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

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 - In 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