Granular Avalanches Research Articles

The Erosion Pattern and Hidden Momentum in Debris‐Flow Surges Revealed by Simple Hydraulic Jump Equations

AbstractThe erosion‐deposition propagation of granular avalanches is prevalent and may increase their destructiveness. However, this process has rarely been reported for debris flows on gentle slopes, and the contribution of momentum hidden under the surge front to debris‐flow destructiveness is ambiguous. Therefore, the momentum carried by the apparent surge front is often used to indicate debris‐flow destructiveness. In this study, the erosion‐deposition propagation is confirmed by surge‐depth hydrographs measured at the Jiangjia Ravine (Yunnan Province, China). Based on simple hydraulic jump equations, the eroded deposition depth of surge flow is quantified, and the erosion pattern can be divided into two patterns (shallow and deep erosion). For surge flows with erosion‐deposition propagation, significant downward erosion potential is confirmed, and debris‐flow surge erosion is considered the deep erosion. The total momentum carried by surge flow is further quantified by two Froude numbers (surge‐front and rearward Froude numbers) and verified through the field observation of surge flows. The total momentum of surge flow not only originates from the apparent surge front, but also includes the momentum within the eroded deposition layer. This study provides a theoretical approach for quantifying the upper limit of erosion depth and revealing the destructiveness of debris‐flow surges. A perspective on the importance of substrate deposition for debris‐flow erosion on gentle slopes is emphasized, as this approach can improve the reliability of debris‐flow risk assessment.

Scale‐Dependent Processes and Runout in Bidisperse Granular Flows: Insights From Laboratory Experiments and Implications for Rock/Debris Avalanches

AbstractThe bidispersity observed in the particle‐size distribution of rock avalanches and volcanic debris avalanches (rock/debris avalanches) has been proposed as a factor contributing to their long runout. This has been supported by small‐scale analog experimental studies, which observe that a small proportion of fine particles mixed with coarser particles enhances granular avalanche runout. However, the mechanisms enabling this phenomenon and their resemblance to rock/debris avalanches have not been directly evaluated. Here, binary mixture granular avalanche experiments are employed to constrain the processes and conditions under which bidispersity enhances the runout of granular avalanches in experiments. Structure‐from‐motion photogrammetry is used to measure center of mass displacement and assess energy dissipation. Subsequently, this study evaluates the dynamic scaling and flow regimes in the lab and field to assess whether the runout‐enhancing mechanism is applicable to rock/debris avalanches. In small‐scale experiments, the granular mass propagates under a collisional regime, enabling kinetic sieving and size segregation. Fine particles migrate to the base where they reduce frictional areas between coarse particles and the substrate and encourage rolling. The reduced energy dissipation increases the kinetic energy conversion and avalanche mobility. However, rock/debris avalanches are unlikely to acquire a purely collisional regime; instead, they propagate under a frictional regime. The size segregation which is essential for the process observed at the lab‐scale is prohibited by the frictional regime, as evident by the sedimentology of rock/debris avalanche deposits. The proposal of bidispersity as a runout‐enhancing mechanism overlooks that scale‐dependent behaviors of natural events are often omitted in small‐scale experiments.

Inner structures of rapid free-surface granular avalanche over a small bump obstacle: Expansion fan, oblique shock wave, and contact anisotropy

This study investigates the inner flow characteristics of a rapid granular avalanche passing over a small bump obstacle fixed on an inclined chute using the discrete element method. Both the cross-sectional mean flow properties, such as free-surface height, mean flow velocity, and mean stresses, and the inner local flow properties, including granular temperature, coordination number, pressure, contact force orientation, and granular fabrics, were comprehensively investigated. Upstream of the obstacle, a wide compression region where mean stresses strengthen and exhibit anisotropy was observed. Employing the kinetic theory of granular gas, we revealed a smooth supersonic-to-subsonic transition near the obstacle, a phenomenon distinct from typical gas dynamics. These upstream flow phenomena are attributed to the generation of stream-wise-oriented contact force chains as the flow impacts the obstacle. Downstream of the obstacle, a complex non-monotonic expansion–compression–expansion process was observed. We demonstrated that this non-monotonic flow process reflects an inner gasdynamic-like phenomenon characterized by an expansion fan followed by an oblique shock wave. Moreover, the force chains and the inner shock structure were found to significantly influence the evolution of stream-wise velocity profiles. These findings underscore the significance of inner flow structures in shaping the dynamics of granular avalanche flow interacting with obstacles.

A continuum model of discrete granular avalanches

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.

The prediction of dynamical quantities in granular avalanches based on graph neural networks.

