An elastic-plastic model for frozen soil from micro to macro scale

Abstract

Frozen soil is a multiphase heterogeneous composite, whose mechanical properties are controlled by the different constituent materials properties and the internal breakage mechanism. In response to this issue, a multiscale incremental elastoplastic constitutive model for frozen soil is derived to reflect this internal mechanical mechanism through micro-thermo-mechanics and homogenization theory, which includes two homogenization steps: breakage stage (I step) and constituent materials stage (II step). Firstly, the nonlinear homogenization process in the first step is transformed into linear homogenization through Hill's linearization method and the incremental constitutive model is given with the elastic/plastic increment strain concentration tensors by the self-consistent theory, which considers the breakage mechanism, and a new method for determining the volumetric breakage ratio is developed by means of thermodynamic theory, which has a more rigorous theoretical framework than previous methods. Secondly, in the second homogenization process, the elastic stiffness tensor of bonded elements, which is composed of unbroken material with elastic properties, is given by M-T method (incremental constitutive model). Meanwhile, the elastical-plastic stiffness tensor of frictional elements is determined by using a new Eshelby's tensor for elastic-plastic medium (incremental constitutive model). Finally, the specific application of this model for frozen soil is given, and the rationality is demonstrated by comparing the computed and tested results under conventional triaxial compression test.