An isotropic-kinematic hardening model for cyclic shakedown and ratcheting of sand

Abstract

Modeling the cyclic shakedown and ratcheting of sand remains a great challenge. An isotropic-kinematic hardening model is presented within the bounding-surface framework. By incorporating new features, a combined isotropic-kinematic hardening rule is extended to the deviatoric stress-ratio space. The hardening rule treats cyclic loading as a sequence of monotonic loading events. The kinematic mechanism of this hardening rule assumes that the bounding surface instantaneously translates from the image point to the stress reversal point when the loading path reverses. Then each stress reversal is regarded as an initiation of a new loading event. In each loading event, the isotropic model, which consists of an open wedge-type surface with a circular deviatoric section, may expand or shrink around a generalized homological center to track the variation in the soil fabric. This isotropic mechanism enables the model to capture the gradual evolution of soil stiffness under numerous loading cycles. By introducing a maximum prestress surface, an additional mechanism is deployed to avoid the overshooting problem and to promote the simulation of the post-cyclic behavior. A unified hardening function is defined in the model for all loading events. After calibrating the basic parameters by monotonic tests, only three extra cyclic parameters are required to describe the cyclic behavior of sand. The model behaviors are validated against serval cyclic triaxial tests. The comparison between experimental and predicted results demonstrates the model capabilities in describing the cyclic shakedown and ratcheting responses of sand.