Crack propagation speeds in weak snowpack layers

For the release of a slab avalanche, crack propagation within a weak snowpack layer below a cohesive snow slab is required. As crack speed measurements can give insight into underlying processes, we analysed three crack propagation events that occurred in similar snowpacks and covered all scales relevant for avalanche release. For the largest scale, up to 400 m, we estimated crack speed from an avalanche movie; for scales between 5 and 25 m, we used accelerometers placed on the snow surface and for scales below 5 m, we performed a propagation saw test. The mean crack speeds ranged from 36 ± 6 to 49 ± 5 m s−1, and did not exhibit scale dependence. Using the discrete element method and the material point method, we reproduced the measured crack speeds reasonably well, in particular the terminal crack speed observed at smaller scales. Finally, we used a finite element model to assess the speed of different elastic waves in a layered snowpack. Results suggest that the observed cracks propagated as mixed mode closing cracks and that the flexural wave of the slab is responsible for the energy transfer to the crack tip.

Dynamic crack propagation in weak snowpack layers: insights from high-resolution, high-speed photography

Dynamic crack propagation in snow is of key importance for avalanche release. Nevertheless, it has received very little experimental attention. With the introduction of the propagation saw test (PST) in the mid-2000s, a number of studies have used particle tracking analysis of high-speed video recordings of PST experiments to study crack propagation processes in snow. However, due to methodological limitations, these studies have provided limited insight into dynamical processes such as the evolution of crack speed within a PST or the touchdown distance, i.e. the length from the crack tip to the trailing point where the slab comes to rest on the crushed weak layer. To study such dynamical effects, we recorded PST experiments using a portable high-speed camera with a horizontal resolution of 1280 pixels at rates of up to 20 000 frames s−1. We then used digital image correlation (DIC) to derive high-resolution displacement and strain fields in the slab, weak layer and substrate. The high frame rates enabled us to calculate time derivatives to obtain velocity and acceleration fields. We demonstrate the versatility and accuracy of the DIC method by showing measurements from three PST experiments, resulting in slab fracture, crack arrest and full propagation. We also present a methodology to determine relevant characteristics of crack propagation, namely the crack speed (20–30 m s−1), its temporal evolution along the column and touchdown distance (2.7 m) within a PST, and the specific fracture energy of the weak layer (0.3–1.7 J m−2). To estimate the effective elastic modulus of the slab and weak layer as well as the weak layer specific fracture energy, we used a recently proposed mechanical model. A comparison to already-established methods showed good agreement. Furthermore, our methodology provides insight into the three different propagation results found with the PST and reveals intricate dynamics that are otherwise not accessible.

Non steady-state intersonic cracks in elastomer membranes under large static strain

International audience Dynamic crack propagation in elastomer membranes is investigated; the focus is laid on cracks reaching the speed of shear waves in the material. The specific experimental setup developed to measure crack speed is presented in details. The protocol consists in (1) stretching an elastomer membrane under planar tension loading conditions, then (2) initiating a small crack on one side of the membrane. The crack speed is measured all along the crack path in both reference and actual configurations, including both acceleration and deceleration phases, i.e. non steady-state crack propagation phases. The influence of the prescribed stretch ratio on crack speed is analysed in the light of both these new experiments and the few previously published studies. Conclusions previously drawn for steady-state crack growth are extended to non steady-state conditions: stretch perpendicular to the crack path governs crack speed in intersonic crack propagation regime, and the role of the stretch in crack direction is minor.

Micro-mechanical modeling using DEM to study the effect of mechanical properties on crack propagation for snow slab avalanches

<p>Dry-snow slab avalanche release is a multi-scale process starting with the formation of localized failure in a highly porous weak snow layer below a cohesive snow slab, which can be followed by rapid crack propagation within the weak layer. Finally, a tensile fracture through the slab leads to its detachment. About 15 years ago, the propagation saw test (PST) was developed. The PST is a fracture mechanical field test that provides information on crack propagation propensity in weak snowpack layers. It has become a valuable research tool to investigate the processes involved in crack propagation. While this has led to a better understanding of the onset of crack propagation, much less is known about the ensuing propagation dynamics. Here, we use the discrete element method to numerically simulate PSTs in 3D and analyze the fracture dynamics using a micro-mechanical approach. Our DEM model reproduced the observed PST behavior extracted from experimental analysis. We developed different indicators to define the crack tip that allowed deriving crack speed. Our results show that crack propagation in level terrain reaches a stationary speed if the snow column is long enough. Moreover, we define stress concentration sections. Their length evolution during crack propagation suggests the development of a steady-state stress regime. Slab and weak layer elastic modulus, as well as weak layer shear strength, are the key input parameters for modeling crack propagation; they affect stress concentrations, crack speed, and the critical length for the onset of crack propagation. The results of our sensitivity study highlight the effect of these mechanical parameters on the emergence of a steady-state propagation regime and consequences for dry-snow slab avalanche release. Our DEM approach opens the possibility for a comprehensive study on the influence of the snowpack mechanical properties on the fundamental processes for avalanche release.</p>

Tensile Crack Speed in Brittle Rocks

<p>An important issue in rapid brittle fracture is the limiting speed of crack propagation. It is widely believed that brittle mode I crack cannot propagate faster than the Rayleigh wave speed, or the speed of sound on a solid surface. Mode II cracks are also limited by longitudinal speed wave. The origin for this belief stems from the predictions of continuum mechanics. Once the crack speed reaches a theoretical upper limit in a material, which is most often larger than one fifth of the Rayleigh wave velocity, branching of a propagating crack occurs. To verify this hypothesis, this paper presents the results of an experimental program aimed at disclosing the size effect on the crack velocity in the Splitting Tensile Strength indirect test (i.e. the Brazilian Test) using high-speed photography techniques. Over 100 Brazilian tests with more than 10 different rock types at various diameters were prepared and tested according to the ASTM standard recommendations using either a servo hydraulic machine or an electromechanical load frame at a wide ranges of load/displacement rates. By adopting a high frame rate of above 100,000 frames per second (fps), crack initiation, propagation, and coalescence were captured to study the size effect on the crack speed and failure mode on the Brazilian test results.</p>

