Influence of slope angle on deposit morphology and propagation of laboratory landslides

Landslide deposits often exhibit surface features, such as transverse ridges and X-shaped conjugate troughs, whose physical formation origins are not well understood. To study the deposit morphology, laboratory studies typically focus on the simplest landslide geometry: an inclined plane accelerating the sliding mass immediately followed by its deceleration on a horizontal plane. However, existing experiments have been conducted only for a limited range of the slope angle θ. Here, we study the effect of θ on the kinematics and deposit morphology of laboratory landslides along a low-friction base, measured using an advanced 3D scanner. At low θ (30°-35°), we find transverse ridges formed by overthrusting on the landslide deposits. At moderate θ (40°-55°), conjugate troughs form. A Mohr-Coulomb failure model predicts the angle enclosed by the X-shaped troughs as 90° - φ, with φ the internal friction angle, in agreement with our experiments and a natural landslide. This supports the speculation that conjugate troughs form due to failure associated with a triaxial shear stress. At high θ (60°-85°), a double-upheaval morphology forms because the rear of the sliding mass impacts the front during the transition from the slope to the horizontal plane. The overall surface area of the landslides increases during their downslope motion and then decreases during their runout.

Debris flow characteristics of the compound channels with vegetated floodplains

Compound cross-sections with vegetated floodplains are a common type of cross-section in debris-flow gullies. Floodplain vegetation participates in large-scale debris flow events and regulates debris-flow discharge. Extensive research has been conducted on the water flow characteristics of compound rivers. However, few studies have investigated the debris flow characteristics of compound channels in mountainous areas, particularly those of debris flow and flash flood inundation areas with vegetation. This study discusses the section characteristics of debris flow gullies with vegetated floodplains, gully evolution processes, and their influence on debris flow. The results show that the compound debris flow gully with a vegetated floodplain is formed in the gully from the mature stage to the old-mature stage. The compound sections are developed in flow areas with a gentle slope, which can be bilateral floodplain, unilateral floodplain, and multi-main gully floodplain types. Owing to the vegetation of the floodplain, the roughness of the channel increases, which makes the beach roughness coefficient much larger than that for the main channel. In the integrated Manning coefficient method, the error in resolving the flow velocity and discharge is large and cannot reflect the difference in velocities of the floodplain and main channel, therefore the sectional splitting method is most applicable. Influencing debris flow movement, limiting channel migration, and retaining debris flow to the main channel were the main contributions of the riparian forest zone.

A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations

The study of rapid free surface granular avalanche flows has attracted much attention in recent years, which is widely modeled using the Savage–Hutter equations. The model is closely related to shallow water equations. We employ a high-order shock-capturing numerical model based on the weighted essential non-oscillatory (WENO) reconstruction method for solving Savage–Hutter equations. Three numerical fluxes, i.e., Lax–Friedrichs (LF), Harten–Lax–van Leer (HLL), and HLL contact (HLLC) numerical fluxes, are considered with the WENO finite volume method and TVD Runge–Kutta time discretization for the Savage–Hutter equations. Numerical examples in 1D and 2D space are presented to compare the resolution of shock waves and free surface capture. The numerical results show that the method proposed provides excellent performance with high accuracy and robustness.

Some Considerations for Using Numerical Methods to Simulate Possible Debris Flows: The Case of the 2013 and 2020 Wayao Debris Flows (Sichuan, China)

Using a numerical simulation method based on physical equations to obtain the debris flow risk range is important for local-scale debris flow risk assessment. While many debris flow models have been used to reproduce processes after debris flow occurrence, their predictability in potentially catastrophic debris flow scenarios has mostly not been evaluated in detail. Two single-phase flow models and two two-phase models were used to reproduce the Wayao debris flow event in 2013. Then the Wayao debris flow event in 2020 was predicted by the four models with the same parameters in 2013. The depth distributions of the debris source and deposition fan were mapped by visual interpretation, electric resistivity surveys, field measurements, and unmanned aerial vehicle (UAV) surveys. The digital elevation model (DEM), rainfall data, and other simulation parameters were collected. These models can reproduce the geometry and thickness distribution of the debris flow fan in 2013. However, the predictions of the runout range and the deposition depth are quite different from the actuality in 2020. The performance and usability of these models are compared and discussed. This could provide a reference for selecting physical models to assess debris-flow risk.

