Uncertainty estimation of rock shear strength parameters based on Gaussian process regression

To address the issue of previous methods for estimating rock shear strength parameters lacking the ability to reflect and quantify uncertainties, a rock shear strength parameter uncertainty estimation method based on Gaussian process regression (GPR) is proposed for conducting probabilistic uncertainty analysis. Utilizing the rock strength parameter dataset, Gaussian process theory is employed to establish the mapping relationship between rock uniaxial compressive strength (UCS) and tensile strength (UTS) with shear strength parameters using various kernel functions. Through maximizing the logarithmic marginal likelihood function, the hyperparameter of the GPR model is optimized, and then the appropriate kernel function and GPR model are determined according to the prediction effect and uncertainty degree. The results indicate that under given UCS and UTS data, it is advisable to utilize the Matern kernel function for developing the cohesion GPR model and the rational quadratic kernel function for constructing the internal friction angle GPR model. Compared with conventional machine learning methods, the GPR method not only provides accurate predictions of rock shear strength parameters but also offers insights into the degree of prediction uncertainty, demonstrating strong scientific validity and interpretability, thereby validating the feasibility and efficacy of the GPR model.