Microparameter calibration is an important problem that must be solved in the discrete element method. The Gaussian process (GP) response surface methodology was proposed to calibrate the microparameters based on the Bayesian principle in machine-learning methods, which addresses the problems of uncertainty, blindness, and repeatability in microparameter calibration methods. Using the particle flow code (PFC) as an example, the effects of the microparameters on the macroparameters were evaluated using the control-variable method, and the range of the microparameters was determined based on the macroparameters. The uniform design (UD) method and numerical calculation were used to obtain training samples, and a GP response surface methodology suitable for multifactor, multilevel, and nonlinear processes was used to establish the response surface relationships for macro–micro parameters of rock-like materials in discrete element method. According to the macroparameters obtained from the uniaxial experiments conducted on rock specimens, the microparameters were calibrated using the GP response surfaces. Numerical calculations of uniaxial compression and Brazilian splitting were performed using microparameters, and the results were compared with laboratory experiments for verification. The results showed that the relative errors of the GP response surface and laboratory test values were 5.3% for the modulus of elasticity, −7.8% for compressive strength, and −2.6% for tensile strength. The nonlinear GP response surface considered the characteristics of multiple interacting factors, and the established nonlinear response surface relationship between the microparameters and macroparameters can be used for the calibration of microparameters. The accuracy of the microparameters was verified according to the stress–strain curve and failure morphology of the rock specimens. The method of using the GP response surface to establish the macro–micro parameter relationship in the discrete element method can also be extended to other numerical simulation methods and can provide a basis for accurately analysing the microdamage mechanism of rock materials under complex loading conditions.

Rock materials failures are accompanied by the co-existence of various failure mechanisms, including rock fracturing, shearing, and compaction yield. These mechanisms manifest macroscopically as multiple failure modes and nonlinear strength characteristics related to stress levels. Considering the limitations of current rock mechanics strength theories, which are primarily derived from single failure mechanisms, this study evaluates the applicability of alternative strength theories. Based on the extensional-strain criterion and the PMC (Paul-Mohr-Coulomb) model, a piecewise linear strength model was proposed that is suitable for analyzing multiple failure mechanisms in rocks, revealing the intrinsic mechanisms of multi-mechanism rock material failure. A multiple failure mechanism strength model in the form of inequalities was proposed, using the generalized shear stress, mean stress, and stress Lode angle as parameters. Strength tests conducted on sandstone and granite rock material samples under different stress conditions revealed distinct piecewise linear strength characteristics for both rock types, validating the rationality and applicability of the multiple failure mechanism model. The findings construct a multi-mechanism failure model for rocks, providing enhanced predictive capabilities and aiding in the prevention of rock structural failures.

Rock materials failures are accompanied by the co-existence of various failure mechanisms, in-cluding rock fracturing, shearing, and compaction yield. These mechanisms manifest macro-scopically as multiple failure modes and nonlinear strength characteristics related to stress levels. Considering the limitations of current rock mechanics strength theories, which are primarily derived from single failure mechanisms, this study evaluates the applicability of alternative strength theories. Based on the extensional-strain criterion and the PMC (Paul-Mohr-Coulomb) model, a piecewise linear strength model was proposed that is suitable for analyzing multiple failure mechanisms in rocks and revealing the intrinsic mechanisms of multi-mechanism rock material failure. A multiple failure mechanism strength model in the form of inequalities was proposed, using the generalized shear stress, mean stress, and stress Lode angle as parameters. Strength tests conducted on sandstone and granite rock material samples under different stress conditions revealed distinct piecewise linear strength characteristics for both rock types, vali-dating the rationality and applicability of the multiple failure mechanism model. The findings construct a multi-mechanism failure model for rocks, providing enhanced predictive capabilities and aiding in the prevention of rock structural failures.