Theoretical Modelling of the State-Dependent Behaviour of Granular Soils Based on Fractional Derivatives

Abstract

The stress-strain behaviour of granular soil was observed to depend on its material state. To consider such state-dependence, different state parameters were empirically proposed and introduced into the existing plastic potential functions, which inevitably resulted in some model parameters with unclear physical origins. The aim of this paper is to present a theoretical modelling of the state-dependent behaviour of granular soils by using fractional derivatives. A novel state-dependent model for granular soils is mathematically developed without any state parameters and plastic potentials as used in other literatures. The soil state in this study is considered via analytical solution. By conducting fractional derivative of the yielding function, a state-dependent plastic flow rule and the corresponding hardening modulus without using plastic potentials and the widely suggested state parameter (ψ) are obtained, where the non-associativity and material hardening are controlled by the fractional order. To validate the model, a series of drained and undrained triaxial test results of different granular soils are simulated, from which a good model performance is observed.