A Bayesian reliability methodology for rock structures considering uncertainties in random field characteristics with limited data of rock properties

Cross-correlated Random Fields (RFs) are often used to simulate the spatial variability of cross-correlated inputs based on the statistical characteristics of RF like auto-correlation functions, cross-correlation structures, and marginal models. Precise estimation of these RF characteristics is often impractical in rock engineering due to limited site-specific data invoking epistemic uncertainties along them. This study proposes a Bayesian Multi-Model Inference (BMMI) coupled with 2D cross-correlated non-normal RF methodology to consider the spatial variation of copula dependent rock properties using their limited data. The proposed methodology constructs the model sets of RF statistical characteristics using BMMI, representing the epistemic uncertainties in the model selection and their parameters along them. Expansion Optimal Linear Estimation (EOLE) method is then used to discretize the RFs for every combination of the model sets which is finally coupled with Fast Lagrangian Analysis of Continua (FLAC)-2D to perform the reliability analysis. The methodology is illustrated for an example rock slope situated within a heavily jointed rock mass susceptible to stress-controlled circular. In addition to this analysis, a traditional cross-correlated non-normal RF analysis is also conducted by ignoring the epistemic uncertainties in the statistical characteristics of RF to assess the impact of these uncertainties. The proposed methodology was concluded to be more effective than the traditional methodology as it is capable of accounting for the spatial variability of copula dependent inputs along with the epistemic uncertainties along them emanating due to their limited data. Proposed methodology provides the confidence interval of reliability index encompassing its fixed-point estimate from the traditional RF analysis, thereby enhancing practitioner's understanding of structural responses.