Cyclic bounding surface model for carbonate sand incorporating particle breakage

The carbonate sand is a crushable granular material formed by the marine organisms, and its foundation is subjected to long-term dynamic loading under the ocean environment. Hence, it is of great significance to simulate the particle breakage of the carbonate sand under cyclic loading and its influences on the stress-strain behavior. The mechanism of particle breakage is decomposed of two parts: the compression mechanism with the increase in the mean effective stress, and the shear mechanism with the change of shear stress ratio. The particle breakage caused by the compression mechanism can be simulated by the Hardin’s formula. In order to adapt to the complex stress path, an incremental compression breakage model is established on the basis of the Hardin’s formula. The shear-induced breakage model includes two "declining rules" under the cyclic loading: (1) The accumulate rate of the particle breakage has a maximum value at the initial phase of the monotonic shear process, but decreases with the increasing shear strain. (2) It continuously descends during the whole shear process with the increasing amount of the particle breakage. The compression and shear breakage models are introduced to the framework of the bounding surface constitutive model, and a novel constitutive model considering the particle breakage is established by reflecting the effects of the particle breakage on the stress-strain behaviors such as modulus, strength and dilatancy through the critical state line moving with the amount of the particle breakage. The simulation capability of the proposed constitutive model is verified by comparing with the experimental results of the carbonate sand which is under the monotonic and cyclic drained triaxial compression tests.