The dynamic behaviour of granular media can be observed widely in nature and in many industrial processes. Yet, the modelling of such media remains challenging as they may act with solid-like and fluid-like properties depending on the rate of the flow and can display a varying apparent friction, cohesion and compressibility. Over the last two decades, the $\mu (I)$-rheology has become well established for modelling granular liquids in a fluid mechanics framework where the apparent friction $\mu$ depends on the inertial number $I$. In the geo-mechanics community, modelling the deformation of granular solids typically relies on concepts from critical state soil mechanics. Along the lines of recent attempts to combine critical state and the $\mu (I)$-rheology, we develop a continuum model based on modified cam-clay in an elastoplastic framework which recovers the $\mu (I)$-rheology under flow. This model permits a treatment of plastic compressibility in systems with or without cohesion, where the cohesion is assumed to be the result of persistent inter-granular attractive forces. Implemented in a two- and three-dimensional material point method, it allows for the trivial treatment of the free surface. The proposed model approximately reproduces analytical solutions of steady-state cohesionless flow and is further compared with previous cohesive and cohesionless experiments. In particular, satisfactory agreements with several experiments of granular collapse are demonstrated, albeit with shear bands which can affect the smoothness of the surface. Finally, the model is able to qualitatively reproduce the multiple steady-state solutions of granular flow recently observed in experiments of flow over obstacles.

Glaciers in High-Mountain Asia are experiencing varying rates and patterns of mass loss due to a complex interplay between glacier surface processes, local conditions and climate forcing. Spatially distributed surface mass balance (SMB) estimates can provide valuable insight into these drivers, but observations are currently limited in both space and time. We used very-high-resolution optical stereo images acquired by commercial satellites to prepare time series of digital elevation models (DEMs), and derived contemporaneous surface velocity and elevation change products for six debris-covered glaciers in Nepal. We developed new methods to produce flow-corrected Lagrangian SMB maps to isolate local surface ablation signals with enough detail to study individual ice cliffs. Our results show reduced ablation under thick debris cover and enhanced ablation over ice cliffs. Ablating ice cliffs were responsible for $10\!-\!38\%$ of the total ablation over debris-covered areas, even though they covered $\leq \!11\%$ of the total area. Seasonal SMB products reveal the timing and patterns of summer accumulation and ablation, underscoring the importance of snow avalanches for low-elevation debris-covered glaciers in the region. Our approach can be applied to other glaciers with repeat high-resolution DEM coverage and extended for regional analyses of SMB on seasonal to interannual timescales.

A simple continuum model is proposed for discrete granular avalanches, as observed in slowly rotating drums. Subject to granular transfer across the basal interface, the model evolves the transient surface inclination and mid-slope velocity profile of the avalanches, from failure to arrest. This is done using new boundary conditions that allow entrainment or detrainment contingent on the basal shear rate. For entrainment to occur, the basal shear stress must overcome the erosion resistance of the jammed deposit, while for detrainment to take place the basal shear rate must vanish. The resulting avalanche dynamics is controlled by a single dimensionless number, the ratio of excess slope at failure to excess resistance to erosion, that can be determined from inclination history data. This number provides a measure of slope brittleness, from which the peak flow rate and arrest inclination can be predicted. Analytical techniques are used to derive model solutions, and clarify the resulting behaviour. Finally, the model is tested by comparing solutions with laboratory experiments and discrete particle simulations.

Avalanche modeling is an essential tool to assess snow avalanche hazard. Today, most popular numerical approaches adopt depth-averaged equations. These methods are computationally efficient but limited in capturing processes occurring in the flow depth direction, e.g. erosion or deposition, which are often considered using ad hoc parameterizations or neglected completely. However, processes such as snow erosion, can crucially influence flow dynamics and run-out and are often not negligible. We address these issues by using a new three-dimensional (3-D) model, based on the material point method and finite strain elastoplasticity. To assess the possibilities and challenges associated with these highly detailed but computationally expensive calculations, we simulated the ‘Salezer’ snow avalanche that released in Davos, Switzerland in 2019. To reproduce the event in our simulations, we use the release areas mapped in a photogrammetric drone survey and estimate the snow conditions on the day of the event. We compare macroscopic features, such as flow outline and snow deposition of the simulated avalanche to field observations. An in-depth analysis of transient 3-D flow structures at the avalanche head not only demonstrates the degree of physical detail in the model, but also highlights challenges which still need to be addressed.

