Modeling Cyclic Volumetric Strain Accumulation in Sand under Drained Simple Shear Conditions

This study presents a critical state two-surface plasticity model formulated such that it accurately simulates the volumetric behavior of sands under drained cyclic simple shear (CSS) loading. The model is based on critical state theory and accounts for the effects of inherent fabric anisotropy and evolving fabric upon cyclic loading. To represent the effects of fabric evolution under cyclic loading, a multiplier is introduced to the plastic modulus equation to express accumulated fabric changes occurring during the dilation phases that manifest as enhanced contraction in subsequent load reversals. Moreover, a conical surface is incorporated into the general stress space, in addition to the yield surface, to capture the experimentally observed cyclic threshold shear strain associated with the onset of volume changes. The model is calibrated using data from low- to high-amplitude CSS tests on Toyoura sand and Ottawa sand. The model manages to reproduce the net contraction that sand experiences during each loading cycle up to a very high number of cycles (of the order of 103 to 105). The magnitude of contraction diminishes progressively over successive cycles, with the compaction process approaching asymptotically a limiting minimum void ratio state at a very large number of cycles. The model accounts for the effects of relative density, anisotropic consolidation, and shear strain amplitude on the rate of accumulation of contractive volumetric strains.