Large mobility of dry snow avalanches: Insights from small-scale laboratory tests on granular avalanches of bidisperse materials

This paper reports small-scale laboratory tests on granular avalanches of bidisperse materials made of fine particles and larger ones. These experiments were motivated by a recent study on the rheology of dense flowing snow which provided evidence for relevant similarities in flow behavior between bidisperse granular materials and dry cold snow [Rognon and others, J. Rheol., 52, 3 ([32])]. The mass proportion of fine particles in the initial binary mixture was systematically varied at constant initial released volume, and we measured the resulting flow depth, the avalanche front velocity and the final avalanche runout. In particular, we show that the avalanche mobility is largely increased, about 40% in our tests, when the mass proportion in fine particles reaches a critical value, around 0.25 in our tests. The avalanche deposit is shallow and lengthened for this critical mass proportion in fine particles. The experimental results are interpreted by the existence of different avalanche mobility regimes on the basis of a heuristic model previously reported in literature. Finally, we discuss their possible implications for the dynamics of full-scale dry snow avalanches.     

Position dependent velocity profiles in granular avalanches

We present velocity profile measurements in granular avalanches flowing down a flat chute with wide rectangular cross section. The flow is recorded through a transparent side-wall by a high-speed camera, which is able to capture 1,825 pictures in a second. Due to the high frame rate of the camera, several flow features can be observed. Quantitative statements can be made by analysing the images with a pattern matching algorithm. This provides us with flow-normal velocity profiles with a very high temporal and spatial resolution. We find that even on flat surfaces, velocity profiles are strongly changing through the flow and for the range of investigated chute angles (from 26° to 36°) clear trends can be recognised. In the head of the avalanche the velocity is highest, decreasing continuously over the length of the avalanche. Thus, the investigated granular avalanches stretch through the flow. The experimental method allows us to study the evolution of characteristic flow properties such as depth averaged velocity, slip velocity, surface velocity, shear rates or flow depth. Side-wall friction effects are estimated.     

Small-scale tests to investigate the dynamics of finite-sized dry granular avalanches and forces on a wall-like obstacle

Small-scale laboratory tests investigate the force from finite-sized granular avalanches on a wall. First, the reference flows, in absence of the wall, were analysed in a wide range of slopes from a minimum angle for which no flow is possible to a critical angle for which the flow becomes very dilute. The changes in thickness and velocity over time exhibit transitions at the minimum slope angle and at intermediate slopes. Then the normal force exerted on a wall spanning the flow was measured. It is notable that the transitions detected in reference flows had a direct effect on the force. The maximum force was equal to the kinetic force of the incoming flow at high slopes, whereas it scaled like hydrostatic force at lower slopes. This is the effect of the dense-to-dilute transition. Furthermore, the maximum force at low slopes was found to be several times greater than the hydrostatic force of the incoming flow. This finding is explained by the considerable contribution of the stagnant zone formed upstream of the wall. Furthermore, the jamming transition was highlighted at the avalanche standstill by the collapse of the residual force on the wall when approaching the minimum angle for which no flow is possible. These results are useful for the design of protection dams against rapid mass movements.     

A cellular automaton for segregation during granular avalanches

Segregation is a complex and poorly understood phenomenon that is prevalent in many industrial and natural granular flows. When grains flow down a slope [1–5], are spun in a rotating drum [6–8] or shaken in a box [9], we observe those grains organising into intriguing patterns. Kinetic sieving is the dominant mode of segregation in granular avalanches, where separation of particles occurs according to size. Using a cellular automaton we have modelled kinetic sieving as the swapping of particles in a one-dimensional system. From the cellular automaton we have deduced a continuum model to describe the segregation.     

Breaking size-segregation waves and mobility feedback in dense granular avalanches

Through experiments and discrete particle method (DPM) simulations we present evidence for the existence of a recirculating structure, that exists near the front of dense granular avalanches, and is known as a breaking size-segregation (BSS) wave. This is achieved through the study of three-dimensional bidisperse granular flows in a moving-bed channel. Particle-size segregation gives rise to the formation of a large-particle-rich front and a small-particle-rich tail with a BSS wave positioned between the tail and front. We experimentally resolve the structure of the BSS wave using refractive-index matched scanning and find that it is qualitatively similar to the structure observed in DPM simulations. Our analysis demonstrates a relation between the concentration of small particles in the flow and the amount of basal slip, in which the structure of the BSS wave plays a key role. This leads to a feedback between the mean bulk flow velocity and the process of particle-size segregation. Ultimately, these findings shed new light on the recirculation of large and small grains near avalanche fronts and the effects of this behaviour on the mobility of the bulk flow.     