The study of granular avalanches in rotating drums is not only essential to understanding various complex behaviors of interest in granular media from a scientific perspective; it also has valuable applications in regard to industrial processes and geological catastrophes. Despite decades of research studies on avalanches, a proper understanding of their dynamic properties still remains a great challenge to scientists due to a lack of state-of-the-art techniques. In this study, we accurately predict the avalanche dynamic features of three-dimensional granular materials in rotating drums, by using graph neural networks on the basis of their initial static microstructures alone. We find that our method is robust to changes in various model parameters, such as the interaction potential, size polydispersity, and noise in particle coordinates. In addition, with the grain-scale velocities obtained either from our network or from numerical simulations, we find an approximately equal and strong correlation between the global velocity and global velocity fluctuation in our 3D granular avalanche systems, which further demonstrates the predictive power of our trained graph neural networks to uncover the fundamental physics of granular avalanches. We expect our method to provide more insight into the avalanche dynamics of granular materials and other amorphous systems in the future.

Velocity effect on the impact dynamics of high-speed granular avalanches based on centrifuge modeling and DEM simulations

The design strategies for barrier structures against high-speed granular impacts are still lacking, because the granular impact dynamics is poorly understood. We have investigated the impact behavior of high-speed granular avalanches with different velocities (7–20 m/s) using the centrifuge modeling and DEM simulation. The results indicate that the peak total impact force should be calculated as the sum of the dynamic and static components, and the impact force distribution mode can be treated as having a rectangular shape. For granular impacts with velocities of 7–20 m/s, the dynamic component can be calculated based on the hydraulic dynamic model fed the maximum values of the flow depth, velocity, and density. The static component can be estimated using Coulomb's earth pressure theory using the dead zone weight based on an assumption of the static failure mode of the dead zone and with the flow–dead zone interaction-induced force being implicitly considered.

Flow pattern of fast granular flow impacting a granular deposit

There are intricate and intriguing flow structures in interaction between fast granular flow and an existing deposit, significantly affecting the development of granular avalanches. This study examines the dynamic interaction for six different steep terrains using the depth-integrated Savage–Hutter model. Results reveal three distinct flow patterns, which are the propagating shock mode, stationary shock mode, and runup mode. In the propagating shock mode, a stable bow shock formed by the fast flow impacting propagates upstream. The stationary shock mode forms a nearly flat, stationary shock upon impact. A new normal shock relationship for granular flow is developed by considering the effect of earth pressure, which can be reduced to classical shock relationship for both stationary and propagating shocks on highly inclined slopes, and agrees well with the numerical predictions. However, on low-degree slopes, the predictions accord with the modified shock relationship accounting for different types of earth pressure.

Experimental and numerical investigation on the collapse of annular columns of dry granular matter

The collapse of a granular column confined in a vertical annulus is investigated through both experiments and DEM. During the collapse of column, an outward-moving avalanche and a unique shape of final deposit are commonly observed. In contrast, the present problem involves an inward granular avalanche towards the center of the annulus along with an outward avalanche. The final deposit profile has been categorized into four different cases involving single or double peaks and valley in between based on the aspect ratio. Apart from the mild effect of the coefficient of friction, no other particle properties influence the shape of the deposit. Removal speed of the confining walls strongly affects the speed of the avalanche but not the deposit shape. Scaling analyses show a power law dependence of runout distance on aspect ratio and a linear dependence of event duration on the free fall time of a grain.

Dune slope, not wind speed, best predicts bare sand in vegetated coastal dunes

Globally vegetation cover on coastal sand dunes has increased since at least the 1950s. With the aim of restoring or increasing biodiversity, land managers in several countries have removed vegetation and/or reprofiled dune slopes to reinvigorate geomorphic activity. However, the longevity of these interventions can be relatively short (on the order of 5 to 10 years), and further active management is required. Hypotheses for controls on geomorphic activity on dunes have frequently suggested that wind speedis the most important controlling factor. Here we show dune slope to be the best predictor of bare sand at four predominantly vegetated coastal sand dunes in England and Wales. We suggest that bare sand on steep dune slopes is maintained by three important factors: (1) Wind erosion, due to topographic acceleration (2) Granular avalanches of unconsolidated sediment and (3) Rotational slumping of unstable slopes. Our results indicate that where land managers wish to ‘rejuvenate’ areas of bare sand, efforts should focus on steep windward dune slopes and reprofiling of the dune slope should mimic the concave profiles of active slope faces on active parabolic dunes with an overall slope angle of between 18° and 23° from the dune toe to the crest.

