Probabilistic Analysis of a Rock Tunnel Face Using Polynomial Chaos Expansion Method

Abstract

The polynomial chaos expansion method was used to perform probabilistic analysis on a tunnel face driven in rock masses. The generalized Hoek-Brown (HB) failure criterion was used to characterize the strength of rock masses. Deterministic calculations of required face pressures were based on the upper bound limit analysis theory. Four HB input parameters, the geological strength index (GSI), the uniaxial compressive strength σc of the intact rock, the constant mi, and the disturbance factor Di, were considered as random variables. The influence of HB input parameter uncertainties on probability density functions of the required face pressures, sensitivity analysis, and failure probabilities were discussed with respect to different coefficients of variance (COVs), distribution types, and correlation coefficients. A reliability-based design was performed to compute probabilistic face pressures under different COVs at a target safety level. The obtained results show uncertainties in the input random variables have an important influence on the required face pressures, and it is necessary to analyze the problem in the probabilistic framework.