Numerical simulations of two-dimensional circular and ellipsoid particulate arrays are carried out based on granular discrete element method. The microscale deformations are measured based on void cells and the deformations occur in them. Deformations within individual voids are computed from the relative motions of surrounding particles. Based on the deformation mechanism

a more physical theory of critical state is developed in terms of valence (number of edges per void cell). Two ultimate cases with large and small friction coefficients are analyzed to define the maximum critical valence. The effects of particle shape

interparticle friction and consolidation stress of the granular assembly on the microscopic fabrics are investigated. The simulation results show that the microscopic critical state can not be characterized by a unique parameter

but depends on the shape and surface characteristic of the individual particles and consolidation stress of the particulate assembly.