Coupled Probabilistic and Numerical Limit Analysis for Stability Assessment of Rock Tunnels Considering Uncertainties of Input Rock Properties

This study presents a stability analysis of circular tunnels in rock masses following the generalized Hoek–Brown (GHB) yield criterion with uncertain rock properties. Hybrid second-order exponential cone programming (HSOECP) is proposed to capture the nonlinear GHB yield criterion in its original form and is implemented within the framework of finite-element lower-bound limit analysis to model the yielding of rock masses. The probabilistic approaches, including Sobol’s global sensitivity analysis (GSA), the radial basis function–response surface method (RBF–RSM), and Monte Carlo simulations (MCSs), are coupled with numerical limit analysis to propagate input uncertainties to the outputs of interest (OIs). The study is conducted in three steps. Initially, the surrogate relationships between inputs and OIs are developed based on numerical limit analysis for the input realizations generated via Latin hypercube sampling (LHS). In the second step, the sensitive inputs are identified via Sobol’s GSA performed using Saltelli’s MCS algorithm. Finally, the uncertainties of the sensitive inputs are propagated to the OIs by performing MCSs on the surrogate RBF–RSM relationships. The coupled analysis is applied to evaluate the stability of an unlined circular tunnel in a rock mass with a surcharge on the ground surface. The geological strength index (GSI) and the Hoek–Brown constant (mi) are estimated to be the most sensitive inputs in Sobol’s GSA. The tunnel cover-depth-to-diameter ratio and the statistics of the sensitive inputs, i.e., GSI and mi, have a significant effect on the probability of failure.