Analytical solution of stress-fabric relationship and failure of granular materials in three dimensions

Based on the macro-micro mechanical analysis, three kinds of tensors are proposed to investigate the stress-fabric relationship. An explicit relationship is derived among applied stress tensor, material fabric tensor and force-fabric tensor in three dimensions. The expressions are also obtained in two dimensions and triaxial stress condition, which are verified by DEM simulation of biaxial and triaxial tests. A concept of “true stress” is adopted to investigate the failure of granular materials. The analytical and numerical results indicate that the stress in granular materials is affected by the three kinds of tensors motioned above. The analytical solution of stress-fabric is coincided with the DEM results and has the same form as that proposed by Rothenburg when the higher order terms are omitted. The strength of granular materials is controlled by the “true stress”, and the apparent mobilized frictional angle is the joint action of friction of particles and anisotropic fabric induced by the applied stress. The proposed stress-fabric relationship is potentially useful for further development of the strength theory and stress-stain behavior for granular materials.