μ(J)-Rheology-based depth-averaged dynamic model for roll waves in granular–fluid avalanches

A depth-averaged two-dimensional mathematical model of granular-fluid avalanches is proposed based on the μ(J) rheology. In the model, a depth-averaged deviatoric viscous stress of granular-fluid mixture is formulated and the corresponding depth-integration term is linearly proportional to the flow depth, which is different from the 1.5th-power law for dry granular avalanches. A basal resistance on the granular-fluid mixture, composed of a Coulomb friction term and a viscous shear term, is adopted in the model. Based on the model, a critical Froude number of 1/2 is obtained for the linear instability of steady-uniform granular-fluid mixture flows. The model is capable of capturing the cutoff frequency for the spatial growth rate of perturbation in the mixture flows. The proposed model is applied to simulate the evolution of imposed perturbations in steady granular-fluid avalanches on an inclined chute. The intensification of imposed perturbations and the generation of final stable roll waves are captured. A parameter sensitivity analysis is conducted to investigate the effects of the depth-averaged in-plane deviatoric viscous stress and the basal resistance on the final stable roll waves. Further, a preliminary analytical solution for the crest/trough heights of the stable roll waves is proposed to verify the numerical findings.

Granular avalanche statistics in rotating drum with varied particle roughness

Granular avalanche statistics in rotating drum with varied particle roughness

Multiscale acoustics in dense granular media; geophysical implications

We overview sound interactions with dense granular packings, dry, wet or saturated by liquid, in which acoustic waves are served not only as a probe to monitor the fragile and heterogeneous contact networks, but also as a pump to fluidize the medium and trigger the shear instability. First, we describe the linear sound propagation in jammed granular solid: coherent waves and multiple scattering [1], as well as acoustic probing of elastic heterogeneities [2], and plastic rearrangements [3]. Then, we investigate the nonlinear acoustic waves dominated by the hysteresis due to micro-slips at contacts [4] and the huge softening of shear wave velocity in transient elastography [5]. Finally, we discuss the triggering of granular avalanches by high-amplitude ultrasound [6], through the acoustic lubrication of contacts (micro-plasticity) without visible grains motions. This work helps to understand landslides triggered by seismicity. [1] X. Jia, Phys. Rev. Lett. 93, 154303 (2004). [2] S. Wildenberg et al., Europhys. Lett. 115, 34005 (2016). [3] Y. Khidas and X. Jia, Phys. Rev. Express 85, 051304 (2012). [4] X. Jia, T. Brunet, and J. Laurent, Phys. Rev. Express 84, 020301(R) (2011). [5] J. Brum et al., Phys. Rev. Eexpress 99, 042902 (2019). [6] J. Léopoldès, X. Jia, A. Tourin, and A. Mangeney, Phys. Rev. Express 102, 042901 (2020).

Keynote lecture. Granular flows

Our understanding of granular flows has progressed considerably over the past two decades. In this talk, I will first review the advances made in the rheology of dense granular media based on the concept of pressure-imposed rheology, discussing the different regimes, from viscous to inertial. I will also illustrate how these rheological descriptions can be used in a two-phase flow approach to model more complex flow configurations, at least in simple small scaled experiments mimicking granular avalanche flows. Can these advances help describe and predict debris flows, is not an easy question, which I will try to discuss by pointing out the limitations and robustness of the rheological models.

Improved Model for Granular Avalanches

A well-posed multilayer model involving a dilatancy law is developed and systematically compared to three different experimental scenarios.

A well-posed multilayer model for granular avalanches: Comparisons with laboratory experiments

Granular avalanches are dangerous phenomena characterized by the rapid gravity-driven motion of granular solids. The complex dynamics of these flows can be effectively modeled by a multilayer approach, which, however, requires particular attention to the derivation of the model equations in order to allow stable solutions. In this work, we use a well-posed multilayer model, in which the μ(I)-rheology is employed and a dilatancy law, depending on the inertial number I, is also taken into account, and systematically compare it with various laboratory experiments. The model, whose well-posedness is guaranteed by a physically based viscous regularization, describes the evolution of a preset number of superimposed granular layers. As the sidewall friction is relevant under most experimental conditions, the model is fitted here with suitable resistance terms. Moreover, non-trivial closures for the mass exchanges are introduced to avoid any unrealistic partitioning of the flow domain during the avalanche evolution, and, hence, guarantee a regular spatial discretization along the normal to flow direction. The velocity fields are compared with different experiments in unsteady state, and comparisons of both velocity and volume fraction profiles are provided with steady uniform flow experiments. The results confirm the good capabilities of the multilayer model and the underlying μ(I)-rheology in capturing the granular flow dynamics. The experimental volume fraction profiles are qualitatively well reproduced by the proposed dilatancy law, while an overestimation is observed only in the upper, more dilute flow region with a thickness of a few grain diameters.