Comparisons of Dynamic Landslide Models on GIS Platforms

Numerical simulation is one of the methods to assess landslide movement processes, which is beneficial for engineering design and urban planning. With the development of computer technology, GIS has gradually become the mainstream platform for landslide simulation due to data availability and algorithm integrability. However, the dynamic processes of landslides are complicated, which makes integration difficult on GIS platforms. Some assumptions are applied to simplify these dynamic processes and solve this problem. Generally, there are two main types of numerical models on GIS platforms: models based on the Eulerian description and models based on the Lagrangian description. Case studies show that Eulerian models are suitable for flow-like movement, and Lagrangian models are suitable for discrete rigid bodies movement. Different models face different problems: the Eulerian-based models show numerical diffusion and oscillation, and the Lagrangian-based model needs to consider complicated shear and collision processes. In addition, the 3-D model can describe more details in the z-direction, while the depth-averaged model can obtain a reasonable range of motion, depth, and speed quickly. From the view of numerical simulation, inappropriate models, assumptions, and numerical schemes will produce errors. The landslide type refers to several forms of mass wasting associated with a wide range of ground movements, which guides establishing dynamic models and numerical schemes on GIS platforms and helps us obtain results accurately.

A Large Old Landslide in Sichuan Province, China: Surface Displacement Monitoring and Potential Instability Assessment

Using advanced Differential Interferometric Synthetic Aperture Radar (InSAR) with small baseline subsets (SBAS) and Permanent Scatter Interferometry (PSI) techniques and C-band Sentinel-1A data, this research monitored the surface displacement of a large old landslide at Xuecheng town, Lixian County, Sichuan Province, China. Based on the MassMov2D model, the effect of the dynamic process and deposit thickness of the potentially unstable rock mass (deformation rate < −70 mm/year) on this landslide body were numerically simulated. Combined with terrain data and images generated by an Unmanned Aerial Vehicle (UAV), the driving factors of this old landslide were analyzed. The InSAR results show that the motion rate in the middle part of the landslide body is the largest, with a range of −55 to −80 mm/year on average, whereas those of the upper part and toe area were small, with a range of −5 to −20 mm/year. Our research suggests that there is a correlation between the LOS (line of sight) deformation rate and rainfall. In rainy seasons, particularly from May to July, the deformation rate is relatively high. In addition, the analysis suggests that SBAS can provide smoother displacement time series, even in areas with vegetation and the steepest sectors of the landslide. The simulation results show that the unstable rock mass may collapse and form a barrier dam with a maximum thickness of about 16 m at the Zagunao river in the future. This study demonstrates that combining temporal UAV measurements and InSAR techniques from Sentinel-1A SAR data allows early recognition and deformation monitoring of old landslide reactivation in complex mountainous areas. In addition, the information provided by InSAR can increase understanding of the deformation process of old landslides in this area, which would enhance urban safety and assist in disaster mitigation.

Operational Estimation of Landslide Runout: Comparison of Empirical and Numerical Methods

A key point of landslide hazard assessment is the estimation of their runout. Empirical relations linking angle of reach to volume can be used relatively easily, but they are generally associated with large uncertainties as they do not consider the topographic specificity of a given study site. On the contrary, numerical simulations provide more detailed results on the deposits morphology, but their rheological parameters can be difficult to constrain. Simulating all possible values can be time consuming and incompatible with operational requirements of rapid estimations. We propose and compare three operational methods to derive scaling power laws relating the landslide travel distance to the destabilized volume. The first one relies only on empirical relations, the second one on numerical simulations with back-analysis, and the third one combines both approaches. Their efficiency is tested on three case studies: the Samperre cliff collapses in Martinique, Lesser Antilles (0.5 to 4×106 m3), the Frank Slide rock avalanche (36×106 m3) and the Samperre cliff collapses in Martinique, Lesser Antilles (0.5 to 4×106 m3) the Fei Tsui debris slide in Hong Kong (0.014×106 m3). Purely numerical estimations yield the smallest uncertainty, but the uncertainty on rheological parameters is difficult to quantify. Combining numerical and empirical approaches allows to reduce the uncertainty of estimation by up to 50%, in comparison to purely empirical estimations. However, it may also induces a bias in the estimation, though observations always lie in the 95% prediction intervals. We also show that empirical estimations fail to model properly the dependence between volume and travel distance, particularly for small landslides (<20,000 <0.02×106 m3).