The objective of this research is to model snow's response to dynamic, impact loading. Two constitutive relationships are considered: elastic and Maxwell-viscoelastic. These material models are applied to laboratory experiments consisting of 1000 individual impacts across 22 snow column configurations. The columns are 60 cm tall with a 30 cm by 30 cm cross-section. The snow ranges in density from 135 to 428 kg m−3 and is loaded with both short-duration (~1 ms) and long-duration (~10 ms) impacts. The Maxwell-viscoelastic model more accurately describes snow's response because it contains a mechanism for energy dissipation, which the elastic model does not. Furthermore, the ascertained model parameters show a clear dependence on impact duration; shorter duration impacts resulted in higher wave speeds and greater damping coefficients. The stress wave's magnitude is amplified when it hits a stiffer material because of the positive interference between incident and reflected waves. This phenomenon is observed in the laboratory and modeled with the governing equations.

The column collapse experiment is a simplified version of natural and industrial granular flows. In this set-up, a column built with grains collapses and spreads over a horizontal plane. Granular flows are often studied with a monodisperse distribution; however, this is not the case in natural granular flows where a variety of grain sizes, known as polydispersity, is a common feature. In this work, we study the effect of polydispersity, and of the inherent changes that polydispersity causes in the initial packing fraction, in dry and immersed columns. We show that dry columns are not significantly affected by polydispersity, reaching similar distances at similar times. In contrast, immersed columns are strongly affected by the polydispersity and packing fraction, and the collapse sequence is linked to changes of the basal pore fluid pressure $P$. At the collapse initiation, negative changes of $P$ beneath the column produce a temporary increase of the column strength. The negative change of $P$ lasts longer in polydisperse columns than in monodisperse columns, delaying the collapse sequence. Conversely, during the column spreading, positive changes of $P$ lead to a decrease of the shear strength. For polydisperse collapses, the excess of $P$ lasts longer, allowing the material to reach farther distances, compared with the collapses of monodisperse materials. Finally, we show that a mobility model that scales the final runout with the collapse kinetic energy remains true for different polydispersity levels in a three-dimensional configuration, capturing the scaling between the micro to macro controlling features.

In the course of an artificially triggered avalanche, a particle tracking procedure is combined with supplementary measurements, including Global Navigation Satellite System (GNSS) positioning, terrestrial laser scanning and Doppler radar measurements. Specifically, an intertial measurement unit is mounted inside a rigid sphere, which is placed in the avalanche track. The sphere is entrained by the moving snow, recording translational accelerations, angular velocities and the flux density of Earth's magnetic field. Based on the recorded data, we present a threefold analysis: (i) a qualitative data interpretation, identifying different particle motion phases which are associated with corresponding flow regimes, (ii) a quantitative time integration algorithm, determining the corresponding particle trajectory and associated velocities on the basis of standard sensor calibration, and (iii) an improved quantitative evaluation relying on a novel in situ sensor calibration technique, which is motivated by the limitations of the given dataset. The final results, i.e. the evolution of the angular orientation of the sensor unit, translational and rotational velocities and estimates of the sensor trajectory, are assessed with respect to their reliability and relevance for avalanche dynamics as well as for future design of experiments.

Spatial variability of snowpack properties adds uncertainty in the evaluation of avalanche hazard. We propose a combined mechanical–statistical approach to study how spatial variation of slab depth affects the skier-triggering probability and possible release size. First, we generate multiple slab depth maps on a plane fictional slope based on Gaussian Random Fields (GRF) for a specific set of mean, variance and correlation length. For each GRF, we derive analytically the Skier Propagation Index (SPI). We then simulate multiple skier tracks and computed the probability based on the number of skier hits where SPI is below 1. Finally, we use a depth-averaged material point method to evaluate the possible avalanche size for given slab depth variations. The results of this analysis show that large correlation lengths and small variances lead to a lower probability of skier-triggering as it reduces the size and the number of areas with low slab depth. Then, we show the effect of skiing style and skier group size on skier-triggering probability. Spatial variability also affects the possible avalanche size by adding stress fluctuation causing early or late tensile failure. Finally, we demonstrate with our models the well-known relationship between the probability and the size in avalanche forecasting.

