Numerical investigation of crack propagation regimes in snow fracture experiments.

A snow slab avalanche releases after failure initiation and crack propagation in a highly porous weak snow layer buried below a cohesive slab. While our knowledge of crack propagation during avalanche formation has greatly improved over the last decades, it still remains unclear how snow mechanical properties affect the dynamics of crack propagation. This is partly due to a lack of non-invasive measurement methods to investigate the micro-mechanical aspects of the process. Using a DEM model, we therefore analyzed the influence of snow cover properties on the dynamics of crack propagation in weak snowpack layers. By focusing on the steady-state crack speed, our results showed two distinct fracture process regimes that depend on slope angle, leading to very different crack propagation speeds. For long experiments on level terrain, weak layer fracture is mainly driven by compressive stresses. Steady-state crack speed mainly depends on slab and weak layer elastic moduli as well as weak layer strength. We suggest a semi-empirical model to predict crack speed, which can be up to 0.6 times the slab shear wave speed. For long experiments on steep slopes, a supershear regime appeared, where the crack propagation speed reached approximately 1.6 times the slab shear wave speed. A detailed micro-mechanical analysis of stresses revealed a fracture principally driven by shear. Overall, our findings provide new insight into the micro-mechanics of dynamic crack propagation in snow, and how these are linked to snow cover properties. Supplementary Information: The online version contains supplementary material available at 10.1007/s10035-024-01423-5.

Transition from sub-Rayleigh anticrack to supershear crack propagation in snow avalanches.

Snow slab avalanches, characterized by a distinct, broad fracture line, are released following anticrack propagation in highly porous weak snow layers buried below cohesive slabs. The anticrack mechanism is driven by the volumetric collapse of the weak layer, which leads to the closure of crack faces and to the onset of frictional contact. Here, on the basis of snow fracture experiments, full-scale avalanche measurements and numerical simulations, we report the existence of a transition from sub-Rayleigh anticrack to supershear crack propagation. This transition follows the Burridge-Andrews mechanism, in which a supershear daughter crack nucleates ahead of the main fracture front and eventually propagates faster than the shear wave speed. Furthermore, we show that the supershear propagation regime can exist even if the shear-to-normal stress ratio is lower than the static friction coefficient as a result of the loss of frictional resistance during collapse. This finding shows that snow slab avalanches have fundamental similarities with strike-slip earthquakes.

Microstructural Origin of Propagating Compaction Patterns in Porous Media.

Porous rocks, foams, cereals, and snow display a diverse set of common compaction patterns, including propagating or stationary bands. Although this commonality across distinct media has been widely noted, the patterns' origin remains debated-current models employ empirical laws for material-specific processes. Here, using a generic model of inelastic structured porous geometries, we show that the previously observed patterns can be attributed to a universal process of pore collapse. Furthermore, the pattern diversity can be mapped in a phase space of only two dimensionless numbers describing material strength and loading rate.

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.

Three-dimensional and real-scale modeling of flow regimes in dense snow avalanches.

Snow avalanches cause fatalities and economic loss worldwide and are one of the most dangerous gravitational hazards in mountainous regions. Various flow behaviors have been reported in snow avalanches, making them challenging to be thoroughly understood and mitigated. Existing popular numerical approaches for modeling snow avalanches predominantly adopt depth-averaged models, which are computationally efficient but fail to capture important features along the flow depth direction such as densification and granulation. This study applies a three-dimensional (3D) material point method (MPM) to explore snow avalanches in different regimes on a complex real terrain. Flow features of the snow avalanches from release to deposition are comprehensively characterized for identification of the different regimes. In particular, brittle and ductile fractures are identified in the different modeled avalanches shortly after their release. During the flow, the analysis of local snow density variation reveals that snow granulation requires an appropriate combination of snow fracture and compaction. In contrast, cohesionless granular flows and plug flows are mainly governed by expansion and compaction hardening, respectively. Distinct textures of avalanche deposits are characterized, including a smooth surface, rough surfaces with snow granules, as well as a surface showing compacting shear planes often reported in wet snow avalanche deposits. Finally, the MPM modeling is verified with a real snow avalanche that occurred at Vallée de la Sionne, Switzerland. The MPM framework has been proven as a promising numerical tool for exploring complex behavior of a wide range of snow avalanches in different regimes to better understand avalanche dynamics. In the future, this framework can be extended to study other types of gravitational mass movements such as rock/glacier avalanches and debris flows with implementation of modified constitutive laws. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10346-021-01692-8.

Micro-mechanical insights into the dynamics of crack propagation in snow fracture experiments.

