Uncertainty quantification of deep-buried tunnels rock system under seismic disturbances based on the GPR-(T)NRBO-Bayesian method

The stability of deep-buried tunnels under seismic disturbances depends on uncertain surrounding-rock parameters and dynamic responses, yet high-fidelity numerical simulations are computationally expensive for repeated uncertainty analyses. This study proposes a systematic uncertainty quantification framework that couples a Gaussian Process Regression (GPR) surrogate with a Tensor-Newton–Raphson Based Optimiser (GPR-(T)NRBO) and Bayesian inference. The GPR surrogate provides both the predictive mean and variance, and NRBO adaptively selects informative samples by maximising the predictive variance. A fourth-order tensor correction is further introduced to refine the Newton update and improve exploration in high-dimensional nonlinear parameter spaces. The resulting emulator provides response predictions along with epistemic uncertainty, which is explicitly propagated into the Bayesian inverse analysis via a likelihood that accounts for measurement noise and surrogate uncertainty. The framework is applied to the D2 laboratory at CJPL-II across multiple seismic-intensity scenarios. Results indicate that the surrogate achieves an average displacement-prediction accuracy of 86.8%, and the posterior mean errors for inferred parameters and displacements remain below 10% and 8%, respectively, even under extended prior ranges. Finally, failure probability under increasing seismic loading is quantified using First-Order Reliability Method (FORM), demonstrating the applicability of the proposed framework for risk-informed stability assessment of deep-buried tunnels.