Multi-objective reliability-based robust design for a rock tunnel support system using Pareto optimality

Abstract

In the context of rock material and modeling uncertainties, the optimization of rock tunnel support systems is often conducted by selecting the most cost-effective solution among several feasible options that typically rely on the engineer's experience, potentially leading to overlooking the most optimal design. To improve such a limitation, this paper presents a multi-objective reliability-based robust design, considering the cost, safety, and design robustness systematically while maintaining the computational efficiency. In this framework, the uncertainty-based reliability constrains is performed using the first-order reliability method (FORM) and an improved Hasofer–Lind–Rackwits–Fiessler recursive algorithm (iHLRF-x). The design robustness, in terms of sensitivity index (SI), is evaluated using the normalized gradient of the system response to the noise factors, which can be efficiently obtained from the output of FORM analysis. Then, the Pareto front revealing the tradeoff between multiple objectives can be directly generated using the proposed optimization framework. To illustrate the effectiveness of this procedure, a set of the optimal design combinations of the shotcrete thickness and installation position for the exampled rock tunnel are obtained, and new perspectives pertaining the success of the reliability-based robust designs are provided.