Prediction of mode I crack propagation in rock based on fracture parameters from the boundary effect Model: Numerical study and experimental Validation

Abstract

Knowledge and accurate prediction of crack extension in rocks that incorporates accurate fracture criterion and fracture parameters are crucial for the stability of rock masses and for safe design of rock structures. While the stress intensity factor (SIF)-based crack propagation criteria have been employed to evaluate the fracture process of concrete, limited research is conducted on the applicability of SIF-based criteria in modelling the crack extension in rocks. In this paper, a numerical model was proposed to evaluate the mode-I crack propagation process in rocks with the consideration of the nil-SIF-based ($K_{\text{IC}}^P-K_{\text{IC}}^{\sigma }=0$) and initial fracture toughness ($K_{\text{IC}}^{\mathrm{ini}}$)-based criteria ($K_{\text{IC}}^P-K_{\text{IC}}^{\sigma }=K_{\text{IC}}^{\mathrm{ini}}$), where $K_{\text{IC}}^P$ and $K_{\text{IC}}^{\sigma }$ represent the SIF induced by external loads and cohesive forces, respectively. To facilitate these simulations, the fracture parameters were analytically calculated using the boundary effect model (BEM) and validated with those measured from experimental tests. Laboratory experiments were carried out on three-point bending (3-p-b) sandstone beam specimens with different initial crack length. After the validity of the proposed model is verified with both the self-conducted experimental results and the test data available in the literature, a comparative analysis was conducted to assess the effectiveness of the two SIF-based criteria by comparing with experimental database given in the literature. The results indicated that the predicted load-crack mouth opening displacement (P-CMOD) response, maximum load, critical CMOD (CMOD_c) at the peak load using the $K_{\text{IC}}^{\mathrm{ini}}$−based criteria showed better agreement with the experimental data, regardless of rock type, specimen configurations and dimensions, while the predictions derived from the nil-SIF-based criterion were underestimated. The crack resistance (K_R) values calculated using the nil-SIF-based criterion were observed to be lower than those determined via the $K_{\text{IC}}^{\mathrm{ini}}$−based criterion during the initial cracking phase, specifically for normalized crack extension lengths near 0.6. Beyond this threshold, the crack resistance becomes predominantly governed by cohesive forces, which results in larger K_R values when the nil-SIF-based criterion is applied.