Flow profile of granular avalanches with imposed vertical vibration

We report experimental results on the effect of imposed vertical vibration on the flow of pentagonal grains in a two-dimensional rotation drum. While dimensionless acceleration $\varGamma $ can be tuned either by increasing vibration frequency or amplitude, the former leads to stabilization an increase in the angle of repose while the latter leads to destabilization and a decrease in the critical angle for failure. Increased vibration amplitude leads to continuous avalanching and a more uniform flow profile, with a flowing layer composed of increasingly long-lived, shallower avalanches before a continuous flow regime is reached. The slope and grain-scale roughness of the surface decrease and interface curvature increases as vibration amplitude is increased and collective motion allows relaxation of the surface. While qualitative flow characteristics are similar both with and without vibration, vibration allows the system to evolve continuously in a nearly steady-state profile.     

Similarity solutions for avalanches of granular materials down curved beds

Summary The present paper investigates similarity solutions for the two-dimensional flow of a mass of cohesionless granular material down rough curved beds having gradually varying slopes. The work is relevant to the motion of rockfalls and loose snow flow avalanches. The depth and velocity profiles for the moving mass are determined in analytical form and the evolution equation for the total length of the pile is integrated numerically using a Runge-Kutta technique. Although similarity solutions can occur for general bed shapes (as long as the curvature is small), specific computations are performed here for two families of bed profiles, one which is in the shape of a circular arc and the other in which the slope decays exponentially with downstream distance. The pile of granular material starts from rest, initially accelerates and then decelerates, finally coming to rest as a result of bed friction and the gradually decreasing bed slope. Depending upon the frictional parameters, the shape of the bed and the initial depth to length of the pile, it is found that the variation of total length with time can exhibit different behaviours. The pile can grow monotonically, it can asymptote to a constant length, it can grow to a maximum and then decrease or it can decrease to a minimum and then increase with time. Furthermore, there are regions in parameter space for which the pile moves as a rigid body either for the whole time of travel or for portions of it.on leave from Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke St. W., Montreal H3A 2K6, Canadaon leave from Institute of Snow and Ice Studies, N.R.C.D.P., Suyoshi, Nagaoka-shi, 940, JapanWith 7 Figures     

Onset mechanism of granular avalanches in inclining layers using a continuum model

What is the onset mechanism of macro scale avalanches? How do macro scale avalanches happen in the granular layers in an inclining box? The answers to these questions are the main part of our article aims. Using 3-dimensional simulation method we show the stresses, the stress ratios and the packing fractions in the processes where the onset of macro scale avalanches takes place. Based on our results the critical conditions of the onset of avalanches are presented. The onset mechanism of granular avalanches is elucidated. The onset of macro scale avalanches occurs in the small area, about 2% of the whole area, in the inclining granular layers. These are the conditions for the onset of macro scale avalanches that the shear and normal stresses and the packing fraction reach the maximum values at the same inclining angle. Then the stress ratio should be larger than the static frictional coefficient of materials. Aggregates of stick-slip like event are formed in the longitudinal direction. The number of aggregates decreases and the physical quantities in the aggregates rapidly increase with increasing inclining angle in the small area in which the onset of macro scale avalanche occurs.     

Erosive granular avalanches: a cross confrontation between theory and experiment

Results on two laboratory scale avalanches experiments taking place both in the air and under-water, are presented. In both cases a family of solitary erosion/deposition waves are observed. At higher inclination angles, we show the existence of a long wavelength transverse instability followed by a coarsening and the onset of a fingering pattern. While the experiments strongly differ by the spatial and time scales, the agreement between the stability diagram, the wavelengths selection and the avalanche morphology suggest a common erosion/deposition scenario. These experiments are studied theoretically in the framework of the “partial fluidization” model of dense granular flows. This model identifies a family of propagating solitary waves displaying a behavior similar to the experimental observation. A primary cause for the transverse instability is related to the dependence of avalanche velocity on the granular mass trapped by the flow.     

