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Modeling of avalanche release processes

 

Models can help us to better understand the driving parameters of avalanche release. But they always need to be calibrated and validated against field data in order to be applicable in practice.

 

Snow is a material with a very complex microstructure and whose properties are strongly heterogeneous at different spatial scales. Besides, snow properties such as density, strength, depth, etc. are generally linked. Hence, in field and laboratory experiments related to snow and avalanche science, it is often hard to precisely control all the parameters driving the phenomenon which is studied. This complicates our task of understanding avalanche release processes.

Models can thus help us to better understand the driving parameters of avalanche release, first since each parameter is well controlled and second since purely homogenous conditions can be simulated, which is not the case in the field. However, a model, as efficient as it can be, will always need to be calibrated and validated against field data in order to be applicable in practice.

We use two main kinds of models: Continuous models based on the finite element method and discontinuous models based on the discrete element method.

 

Finite element method (FEM)

The finite element method allows computing numerically the behavior of complex materials, if this material can be assumed as continuous at the scale of the simulation.

Skier stability

The skier stability index, as it implemented in SNOWPACK takes into account the overload due to a skier on the weak layer assuming a homogenous snowpack. However, it does not take into account the individual mechanical properties of the overlying slab layers which can induce a so-called “bridging effect” i.e. an increase of stability if a hard slab prevents the transmission of the additional stress due to the skier on the WL. Simulations using the FEM (Figure 1a) showed that this additional stress can decrease by a factor 2 if this effect is taken into account. Based on these results a new skier stability index is currently tested before being implemented into SNOWPACK.

Onset of crack propagation: evaluation of the critical length

The propagation saw test allows evaluating the size of the initial crack in the WL necessary for the onset of crack propagation but also how far this crack can propagate. The FEM is thus used to study the influence of snowpack properties on the stress distribution in the WL and the slab assuming a preexisting crack (Figure 1b,c and movie 1) in order to better understand those processes.

Influence of spatial variability on slope stability

In order to take into account the important spatial variability of the mechanical properties of the WL at the slope scale, we use the FEM to model a slope with heterogeneous properties of the strength of the WL (Movie 2). This variability induces a reduction of the stability (knock-down effect) compared to the case of a homogeneous slope. Some work is currently undergoing to take those effects into account in SNOWPACK.

 

Discrete Element Method (DEM)

One of the main drawbacks of the finite element method is that is assumes a continuous material and generally a linear elastic behavior. Hence, it might give an interesting first insight of the mechanical processes at play, in an engineering point of view. However, to go deeper in the analysis, the porosity of snow as well as the failure behavior at the grain scale which induces the brittle character of snow needs to be accounted for.

This can be done by using the discrete element method, which is grain-based and allows simulating the behavior of any granular material by solving dynamic equations for each grain and assessing a contact law between the grains (including cohesion).

Failure criterion of weak snow layers

We perform mixed-mode shear-compression loading tests on different types of WLs (Figure 1a) until failure using the discrete element method which allows mimicking the high porosity of snow. These simulations, together with similar experiments made on real WLs in the cold laboratory using a shear apparatus (Figure 1b) will help find more accurate failure criterion for weak snowpack layers.

Crack propagation

Today, our understanding of the dynamic phase of crack propagation as well as fracture arrest propensity is still very limited. However, these processes strongly affect the potential avalanche release size and thus, the avalanche danger. For instance, it is not uncommon to perform measurements with widespread crack propagation on one day, while a few days later, with very little change to the snowpack, crack propagation does not occur anymore. Thus far, there is no clear theoretical framework to interpret such observation, and it is not clear how and which snowpack properties affect crack propagation. To shed more light on this issue we perform numerical propagation saw tests using the DEM and study the effect of the different system parameters on the crack propagation velocity as well as on the propagation distance (Movie 3).

 

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