In this paper, transient granular flows are examined both numerically and experimentally. Simulations are performed using the continuous three-dimensional (3-D) granular model introduced in Daviet & Bertails-Descoubes (ACM Trans. Graph., vol. 35, no. 4, 2016b, p. 102), which represents the granular medium as an inelastic and dilatable continuum subject to the Drucker–Prager yield criterion in the dense regime. One notable feature of this numerical model is to resolve such a non-smooth rheology without any regularisation. We show that this non-smooth model, which relies on a constant friction coefficient, is able to reproduce with high fidelity various experimental granular collapses over inclined erodible beds, provided the friction coefficient is set to the avalanche angle – and not to the stop angle, as generally done. In order to better characterise the range of validity of the fully plastic rheology in the context of transient frictional flows, we further revisit scaling laws relating the shape of the final collapse deposit to the initial column aspect ratio, and accurately recover established power-law dependences up to aspect ratios of the order of 10. The influence of sidewall friction is then examined through experimental and simulated collapses with varying channel widths. The analysis offers a comprehensive framework for estimating the effective flow thickness in relation to the channel width, thereby challenging previously held assumptions regarding its estimation in the literature. Finally, we discuss the possibility to extend the constant coefficient model with a hysteretic model in order to refine the predictions of the early-stage dynamics of the collapse. This illustrates the potential effects of such phenomenology on transient flows, paving the way to more elaborate analysis.

Understanding the dynamics of snow avalanches is crucial for predicting their destructive potential and mobility. To gain insight into avalanche dynamics at a particle level, the AvaNode in-flow sensor system was developed. These synthetic particles, equipped with advanced and affordable sensors such as an inertial measurement unit (IMU) and global navigation satellite system (GNSS), travel with the avalanche flow. This study focuses on assessing the feasibility of the in-flow measurement systems. The experiments were conducted during the winter seasons of 2021–2023, both in static snow cover and dynamic avalanche conditions of medium-sized events. Radar measurements were used in conjunction with the particle trajectories and velocities to understand the behaviour of the entire avalanche flow. The dynamic avalanche experiments allowed to identify three distinct particle flow states: (I) initial rapid acceleration, (II) a steady state flow with the highest velocities (9–17 ms−1), and (III) a longer deceleration state accompanied by the largest measured rotation rates. The particles tend to travel towards the tail of the avalanche and reach lower velocities compared to the frontal approach velocities deduced from radar measurements (ranging between 23–28 ms−1). The presented data give a first insight in avalanche particle measurements.

Liquid water at the ground–snow interface is thought to play a crucial role in the release of glide-snow avalanches, which can be massive and threaten infrastructure in alpine regions. Several mechanisms have been postulated to explain the formation of this interfacial water. However, these mechanisms remain poorly understood, in part because suitable measurement techniques are lacking. Here, we demonstrate the use of neutron radiography for imaging water transport in soil–snow systems. Columns of sand, gravel and snow were used to simulate the capillary forces of the soil–vegetation–snow layering found in nature. The columns were connected to a water reservoir to maintain a constant-pressure boundary condition and placed in a climatic chamber within the neutron beam. We show that neutron radiography is capable of measuring changes in the optical density distribution (related to liquid water content) within all three layers of the model system. Results suggest that a porous interface between the sand and snow may induce the formation of a water layer in the basal snowpack. Improved understanding of the water transport in soil–snow systems should lead to better prediction of glide-snow avalanche release and could also benefit other fields such as snow hydrology.

Hydrodynamic approaches that treat granular materials as a continuum via the homogenization of discrete flow properties have become viable options for efficient predictions of bulk flow behaviours. However, simplified boundary conditions in computational fluid dynamics are often adopted, which have difficulty in describing the complex stick–slip phenomenon at the boundaries. This paper extends the lattice Boltzmann method for granular flow simulations by incorporating a novel frictional boundary condition. The wall slip velocity is first calculated based on the shear rate limited by the Coulomb friction, followed by the reconstruction of unknown density distribution functions through a modified bounce-back scheme. Validation is performed against a unique plane Couette flow configuration, and the analytical solutions for the flow velocity profile and the wall slip velocity, as functions of the friction coefficient, are reproduced by the numerical model. The transition between no-slip and partial-slip regimes is captured well, but the convergence rate drops from second order to first order when slip occurs. The rheological parameters and the basal friction coefficient are calibrated further against the discrete element simulation of a square granular column collapsing over a horizontal bottom plane. It is found that the calibrated continuum model can predict other granular column collapses with different initial aspect ratios and slope inclination angles, including the basal slip and the complex internal flow structures, without any further adjustments to the model parameters. This highlights the generalization ability of the numerical model, which has a wide range of application in granular flow predictions and controls.

