An efficient Bayesian multi-model framework to analyze reliability of rock structures with limited investigation data

Availability of insufficient data is a frequent issue resulting in the inaccurate probabilistic characterization of properties and, finally the inaccurate reliability estimates of rock structures. This study presents a Bayesian multi-model inference methodology which couples multi-model inference with traditional Bayesian approach to characterize uncertainties in both—(1) probability models, and (2) model parameters of rock properties arising due to insufficient data, and to estimate the reliability of rock slopes and tunnels considering their effect. Further, this methodology was coupled with Sobol’s sensitivity, metropolis–hastings Markov chain Monte Carlo sampling and moving least square-response surface method to improve the computational efficiency and applicability for problems with implicit performance functions (PFs). Methodology is demonstrated for a Himalayan rock slope (implicit PF) prone to stress-controlled failure in India. Analysis is also performed using recently developed limited data reliability methods, i.e., traditional Bayesian (considers uncertainty in model parameters only) and bootstrap-based re-sampling reliability methods (considers uncertainties in model types and parameters). Proposed methodology is concluded to be superior to other methods due to its capability of considering uncertainties in both model types and parameters, and to include the prior information in the analysis.