Dynamic crack propagation in weak snowpack layers: Insights from high-resolution, high-speed photography

To assess snow avalanche release probability, information on failure initiation and crack propagation in weak snowpack layers underlying cohesive slab layers are required. With the introduction of the Propagation Saw Test (PST) in the mid-2000s, various studies used particle tracking analysis of high-speed video recordings of PST experiments to gain insight into crack propagation processes, including slab bending, weak layer collapse, crack propagation speed and the frictional behavior after weak layer fracture. However, the resolution of the videos and the methodology used did not allow insight into dynamic processes such as the evolution of crack speed within a PST or the touchdown distance, which is the length from the crack tip to the trailing point where the slab sits on the crushed weak layer at rest again. Therefore, to study the dynamics of crack propagation we recorded PST experiments using a powerful portable high-speed camera with a horizontal resolution of 1280 pixels at rates up to 20,000 frames per second. By applying a high-density speckling pattern on the entire PST column, we then used digital image correlation (DIC) to derive high-resolution displacement and strain fields in the slab, weak layer, and substrate. The high frame rates allowed time derivatives to obtain velocity and acceleration fields. On the one hand, we demonstrate the versatile capabilities and accuracy of the DIC method by showing three PST experiments resulting in slab fracture, crack arrest and full propagation. On the other hand, we present a methodology to determine relevant characteristics of crack propagation: the crack speed and touchdown distance within a PST, and the specific fracture energy of the weak layer. To estimate the effective elastic modulus of the slab and weak layer as well as the weak layer specific fracture energy we used a recently proposed mechanical model. A comparison to already established methods showed good agreement. Furthermore, our methodology also provides insight into the three different propagation results found with the PST and reveals intricate dynamics that are otherwise not accessible.

Measuring slope-scale crack propagation in weak snowpack layers

<p>For a snow avalanche to release, a weak layer has to be buried below a cohesive snow slab. The slab-weak layer configuration must not only allow failure initiation but also crack propagation across a slope. While in the past failure initiation was extensively studied, research focusing on the onset and dynamics of crack propagation only started with the introduction of the Propagation Saw Test (PST), a meter scale fracture mechanical field test. Since then, various studies used particle tracking analysis of high-speed video recordings of PST experiments to gain insight into crack propagation processes and to measure crack propagation speeds. At the slope scale, a few crack speed estimates have been obtained from seismic sensors, videos or visual observation. However, due to experimental limitations, these latter studies can only provide rather crude crack speed estimates and direct comparisons to PST measurements are still missing. Sure, performing experiments in avalanche terrain is challenging and limited for security reasons, but crack propagation occurs also in slopes not sufficiently steep to release an avalanche. This phenomena is called a whumpf. Since crack propagation in whumpfs is presumably similar to that in avalanches, we developed instrumentation to measure crack speeds on artificially triggered whumpfs. We designed small wireless time synchronized accelerometers with a sampling rate of 400 Hz that can be placed on the snowpack. These measure the downward acceleration of the slab when a crack in the weak layer below passes by. Though triggering whumpfs is difficult and unpredictable, we performed a successful experiment with seven sensors placed over a distance of 25 m. Our experiment revealed a crack speed around 50 ms<sup>-1</sup>. In addition, we obtained very similar crack speed measurements from a 5.3 m long PST carried out close-by (42 ms<sup>-1</sup>) and a video-based speed estimate of an avalanche triggered two days later (42 – 55 ms<sup>-1</sup>). Our unique whumpf measurement is the first slope scale speed value that can be directly compared to results obtained with other speed measurement techniques. The similarity between the measured speeds suggests that the one-dimensional crack propagation in PSTs is also similar to the 2-dimensional crack propagation in Whumpfs and real avalanches. PSTs are therefore well suited to investigate crack propagation processes of dry snow slab avalanches.</p>

Poroelastic Effects on the Time- and Rate-Dependent Fracture of Polymer Gels

Fracture of polymer gels is often time- and rate-dependent. Subject to a constant load, a gel specimen may fracture immediately or after a delay (time-dependent, delayed fracture). When a crack grows in a gel, the fracture energy may depend on the crack speed (rate-dependent). The underlying mechanisms for the time- and rate-dependent fracture of gels could include local molecular processes, polymer viscoelasticity, and solvent diffusion coupled with deformation (poroelasticity). This paper focuses on the effects of poroelasticity. A path-independent, modified J-integral approach is adopted to define the crack-tip energy release rate as the energetic driving force for crack growth in gels, taking into account the energy dissipation by solvent diffusion. For a stationary crack, the energy release rate is time-dependent, with which delayed fracture can be predicted based on a Griffith-like fracture criterion. For steady-state crack growth in a long-strip specimen, the energy release rate is a function of the crack speed, with rate-dependent poroelastic toughening. With a poroelastic cohesive zone model, solvent diffusion within the cohesive zone leads to significantly enhanced poroelastic toughening as the crack speed increases, rendering a rate-dependent traction-separation relation. While most of the results are based on a linear poroelastic formulation, future studies may extend to nonlinear theories with large deformation. In addition to the poroelastic effects, other mechanisms such as viscoelasticity and local fracture processes should be studied to further understand the time and rate-dependent fracture of polymer gels.