Dry-snow slab avalanches are generally caused by a sequence of fracture processes, including failure initiation in a weak snow layer underlying a cohesive slab followed by crack propagation within the weak layer (WL) and tensile fracture through the slab. During past decades, theoretical and experimental work has gradually increased our knowledge of the fracture process in snow. However, our limited understanding of crack propagation and fracture arrest propensity prevents the evaluation of avalanche release sizes and thus impedes hazard assessment. To address this issue, slab tensile failure propensity is examined using a mechanically based statistical model of the slab–WL system based on the finite element method. This model accounts for WL heterogeneity, stress redistribution by slab elasticity and possible tensile failure of the slab. Two types of avalanche release are distinguished in the simulations: (1) full-slope release if the heterogeneity is not sufficient to stop crack propagation and trigger a tensile failure within the slab; (2) partial-slope release if fracture arrest and slab tensile failure occur due to the WL heterogeneity. The probability of these two release types is presented as a function of the characteristics of WL heterogeneity and the slab. One of the main outcomes is that, for realistic values of the parameters, the tensile failure propensity is mainly influenced by slab properties. Hard and thick snow slabs are more prone to wide-scale crack propagation and thus lead to larger avalanches (full-slope release). In this case, the avalanche size is mainly influenced by topographical and morphological features such as rocks, trees, slope curvature and the spatial variability of the snow depth as often claimed in the literature.

Dry-snow slab avalanches are generally caused by a sequence of fracture
processes including (1) failure initiation in a weak snow layer underlying a
cohesive slab, (2) crack propagation within the weak layer (WL) and (3)
tensile fracture through the slab which leads to its detachment

Avalanche hazard mapping procedures have recently seen growing popularity of
coupled statistical–deterministic models in order to evaluate the runout
distance distribution and the probability of exceedance of a threshold
pressure at any location of the runout zone

In this paper, we extend a mechanically based probabilistic model developed
in a previous study

In this paper, the mechanical model proposed by

The simulated system is a uniform slope composed of a slab and a weak layer
of length

Parameters used in the model and typical values for snow from
field and laboratory experiments. For more details about these parameters and
a more complete review of the different related studies, see Sect. 3.3.2 in

Besides the evaluation of avalanche release depth distributions, this model
formerly enabled us to evidence a heterogeneity smoothing effect caused by
stress redistributions due to slab elasticity. This elastic smoothing effect
is characterized by a typical length scale of the system

Schematic representing the two types of failure
observed in the simulations.

Two types of avalanche release were obtained in the simulations: (1)
full-slope release when the entire simulated slope becomes unstable without
tensile failure within the slab (Fig.

In the case of a full-slope release, the heterogeneity magnitude is not
sufficient to trigger a tensile failure within the slab. The basal crack in
the weak layer thus propagates until reaching the top boundary condition
which can be seen as an anchor point (Fig.

In contrast, for partial-slope releases the cohesion variability in the weak layer is sufficient to generate the tensile failure of the slab within the simulated system. Local strong zones can effectively stop the propagation of the crack and the excess of stress is redistributed in the slab and induces slab tensile opening.

For a constant slab failure strength and a constant average cohesion of the
WL, the occurrence of full- or partial-slope release is intimately linked to
the heterogeneity of WL cohesion as well as smoothing effects due to the
elasticity of the slab. These combined mechanisms lead to shear stress
heterogeneities in the WL which modulate the shear stress differences,

Note that the position of the tensile failure in the slab, if existent,
also depends on the position of the initial basal failure in the weak layer.
This is due to the fact that the stress concentration at the crack tip
increases naturally with the crack size. Hence, the shear stress difference

For each set of the model parameters, 100 finite element (FE) simulations were performed for
different realizations of the WL heterogeneity with a constant average
cohesion

In the first part of this section (parametric analysis), the influence of the
characteristics of WL heterogeneity (cohesion standard deviation

Probability of slab tensile failure

Figures

The influence of the correlation length

The correlation length

The influence of the standard deviation

Indeed, a large value of the coefficient of variation induces large local variations of the WL shear stress, resulting in high tensile stresses within the slab, and ultimately favors fracture arrest. As a consequence, the tensile failure probability increases with increasing variability.

As shown in Fig.

In more detail, Fig.

It has previously been shown

Figure

Moreover, as shown in

The results of the previous parametric analysis should be interpreted with
care and one should keep in mind that, for snow, several of the previous
parameters are linked which may lead to more complex interactions. For
instance, the result of the influence of Young's modulus on the tensile
failure probability might seem contradictory to avalanche observations.
Indeed, taken as it is, this result would imply that it is easier to trigger
a tensile failure in stiff and strong snow than in softer snow. If this
line of reasoning is pursued, hard snow slabs would result in smaller
avalanche size than soft slabs, which is clearly in contradiction to
avalanche observations. Hence, even if the result behind Fig.

Slab tensile failure probability

New simulations were therefore performed, for which the dependence among

Slab tensile failure probability ^{©}Anchorage
Avalanche Center); (right) hard and thick slab with a very large extent
(^{©}Grant Gunderson).

In both cases, the slab tensile failure probability

Cumulative exceedance probability of the width

The proposed approach allows us to compute the slab tensile failure
probability from WL spatial variability characteristics and slab properties
using the finite element method. First, a parametric analysis showed the
influence of each model parameter on the tensile failure probability. Then,
more realistic simulations were performed, taking into account the link
between the mechanical properties of the slab. These simulations explained
why hard and thick snow slabs are more prone to wide-scale crack propagation
than soft slabs. However, one might also argue that the density is generally
linked to the thickness: the higher the thickness, the higher the density due
to settlement. Nevertheless, even if this link was taken into account, the
main finding of Fig.

From the presented approach, a rough estimate of the avalanche release area
can also be proposed. For a tensile failure probability equal to zero, the
avalanche release area would be equal to the maximum area

Figure

Finally, the results of the presented model suggest that the majority of the
releases would be full slope, i.e., not influenced by WL heterogeneity,
especially for high densities. Hence, the potential extent of slab avalanche
release areas will be controlled by topographical and geomorphological
features of the path such as rocks, trees, ridges or local curvatures induced
by the terrain and the snow cover distribution. As a consequence, GIS methods
based on terrain characteristics such as those developed by

We used a coupled mechanical–statistical approach to study the probability of the occurrence of slab tensile failure of a slab–WL system using the finite element method. Two different release types were observed in the simulations: (1) Full-slope release when the WL heterogeneity is not sufficient to arrest crack propagation and trigger a tensile failure within the slab, and hence the crack propagates across the whole system; (2) partial-slope release when the local variations of WL cohesion are substantial and can stop crack propagation and trigger the slab tensile failure. Importantly, for both release types the primary failure process observed is always the basal shear failure of the weak layer. Hence slab fracture systematically constitutes a secondary process.

We have shown that the slab tensile failure propensity strongly depends on
the model parameters such as the tensile strength

For realistic values of the parameters and taking the link between the
mechanical properties of the slab into account, the model results suggest
that the releases are partial slope only for low slab densities and full
slope for densities higher than about 150 kg m

We wish to express our gratitude to Claude Schneider, snow expert in La Plagne, for providing the database of avalanche sizes. J. Gaume was supported by a Swiss Excellence Government Scholarship and is grateful for support by the State Secretariat for Education, Research and Innovation (SERI) of the Swiss government. We thank two anonymous reviewers for their constructive comments that helped to improve our paper. Edited by: F. Dominé