Constitutive relations for sand under cyclic loading based on elasto-plasticity theory

Constitutive relations are proposed for expressing the inelastic behavior of sandy ground expected at the time of a strong earthquake. These relations are formulated by a yield function in terms of effective stress ratio and by a plastic potential function which is derived from the stress-ratio-plastic-strain incremental ratio defined as a function of accumulated volumetric strain. These constitutive relations employ Sekiguchi and Ohta's stress parameter to account for the effects of rotation of principal stress axis on the deformation characteristics of sand. The Masing rule is modified so that it can be used in the multidimensional stress field and employed in the hardening function in order to express hysteretic damping. Behavior predicted using the constitutive relations and the results of undrained cyclic shear tests are compared.