3D elastoplastic simulation of ski-triggered snow slab avalanches

The stability of dry-snow avalanches is strongly dependent on the interaction between the snow slab above a weak-layer and, as presented in this work, the skier induced load. This induced load causes an additional stress field on the slab which eventually triggers an avalanche. I present the results of 3D finite element simulations in an elastoplastic domain. The plastic deformation of the weak-layer follows the Mohr-Coulomb-Cap model which provides a more realistic model as a pure elastic approach. I investigate how the stress field on top of the weak-layer changes if one is skiing down-slope or parallel to the slope. A layered snow slab changes the stress on top of the weak-layer and to investigate these changes I simulated two different representative layered slabs. One containing only soft layers to investigate how the weak layer is affected by the ski induced stress and the other hard-soft-hard layer to examine bridge effects caused by the hard layers. A hard layer in the snow slab forms a sort of bridge which spreads the induced stress over a larger lateral distance, at the same time decreasing the stress to the layers below the bridge. Furthermore, I show a possible connection between the plastic deformation and the critical crack length.

💡 Research Summary

This paper presents a three‑dimensional finite‑element (FE) study of how a skier’s load influences the stress state within a snow slab and its underlying weak layer, a key factor in dry‑snow avalanche triggering. Unlike earlier works that treated the slab as purely elastic or considered only failure initiation, the author incorporates both elastic‑plastic behavior of the weak layer using a Mohr‑Coulomb‑Cap (MCC) constitutive model, smoothed with a Drucker‑Prager approximation to avoid numerical difficulties at the yield surface corners.

Two representative snowpack configurations are examined: (1) a homogeneous “Soft‑Soft‑Soft” stack where three identical soft layers have the same density, Young’s modulus, and shear strength, and (2) a “Hard‑Soft‑Hard” stack where hard layers sandwich a softer middle layer, creating a “bridge” that can redistribute load. For each configuration the skier is modeled as a static rectangular load (1.75 m × 0.05 m × 0.015 m) split evenly between two skis spaced 0.08 m apart. Two skiing orientations are simulated: skis pointing down‑slope and skis aligned parallel to the slope.

The FE model (≈ 901 000 degrees of freedom) is built in COMSOL Multiphysics, meshed densely near the skis and the weak layer, and solved on a 16‑core cluster (≈ 10 min per run). Bottom boundary is fixed to represent a rock base; all other faces are free. Gravity is omitted during the simulation and added back analytically afterward.

Results show that in the Soft‑Soft‑Soft case the normal compressive stress directly beneath the skis reaches about –2330 Pa and decays to –414 Pa at the top of the weak layer. Shear stresses τ_xz and τ_yz are strongly localized at the ski edges, with τ_xz reaching +290 Pa on one side and near zero on the other. In the Hard‑Soft‑Hard case the hard upper layer reduces the stress transmitted to the weak layer: normal stress at the weak‑layer surface is only –108 Pa, a reduction of roughly 70 % compared with the homogeneous slab. The hard layers act as a bridge, spreading the load laterally and causing a faster decay of both normal and shear stresses in the deeper hard layer. Consequently, the volumetric plastic strain in the weak layer is markedly lower when a hard bridge is present.

The study also links the computed volumetric plastic strain to the critical crack length a_c, using a formulation derived from Gaume & Reuter (2017). Larger plastic‑strain zones correspond to smaller a_c, indicating that the weak layer becomes more susceptible to crack propagation when the plastic zone expands.

Orientation effects are modest but noticeable: when skis are parallel to the slope, the compressive stress on the weak layer is about 10 % lower than when the skis point down‑slope, suggesting that skier direction can influence avalanche risk.

Limitations include the use of a static load (ignoring dynamic impact), omission of temperature‑dependent snow properties, and the assumption of isotropic, homogeneous material parameters within each layer. Future work should incorporate dynamic loading, thermomechanical coupling, and validation against field measurements.

Overall, the paper provides the first 3‑D elastoplastic FE analysis of skier‑triggered slab avalanches, demonstrates the “bridge” effect of hard layers in reducing stress transmission to the weak layer, and proposes a quantitative link between plastic deformation and critical crack length. These insights can improve avalanche stability indices, inform skier behavior guidelines, and guide more realistic numerical models for back‑country safety assessments.