A bedform phase diagram for dense granular currents

Pyroclastic density currents (PDCs) are a life-threatening volcanic hazard. Our understanding and hazard assessments of these flows rely on interpretations of their deposits. The occurrence of stratified layers, cross-stratification, and bedforms in these deposits has been assumed as indicative of dilute, turbulent, supercritical flows causing traction-dominated deposition. Here we show, through analogue experiments, that a variety of bedforms can be produced by denser, aerated, granular currents, including backset bedforms that are formed in waning flows by an upstream-propagating granular bore. We are able to, for the first time, define phase fields for the formation of bedforms in PDC deposits. We examine how our findings impact the understanding of bedform features in outcrop, using the example of the Pozzolane Rosse ignimbrite of the Colli Albani volcano, Italy, and thus highlight that interpretations of the formative mechanisms of these features observed in the field must be reconsidered.

In this study, Smith and colleagues employ analogue experiments to show the controlling parameters on sediment bedforms in pyroclastic density current deposits. The findings are applied and validated on natural deposits.

Experimental Analysis of Velocity Distribution in a Coarse-Grained Debris Flow: A Modified Bagnold’s Equation

Today, Bagnold’s theory is still applied to gravity-driven flows under the assumption of uniform sediment concentration. This study presents findings of flume experiments conducted to investigate the velocity and concentration distributions within the debris body by using high-resolution images. The analysis has shown that the concentration and mobility of grains vary along the depth. A linear law to interpret the grains concentration distribution, starting from the knowledge of the packing concentration and of the surface concentration, Cs, has been identified. By considering such a law, modified expressions of the Bagnold’s number and the velocity in stony-type debris flows are also presented. By using these expressions, three regimes of motion have been identified along the depth, and the velocity profile within the debris body is determined as a function of the parameter Cs. It has been verified that the velocity profiles estimated by using the modified equation compare well (mean square error less than 0.1) with the literature’s measured profiles when Cs is correctly measured or estimated. Results of cutting tests, conducted for a sample of the used material, have also allowed us to verify that Cs could be determined as a function of the static friction angle of the material.

Numerical Runout Modeling Analysis of the Loess Landslide at Yining, Xinjiang, China

The Panjinbulake loess landslide is located in the western part of the Loess Plateau, in Yining County, Xinjiang, China. It is characterized by its long runout and rapid speed. Based on a field geological survey and laboratory test data, we used the DAN-W dynamic numerical simulation software (Dynamic Analysis Of Landslides, Release 10, O. Hungr Geotechnical Research Inc, West Vancouver, BC, Canada) and multiple sets of rheological models to simulate the whole process of landslide movement. The best rheological groups of the features of the loess landslide process were obtained by applying the Voellmy rheological model in the debris flow area and applying the Frictional rheological model in the sliding source area and accumulation area. We calculated motion features indicating that the landslide movement duration was 22 s, the maximum movement speed was 20.5 m/s, and the average thickness of the accumulation body reached 5.5 m. The total accumulation volume, the initial slide volume and the long runout distance were consistent with the actual situation. In addition, the potential secondary disaster was evaluated. The results show that the DAN-W software and related model parameters can accurately simulate and predict the dynamic hazardous effects of high-speed and long runout landslides. Together, these predictions could help local authorities make the best hazard reduction measures and to promote local development.

Source areas, connectivity, and delivery rate of sediments in mountainous-forested hillslopes: A probabilistic approach

In mountainous-forested landscape, quantifying the materials produced at hillslope scale that effectively reach the channel network with a given probability is currently challenging, due to the uncertainties in modelling the frequency-magnitude distribution of failures and in determining the sediment connectivity between unstable areas and channel network. The purpose of this study is to develop a modular approach to assess the sediment source areas and the probability of mobilization from hillslope, and to estimate the probability of sediment input to the streams proposing a new connectivity index. The first goal was faced adopting a 3D probabilistic slope stability method that includes the spatially distributed characteristics of forest coverage. The second aim was tackled by comparing sediment travel distance and the minimum-topographic distance to reach the nearest stream. A simple deposition model was applied to estimate the percentage of the sediment entering into the stream network. The methodology was tested on three headwater catchments in northern Italian Alps. The outputs were landslide susceptibility maps, which showed robust performances when compared to the available landslide inventories (AUC > 0.726), and maps of the probability that sediment reaches the channel network. In this way, it was possible to identify which areas are the most susceptible to landsliding, how many sediment materials can be mobilised with a given probability, and which is the degree of sediment connectivity with the channel system. Results obtained for the tested catchments, compared with data available from the literature, showed that the proposed methodology is of general validity, especially for those territories characterized by rainfall-triggered landslides and forest coverage. This study, then, provides a robust framework to improve debris-flow risk management and to implement watershed management strategies, such as planning forestry operations or positioning retention structures addressed to increase slope stability and to reduce sediment delivery.

