutes of the May 18, 1980, eruption of Mount St. Helens. The initial surge cloud evolved progressively by gravity segregation from a gas-mobilized, highly inflated density flow to a dense, water-mobilized, basal debris flow (lahar) and accompanying ash cloud as it flowed down the east flank of the volcano. The main source of the water for the lahars was probably from eroded snow and ice incorporated into the flow by turbulent mixing, but ground water, expelled together with the rock debris by the initiating volcanic explosions, also may have contributed. Peak lahar discharge from the Pine-Muddy fan, upper Smith Creek, and Ape Canyon probably exceeded 250,000 m 3 /s initially but decreased exponentially in the downstream direction. Total volume of the lahars was in excess of 1.4 × 10 7 m 3 . Initial peak-flow velocities in excess of 30 m/s also decreased markedly downstream. Where flow was not impeded, velocity was strongly related to the depth-slope term (R 2/3 S 1/2 ) from the Manning uniform-flow equation as a power-law function. During much of the route traveled, lahar flow appears to have been supercritical. Deposits left in channels were generally thin relative to flow depth (0 to 2.5 m). Particles up to small boulder size were randomly distributed in the poorly sorted, nonstratified matrix, indicating complete suspension in a fully developed debris-flow slurry; however, much larger clasts were transported as “bed-load.” Computed sediment concentrations of matrix slurry samples ranged from 84% to 91% solids by weight and were similar for the two lahars. Two indirect methods for computing peak-flow velocity, previously only tentatively applied to debris flows, were tested for accuracy by comparing computed lahar arrival times with recorded arrival times at Swift Reservoir. The computed velocities appear to be ∼15% slower than the recorded velocities, which is consistent with the restriction that the velocity formulas produce only minimum values.

Thomas C. Pierson

Papers

A rheologic classification of subaerial sediment-water flows

Downstream dilution of a lahar : transition from debris flow to hyperconcentrated streamflow.

Perturbation and melting of snow and ice by the 13 November 1985 eruption of Nevado del Ruiz, Colombia, and consequent mobilization, flow and deposition of lahars

Debris Flow Rheology: Experimental Analysis of Fine-Grained Slurries

Initiation and flow behavior of the 1980 Pine Creek and Muddy River lahars, Mount St. Helens, Washington