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To capture the state-dependent behaviour of granular soil, an interdisciplinary approach, fractional plasticity, was proposed. However, the permissible value of the fractional-derivative order has not been evaluated. This technical note aims to analyse the permissible range of fractional order from the perspective of modelling flow liquefaction of sand. A state-dependent fractional elastoplastic model without using predefined state parameters is proposed. Then, a series of test results of different sands under flow liquefactions are simulated. Permissible range of the fractional order is analysed by evaluating the second-order work for predicting flow liquefaction instability of sand, where it is suggested that the fractional order should be less than two. [ABSTRACT FROM AUTHOR]

The strength and deformation behaviour of granular soil is strongly dependent on its stress state and loading history. Due to the change of soil state, the plastic flow direction and loading direction are usually non-coaxial and a plastic potential different from the plastic loading function is generally mandatory for capturing correctly volumetric deformation. For that, some state variables have been involved phenomenologically in plastic equations, bringing about some complexity in model formulations and physically meaninglessness of certain parameters. This paper presents a new approach to describing the state-dependent stress-dilatancy behaviour of granular soil using fractional order derivations. Unlike integer-order derivative in the classical plasticity theory, the fractional order derivative is defined in an integral form. Originally, we relate the description of soil state to the definition of the integral lower and upper limits respectively as the current and critical stress states. By performing a fractional order derivative of the plastic yield function, a state-dependent stress-dilatancy equation is set up without additional state variables. As the integration range increases, the flow direction deviates gradually from the loading direction. However, they coincide with each other when critical state is reached where the lower and upper limits merge. For validation, an elastoplastic constitutive model is developed by incorporating the fractional equation into the modified Cam-clay model. A series of drained and undrained triaxial test results for different granular soils are simulated, and the issue of plastic energy dissipation in each simulation is also addressed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]