Dry-snow slab avalanches result from crack propagation in a highly porous weak layer buried within a stratified and metastable snowpack. While our understanding of slab avalanche mechanisms improved with recent experimental and numerical advances, fundamental micro-mechanical processes remain poorly understood due to a lack of non-invasive monitoring techniques. Using a novel discrete micro-mechanical model, we reproduced crack propagation dynamics observed in field experiments, which employ the propagation saw test. The detailed microscopic analysis of weak layer stresses and bond breaking allowed us to define the crack tip location of closing crack faces, analyze its spatio-temporal characteristics and monitor the evolution of stress concentrations and the fracture process zone both in transient and steady-state regimes. Results highlight the occurrence of a steady state in crack speed and stress conditions for sufficiently long crack propagation distances (> 4 m). Crack propagation without external driving force except gravity is possible due to the local mixed-mode shear-compression stress nature at the crack tip induced by slab bending and weak layer volumetric collapse. Our result shed light into the microscopic origin of dynamic crack propagation in snow slab avalanche release that eventually will improve the evaluation of avalanche release sizes and thus hazard management and forecasting in mountainous regions.

Microscopic Origin of Nonlocal Rheology in Dense Granular Materials.

We study the microscopic origin of nonlocality in dense granular media. Discrete element simulations reveal that macroscopic shear results from a balance between microscopic elementary rearrangements occurring in opposite directions. The effective macroscopic fluidity of the material is controlled by these velocity fluctuations, which are responsible for nonlocal effects in quasistatic regions. We define a new micromechanically based unified constitutive law describing both quasistatic and inertial regimes, valid for different system configurations.

Microstructural controls of anticrack nucleation in highly porous brittle solids.

Porous brittle solids have the ability to collapse and fail even under compressive stresses. In fracture mechanics, this singular behavior, often referred to as anticrack, demands for appropriate continuum models to predict the catastrophic failure. To identify universal controls of anticracks, we link the microstructure of a porous solid with its yield surface at the onset of plastic flow. We utilize an assembly method for porous structures, which allows to independently vary microstructural properties (density and coordination number) and perform discrete element simulations under mixed-mode (shear-compression) loading. In rescaled stress coordinates, the concurrent influence of the microstructural properties can be cast into a universal, ellipsoidal form of the yield surface that reveals an associative plastic flow rule, as a common feature of these materials. Our results constitute a constructive approach for continuum modeling of anticrack nucleation and propagation in highly porous brittle, engineering and geo-materials.

Numerical investigation of the mixed-mode failure of snow.

The failure of a weak snow layer underlying a cohesive slab is the primary step in the release process of a dry snow slab avalanche. The complex and heterogeneous microstructure of snow limits our understanding of failure initiation inside the weak layer, especially under mixed-mode shear-compression loading. Further complication arises from the dependence of snow strength on the loading rate induced by the balance between bond breaking and bond formation (sintering) during the failure process. Here, we use the discrete element method to investigate the influence of mixed-mode loading and fast sintering on the failure of a weak layer generated using cohesive ballistic deposition. Both fast and slow loading simulations resulted in a mixed-mode failure envelope in good agreement with laboratory experiments. We show that the number of broken bonds at failure and the weak layer strength significantly decreases with increasing loading angle, regardless of the loading rate. While the influence of loading rate appears negligible in shear-dominant loading (for loading angles above 30 ∘ ), simulations suggest a significant increase in the weak layer strength at low loading angles and low loading rates, characteristic of natural avalanches, due to the presence of an active sintering mechanism.

Scaling laws for the mechanics of loose and cohesive granular materials based on Baxter's sticky hard spheres.

We have conducted discrete element simulations (pfc3d) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxter's sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number z_{c} of cohesive contacts and particle volume fraction ϕ of the initial states. We focus on discerning the role of z_{c} and ϕ for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density ν_{c}=z_{c}ϕ of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure.

Quasistatic to inertial transition in granular materials and the role of fluctuations.

On the basis of discrete element numerical simulations of a Couette cell, we revisit the rheology of granular materials in the quasistatic and inertial regimes, and discuss the origin of the transition between these two regimes. We show that quasistatic zones are the seat of a creep process whose rate is directly related to the existence and magnitude of velocity fluctuations. The mechanical behavior in the quasistatic regime is characterized by a three-variable constitutive law relating the friction coefficient (normalized stress), the inertial number (normalized shear rate), and the normalized velocity fluctuations. Importantly, this constitutive law appears to remain also valid in the inertial regime, where it can account for the one-to-one relationship observed between the friction coefficient and the inertial number. The abrupt transition between the quasistatic and inertial regimes is then related to the mode of production of the fluctuations within the material, from nonlocal and artificially sustained by the boundary conditions in the quasistatic regime, to purely local and self-sustained in the inertial regime. This quasistatic-to-inertial transition occurs at a critical inertial number or, equivalently, at a critical level of fluctuations.