Fractional-order bounding surface model considering breakage of calcareous sand

The calcareous sand is widely used as the construction materials in marine engineering. Particle breakage will reduce the strength and dilatancy, and increase the compressibility, which affects the security and stability of the constructions. In this study, the influences of breakage on the position and shape of the critical state line are described by introducing the crushing stress. A unified state-dependent fractional plastic flow rule is established based on fractional differential and state-dependent theory. A fractional-order plasticity boundary surface constitutive model considering the particle breakage and state-dependent behavior of the calcareous sand is established under the framework of the boundary surface plasticity and the critical state theory. The model can simulate the drained triaxial test results of the calcareous sand under different initial densities and confining pressures and reflect the state-dependent behavior under the influences of the particle breakage, which verifies the applicability of the proposed model.