Triggering of dry snow slab avalanches: stress versus fracture mechanical approach

This paper analyses the conditions for triggering of dry snow slab avalanches. As suggested by several Authors, we assume as a basic mechanism for avalanche triggering the mode II fracture of the weak layer lying beneath the stiff snow slab, i.e. we assume the presence of super-weak zones in the basal layer. By means of a linear elastic analysis, the shear stresses in the weak layer as well as the strain energy release rate caused by an increment of the super-weak zone are evaluated. Hence we introduce a stress failure criterion as well as an energy one. It is shown that the latter criterion can be seen as an extension of the criterion firstly proposed by McClung [McClung, D.M., 1979. Shear fracture precipitated by strain softening as a mechanism of dry slab avalanche release. Journal of Geophysical Research, 84(B7), 3519-3526.] for dry snow slab avalanche release. Finally we couple the two criteria, showing that the weak layer can fail only in a min–max band of thickness.     

Flow–obstacle interaction in rapid granular avalanches: DEM simulation and comparison with experiment

This paper investigates the interaction between rapid granular flow and an obstacle. The distinct element method (DEM) is used to simulate the flow regimes observed in laboratory experiments. The relationship between the particle properties and the overall flow behaviour is obtained by using the DEM with a simple linear contact model. The flow regime is primarily controlled by the particle friction, viscous normal damping and particle rotation rather than the contact stiffness. Rolling constriction is introduced to account for dispersive flow. The velocity depth-profiles around the obstacles are not uniform but varying over the depth. The numerical results are compared with laboratory experiments of chute flow with dry granular material. Some important model parameters are obtained, which can be used to optimize defense structures in alpine regions.     

Snowpack properties associated with fracture initiation and propagation resulting in skier-triggered dry snow slab avalanches

This study investigates snowpack properties associated with skier-triggered dry slab avalanches, with a particular view on snowpack conditions favoring fracture propagation. This was done by analyzing a data set of over 500 snow profiles observed next to skier-triggered slabs (including remotely triggered slab avalanches and whumpfs) and on skier-tested slopes that did not release a slab avalanche. The relation of the snowpack variables with fracture initiation and fracture propagation, both of which are required for skier-triggering, was investigated. Specific snowpack characteristics, including hardness difference and difference in crystal size across the failure layer, associated with skier-triggered dry slab avalanches were identified and the frequency of skier-triggering was determined. In order to assess snowpack variables favouring fracture propagation, variables from failure layers associated with skier-triggered slabs that were not remotely triggered and relatively small were contrasted with snowpack variables from failure layers of remotely triggered slab avalanches, whumpfs and relatively large slab avalanches. The properties of the slab overlying the weak layer, as well as the layer above the weak layer, were found to affect fracture propagation. Stiffer slabs were associated with large avalanches as well as whumpfs and remotely triggered avalanches. Furthermore, a correlation analysis of snowpack variables with the size and width of the investigated slab avalanches further accentuated the importance of these slab properties with regards to fracture propagation.     

A two-phase model for dry density-varying granular flows

A granular flow is normally comprised of a mixture of grain-particles (such as sand, gravel or rocks) of different sizes. In this study, dry granular flows are modeled utilizing a set of equations akin to a two-phase mixture system, in which the interstitial fluid is air. The resultant system of equations for a two-dimensional configuration includes two continuity and two momentum balance equations for the two respective constituents. The density variation is described considering the phenomenon of air entrainment/extrusion at the flow surface, where the entrainment rate is assumed to be dependent on the divergent or convergent behavior of the solid constituent. The density difference between the two constituents is extremely large, so, as a consequence scaling analysis reveals that the flow behavior is dominated by the solid species, yielding small relative velocities between the two constituents. A non-oscillatory central (NOC) scheme with total variation diminishing (TVD) limiters is implemented. Three numerical examples are investigated: the first being related to the flow behaviors on a horizontal plane with an unstable initial condition; the second example is devoted to simulating a dam-break problem with respect to different initial conditions; and in the third one investigates the behavior of a finite mass of granular material flowing down an inclined plane. The key features and the capability of the equations to model the behavior are illustrated in these numerical examples.     

Electron-hole avalanches in semiconductors

An analytical theory of the development of electron-hole avalanches in semiconductors, which qualitatively differ from the electron avalanches in gases, is proposed and the spatiotemporal distributions of the field and charge in such avalanches are determined. It is suggested to identify the onset of the avalanche-streamer transition as the moment (t _a) corresponding to a 20% decrease in the impact ionization coefficient α at the avalanche center. A transcendent equation is obtained for the calculation of t _a as a function of the unperturbed coefficient α(E _ext) determined by the external field E _ext. It is established that, as the α(E _ext) value is increased in from 10³ to 10⁵ cm^?1, the total number of electron-hole pairs generated by the t _a moment decreases by almost three orders of magnitude.     

