Dynamic anticrack propagation in snow

Fracture toughness of mixed-mode anticracks in highly porous materials

When porous materials are subjected to compressive loads, localized failure chains, commonly termed anticracks, can occur and cause large-scale structural failure. Similar to tensile and shear cracks, the resistance to anticrack growth is governed by fracture toughness. Yet, nothing is known about the mixed-mode fracture toughness for highly porous materials subjected to shear and compression. We present fracture mechanical field experiments tailored for weak layers in a natural snowpack. Using a mechanical model for interpretation, we calculate the fracture toughness for anticrack growth for the full range of mode interactions, from pure shear to pure collapse. The measurements show that fracture toughness values are significantly larger in shear than in collapse, and suggest a power-law interaction between the anticrack propagation modes. Our results offer insights into the fracture characteristics of anticracks in highly porous materials and provide important benchmarks for computational modeling.

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.

Graphical Abstract

Supplementary Information

The online version contains supplementary material available at 10.1007/s10035-024-01423-5.

Towards a holistic paradigm for long-term snow avalanche risk assessment and mitigation

In mountain territories, snow avalanches are a prevalent threat. Long-term risk management involves defining meaningful compromises between protection and overall sustainability of communities and their environment. Methods able to (i) consider all sources of losses, (ii) account for the high uncertainty levels that affect all components of the risk and (iii) cope for marked non-stationarities should be employed. Yet, on the basis of a literature review and an analysis of relations to Sustainable Development Goals (SDGs), it is established that snow avalanche risk assessment and mitigation remain dominated by approaches that can be summed up as deterministic, hazard oriented, stationary and not holistic enough. A more comprehensive paradigm relying on formal statistical modelling is then proposed and first ideas to put it to work are formulated. Application to different mountain environments and broader risk problems is discussed.

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.

A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution

We develop a generalized interpolation material point method (GIMPM) for the shallow shelf approximation (SSA) of ice flow. The GIMPM, which can be viewed as a particle version of the finite element method, is used here to solve the shallow shelf approximations of the momentum balance and ice thickness evolution equations. We introduce novel numerical schemes for particle splitting and integration at domain boundaries to accurately simulate the spreading of an ice shelf. The advantages of the proposed GIMPM-SSA framework include efficient advection of history or internal state variables without diffusion errors, automated tracking of the ice front and grounding line at sub-element scales, and a weak formulation based on well-established conventions of the finite element method with minimal additional computational cost. We demonstrate the numerical accuracy and stability of the GIMPM using 1-D and 2-D benchmark examples. We also compare the accuracy of the GIMPM with the standard material point method (sMPM) and a reweighted form of the sMPM. We find that the grid-crossing error is very severe for SSA simulations with the sMPM, whereas the GIMPM successfully mitigates this error. While the grid-crossing error can be reasonably reduced in the sMPM by implementing a simple material point reweighting scheme, this approach it not as accurate as the GIMPM. Thus, we illustrate that the GIMPM-SSA framework is viable for the simulation of ice sheet-shelf evolution and enables boundary tracking and error-free advection of history or state variables, such as ice thickness or damage.

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.

Mesoscale inertial transition in granular materials

Granular assemblies can experience complex failure patterns along a given loading path, with a distribution of ephemeral inertial events marked by local outbursts in kinetic energy. However, investigating such mechanisms appears to be necessary to understand how a certain failure mode develops in a granular material. Using a discrete element method, this study highlights several microstructure reorganizations before the specimen reaches a proper failure state. Meso structures have proven to be efficient to understand the elementary mechanisms responsible for these outbursts in kinetic energy. Strain–like and stress-like quantities are thus defined at a mesoscale and they are used to characterize the nucleation and propagation of these local microstructural events.

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.

The mechanism of delayed release in earthquake-induced avalanches

Snow avalanches can be triggered by strong earthquakes. Most existing models assume that snow slab avalanches happen simultaneously during or immediately after their triggering. Therefore, they cannot explain the plausibility of delayed avalanches that are released minutes to hours after a quake. This paper establishes the basic mechanism of delays in earthquake-induced avalanche release using a novel analytical model that yields dynamics consistent with three documented cases, including two from Western Himalaya and one from central Italy. The mechanism arises from the interplay between creep, strain softening and strain-rate sensitivity of snow, which drive the growth of a basal shear fracture. Our model demonstrates that earthquake-triggered delayed avalanches are rare, yet possible, and could lead to significant damage, especially in long milder slopes. The generality of the model formulation opens a new approach for exploring many other problems related to natural slab avalanche release.

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.