Abstract
It was found that the constitutive behaviour of granular soil was dependent on its density and pressure (i.e. material state). To capture such state dependence, a variety of state variables were empirically proposed and introduced into the existing plastic potential functions, which inevitably resulted in the complexity and meaninglessness of some model parameters. The purpose of this study is to theoretically investigate the state-dependent non-associated behaviour of granular soils without using predefined plastic potential and state variable. A novel state-dependent non-associated model for granular soils is mathematically developed by incorporating the stress-fractional operator into the bounding surface plasticity. Unlike previous studies using empirical state variables, the soil state and non-associativity in this study are considered via analytical solution, where a state-dependent plastic flow rule and the corresponding hardening modulus without using additional plastic potentials are obtained. Possible mathematical connection with a well-known empirical state variable is also discussed. The non-associativity between plastic flow and loading directions as well as material hardening is found to be controlled by the fractional-derivative order. To validate the proposed approach, a series of drained and undrained triaxial test results of different granular soils are simulated and compared, where a good agreement between the model predictions and the corresponding test results is observed.
Highlights
It has been widely acknowledged that the strength and deformation behaviour of granular soil, such as sand and rockfill, is significantly dependent on its density and pressure [1]
Before the proper consideration of state dependence during constitutive modelling, different model parameters were often required for modelling the stress-strain behaviour of granular soils with different initial densities or subjected to different confining pressures [2,3,4]
To consider the state dependence, the state-dependent fractional plasticity model was proposed [14] by empirically incorporating ψ, which made the parameters of the obtained stress-dilatancy equation lack physical meaning
Summary
It has been widely acknowledged that the strength and deformation behaviour of granular soil, such as sand and rockfill, is significantly dependent on its density and pressure (material state) [1]. To reduce the number of model parameters without the loss of modelling capability, Sun and Shen [21] proposed a non-associated plastic flow rule for granular soil by conducting fractional-order derivatives of the yielding surface, where the obtained vector (plastic flow direction) was no longer normal to the yielding surface, even without using an additional plastic potential. This non-normality increased as the fractional order (α) decreased [14, 22, 23]. To consider the state dependence, the state-dependent fractional plasticity model was proposed [14] by empirically incorporating ψ, which made the parameters of the obtained stress-dilatancy equation lack physical meaning
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
