The macro- and micro-numerical simulations of biaxial shear tests for ideal granular samples with different initial densities were carried out using discrete element method. Loop structures

represented by Voronoi polygons

were taken as the basic meso-mechanical unit of granular material by mesh-subdivision. The evolution of numbers

geometrical morphology and mechanical characteristic for different loops were simulated. The meso-mechanical characteristic at critical state for granular media was especially analyzed. Numerical results show that the evolution of higher-order loops and lower-order loops are different. The evolution of same types of loops in granular samples with different initial densities are different before critical state reaching. The number proportions

geometrical morphology

contact forces of side particles and inner sliding rates of same kinds of loops in granular samples with different initial densities have reached critical state respectively. From mesoscopic point of view

critical state of granular media is the consequence of mutual transformation for higher-order loops and lower-order loops

and is the combined average and external manifestation of all loops. Meso-scale loop structures under a state of dynamic equilibrium at critical state reflected by the constant shear stress and development of shear deformation under constant volume on macro-scale. Numerical results also show the evolution of numbers

geometrical morphology

mechanical characteristic and contact stabilities of meso-scale loop structures

are closely related to the development of strength

dilatancy and critical state for granular material. So it can be taken as the basic unit of meso-mechanism for granular media.