A bounding surface visco-plasticity model considering generalized spacing ratio of soils

The non-unique critical state of soils with time-dependent behaviors is a significant issue in geotechnical engineering problems. However, previous bounding surface plasticity models cannot predict accurately the non-unique critical state of soils, because the distance between the compression line and critical state line charged by strain-rate effect is basically neglected. To fill this gap, a generalized spacing ratio of soils is defined in the elasto-viscoplastic framework, and a bounding surface visco-plasticity model is formulated and verified, which can consider the generalized spacing ratio. Specifically, the generalized spacing ratio of soils reflects the distance between the compression line and the critical state line of soils with time-dependent behaviors. Then, the generalized spacing ratio is introduced into an improved anisotropic bounding surface. A new expression of the visco-plastic multiplier is derived by solving the consistency equation of an anisotropic bounding surface. In the expression, a strain rate index is proposed to account for the strain-rate effect on visco-plastic strain increment, and a visco-plastic hardening modulus is derived to predict the visco-plastic response of soils in overconsolidation conditions. The model is then verified through constant strain rate tests and creep tests. Notably, it can capture the non-unique critical states of soils with time-dependent behaviors due to the generalized spacing ratio and the creep rupture of soils due to the visco-plastic multiplier that considers the stress ratio and visco-plastic strain rate.