Probabilistic characterization of joint roughness coefficient through a novel Bayesian sequential updating framework

The probabilistic characteristics of joint roughness coefficient (JRC) are critical for risk assessment and reliability-based design in rock engineering involving jointed rock masses. Direct measurements are often laborious and limited, while empirical models using various topographic metrics typically yield inconsistent JRC estimates, posing challenges for reliable result selection. Thus, effectively combining multi-metric evaluations for reasonable probabilistic JRC characterization remains an urgent task. For this purpose, this paper proposes a novel Bayesian sequential updating (BSU) framework that considers the inherent uncertainties in various JRC estimation models and innovatively incorporates correlations among multi-source metrics using multivariate normal, Gaussian copula, and Vine copula models, respectively. Furthermore, the Bayesian model averaging (BMA) technique is employed for the first time to address the selection uncertainty in Vine copula-based dependence structures. Three real-life datasets of root mean square of the average local slope ($Z_{\text{2}}$), ultimate slope of the profile (${\text{R}}_{\max }$), and standard deviation of undulation angle (${\text{SD}}_{\text{i}}$) are sequentially integrated into the proposed BSU framework to generate massive equivalent JRC sample sets, through which the statistics and probability distribution of JRC are analyzed. The results show that the proposed BSU framework significantly outperforms the conventional BSU with independence assumptions. As more multi-source information is integrated, it achieves better BSU results with comparable or superior accuracy to individual empirical models, circumventing the model selection challenge. The proposed approach demonstrates enhanced adaptability to limited datasets and broad generality for probabilistic characterization of data-constrained geotechnical parameters with correlated multi-source indirect information.