General Stress‐Dependent Elastic Moduli for Cross‐Anisotropic Soils

Abstract

A new general nonlinear model for the dependence of the elastic moduli of a cross‐anisotropic soil on the stress state is presented. In agreement with experimental evidence, the model considers that the Young's modulus, the shear modulus and the bulk modulus of soil depend on the stress state, while the three Poisson's ratios are practically constant. The expressions for the stress dependence of the moduli are derived in a rigorous way by considering the conservation of energy during a cycle of loading along any arbitrary closed stress path, assuming purely elastic behavior. For the special case of isotropic soil, the model reduces to an earlier solution, developed by Lade and Nelson in 1987. A parametric study elucidates the effects of normal stresses, deviatoric stresses, Poisson's ratios, and degree of cross anisotropy on the elastic behavior of soil. Furthermore, simulations of undrained triaxial compression tests demonstrate that anisotropy may have a substantial effect on the development of excess pore‐water pressure and the direction of the stress path.