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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]