The dynamics of avalanches of granular materials from initiation to runout. Part II. Experiments

Summary This paper describes a model to predict the flow of an initially stationary mass of cohesionsless granular material down a rough curved bed and checks it against laboratory experiments that were conducted with two different kinds of granular materials that are released from rest and travel in a chute consisting of a straight inclined section, a curved segment that is followed by a straight horizontal segment. This work is of interest in connection with the motion of landslides, rockfalls and ice and dense flow snow avalanches. Experiments were performed with two different granular materials, nearly spherical glass beads of 3 mm nominal diameter, Vestolen particles (a light plastic material) of lense type shape and 4 mm nominal diameter and 2,5 mm height. Piles of finite masses of these granular materials with various initial shapes and weight were released from rest in a 100 mm wide chute with the mentioned bent profile. The basal surface consisted of smooth PVC, but was in other experiments also coated with drawing paper and with sandpaper. The granular masses under motion were photographed and partly video filmed and thus the geometry of the avalanche was recorded as a function of position and time. For the two granular materials and for the three bed linings the angle of repose and the bed friction angle were determined. The experimental technique with which the laboratory avalanches were run are described in detail as is the reliability of the generated data. We present and use the depth-averaged field equations of balance of mass and linear momentum as presented by Savage and Hutter [28]. These are partial differential equations for the depth averaged streamwise velocity and the distribution of the avalanche depth and involve two phenomenological parameters, the internal angle of friction, ø, and a bed friction angle, , both as constitutive properties of Coulomb-type behaviour. We present the model but do not derive its equations. The numerical integration scheme for these equations is a Lagrangian finite difference scheme used earlier by Savage and Hutter [27],[28]. We present this scheme for completeness but do not discuss its peculiarities. Comparison of the theoretical results with experiments is commenced by discussing the implementation of the initial conditions. Observations indicate that with the onset of the motion a dilatation is involved that should be accomodated for in the definition of the initial conditions. Early studies of the temporal evolution of the trailing and leading edges of the granular avalanche indicate that their computed counterparts react sensitively to variations in the bed friction angle but not to those of the internal angle of friction. Furthermore, a weak velocity dependence of the bed friction angle, , is also scen to have a small, but negligible influence on these variables. We finally compare the experimental results with computational findings for many combinations of the masses of the granular materials and bed linings. It is found that the experimental results and the theoretical predictions agree satisfactorily. They thus validate the simple model equations that were proposed in Savage and Hutter [28].     

The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis

Summary This paper describes a model to predict the flow of an initially stationary mass of cohesion-less granular material down rough curved beds. This work is of interest in connection with the motion of rock and ice avalanches and dense flow snow avalanches. The constitutive behaviour of the material making up the pile is assumed to be described by a Mohr-Coulomb criterion while the bed boundary condition is treated by a similar Coulomb-type basal friction law assumption. By depth averaging the incompressible conservation of mass and linear momentum equations that are written in terms of a curvilinear coordinate system aligned with the curved bed, we obtain evolution equations for the depthh and the depth averaged velocity. Three characteristic length scales are defined for use in the non-dimensionalization and scaling of the governing equations. These are a characteristic avalanche lengthL, a characteristic heightH, and a characteristic bed radius of curvatureR. Three independent parameters emerge in the non-dimensionalized equations of motion. One, which is the aspect ratio -H/L, is taken to be small. By choosing different orderings for the other two, the tangent of the bed friction angle and the characteristic non-dimensional curvature =L/R, we can obtain different sets of equations of motion which appropriately display the desired importance of bed friction and bed curvature effects. The equations, correct to order for moderate curvature, are discretized in the form of a Lagrangian-type finite difference representation which proved to be successful in the earlier studies of Savage and Hutter [24] for granular flow down rough plane surfaces. Laboratory experiments were performed with plastic particles flowing down a chute having a bed made up of a straight, inclined portion, a curved part and a horizontal portion. Numerical solutions are presented for conditions corresponding to the laboratory experiments. It is found that the predicted temporal-evolutions of the rear and front of the pile of granular material as well as the shape of the pile agree quite well with the laboratory experiments.     

