Modeling of crack propagation in weak snowpack layers using the discrete element method

Abstract

Abstract. 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 and (3) tensile fracture through the slab which leads to its detachment. During the past decades, theoretical and experimental work has gradually led to a better understanding of the fracture process in snow involving the collapse of the structure in the weak layer during fracture. This now allows us to better model failure initiation and the onset of crack propagation, i.e., to estimate the critical length required for crack propagation. On the other hand, our understanding of dynamic crack propagation and fracture arrest propensity is still very limited.To shed more light on this issue, we performed numerical propagation saw test (PST) experiments applying the discrete element (DE) method and compared the numerical results with field measurements based on particle tracking. The goal is to investigate the influence of weak layer failure and the mechanical properties of the slab on crack propagation and fracture arrest propensity. Crack propagation speeds and distances before fracture arrest were derived from the DE simulations for different snowpack configurations and mechanical properties. Then, in order to compare the numerical and experimental results, the slab mechanical properties (Young's modulus and strength) which are not measured in the field were derived from density. The simulations nicely reproduced the process of crack propagation observed in field PSTs. Finally, the mechanical processes at play were analyzed in depth which led to suggestions for minimum column length in field PSTs.

Snow fracture in relation to slab avalanche release: critical state for the onset of crack propagation

“…The slab is modeled with spherical elements of radius r = 0.01 m with a square packing. As explained in Gaume et al (2015b), these elements are not intended to represent the real snow grains. They constitute entities of discretization used to model an elastic continuum of density ρ, Young's modulus E, and Poisson's ratio ν.…”

“…The simulations are performed using PFC2D (by Itasca), implementing the original soft-contact algorithm of Cundall and Strack (1979). The numerical setup and the cohesive contact law implemented is fully described in Gaume et al (2015b). We recall here the main characteristics of the DEM model.…”

“…DEM is well suited to represent large deformations as well as the evolution of the microstructure of materials in a dynamic context (Radjai and Dubois, 2011;Hagenmuller et al, 2015;Gaume et al, 2011Gaume et al, , 2015b. The simulations are performed using PFC2D (by Itasca), implementing the original soft-contact algorithm of Cundall and Strack (1979).…”

“…We used the cohesive contact law detailed in Gaume et al (2015b). The bonds are characterized by specific elasticity and strength parameters which have been calibrated to obtain the desired macroscopic (bulk) properties.…”

Fiber-bundle model with time-dependent healing mechanisms to simulate progressive failure of snow

“…Model improvements may include introducing local load-sharing rules (e.g., [2,26]) and using a more complex model for the load rheology instead of the Maxwell model (e.g., power-law creep [13,38]). Moreover, with a model capable of reproducing a more complex three-dimensional geometry (e.g., discrete element model DEM (e.g., [39,40]) the effect of the complex structure of the ice matrix could be studied. Snow failure leading to snow avalanches occurs under mixed-mode loading (shear and compression) [41].…”