Abstract: Macroscopic mechanical characteristics of granular materials are closely related to the microscopic contact force and fabric. Generally speaking, the strong contact system contributes to the force transmission of internal granular system, and then its corresponding fabric tensor has important influence on the macroscopic stress. Microscopic numerical methods, such as discrete element method, can reproduce the laboratory tests with reasonable macroscopic responses and extract macro- and micro-data conveniently for investigating the underlying mechanism of the granular system. Based on discrete element method (DEM), a series of true triaxial tests for granular materials under constant p and constant b stress paths are carried out, and the evolutions of macro- and micro-mechanical parameters of granular materials, the multiple relationship between three-dimensional fabric tensor and stress tensor and the macro-stress characteristics reflected by strong contact system are studied. The results demonstrate that some macro- and microscopic parameters at the stress peak and critical state in the granular system are independent on the loading path. Non-coaxiality between fabric tensor and stress tensor is observed under three-dimensional stress path, but the evolution of the joint invariant of the two tensors is independent on the 3D loading path. Compared to fabric tensor of weak contact system, the fabric tensor of strong contact system reflects better the characteristics of macroscopic stress tensor. Fabric tensors of strong and weak contact systems contribute differently to the granular macroscopic response. To divide the strong and weak contact system, there is a range for the threshold, however adopting the average contact force is relatively simple and reasonable.