Explanation and limitations of study plot stability indices for forecasting dry snow slab avalanches in surrounding terrain

In the Columbia Mountains of western Canada, some snow avalanche forecasting programs use slab stability indices calculated from study plot measurements near tree-line and find these indices helpful for forecasting dry slab avalanching many kilometers from the study plot. Research in the same mountain range has confirmed the correlation between the indices and avalanche occurrence. Due to spatial variability and scale issues, the explanation for the correlation between the indices, which are based on measurements over a small area, and avalanching many kilometers away has been unclear. The stability indices for natural (spontaneous) avalanches are ratios of shear strength of a weak snowpack layer to the shear stress on the weak layer applied by the overlying slab. The denominator of these ratios is proportional to vertical overburden pressure (load). One time series of overburden and shear strength measurements shows that neither measurement can be extrapolated from one site to another. A second time series shows a substantial difference in the stability index between the two sites, which is likely due to different initial crystal sizes in the weak layer at the two sites. However, different sites exhibit concurrent decreases in the strength–load ratio during snowfall and concurrent increases in the ratio after snowfall. The increases after snowfall are explained by lagged densification of weak layers and pressure sintering between grains. Critical values of stability indices are shown to be less useful than their trends for forecasting natural dry slab avalanches. The potential correlation of study plot stability indices with avalanching in surrounding terrain is also limited by the spatial extent of the weather system that forms the weak snowpack layer.     

Effect of base roughness on size segregation in dry granular flows

This paper presents simulations of dry granular flows along a sloping channel using the discrete element method. The kinetic sieving and squeeze expulsion theories are utilized to study the effects of base roughness on size segregation and the underlying mechanisms. Basal friction has a significant influence on flowing regimes inside the granular body, and a larger base friction accelerates the size segregation process. The front zone of the granular body is more likely to be collision dominated with increasing base friction; as a result, the energy dissipated by frictional shearing decreases, and damping energy due to particles collisions is enhanced. Meanwhile, granular flows become much looser, and collisions between particles increase rapidly. It is shown that the differences in the kinetics among grains of mixed sizes and the mechanical effects of particle contacts can explain the mechanism of size segregation. The parameter representing the intensity of particles exchange also increases as base friction increases. The forces acting on particles are also affected by base friction. The dimensionless contact force describing the contribution of contact channel-normal stress increases as base friction increases, which indicates that a higher dispersive trend has developed inside the granular body.     

Explanation and limitations of study plot stability indices for forecasting dry snow slab avalanches in surrounding terrain

In the Columbia Mountains of western Canada, some snow avalanche forecasting programs use slab stability indices calculated from study plot measurements near tree-line and find these indices helpful for forecasting dry slab avalanching many kilometers from the study plot. Research in the same mountain range has confirmed the correlation between the indices and avalanche occurrence. Due to spatial variability and scale issues, the explanation for the correlation between the indices, which are based on measurements over a small area, and avalanching many kilometers away has been unclear. The stability indices for natural (spontaneous) avalanches are ratios of shear strength of a weak snowpack layer to the shear stress on the weak layer applied by the overlying slab. The denominator of these ratios is proportional to vertical overburden pressure (load). One time series of overburden and shear strength measurements shows that neither measurement can be extrapolated from one site to another. A second time series shows a substantial difference in the stability index between the two sites, which is likely due to different initial crystal sizes in the weak layer at the two sites. However, different sites exhibit concurrent decreases in the strength–load ratio during snowfall and concurrent increases in the ratio after snowfall. The increases after snowfall are explained by lagged densification of weak layers and pressure sintering between grains. Critical values of stability indices are shown to be less useful than their trends for forecasting natural dry slab avalanches. The potential correlation of study plot stability indices with avalanching in surrounding terrain is also limited by the spatial extent of the weather system that forms the weak snowpack layer.     

Dynamical stress in force chains of granular media traveling on a bumpy terrain and the fragmentation of rock avalanches

The dynamics of grain fragmentation is usually ignored in the study of rapid granular flows. This is realistic for experiments on small-scale chutes or in many industrial processes where the specific granular energy is too small for particles to break but is unrealistic for natural rock avalanches, where the extremely comminuted state is perhaps the most evident aspect of the deposit. Based on observations of natural landslide deposits, it has been suggested that the stress may increase along a sequence of force chains formed by the granular material. However, simple calculations show that rock avalanche deposits exhibit a much more advanced degree of fragmentation than explainable with the static chain model. It is thus deduced that fragmentation along force chains must be combined with the effect of a bumpy topography. A simple model of a force chain moving on a rugged incline is then introduced, which exhibits increased fragmentation rate in the presence of a bumpy topography. It is shown that both the wave number and amplitude of the topographic undulations are significant in the efficiency of fragmentation.