Abstract
Abstract. While the homogenization of snow elastic properties has been widely reported in the literature, homogeneous rate-dependent behavior responsible for the densification of the snowpack has hardly ever been upscaled from snow microstructure. We therefore adapt homogenization techniques developed within the framework of elasticity to the study of snow viscoplastic behavior. Based on the definition of kinematically uniform boundary conditions, homogenization problems are applied to 3-D images obtained from X-ray tomography, and the mechanical response of snow samples is explored for several densities. We propose an original post-processing approach in terms of viscous dissipated powers in order to formulate snow macroscopic behavior. Then, we show that Abouaf models are able to capture snow viscoplastic behavior and we formulate a homogenized constitutive equation based on a density parametrization. Eventually, we demonstrate the ability of the proposed models to account for the macroscopic mechanical response of snow for classical laboratory tests.
Highlights
Predicting the macroscopic behavior of snow in a wide range of loads, strain rates and temperatures is of a particular interest with respect to avalanche risk forecasting or to structural design of avalanche defense structures
Based on the definition of kinematically uniform boundary conditions, homogenization problems are applied to 3-D images obtained from X-ray tomography, and the mechanical response of snow samples is explored for several densities
As the snow samples are often extracted from the snowpack thanks to hollow cylinders, the oedometric compression test is one of the most convenient mechanical laboratory tests to perform on snow
Summary
Predicting the macroscopic behavior of snow in a wide range of loads, strain rates and temperatures is of a particular interest with respect to avalanche risk forecasting or to structural design of avalanche defense structures. The relation (Eq 20) shows that, for a given snow porosity, the equivalent macroscopic stress eq can be fitted on iso-volumetric mechanical dissipation curves in the plane (S1/3, S2) These iso-dissipation curves can be obtained by plotting the values (S1/3, S2) corresponding to different loading conditions defined by (E1, E2). Given an arbitrary value of Pv◦ = 1 Pa s−1, the corresponding macroscopic strain and stress invariants are computed as (E1◦, E◦2) = Thanks to this rescaling, the seven homogenization tests (Eq 21) enable the description of an iso-dissipation curve in the plane of the stress invariants (S1/3, S2) as illustrated in Fig. 2 (Step b). Optimal values for f (φ) and c(φ) were obtained in the range φ ∈ [0.43, 0.87] by minimizing the quadratic error between the model (Eq 28) and the numerical points (S1◦(θ )/3, S◦2(θ ))
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