Modelling of Fluidised Geomaterials: The Case of the Aberfan and the Gypsum Tailings Impoundment Flowslides

The choice of a pure cohesive or a pure frictional viscoplastic model to represent the rheological behaviour of a flowslide is of paramount importance in order to obtain accurate results for real cases. The principal goal of the present work is to clarify the influence of the type of viscous model—pure cohesive versus pure frictional—with the numerical reproduction of two different real flowslides that occurred in 1966: the Aberfan flowslide and the Gypsum tailings impoundment flowslide. In the present work, a depth-integrated model based on the v-pw Biot–Zienkiewicz formulation, enhanced with a diffusion-like equation to account for the pore pressure evolution within the soil mass, is applied to both 1966 cases. For the Aberfan flowslide, a frictional viscous model based on Perzyna viscoplasticity is considered, while a pure cohesive viscous model (Bingham model) is considered for the case of the Gypsum flowslide. The numerical approach followed is the SPH method, which has been enriched by adding a 1D finite difference grid to each SPH node in order to improve the description of the pore water evolution in the propagating mixture. The results obtained by the performed simulations are in agreement with the documentation obtained through the UK National Archive (Aberfan flowslide) and the International Commission of large Dams (Gypsum flowslide).

Numerical Simulation of Dry Granular Flow Impacting a Rigid Wall Using the Discrete Element Method

This paper presents a clump model based on Discrete Element Method. The clump model was more close to the real particle than a spherical particle. Numerical simulations of several tests of dry granular flow impacting a rigid wall flowing in an inclined chute have been achieved. Five clump models with different sphericity have been used in the simulations. By comparing the simulation results with the experimental results of normal force on the rigid wall, a clump model with better sphericity was selected to complete the following numerical simulation analysis and discussion. The calculation results of normal force showed good agreement with the experimental results, which verify the effectiveness of the clump model. Then, total normal force and bending moment of the rigid wall and motion process of the granular flow were further analyzed. Finally, comparison analysis of the numerical simulations using the clump model with different grain composition was obtained. By observing normal force on the rigid wall and distribution of particle size at the front of the rigid wall at the final state, the effect of grain composition on the force of the rigid wall has been revealed. It mainly showed that, with the increase of the particle size, the peak force at the retaining wall also increase. The result can provide a basis for the research of relevant disaster and the design of protective structures.

Unsteady granular flows down an inclined plane

The continuum description of granular flows is still a challenge despite their importance in many geophysical and industrial applications. We extend previous works, which have explored steady flow properties, by focusing on unsteady flows accelerating or decelerating down an inclined plane in the simple shear configuration. We solve the flow kinematics analytically, including predictions of evolving velocity and stress profiles and the duration of the transient stage. The solution shows why and how granular materials reach steady flow on slopes steeper than the angle of repose and how they decelerate on shallower slopes. The model might facilitate development of natural hazard assessment and may be modified in the future to explore unsteady granular flows in different configurations.

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. I. Physical basis

To simulate debris-flow behaviour from initiation to deposition, we derive a depth-averaged, two-phase model that combines concepts of critical-state soil mechanics, grain-flow mechanics and fluid mechanics. The model's balance equations describe coupled evolution of the solid volume fraction, m , basal pore-fluid pressure, flow thickness and two components of flow velocity. Basal friction is evaluated using a generalized Coulomb rule, and fluid motion is evaluated in a frame of reference that translates with the velocity of the granular phase, v s . Source terms in each of the depth-averaged balance equations account for the influence of the granular dilation rate, defined as the depth integral of ∇⋅ v s . Calculation of the dilation rate involves the effects of an elastic compressibility and an inelastic dilatancy angle proportional to m − m eq , where m eq is the value of m in equilibrium with the ambient stress state and flow rate. Normalization of the model equations shows that predicted debris-flow behaviour depends principally on the initial value of m − m eq and on the ratio of two fundamental timescales. One of these timescales governs downslope debris-flow motion, and the other governs pore-pressure relaxation that modifies Coulomb friction and regulates evolution of m . A companion paper presents a suite of model predictions and tests.

