Graph theoretical analysis of limestone fracture network damage patterns based on uniaxial compression test

The topological attributes of fracture networks in limestone, subject to intense hydrodynamics and intricate geological discontinuities, substantially influence the mechanical and hydraulic characteristics of the rock mass. The dynamical evolution of fracture networks under stress is crucial for unveiling the interaction patterns among fractures. However, existing models are undirected graphs focused on stationary topology, which need optimization to depict fractures' dynamic development and rupture process. To compensate for the time and destruction terms, we propose the damage network model, which defines the physical interpretation of fractures through the ternary motif. We focus primarily on the evolution of node types, topological attributes, and motifs of the fracture network in limestone under uniaxial stress. Observations expose the varying behavior of the nodes' self-dynamics and neighbors' adjacent dynamics in the fracture network. This approach elucidates the impact of micro-crack behaviors on large brittle shear fractures from a topological perspective and further subdivides the progressive failure stage into four distinct phases (isolated crack growth phase, crack splay phase, damage coalescence phase, and mechanical failure phase) based on the significance profile of the motif. Regression analysis reveals a positive linear and negative power correlation between fracture network density and branch number to the rock damage resistance, respectively. The damage network model introduces a novel methodology for depicting the interaction of two-dimensional (2D) projected fractures, considering the dynamic spatiotemporal development characteristics and fracture geometric variation. It helps dynamically characterize properties such as connectivity, permeability, and damage factors while comprehensively assessing damage in rock mass fracture networks.