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

• Critical conditions for the onset of macro scale avalanches are presented. • Onset of macro scale avalanches occur in the small area in granular layers. • Stresses and packing fractions reach the maxima at the onset of avalanches. • Both of dilatancy and densification occur at the same time in granular layers. • Aggregates of stick-slip like events are formed in the longitudinal direction. 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.

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.

A bed pressure correction of the friction term for depth-averaged granular flow models

Depth-averaged models, such as the Savage-Hutter model with Coulomb or Pouliquen friction laws, do not in some cases preserve the physical threshold of motion. In particular, the simulated granular mass can start to flow (or stay at rest) even if the slope angle of its free surface is lower (or higher) than the repose angle of the granular material involved. The problem is related to the hydrostatic pressure assumption, associated with the direction of integration, which is orthogonal to a reference plane or a reference bottom. We propose here an initial method to correct this misleading behavior. Firstly, we define a correction of the friction term that accounts for the Jacobian of a change of coordinates, making it possible to reproduce the physical threshold of motion and thus the solutions at rest. Secondly, we observe that the 3D model presented in [F. Bouchut, I. Ionescu, and A. Mangeney. An analytic approach for the evolution of the static-flowing interface in viscoplastic granular flows. Commun, Math. Sci., 14(8):2101–2126, 2016] verifies the physical thresholds of motion because it is based on a second order correction of the pressure valid for slow granular flows. The correction proposed here ensures that the model preserves, up to the second order, the physical threshold of motion defined by the repose angle of the material. Several numerical tests are presented to illustrate certain problems related to classical depth averaged models and the remedial effect of the proposed correction, in particular through comparisons with experimental data. We finally show that this correction is not exact far from the starting and stopping phases of the granular avalanche and should be improved by adding other second order terms in the pressure approximation.

Numerical investigation of the effect of cohesion and ground friction on snow avalanches flow regimes.

With ongoing global warming, snow avalanche dynamics may change as snow cohesion and friction strongly depend on temperature. In the field, a diversity of avalanche flow regimes has been reported including fast, sheared flows and slow plugs. While the significant role of cohesion and friction has been recognized, it is unclear how these mechanical properties affect avalanche flow regimes. Here, we model granular avalanches on a periodic inclined plane, using the distinct element method to better understand and quantify how inter-particle cohesion and ground friction influences avalanche velocity profiles. The cohesion between particles is modeled through bonds that can subsequently break and form, thus representing fragmentation and aggregation potentials, respectively. The implemented model shows a good ability to reproduce the various flow regimes and transitions as observed in nature: for low cohesion, highly sheared and fast flows are obtained while slow plugs form above a critical cohesion value and for lower ground frictions. Simulated velocity profiles are successfully compared to experimental measurements from the real-scale test site of Vallée de la Sionne in Switzerland. Even though the model represents a strong simplification of the reality, it offers a solid basis for further investigation of relevant processes happening in snow avalanches, such as segregation, erosion and entrainment, with strong impacts on avalanche dynamics research, especially in a climate change context.

The concept of the mobilized domain: how it can explain and predict the forces exerted by a cohesive granular avalanche on an obstacle

The calculation of the impact pressure on obstacles in granular flows is a fundamental issue of practical relevance, e.g. for snow avalanches impacting obstacles. Previous research shows that the load on the obstacle builds up, due to the formation of force chains originating from the obstacle and extending into the granular material. This leads to the formation of a mobilized domain, wherein the flow is influenced by the presence of the obstacle. To identify the link between the physical mobilized domain properties and the pressure exerted on obstacles, we simulate subcritical cohesionless and cohesive avalanches of soft particles past obstacles with circular, rectangular or triangular cross-section using the Discrete Element Method. Our results show that the impact pressure decreases non-linearly with increasing obstacle width, regardless of the obstacle’s cross-section. While the mobilized domain size is proportional to the obstacle width, the pressure decrease with increasing width originates from the jammed material inside the mobilized domain. We provide evidence that the compression inside the mobilized domain governs the pressure build-up for cohesionless subcritical granular flows. In the cohesive case, the stress transmission in the compressed mobilized domain is further enhanced, causing a pressure increase compared with the cohesionless case. Considering a kinetic and a gravitational contribution, we are able to calculate the impact pressure based on the properties of the mobilized domain. The equations used for the pressure calculation in this article may be useful in future predictive pressure calculations based on mobilized domain properties.Graphic