Articles | Volume 11, issue 3
The Cryosphere, 11, 1465–1485, 2017
The Cryosphere, 11, 1465–1485, 2017

Research article 28 Jun 2017

Research article | 28 Jun 2017

Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

Antoine Wautier1,2,a,b,c, Christian Geindreau1, and Frédéric Flin2 Antoine Wautier et al.
  • 1Université Grenoble Alpes, CNRS, Grenoble INP (Institute of Engineering), 3SR, 38000 Grenoble, France
  • 2Météo-France – CNRS, CNRM UMR 3589, CEN, 38400 Saint Martin d'Hères, France
  • anow at: AgroParisTech-ENGREF, 19 avenue du Maine, 75732 Paris, France
  • bnow at: Irstea UR RECOVER, 3275 Rte Cézanne, CS 40061, 13182 Aix-en-Provence CEDEX 5, France
  • cnow at: Université Grenoble Alpes, Irstea, UR ETGR, 2 rue de la Papeterie-BP 76, 38402 St-Martin-d'Hères, France

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.

Short summary
The results shown in the present paper consist in predicting the overall viscous behavior of snow from the sole knowledge of the microstructure and the ice viscous behavior. This is done thanks to multi-scale modeling techniques and an original approach is used to handle the nonlinearity of the ice behavior. An application of the developed formulation can be found in the simulation of the densification of the snowpack in order to enhance avalanche risk forecasting.