The snow compression test is a snow stability test where an isolated column of snow is progressively loaded by tapping on it to induce failure in a possible weak layer. The test result provides valuable information about the propensity of failure initiation within the snowpack. However, different persons might tap with different force and thus reduce the reproducibility of the test results. The aim of this work was to quantify the influence of different test persons and different snowpacks on snow compression test results. We therefore let 62 persons tap on a stress measurement plate during a workshop of the European Avalanche Warning Services. Moreover, in the field, we performed stress measurements during 116 snow compression tests with 13 persons at eight different locations in the Alps. Data on persons’ body features and snow properties were also collected. Our results show that the stresses that reach a weak snow layer due to tapping are influenced by both the snowpack as well as different persons. Still, the data's scattering is surprisingly small for lower loading steps and decreases with depth. Therefore, we can deduce that, especially when avalanche conditions are particularly dangerous, snow compression test results are quite reproducible.

Glide-snow avalanches release due to a loss of friction at the snow–ground interface, which can result in large avalanches that endanger infrastructure in alpine regions. The underlying processes are still relatively poorly understood, in part due to the limited data available on glide processes. Here, we introduce a pixel-based algorithm to detect glide cracks in time-lapse photographs under changing illumination and shadow conditions. The algorithm was applied to 14 years of time-lapse images at Dorfberg (Davos, Switzerland). We analysed 947 glide-snow events at a high-spatial (0.5 m) and temporal (2–15 min) resolution. Avalanche activity and glide-crack opening dynamics were investigated across timescales ranging from seasonally to hourly. Events were separated into surface (meltwater percolation) and interface events (no meltwater percolation). The results show that glide activity is highly variable between and within seasons. Most avalanches released without crack formation or within 24 h after crack opening, and release was favoured in the afternoon hours. Glide rates often showed a stick–slip behaviour. The acceleration of glide rates and non-constant increases in glide crack aspect ratio were indicators for avalanche release. This comprehensive dataset provides the basis for further investigations into glide-snow avalanche drivers.

Viscous flow around two spherical macroscopic cavities (or void spaces) in a granular material, which is exposed to an otherwise uniform flow at infinity, is investigated. The flow field is obtained analytically by solving the Stokes equation inside and the Darcy–Brinkman equation outside of the cavities, where continuity of the velocity and that of the stress are assumed on the boundary. In our previous complementary paper (Sano, Karmakar & Sekhar, J. Fluid Mech., vol. 931, 2022, A20), we obtain that two cavities of equal size in a tandem position are more prone to collapse for a shorter centre-to-centre distance with low permeability. In the present study, the asymptotic analysis of the interaction of two spherical cavities of different sizes with arbitrary configuration is presented. Particular attention is paid to the configuration dependence of two cavities of equal radius. The velocity field and the volume flux into respective cavities are calculated, which reveal that two cavities with orientation less than a certain critical angle are given a larger volume flux and are more prone to collapse. The present results are applicable to predicting the behaviour in a fixed-bed regime of a solid–gas transport system, microscale waterway formation in a granular material, onset of landslides, collapse of cliffs and river banks, etc.

Dry-snow slab avalanches release due to crack propagation in a weak snow layer under a cohesive snow slab. Crack propagation speeds can provide insights into the potential size of avalanches and inform fracture and avalanche release models. Despite their importance, slope-scale crack speed measurements from real avalanches are limited. Further, most existing slope-scale measurements utilize the appearance of slab fractures on the snow surface. However, we have no evidence that the appearance of surface cracking is a good indicator of the weak layer crack propagation tip. Here we present a novel method to estimate crack propagation speed from snow surface movements in avalanche videos. Our technique uses changes in frame pixel intensity, allowing us to detect the location of weak layer cracks well before slab fractures appear on the snow surface. We use field experiments and numerical simulations to validate our method before applying it to five avalanches. Our estimates show that cracks propagate faster up and down the slope than in the cross-slope direction; this suggests that different propagation regimes likely govern crack propagation up/down the slope, cross-slope and in flat terrain.