A depth-averaged debris-flow model that includes the effects of evolving dilatancy. II. Numerical predictions and experimental tests

We evaluate a new depth-averaged mathematical model that is designed to simulate all stages of debris-flow motion, from initiation to deposition. A companion paper shows how the model's five governing equations describe simultaneous evolution of flow thickness, solid volume fraction, basal pore-fluid pressure and two components of flow momentum. Each equation contains a source term that represents the influence of state-dependent granular dilatancy. Here, we recapitulate the equations and analyse their eigenstructure to show that they form a hyperbolic system with desirable stability properties. To solve the equations, we use a shock-capturing numerical scheme with adaptive mesh refinement, implemented in an open-source software package we call D-Claw. As tests of D-Claw, we compare model output with results from two sets of large-scale debris-flow experiments. One set focuses on flow initiation from landslides triggered by rising pore-water pressures, and the other focuses on downstream flow dynamics, runout and deposition. D-Claw performs well in predicting evolution of flow speeds, thicknesses and basal pore-fluid pressures measured in each type of experiment. Computational results illustrate the critical role of dilatancy in linking coevolution of the solid volume fraction and pore-fluid pressure, which mediates basal Coulomb friction and thereby regulates debris-flow dynamics.

Bidisperse granular avalanches on inclined planes: a rich variety of behaviors

Experiments were performed to provide insight into the flow behavior and structure of bimodal mixtures of grains in gravity-driven, free-surface flows. Unsteady unconfined flows were produced by releasing instantaneously a dry granular mass, composed of two particle sizes, over a rough inclined plane. As a result of size segregation, the small particles are found at the bottom of the flow and final deposit, the large particles are found at the free surface, but also on the lateral borders and at the front of the flow. The lateral and vertical inhomogeneous repartitions of particles lead to two main effects that are completely absent in monodispersed flows. The outline effect results from the accumulation of large beads on the periphery of the flow depending on the value of the relative friction of each particle species on the plane. This effect in turn causes a narrowing of the flow and/or an increase of length of the final deposit. The interface effect results of the interaction between layers of different size particles and causes the modification of the thickness of the deposit. These effects occur simultaneously and their combination leads to a great variety of behaviors. In this investigation, evidence of the diversity of behaviors is presented as the size ratio, relative friction and concentration of each particle species are varied.

Techniques, issues and advances in numerical modelling of landslide hazard

Slope movements (e.g. landslides) are dynamic systems that are complex in time and space and closely linked to both inherited and current preparatory and triggering controls. It is not yet possible to assess in all cases conditions for failure, reactivation and rapid surges and successfully simulate their transient and multi-dimensional behaviour and development, although considerable progress has been made in isolating many of the key variables and elementary mechanisms and to include them in physically-based models for landslide hazard assessments. Therefore, the objective of this paper is to review the state-of-the-art in the understanding of landslide processes and to identify some pressing challenges for the development of our modelling capabilities in the forthcoming years for hazard assessment. This paper focuses on the special nature of slope movements and the difficulties related to simulating their complex time-dependent behaviour in mathematical, physically-based models. It analyses successively the research frontiers in the recognition of first-time failures (pre-failure and failure stages), reactivation and the catastrophic transition to rapid gravitational processes (post-failure stage). Subsequently, the paper discusses avenues to transfer local knowledge on landslide activity to landslide hazard forecasts on regional scales and ends with an outline how geomorphological investigations and supporting monitoring techniques could be applied to improve the theoretical concepts and the modelling performance of physically-based landslide models at different spatial and temporal scales.

Collapses of two-dimensional granular columns

The first detailed quantitative observations of the two-dimensional collapse of a granular column along a horizontal channel are presented for a variety of materials. Together with the complementary study for the axisymmetric situation, we conclude that for granular collapses the generally accepted approaches, that are highly dependent on frictional parameters, do not describe the main flow phenomena. The motion divides in two main flow regimes at a approximately 1.8, where the aspect ratio a = hi/di and hi and di are the initial height and width of the column. We describe the details of collapse by emphasizing the sequential occurrence of a main spreading followed by a final avalanching phase. For the low a regime, a < 1.8, we derive descriptions of the final geometry by direct physical arguments. For the large a regime, a > 1.8, we determine that nearly all details of the collapse, including the position of the flow front as a function of time, the emplacement time, the self-similar final profiles, and especially their maximum vertical and horizontal extension, are established during the spreading phase and can be expressed in terms of the initial geometrical parameters but are independent of basal and internal friction parameters.

