Probability Quantification of GSI and D in Hoek–Brown Criterion Using Bayesian Inversion and Ultrasonic Test in Rock Mass

The Hoek–Brown criterion is widely utilized in rock mass engineering. However, determining the geological strength index (GSI) and disturbance factor ( D ), essential parameters of the Hoek–Brown criterion, can be challenging. This study addresses this issue by establishing a quantitative expression for D based on the theoretical relationship between the P-wave velocity of rock mass ( V_p ) and dynamic elastic modulus ( E_md ). Furthermore, a probability inversion framework employing Bayesian theory is developed to derive the probability distribution of Hoek–Brown criterion parameters using field monitoring data. To validate the effectiveness of the framework, time-series data obtained during the excavation of the main powerhouse at the Yingliangbao Hydropower Station are utilized. The results demonstrate that the updated GSI and D parameters conform to normal distributions, specifically Normal (57.01, 4.04) for GSI and Normal (0.43, 0.10) for D , respectively. By incorporating the updated rock mass parameters, the accuracy of predicting excavation deformation is significantly improved. Overall, the developed framework offers a dynamic and probabilistic approach for determining Hoek–Brown criterion parameters, enabling more accurate deformation predictions and risk assessments during excavation projects.