Strength Equivalence of Two Stiffness Calibrations in Particle Flow Code: An Insight from Micro-Cracking Evolution

Geohazards in rock mass are essentially results of fracturing evolution. Regarding deeper exploration, to better contribute to evaluating and predicting instability, Particle Flow Code (PFC) has gained increasing popularity because of its logical resemblance in simulating rock composition and cracking processes. However, micro-parameter calibrations in PFC mainly focus on both the peak strength and macroscopic cracks in many previous, as well as current, studies, resulting in the existence of two widely used yet distinct strategies in stiffness calibration. The first is to ensure the consistency of the elastic modulus, and the second is to ensure the deformation consistency at peak-stress states. Do these two stiffness calibrations have a strength equivalence? To explore it, several rock mechanical tests—with and without confining pressures and a pre-existing flaw—were numerically conducted using PFC for two materials produced by these two distinct stiffness-calibration strategies. The results demonstrate that the two stiffness calibrations can yield equivalent strength parameters, including tensile strength, cohesion, and internal friction angle. This strength equivalence could be attributed to the evolutionary process of micro-crack initiation, accumulation, nucleation, and global failure (coalescence). Fracture mechanics analysis demonstrates that crack initiation is independent of the elastic modulus and marginally influenced by Poisson’s ratio, leading to a negligible impact of stiffness-calibration distinction on crack-initiation stress. Subsequent micro-crack accumulation follows a nearly identical non-linear increasing trend, with a high consistency of spatial distributions in stress concentration, displacement gradient, and strain localization. As a result, the near-identical structural logic in micro-crack nucleation results in failure-pattern consensus and governs the macro-scale strength equivalence of these two distinct stiffness-calibration strategies. These findings could help us to better comprehend those previous, as well as current, research results based on the two stiffness-calibration strategies.