Wet-snow avalanches are triggered by the infiltration of liquid water which weakens the snowpack. Wet-snow avalanches are among the most destructive avalanches, yet their release mechanism is not sufficiently understood for a process-based prediction model. Therefore, we followed a data-driven approach and developed a random forest model, depending on slope aspect, to predict the local wet-snow avalanche activity at the locations of 124 automated weather stations distributed throughout the Swiss Alps. The input variables were the snow and weather data recorded by the stations over the past 20 years. The target variable was based on manual observations over the same 20-year period. To filter out erroneous reports, we defined the days with wet-snow avalanches in a stringent manner, selecting only the most extreme active or inactive days, which reduced the size of the dataset but increased the reliability of the target variable. The model was trained with weather variables and variables computed from simulated snow stratigraphy in 38$^\circ$ slopes facing the 4 cardinal directions. While model development and validation were done in nowcast mode, we also studied model performance in 24-hour forecast mode by using input variables computed from a numerical weather prediction (NWP) model. Overall, the performance was good in both nowcast and forecast mode (f1-score around 0.8). To assess model performance beyond the stringent definition of wet-snow avalanche days, we compared model predictions to wet-snow avalanche activity over the entire Swiss Alps, based on the raw data over 8 winters. We obtained a Spearman correlation coefficient of 0.71. Hence, our model represents a step toward the application of support tools in operational wet-snow avalanche forecasting.

It has been reported that, in submarine landslides down a slope, only a small part of the landslide momentum was transferred to the tsunami while most was lost in the further propagation over the flat bed. The high momentum of landslides off a slope meant a long run-out and a great impact on underwater infrastructure. Nevertheless, little attention has been paid to the variation of momentum of deformable submarine landslides off a slope, i.e. the loss of momentum when the slides flow away from the slope over a flat bottom. In this paper, the translational momentum of deformable submarine granular landslides running down a non-erodible inclined bed is investigated with a two-phase smoothed particle hydrodynamics model. After flowing down the slope, the transport rate and flux of the landslide translational momentum along the propagation over the flat bottom are examined. The effects of physical variables of the slide, particularly the grain size, the initial compaction and the front intrusion angle on the variation of the translational momentum, are explored. Accordingly, scaling relations of the spatial-temporal maximum transport rate and flux of the landslide translational momentum, as well as those of the slide final run-out and the generated leading wave height, are proposed. These scaling relations, although based on numerical data of small-scale granular landslides, demonstrate a preliminary attempt to develop practical expressions in the framework of momentum for estimating the run-out of real submarine landslides and the impact on underwater infrastructure.

Many granular surface flows occur as shear flows of finite thickness, over erodible beds composed of the same granular material. Such beds may be fragile, and offer no more resistance to erosion than to sustained shear. Or they may be brittle, and offer instead an excess resistance to erosion. To take this contrast into account, new basal boundary conditions are proposed. Their implications for parallel flows down infinite slopes are then examined for three different cases: stationary flows; starting; and stopping transients. For all three cases, flow behaviour is altered significantly when beds present an excess resistance to erosion. For stationary flows, non-unique velocity profiles are obtained, implying hysteresis or history-dependence. For starting transients, a power law growth of the flow thickness is predicted, instead of the jump to finite or infinite depth that would otherwise occur. For stopping transients, flows start to decelerate with a finite basal shear rate, even over erodible substrates. Analytical solutions to the corresponding free and moving boundary problems are obtained, and checked against numerical results. Model predictions are then compared with experimental measurements. Overall, good agreement is obtained. In particular, the model describes well the very different erosional responses observed for fragile and brittle beds.

Geophysical mass flows such as debris flows, dense pyroclastic flows and snow avalanches can self-channelize on shallow slopes. The confinement afforded by formed levees helps to maintain the flow depth, and hence mobility, allowing self-channelized flows to run out significantly farther than unconfined, spreading flows. Levee formation and self-channelization are strongly associated with particle-size segregation, but can also occur in monodisperse flows. This paper uses the monodisperse depth-averaged theory of Rocha et al. (J. Fluid Mech., vol. 876, 2019, pp. 591–641), which incorporates a hysteretic friction law and second-order depth-averaged viscous terms. Both of these are vital for the formation of a travelling wave that progressively deposits a pair of levees just behind the front. The three-dimensional velocity field is reconstructed in a frame moving with the front assuming Bagnold flow. This enables a bidisperse particle-size segregation theory to be used to solve for the large and small particle concentrations and particle paths in three-dimensions, for the first time. The model shows that the large particles tend to segregate to the surface of the flow, forming a carapace that extends over the centre of the channel, as well as along the external sides and base of the levee walls. The small particles segregate downwards, and are concentrated in the main channel and in the inner levee walls. This supports the contention that a low-friction channel lining provides a secondary mechanism for run-out enhancement. It is also shown that the entire theory scales with particle diameter, so experiments with millimetre-sized particles provide important insights into geophysical-scale flows with boulders and smaller rock fragments. The model shows that self-channelization does not need particle-size segregation to occur, but supports the hypothesis that particle-size segregation and the associated frictional feedback can significantly enhance both the flow mobility and the levee strength.