Study on the evolution law and quantitative characterization of micro-crack propagation in the compressive failure process of rocks

Quantitative characterization of the evolution law of micro-crack propagation in rocks is important for understanding the rock failure mechanism. This study aims to establish a theoretical method for quantitatively characterizing the evolution of micro-crack propagations during the compressive failure of rocks. Mechanical properties and failure characteristics of carbonaceous mudstone were investigated by triaxial compression tests. In order to study the evolution law of crack propagation morphology and quantity, numerical simulations of micro-crack propagation in rocks during triaxial compression were performed using the particle flow code (PFC). Based on the phenomenological theory, we proposed to define the rock damage increment by crack propagation quantity. The evolution law of crack quantity was characterized using the Logistic growth model. Furthermore, an equation for the evolution of micro-crack propagation quantity during compressive failure was established, and the rationality of the equation was verified. The results show that micro-cracks initiate in weak areas of rocks and develop and converge around existing cracks, eventually leading to localized failure through propagation and connection. The number of micro-cracks grows in an “S-shaped” pattern, accelerating before the peak stress, reaching a maximum growth rate at the peak stress, and decelerating in the post-peak stage. As the confining pressure increases, the number of rock micro-cracks increases, the propagation morphology becomes more complex, and the failure localization weakens. The proposed equation accurately characterizes the evolution of micro-crack propagation quantity in the rock failure process. In addition, the calculation results are in good agreement with the numerical analysis results, verifying the rationality of the equation.