The Random RFPA Method for Modelling Rock Failure.

The random rock failure process analysis (RRFPA) method was developed in this research to characterize the material spatial variability and uncertainty in rock failure modelling. The random field theory (RFT) was integrated with the traditional rock failure process analysis (RFPA) to model rock heterogeneity. In this approach, the variation of rock properties is represented as a function of relative distance, such that the influence of material intrinsic correlation on its fracturing behaviour can be appropriately captured. To validate the theory, 300 RRFPA simulations were conducted to investigate the failure characteristics of rock samples under compressive loading. The results showed that by incorporating a spectrum of material properties, the numerical outcomes exhibited distinct upper and lower bounds of stress across all testing scenarios, closely aligning with the experimental relationships. The histograms for uniaxial compressive strength and elastic modulus showed that both properties followed normal distributions, with the average values of 10.099 MPa and 1.818 GPa, respectively. The corresponding coefficients of variation were 0.450 and 0.038. The localized failure tended to result in a more rapid release of acoustic emission energy, but generated smaller cumulative energy compared to the overall failure pattern. In general, the maximum relative error of the RRFPA model was only 0.66% for uniaxial compressive strength, elastic modulus, and critical axial strain.