The mechanical origin of snow avalanche dynamics and flow regime transitions

Abstract

Abstract. Snow avalanches cause fatalities and economic damage. Key to their mitigation is the understanding of snow avalanche dynamics. This study investigates the dynamic behavior of snow avalanches, using the material point method (MPM) and an elastoplastic constitutive law for porous cohesive materials. By virtue of the hybrid Eulerian–Lagrangian nature of the MPM, we can handle processes involving large deformations, collisions and fractures. Meanwhile, the elastoplastic model enables us to capture the mixed-mode failure of snow, including tensile, shear and compressive failure. Using the proposed numerical approach, distinct behaviors of snow avalanches, from fluid-like to solid-like, are examined with varied snow mechanical properties. In particular, four flow regimes reported from real observations are identified, namely, cold dense, warm shear, warm plug and sliding slab regimes. Moreover, notable surges and roll waves are observed peculiarly for flows in transition from cold dense to warm shear regimes. Each of the flow regimes shows unique flow characteristics in terms of the evolution of the avalanche front, the free-surface shape, and the vertical velocity profile. We further explore the influence of slope geometry on the behavior of snow avalanches, including the effect of slope angle and path length on the maximum flow velocity, the runout angle and the deposit height. Unified trends are obtained between the normalized maximum flow velocity and the scaled runout angle as well as the scaled deposit height, reflecting analogous rules with different geometry conditions of the slope. It is found that the maximum flow velocity is mainly controlled by the friction between the bed and the flow, the geometry of the slope, and the snow properties. We reveal the crucial effect of both flow and deposition behaviors on the runout angle. Furthermore, our MPM modeling is calibrated and tested with simulations of real snow avalanches. The evolution of the avalanche front position and velocity from the MPM modeling shows reasonable agreement with the measurement data from the literature. The MPM approach serves as a novel and promising tool to offer systematic and quantitative analysis for mitigation of gravitational hazards like snow avalanches.

Detrainment and braking of snow avalanches interacting with forests

“…Based on the calibration case reported in section 3 (Case 2 in Table 2), a more cold snow and a warmer snow are adopted respectively in Cases 1&3 (Table 2) to investigate the influence of snow properties on the avalanche-forest interaction. The cold snow in Case 1 gives a dry cohesionless granular flow with a continuous and smooth free surface, which resembles avalanches in the cold dense regime (Li et al, 2020). In comparison, the warm snow in Case 3 leads to an avalanche with granules and blocks due to the higher internal friction and cohesion, sharing features of a wet snow.…”

“…We define h 0 = 1 m, l 0 = 20 m and w 0 = 20 m as respectively the height, length, and width of the released snow. For all the snow types simulated in this study, they share the same Young's modulus (E = 3 MPa), Poisson's ratio (ν = 0.3) and density (ρ = 200 kg/m 3 ) (Li et al, 2020). In addition to the different tree arrangements, the forest density ρ forest and the tree diameter d are also varied to study their effect on snow detrainment.…”

“…Hence, the total dissipation in the case without forest is ∆e 0 = w b0 + w int0 ≈ w b0 , as the internal dissipation can be negligible compared to the bed friction dissipation (Li et al, 2020). Similarly, in the forest case…”

“…This study aims to quantify the amount of snow caught in forests and explore the mechanism of the detrainment, with comprehensive consideration of different avalanche features and forest configurations. We use a three-dimensional Material Point Method (3D MPM), by which the fractures, collisions, and large deformations involved in snow avalanches can be well captured (Gaume et al, 2018(Gaume et al, , 2019Li et al, 2020Li et al, , 2021. More importantly, individual trees and their interactions with snow avalanches can be explicitly modelled without relying on empirical laws.…”

“…Appendix A: Calculation of energy dissipation due to forest By defining ∆e the additional dissipation at each time step, it is possible to separate it into two parts (Li et al, 2020): the dissipation inside the flow w int and through the boundary bed w b , and in the case with forest, the dissipation ẽf is added.…”