An Incremental Formulation of Constitutive Equations for Deposited Snow

Abstract

The behaviour of a snow mass under natural loadings (gravity forces, boundary conditions) can be computed by the finite-element method, in so far as a convenient formulation of the stress–strain relationship for snow is available. This paper deals with such a formulation given in incremental form.Experiments have been performed, which show that deposited snow can be considered as a non-linear visco-elastic material with memory effect. The proposed theoretical formulation takes into account these properties. The elastic part of the deformation is assumed to be isotropic and non-linear; the viscous part is expressed in terms of a creep-rate, which results from a superposition of elementary creep-rates according to Boltzmann’s principle.The values of parameters can be obtained from isotropic creep experiments. The experimental data and the resulting parameters are reported.Since the parameters were determined, the formulation of the rheological law was then tested by integration on “stress–strain paths" corresponding to other experiments of a different type, performed on the same snow. The experiments are triaxial tests at constant axial strain-rate, with a preliminary stage of isotropic compression. Experimental data are compared to theoretical curves obtained by integration of the rheological law. The calculated behaviour is consistent with the experimental results.

Dynamic anticrack propagation in snow

“…Note that in the PST, the slab fails only under tension and thus the absolute value of p 0 has no effect on the results, only βp 0 does. The hardening factor ξ of the slab was chosen based on laboratory experiments of triaxial tests of snow 34 , 58 , 59 but could also be derived from strength–density relationships 57 , 60 .…”

Postglacial colluvium in western Norway: depositional processes, facies and palaeoclimatic record

“…At a very low rate, snow creeps due to the rupture of interparticle bonds and the localized melting and slip within the ice crystals and their aggregates. The creep is often approximated as a linear viscous deformation ( Brown & Lang, 1973; Salm, 1982), although the strain rate decreases with depth, roughly linearly, as the viscosity increases linearly with the normal stress ( Desrues et al , 1980 ; McClung, 1980; Watanabe, 1980). The constitutive relationship is nonlinear once the snow mass has detached itself and flows at a low rate.…”

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

“…The proposed homogenization model can be easily used to predict the viscous behavior of snow in classical laboratory tests as illustrated in the last section of this paper. However, the uncertainties made on our model parameters should be quantified through a sensitivity analysis, in order to reckon the ability of our homogenized law for snow viscosity to quantitatively 5 recover the experimental results of Desrues et al (1980); Bartelt and von Moos (2000); Moos et al (2003); Scopozza and Bartelt (2003b).…”

“…During the last decades, numerous experimental studies have been performed in order to characterize the macroscopic behavior of different types of snow under various loading conditions and temperatures (Mellor, 1974;Salm, 1982;Desrues et al, 1980;Shapiro et al, 1997; Bartelt and von Moos, 2000;Moos et al, 2003;Scopozza and Bartelt, 2003a). In the framework of the continuum mechanics, several models have been then proposed in order to reflect these experimental data (Desrues et al, 1980;Scopozza and Bartelt, 2003b;Cresseri and Jommi, 2005;Navarre et al, 2007;Cresseri et al, 2009). However, the fitted material parameters arising in these models often characterize the mean properties of a few types of snow in a restricted density range.…”