Abstract: Under prolonged shear, granular systems reach a critical state with constant macroscopic volume fraction and shear stress, which is commonly described and modeled by the macroscopic critical state theory. However, the mesoscopic origin of the critical state of granular materials remains to be further investigated. Biaxial shear tests were carried out on granular specimens with different initial densities by the discrete element method, and a dynamic evolution analysis method for contact networks based on persistent homology was introduced, which effectively overcomes the difficulty of quantitative characterization caused by the high-dimensional heterogeneity of contact networks. Based on the evolution law of network topology during spatial filtration, the highly heterogeneous composition of the contact network was quantitatively analyzed, and the optimal partition threshold for strong and weak contact systems was proposed. It is found that this threshold is mainly determined by the current shear state of the system and has little correlation with the initial density. Although the contact networks of specimens with different initial densities differ significantly at the early stage of shearing, they all evolve towards the same "mesoscopic critical state" as shearing proceeds, characterized by constant topological structural properties and dynamic evolution rate; moreover, this state is unique and independent of the initial density. It is revealed that the evolution of the contact network towards the critical topological structure and dynamic behavior is the mesoscopic topological origin of the macroscopic critical state of granular systems.

Key words: granular material, contact network, critical state, topological data analysis, discrete element method