Simulation Of Macro-meso Mechanical Behaviors For Granular Materials Based On Cosserat Continuum Model

Granular materials are closely linked to human beings’ daily life and are widely used in engineering, such as gravel, grainy pharmacy and so on. Generally speaking, granular materials are composed of randomly packed discrete particles partially or fully filled with void fluids and they have many complex charateristics. So many researchers devote themselves to theoretical and numerical studies of mechanical behaviors of granular materials.Many features of granular materials, such as the reduction of friction angle with increasing stress level, are related to dilatancy; therefore the understanding of dilatancy is the key to investigating behaviors of granular materials. In most engineering analysis, effect of dilatancy is usually taken into account by introducing the dilatancy angle. Dilatancy angle is generally considered by the following approaches:(1) assuming that the dilatancy angle is equal to zero;(2) assuming that the dilatancy angle is equal to the internal friction angle;(3) assuming that the dilatancy angle is a constant in the range from zero to the internal fricition angle. However, these approaches all have obvious drawbacks:the first method completely ignores dilatancy of granular materials; the second method expands dilatancy of granular materials and it also conflicts with the plastic energy dissipation theory; the last method is a way of over-reliance on engineering experience. While dilatancy angle in all three methods is kept as a constant, which causes that dilatancy increases linearly with the shear strain increasing. And this phenomenon is not consistent with that the plastic volume does not increase after achieving the critical state. In this paper, the specify formula about dilatancy angle given by Houlsby is introduced into plastic potential function in conjunct with Drucker-Prager yield function for Cosserat continuum model for granular materials. Based on two simple numerical examples, it has been show that evolution of dilatancy angle has some effect on the bearing capacity and strain localization. For the bearing capacity, with evolution of dilatancy angle, the larger dilatancy angle will lead to larger bearing capacity, and after the peak of the bearing capacity it will exhibit obvious nonlinear behaviors. For the strain localization, especially for slope stability problem, the larger dilatancy angle causes a more obvious slide band.At the same time, particles’ breakage has an important effect on macroscopic mechanical behaviors of granular materials. Cosserat continuum model contains the internal length scale which represents the average particles’ size of micro structure in granular materials to some extent. So the internal length scale can reflect changes of particles’ radius caused by particles’ breakage. In this paper, an elastoplastic model combined with an experiential crushing equation is suggested for crushable granular materials based on Cosserat continuum model, Hardin’s definition of relative breakage Br, which is used to quantify the extent of crushing, can be obtained from the crushing equation according to normal crushing stress. Numerical examples mainly focus on the effect of particle crushing on the bearing capacity and localization of plastic strain. Numerical results illustrate that particles crush mainly in shear band, and shear band obviously becomes narrow and the equivalent plastic strain gradient increases when considering crushing.In addition, multiscale method for granular materials provides a new approach for the study of granular materials. The macro-micro mechanical behavior of granular materials is investigated based on a two-scale method (Finite Element Method-Discrete Element Method, FEM-DEM). In this method, the macro-stresses are obtained from the average of contact forces between discrete particles in RVE (Representative Volume Element) and the macro deformation provides the boundary condition for RVE, meanwhile the micro behavior of granular materials is modeled by the DEM. So RVE is the key point for this method and it needs to choose a micro structure which has an appropriate size to become RVE. Part of this paper’s content is mainly focused on the influence of the size of micro structure on the deformation stiffness, the bearing capacity and the residual strength of the numerical model and suggests the corresponding fitting formulas according to the results. In addition, the micro structure’s configuration and the particles’ displacement fluctuation in the loading process are also concerned. Comparing the results under the same vertical loading displacement, it can be found that the macro deformation is closely associated with the evolution of the micro structure:because the micro structure’s configuration and closely packed form both don’t change obviously before the ultimate bearing capacity, the bearing capacity increases as the load displacement’s increasement. After the ultimate bearing capacity, the micro structure’s area becomes bigger apparently and closely packed form gradually disappears. As results of these changes, the bearing capacity has a significant softening and the particles’ displacement fluctuation includes some slip bands.