Modeling snow slab avalanches caused by weak-layer failure – Part 2: Coupled mixed-mode criterion forskier-triggered anticracks

Using the analytical model presented in Part 1 ofthis two-part paper, a new conceptual understanding of an-ticrack nucleation in weak layers is proposed. To obtain asufficient condition for onset of failure, two necessary con-ditions must be satisfied simultaneously: (i) the weak layermust be overloaded in terms of stress and (ii) the initiatingcrack must release enough energy for the formation of newsurfaces. This so-called coupled criterion was proposed byLeguillon (2002). No assumptions on initial defects withinthe weak layer are needed. Instead, the failure criterion pro-vides both critical loading and the size of initiating cracks.It only requires the fundamental material properties strengthand fracture toughness as inputs. Crack initiation and sub-sequent propagation are covered by a single criterion con-taining both a strength-of-materials and a fracture mechanicscondition.Analyses of skier-loaded snowpacks show the impact ofslab thickness and slope angle on critical loading and crackinitiation length. In the limit cases of very thick slabs andvery steep slopes, we obtain natural avalanche release. A dis-cussion of different mixed-mode stress and energy criteriareveals that a wrong choice of mixed-mode hypotheses canyield unphysical results. The effect of material parameterssuch as density and compliance on weak-layer collapse is il-lustrated.The framework presented in this two-part series harnessesthe efficiency of closed-form solutions to provide fast andphysically sound predictions of critical snowpack loads us-ing a new conceptual understanding of mixed-mode weak-layer failure. It emphasized the importance of both stress andenergy in avalanche release.