Bayesian Inference of Rock Rheological Constitutive Model with NUTS-MCMC: A Case Study on Baihetan’s Slope Engineering

In evaluating the safety of rock slopes engineering, it is imperative to account for rheological effects. These effects can lead to significant deformations that may adversely impact the overall structural integrity. Consequently, accurate determination of the rheological mechanical parameters of slope rocks is essential. However, the application of rheological parameters obtained from laboratory tests encounters limitations due to the rock’s inherent heterogeneity, scale effects, and inevitable sample dispersion. By contrast, on-site monitoring data serve as critical assets for real-time calibration and risk assessment in the evaluation of rheological parameters and prediction of slope deformation. To integrate on-site monitoring data with rheological mechanical mechanisms, this study introduces a probabilistic inverse model for evaluating rock slope rheological parameters, grounded in Bayesian theory, and incorporating a No-U-Turn Sampler (NUTS) based on Markov Chain Monte Carlo (MCMC) sampling algorithm. In terms of methodological efficiency, we compared the NUTS method with the traditional Metropolis–Hastings (M-H) approach, demonstrating the superior efficiency of the former. Additionally, sensitivity analysis of rheological parameters was conducted using the Burgers constitutive model. By combining the NUTS-based MCMC method with this model, the uncertainty of creep parameters was successfully evaluated. Utilizing these updated posterior parameters, up to 3-year deformation forecast for the slope was executed, the findings demonstrate that the deformation on the left bank slope is slight, indicating a state of safety. This study integrates monitoring data with rheological mechanics to establish a physical-data-driven rheological safety assessment mechanism. It offers a scientifically robust and effective approach for the uncertainty evaluation of rheological parameters and deformation prediction, providing significant support for the safety assessment of the left bank slope of the Baihetan hydropower station, China.