Numerical investigation of granular material behaviour under rotational shear

Abstract

This paper presents numerical experimental results with respect to the responses of two-dimensional granular materials under principal stress rotations. The tests were carried out using the discrete element method. A numerical procedure has been developed to apply arbitrary stress or strain paths and to measure the induced strain or stress changes. The procedure is used to investigate the elementary behaviour of granular materials undergoing pure stress rotation. In this kind of test, the mean stress and the shear stress are kept constant while the principal stress direction continuously rotates. Two series of numerical experiments have been conducted, one with varying stress ratios and the other with different initial void ratios. Material dilatancy and non-coaxiality are explained based on the knowledge of the internal structure and its evolution. The material internal structure is mathematically described in terms of a geometrical system, called the void cell system. The internal structure size and material anisotropy are characterised by the statistical measures of the void cell geometries. The observations show that granular materials develop an anisotropic structure when sheared. In rotational shear, the internal structure rotates following the rotation of principal stress, only lagging behind by a few degrees. The rotation of the internal structure produces strain components normal to the stress direction. Hence, the material behaviour is non-coaxial. When principal stress rotation continues, granular materials approach an ultimate internal structure, the strain trajectory in the deviatoric plane approaches a circle. The material anisotropy and the internal structure size at the ultimate state are dependent on the stress ratio, but independent of the initial void ratio. The larger the stress ratio is, the more anisotropic would the ultimate internal structure become. The ultimate internal structure size under stress rotation is found to be much smaller than the internal structure size achieved in biaxial shearing at the critical state. In other words, the void ratio at the ultimate state undergoing rotational shear is much smaller than that at the critical state undergoing biaxial shearing. Hence, the material behaviour under principal stress rotation is more contractive.