Bounding surface plasticity for sand using fractional flow rule and modified critical state line

Abstract

Bounding surface plasticity has been widely used for capturing the stress–strain behaviour of geomaterials. However, it may require multiple sets of model parameters for constitutive modelling of sands with a wide range of initial states, because of the distinct critical state characteristics under low and high densities or pressures in the $$e-\ln {p}'$$ plane. In this study, an enhanced bounding surface plasticity approach for sand with a wide range of initial material states is developed. A fractional plastic flow rule and a modified critical state line are suggested, which ensures that without using any predefined state indices, the developed model can consider the state-dependent dilatancy and hardening behaviours of sand subjected to low and high pressures/densities. The approach is validated by simulating the well-documented test results of Toyoura sand and Sacramento River sand. For comparison, the original state-dependent dilatancy approach in Li and Dafalias (Geotechnique 50(4):449–460, 2000. https://doi.org/10.1680/geot.2000.50.4.449 ) is also adopted and implemented. It is found that the two approaches can reasonably capture the typical stress–strain behaviour, e.g. hardening/contraction, softening/dilation, liquefaction, quasi-steady state flow, and non-flow, of sands with different initial material states, by using a single set of model parameters. However, compared to the current work, Li and Dafalias (2000) model relied on a predefined state parameter, for capturing the state-dependent behaviour of sand under a wide range of initial states