A dilatant double shearing model for granular materials including the effects of fabric
Description
In the present study, we develop a dilatant double shearing model for granular materials incorporating the effects of fabric and its evolution in order to capture the inherent and induced anisotropic behavior and the complex cyclic shear loading response of granular materials. Unlike Anand and Gu's (2000) model where the two shearing rates are taken to be equal, we can have different shearing rates along the two slip systems by considering the fabric. This property leads to non-coaxiality of the principal axes of stress and strain rate, which is more appropriate for a material that exhibits initial and induced anisotropy. We also propose an evolution equation for the fabric tensor. In addition, we assume an orthotropic elasticity tensor with the axes of orthotropy coincident with the principal axes of the fabric tensor and the components of the elasticity tensor dependent on the invariants of the fabric tensor. The model developed in this paper also includes the experimentally observed characteristics of granular materials: the gradual concentration of the contact normals towards the maximum compressive principal stress direction. We then implement the constitutive equation of the model into ABAQUS/Explicit by writing a user material subroutine and use it to conduct the biaxial compression tests under different initial bedding angles and investigate the responses of this model under the cyclic shear loading conditions. The predictions of this model show good quantitative agreement with the experiments of Park (1990), Park and Tatsuoka (1994) and Okada (1992) We then extend the plain strain dilatant double shearing model to three dimensions. We use this model to conduct the numerical triaxial compression tests for granular samples with different initial anisotropy and the numerical computations for the stress state in a static conical sand pile. The numerical results show that the extended constitutive model is able to capture the strength anisotropy behavior of granular materials We finally make a comparative study of the responses of the present model and the hypoplastic model. We find our newly developed model is easy to calibrate and gives close stress ratio and void ratio responses to the predictions of hypoplastic model under most conditions