Finite-Deformation Cam-Clay Model Considering Elastic Dilatancy and Soil Skeleton Structure

Abstract

Elastoplastic constitutive equations for soils often employ the nonlinear rate-type isotropic Hooke’s law, which is based on the additive decomposition of strain rate and considers the pressure dependency in the elastic part. Hooke’s law has independent isotropic and deviatoric components, and therefore, it cannot express elastic dilatancy as confirmed in experiments. In this model, although the elastic volume change is path-independent, the shear strain exhibits a significant residual when subjected to an effective stress cycle. This study proposes a rate-type elastic constitutive equation for soil applicable to elastoplastic constitutive equations based on finite deformation theory using an objective stress rate and additive decomposition of stretching; these equations cover these shortcomings of the rate-type Hooke’s law. The proposed rate-type elasticity constitutive equation is based on the hyperelastic body in the infinitesimal deformation theory proposed by Einav and Puzrin or Houlsby et al. and has confining pressure dependence, path independence of elastic volume change, and elastic dilatancy. Further, the residual strain is considerably smaller than that of the rate-type Hooke’s law. Moreover, this study improves the elasto-plastic constitutive equation, SYS Cam-Clay model, based on the skeleton structure concept by introducing the proposed elastic constitutive equation. The basic behavior of the elastoplastic constitutive equation for clay and sand is demonstrated to show that the newly acquired elastic dilatancy improves the mean effective stress reduction behavior during shear stress unloading under undrained conditions and the stiffness recovery behavior during liquefaction, which is essential for describing cyclic mobility.