Crack-closure behavior and stress-sensitive wave velocity of hard rock based on flat-joint model in particle-flow-code (PFC) modeling

Micro cracks inside rocks can open or close under variable external forces, which significantly affects the rock modulus and wave velocity. However, conventional simulations typically ignore or homogenize micro cracks primarily because of statistical intricacy and implementation difficulties. A micro -cracked rock model was proposed - characterized by the inclusion of unbonded contacts with an initial gap, based on the flat -joint contact model - to study the mechanisms of micro -cracked rocks and rock masses. The relationship between the static modulus and crack parameters in the proposed model was estimated based on the energy additive theory. Additionally, the macromechanical properties affected by the crack intensity and width were investigated using uniaxial compression, wave velocity measurements, Brazilian splitting, and direct shear simulations. Based on the simulated results, a new calibration procedure was formulated to efficiently calibrate the crack -closure stage under uniaxial compression. Furthermore, the relationships between the P -wave velocity, cracks, and biaxial stresses were investigated. The results indicate that existing micro cracks can transition between open and closed states under variable biaxial -stress conditions, influencing wave propagation and resulting in anisotropy. The performance observed during the transient unloading of a tunnel validated the capability of the proposed method for dynamic analysis in jointed -rock -mass engineering.