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.

中文翻译：

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基于帕累托最优的岩石隧道支护系统的多目标可靠性鲁棒设计


在岩石材料和建模不确定性的情况下，岩石隧道支护系统的优化通常是通过在通常依赖于工程师经验的几个可行选项中选择最具成本效益的解决方案来进行的，这可能导致忽视最佳设计。为了改善这一限制，本文提出了一种基于多目标可靠性的鲁棒设计，在保持计算效率的同时系统地考虑成本、安全性和设计鲁棒性。在此框架中，使用一阶可靠性方法（FORM）和改进的 Hasofer-Lind-Rackwits-Fiessler 递归算法（iHLRF-x）执行基于不确定性的可靠性约束。使用系统对噪声因素响应的归一化梯度来评估灵敏度指数 (SI) 方面的设计鲁棒性，该梯度可以从 FORM 分析的输出中有效获得。然后，可以使用所提出的优化框架直接生成揭示多个目标之间权衡的帕累托前沿。为了说明该程序的有效性，获得了示例岩石隧道的一组喷射混凝土厚度和安装位置的最佳设计组合，并提供了有关基于可靠性的稳健设计成功的新视角。