Probability distribution of energetic-statistical strength size effect in alpine snow

Alpine snow in which avalanches form is a quasi-brittle material with an energetic (or fracture mechanical) strength size effect. However, there is also a probabilistic aspect to the size effect. In this paper, we present field data for unnotched tensile fracture of uniaxially stressed samples and 3 point bending tensile experiments from a cold laboratory. In addition, we summarize field data on shear fracture tests of avalanche weak layers. Taken together, the argument is derived from about 1300 tests, 90% of which are from field data. On the basis of the data, as well as simple theory relevant to unnotched quasi-brittle fracture, we suggest that the tensile and shear fracture data follow a gamma probability density function (pdf). For our data, the gamma pdf is essentially equivalent to a normal pdf as in Daniels’ fibre bundle model for the implied distribution shape factors. However, the physical description of the failure process to derive the gamma pdf for alpine snow differs substantially from that in Daniels’ classical fibre bundle model.

► We present 1300 fracture strength tests in tension and shear from un-notched samples in alpine snow.
► Assuming quasi-brittle fracture, the strength size effect follows a gamma function.
► From physical principles, the classical Weibull and fibre bundle models are unlikely.
► Implications for avalanche release are given.