Uncertainty quantification and propagation for spatial variability of rock mass parameters for grottoes under limited data conditions

Accurately characterizing the spatial variability of rock mass mechanical parameters is essential for the reliability assessment of cultural heritage sites such as grottoes. To address the parameter non-identifiability caused by sparse data and high measurement noise, this study develops an integrated analytical framework based on hierarchical Bayesian inference. The framework introduces nugget effect to separate signal and noise components and incorporates informative priors to enhance model identifiability. Conditional random field simulations are employed to propagate posterior uncertainties of the parameters and, combined with probabilistic failure criteria, to evaluate spatial reliability. The proposed five-parameter model exhibits excellent convergence and robustness in MCMC posterior inference, while prior sensitivity analysis quantitatively reveals the critical regularization role of informative priors. The resulting spatial failure probability map aligns well with observed damage patterns, identifying potential high-risk zones with a maximum failure probability of 32.9%. Overall, the proposed Bayesian framework enables robust inference and comprehensive uncertainty quantification of geotechnical parameters under limited and noisy data conditions, providing a rigorous quantitative basis for risk identification and dynamic preservation of grotto cultural heritage.