An Efficient Probabilistic Approach to Tunnel Reliability Problems Considering Properties of Performance Functions

With the advancement of reliability‐based design in tunnelling engineering, tunnel reliability analysis is becoming increasingly important. The performance function is the cornerstone and pivotal element in reliability analysis. However, they are found to be predominantly cumbersome, implicit, or derived from numerical simulations in tunnel reliability problems, thereby presenting significant challenges. Focusing on the direct approach to these performance functions, an efficient probabilistic method with a recursion procedure based on a revised Hasofer–Lind–Rackwits–Fiessler (HLRF)‐Broyden–Fletcher–Goldfarb–Shan (BFGS) algorithm and the finite difference method (FDM) is proposed, considering properties of performance functions in tunnel reliability problems and convergence problems of the direct approach itself. Numerical performance functions with diverse degrees of nonlinearity are presented and validated, and it is suggested that the value of the step length coefficient involved in the FDM should not exceed 0.2. Subsequently, tunnel reliability problems with different performance functions are illustrated and verified. For the first scenario involving a complicated power exponential function, the proposed approach could converge for some cases that the HLRF cannot, and the relative errors are less than 3.0% compared with Monte Carlo simulation (MCS). For the second scenario concerning numerical simulations with a horseshoe‐shaped cross‐section, the required computational costs of the proposed approach could potentially be reduced by 50% compared to the HRLF method. For the third scenario involving the support capacity for tunnel reliability‐based design, the required computational costs of the proposed approach could be 72% less than those of some classical first‐order reliability methods, and the relative error is less than 0.5% compared with MCS.