基于滑移线场理论的概率边坡设计

基于可靠度的最优化设计能有效地处理岩土工程中存在的不确定性，在工程界和学界日益得到重视。然而，传统的基于可靠度的分析方法需要进行多次计算并不断重构计算模型，计算量巨大且难以实施。本文提出了一个基于滑移线场理论的概率边坡优化设计方法。该方法采用了更加高效的拟蒙特卡罗模拟（QMCS）来确定边坡的失效概率，而在每次模拟过程中采用滑移线场理论来分析边坡的稳定性。为了更加高效的确定满足目标失效概率的设计坡角，本文提出了一个简单而有效地二分搜索方法。最后，以一个边坡为例设计了不同目标失效概率的坡角，并验证了所提方法的有效性。结果表明所提方法最多只需36.29 min就能得到满足目标失效概率的坡角。本文提出的边坡概率优化设计方法避免了计算模型的反复重构，计算效率较好，可为基于可靠度边坡设计提供新的可选手段。

Probabilistic design of slopes based on slip line field theory

Reliability-based optimum design can effectively deal with the uncertainty existing in geotechnical engineering, which gains increased attention in the engineering and academic communities. However, the traditional reliability-based analysis method necessitates a large number of computations and requires continuous reconstruction of the calculation model, making it challenging to execute. In this paper, a slip-line theory-based probabilistic method is developed for slope design. In order to quickly and accurately identify the slope angle of the design under the condition of satisfying the objective failure probability, a binary search method is proposed to determine the slope angle of the design. In each search, the slip-line theory is applied to assess the stability of slopes, and the efficient quasi-Monte Carlo simulation is employed to estimate the failure probability of slopes. The effectiveness of the proposed method is verified using a real engineering slope with thickly layered soil. The results show that the proposed method can obtain the design slope angle satisfying the objective failure probability in only 36.29 min, demonstrating the efficiency of the proposed method. The proposed method for slope design reduces the need for repetitive reconstruction of the calculation model and improves the calculation efficiency of design work. It has the potential to provide a new approach to slope design based on reliability.