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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 stress–dilatancy relation is of critical importance for constitutive modelling of geomaterial. A novel fractional-order stress–dilatancy equation had been developed for granular soil, where a nonlinear stress–dilatancy response was always predicted. However, it was experimentally observed that after a certain extent of shearing, an almost linear response between the stress ratio and the dilatancy ratio, rather than the nonlinear response, usually existed. To capture such stress–dilatancy behaviour, a new fractional stress–dilatancy model is developed in this study, where an apparent linear response of the stress–dilatancy behaviour of soil after sufficient shearing is obtained via analytical solution. As the fractional order varies, the derived stress–dilatancy curve and the associated phase transformation state stress ratio keep changing. But, unlike existing researches, no other specific parameters, except the parameter related to fractional order, concerning such shift are required. Then, the developed stress–dilatancy model is applied to constitutive modelling of granular soil and soil–structure interface, for further validation. A series of test results of different granular soils and soil–structure interfaces under different loading conditions are simulated and compared, where a good model performance is observed. [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]

This paper presents a fractional order plasticity model by using the concept of fractional order plastic flow. The flow direction is obtained by performing fractional order derivative of the plastic potential function with respect to loading stress. Unlike the classical model, the obtained flow direction changes with the changing fractional order, which makes the model capable for modelling various kinds of plastic flow patterns of different granular soils without changing the details of the potential function. The flexible ability of the proposed model is further validated by simulating multiple series of experimental results of different granular soils subjected to drained and undrained triaxial compressions. [ABSTRACT FROM AUTHOR]

Due to the distinct integral definitions of the fractional derivatives for compression and extension, a generalised state-dependent fractional plasticity model suitable for both loading cases is derived analytically to simulate the drained and undrained behaviour of granular soils. A series of triaxial tests on different granular soils are then used to validate the model. It is found that material responses, such as hardening and softening, contraction and dilation, liquefaction and steady state flow, etc., under compressive and extensive loads is well described by the proposed model. [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]

The influence of the intermediate principal stress ratio (i.e., the b -value) on the stress–dilatancy relation of coarse granular soils was investigated by a series of true triaxial compression tests conducted under the constant- p ′ and constant- b loading conditions. It was observed that the peak and critical state friction angles increased with decreasing confining pressure or increasing b -value. An increase in the confining pressure or b -value resulted in a decrease in the maximum dilatancy angle. In addition, the relationship between the excess friction angle (i.e., the difference between the peak and critical state angles) and maximum dilatancy angle was greatly influenced by the b -value. A linear equation incorporating the effect of the b -value was proposed for this stress–dilatancy relationship. The perditions of the proposed equation could be in good agreement with the test data of coarse granular soils. The proposed b -dependent stress–dilatancy equation could be useful in the foundation of a constitutive model for granular soils. [ABSTRACT FROM AUTHOR]