Efficient Probabilistic Approach to Analyze Tunnel Support with Uncertain Probability Distribution Function of Input Parameters

Due to the inherent random variations in the engineering properties of soils and rocks, considering probabilistic analysis rather than the deterministic one is a safer option for the design of geotechnical structures. However, the probabilistic methodologies often rely on prior knowledge of probability density function (PDF) of the considered random variables (RVs). In this study, a new formulation called the fourth-moment pseudo-normal transformation (FMNT) is employed to perform the probabilistic analysis of a tunnel support system. FMNT requires only the first four statistical moments of the random variables instead of complete information about their PDF to calculate the failure probability (Pf). Further, it is an efficient technique that is demonstrated by performing analytical as well as numerical probabilistic analysis of circular and noncircular tunnels using FLAC 3D. FMNT is used in two different ways to highlight its flexibility: (1) with the first-order reliability method (FORM) called FORM-based FMNT; and (2) with point estimated method (PEM) called PEM-based FMNT. The results of the latter align adequately with the results of Monte Carlo simulation (MCS) and the analysis requires only 21 and 26 simulations for four and five random variables, respectively, instead of 100,000 simulations required by the MCS. The compatibility of this framework in actual field settings is demonstrated through an exercise using the nonnormal random variables.