Mathematical aspect of the state-dependent stress–dilatancy of granular soil under triaxial loading Available to Purchase

The stress–dilatancy of granular soil is highly dependent on its material state. To understand and model such behaviour, a variety of state-dependent stress–dilatancy equations have been proposed by empirically incorporating different state parameters. Even though a good performance was often observed when using these equations, the basic mathematical origins were missing. The purpose of this note is to provide one possible mathematical interpretation of the state-dependent stress–dilatancy. A novel state-dependent stress–dilatancy equation without using any state parameters is derived step by step based on fractional stress operators. As mathematically proved, the plastic flow of granular soil is determined not only by the current load state but also by the memory distance from the current state to the corresponding critical state, which conforms to the concept indicated by state parameters. Possible mathematical and physical meanings of the fractional order are also discussed. To verify the proposed approach, a series of stress–dilatancy data of granular soils with different material states from the literature are simulated and compared, from which a good agreement can be observed. To further demonstrate the capability of the approach, the developed state-dependent stress–dilatancy equation is then incorporated into the well-known model developed by X. Li and Y. Dafalias in 2000; here also a good performance is observed.