Revisiting snow settlement with microstructural knowledge

Abstract. Snow settlement under gravity is primarily driven by the slow creep of its ice matrix, which exhibits a viscoplastic behaviour. Knowledge of the viscoplastic properties of snow is thus crucial for understanding and predicting the snowpack seasonal and perennial evolution. However, different approaches have yielded disparate constitutive viscoplastic laws. Field experiments and snowpack models typically described snow settlement with a linear model and an apparent compaction viscosity. Dedicated laboratory experiments exhibited non-linear relationships between stress and strain rate, with a stress exponent ranging from 1.8 to 4. Microstructure-based simulations showed that the viscoplastic behaviour likely results from the interaction of glides on various intra-crystalline slip systems within ice crystals, yielding an exponent between 2 and 3. The paper aims to reconcile these approaches. To do so, we conducted microstructure-based simulations on 37 three-dimensional snow images and established that the viscoplastic behaviour follows a power-law relation, with a stress exponent almost constant around 2.15, and a reference stress that depends mostly on the solid fraction. Analysing a dataset from previous viscoplastic tests (178 points) revealed that applying the stress exponent from the simulations significantly reduces variability in the reference stress between independent studies and led to a simplified constitutive relation. Lastly, we showed that the linear settlement laws of snowpack models, such as Crocus, align with the proposed constitutive relation under natural loading conditions typically encountered on alpine sites, due to correlations between stress and density. However, considerable differences emerge under "non-standard" scenarios, such as elevated loads on light snow or reduced loads on dense snow, where our model demonstrates superior qualitative performance.