Rapid motions of free-surface avalanches down curved and twisted channels and their numerical simulation

This paper presents a new model and discussions about the motion of avalanches from initiation to run-out over moderately curved and twisted channels of complicated topography and its numerical simulations. The model is a generalization of a well established and widely used depth-averaged avalanche model of Savage & Hutter and is published with all its details in Pudasaini & Hutter (Pudasaini & Hutter 2003 J. Fluid Mech. 495, 193-208). The intention was to be able to describe the flow of a finite mass of snow, gravel, debris or mud, down a curved and twisted corrie of nearly arbitrary cross-sectional profile. The governing equations for the distribution of the avalanche thickness and the topography-parallel depth-averaged velocity components are a set of hyperbolic partial differential equations. They are solved for different topographic configurations, from simple to complex, by applying a high-resolution non-oscillatory central differencing scheme with total variation diminishing limiter. Here we apply the model to a channel with circular cross-section and helical talweg that merges into a horizontal channel which may or may not become flat in cross-section. We show that run-out position and geometry depend strongly on the curvature and twist of the talweg and cross-sectional geometry of the channel, and how the topography is shaped close to run-out zones.

Geophysical granular and particle-laden flows: review of the field

An introduction is given to the title theme, in general, and the specific topics treated in detail in the articles of this theme issue of the Philosophical Transactions. They fit into the following broader subjects: (i) dense, dry and wet granular flows as avalanche and debris flow events, (ii) air-borne particle-laden turbulent flows in air over a granular base as exemplified in gravity currents, aeolian transport of sand, dust and snow and (iii) transport of a granular mass on a two-dimensional surface in ripple formations of estuaries and rivers and the motion of sea ice.

A two-fluid model for avalanche and debris flows

Geophysical mass flows--debris flows, avalanches, landslides--can contain O(10(6)-10(10)) m(3) or more of material, often a mixture of soil and rocks with a significant quantity of interstitial fluid. These flows can be tens of meters in depth and hundreds of meters in length. The range of scales and the rheology of this mixture presents significant modelling and computational challenges. This paper describes a depth-averaged 'thin layer' model of geophysical mass flows containing a mixture of solid material and fluid. The model is derived from a 'two-phase' or 'two-fluid' system of equations commonly used in engineering research. Phenomenological modelling and depth averaging combine to yield a tractable set of equations, a hyperbolic system that describes the motion of the two constituent phases. If the fluid inertia is small, a reduced model system that is easier to solve may be derived.

Monte Carlo calibration of avalanches described as Coulomb fluid flows

The idea that snow avalanches might behave as granular flows, and thus be described as Coulomb fluid flows, came up very early in the scientific study of avalanches, but it is not until recently that field evidence has been provided that demonstrates the reliability of this idea. This paper aims to specify the bulk frictional behaviour of snow avalanches by seeking a universal friction law. Since the bulk friction coefficient cannot be measured directly in the field, the friction coefficient must be calibrated by adjusting the model outputs to closely match the recorded data. Field data are readily available but are of poor quality and accuracy. We used Bayesian inference techniques to specify the model uncertainty relative to data uncertainty and to robustly and efficiently solve the inverse problem. A sample of 173 events taken from seven paths in the French Alps was used. The first analysis showed that the friction coefficient behaved as a random variable with a smooth and bell-shaped empirical distribution function. Evidence was provided that the friction coefficient varied with the avalanche volume, but any attempt to adjust a one-to-one relationship relating friction to volume produced residual errors that could be as large as three times the maximum uncertainty of field data. A tentative universal friction law is proposed: the friction coefficient is a random variable, the distribution of which can be approximated by a normal distribution with a volume-dependent mean.

The Savage-Hutter avalanche model: how far can it be pushed?

The Savage-Hutter (SH) avalanche model is a depth-averaged dynamical model of a fluid-like continuum implementing the following simplifying assumptions: (i) density preserving, (ii) shallowness of the avalanche piles and small topographic curvatures, (iii) Coulomb-type sliding with bed friction angle delta and (iv) Mohr-Coulomb behaviour in the interior with internal angle of friction phi> or =delta and an ad hoc assumption reducing the number of Mohr's circles in three-dimensional stress states to one. We scrutinize the available literature on information regarding these assumptions and thus delineate the ranges of validity of the proposed model equations. The discussion is limited to relatively large snow avalanches with negligible powder snow component and laboratory sand avalanches starting on steep slopes. The conclusion of the analysis is that the SH model is a valid model for sand avalanches, but its Mohr-Coulomb sliding law may have to be complemented for snow avalanches by a second velocity-dependent contribution. For very small snow avalanches and for laboratory avalanches starting on moderately steep and bumpy slopes it may not be adequate.