Abstract: Based on the bounding surface model developed for saturated sand under cyclic loading, a 3D model is introduced into three-dimensional stress space by means of the modified generalized Mises method. The model incorporates the state-dependent dilatancy and the hardening rule of using historically maximum loading surface as the bounding-surface to simulate the changes of stiffness and dilatancy and contraction of saturated sand under drained conditions. In virtue of the concept of substepping integration scheme, an explicit integration procedure of the bounding-surface model for saturated sand under cyclic loading is proposed. By utilizing user subroutine interface of finite element method (FEM) software, the explicit integration procedure is incorporated into FEM software. Hence, a finite element model consists of one single soil element is created to simulate triaxial compression experiments of Toyoura sand subjected under monotonic and cyclic loading respectively. As a result, the effectiveness of the explicit integration scheme demonstrated its performances in accurately obtaining stress-strain relation and dilatancy and contraction phenomenon of Toyoura sand under both monotonic and cyclic loading. Moreover, the high stability and convergence of the explicit integration scheme are validated for relatively small strain increments by setting up increments with various sizes.

Key words: substepping, explicit integration algorithm, bounding surface model, cyclic loading, saturated sand, drained condition