Size scaling for dry snow slab release

[1] Sandpile avalanches were used first to illustrate the concept of self-organized criticality (SOC). Snow avalanches consist of two types: (1) loose snow avalanches which release in cohesionless material at the top of the snowpack and (2) slab avalanches which release by propagation of shear fractures originating in a thin weak layer at depth in the snowpack. Loose snow avalanches are analogous to sandpile avalanches with a similar release mechanism, whereas slab avalanches have an entirely different release mechanism, namely, propagation of mode II shear fractures. This paper is concerned with scaling the magnitude (or size) for dry snow slabs. The argument is made that the fundamental parameter for scaling is the slab thickness based on fracture mechanics principles. The probability density function implied for the fundamental size parameter is derived from field measurements of slab thickness. An asymptotic power law is related empirically to slab fracture toughness derived from field measurements and fracture mechanical scaling. The results suggest that the power law is inversely proportional to the fracture toughness squared or, equivalently, it is inversely proportional the product of the energy to generate a unit area of fracture surface in the weak layer and the effective modulus at the base of the slab. The combined results suggest that the scaled power law is mainly explained by two components of the slab fracture toughness: (1) the fracture mechanical size effect and (2) increase in toughness due to creep, bonding, and normal pressure induced by the slab on top of the weak layer. Both components are needed to explain why fracture toughness increases with slab thickness. A further result is that release of individual slab avalanches involves a well-defined length scale which governs size and scale invariance is not satisfied. Thus slab avalanches do not conform to the original description of self-organized criticality.