Stress-fractional modelling of dilatancy behavior under monotonic loading based on a new yield surface of coarse-grained soil

Fractional calculus has been proven to be a powerful modeling tool for soil, which is often used to develop the dilatancy equation in the model construction. However, the existing fractional-order dilatancy equation incorporating the state parameter has the unsatisfying simulations on the dilatancy behaviors of coarse-grained soil, which strongly depends on the material state, i.e., the stress and void ratio. For that, a new fractional-order dilatancy model incorporating the stress and strain states is developed for coarse-grained soil. Originally, a new yield function applicable to coarse-grained soil is proposed by modifying the yield function of Cam-clay model, in which a parameter controlling the shape of the yield surface is introduced. Then, a fractional-order dilatancy model for coarse-grained soil is derived by using the fractional derivative of the new yield function. Meanwhile, an evolution law for the order of fractional derivative is put forward, which shows the development with the shear strain. Ulteriorly, drained triaxial compression test results of three coarse-grained soils with only one void ratio and two coarse-grained soils with three void ratios are simulated, and it is found that there is a good agreement between the model simulations and test results. Finally, the elastoplastic model developed by incorporating the modified yield function and fractional-order dilatancy model into Cam-clay model is used to simulate the bearing capacity of one foundation, and the result reveals that the introduction of fractional calculus will not encounter convergence issue in finite element analysis.