Abstract
Uncertainty is an important prosperity to rock tunnel. Reliability analysis is widely used to deal with the uncertainty. But it is difficult to be adopted in rock tunnel using the traditional reliability method because the limit state function is an implicit function. High dimension model representation (HDMR) can approximate the high dimensional, nonlinear, and implicit function using the low dimensional function. In this study, the HDMR method was adapted to approximate the limit state function through combining with response surface method (RSM). A new reliability analysis approach of HDMR-based response surface method, combined with the first-order reliability method (FORM), is developed to calculate the reliability index of tunnel, and implementation of the method is explained briefly. A circular tunnel with analytical solution and horseshoe tunnel with numerical solution are used to demonstrate the proposed method. The obtained reliability index is in excellent agreement with Low and Tang’s (2007) method and traditional RSM. It shows that HDMR-based response surface can approximate well the limit state function, and the proposed method is an efficient and effective approach for reliability analysis in tunnel engineering. It is very useful for reliability analysis of practical large-scale rock engineering.
Highlights
Stability analysis of tunnel is very important to optimization design and safety construction
High dimension model representation (HDMR) was adopted to approximate the response of tunnel, and that combined with response surface method to build the limit state function
The HDMR-based reliability analysis was applied to two tunnels
Summary
Stability analysis of tunnel is very important to optimization design and safety construction. Other researchers have applied ANN to reliability analysis by combining it with Monte Carlo simulation, FORM, response surface method, etc. The HDMR was adopted to approximate the limit state function, and FORM was used to compute the reliability index of tunnels. We use a practical FORM method, which was presented by Low (2004) based on the Hasofer–Lind index [19, 20]. To obviate the computations of equivalent normal means and equivalent normal standard deviations, Low and Tang (2007) proposed a new efficient algorithm for the FORM via varying dimensionless number ni to estimate the reliability index as follow [21]:. In this study, (1) was adopted to compute the reliability analysis based on FORM proposed by Low and Tang
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