Locating a critical slip surface or calculating the minimum safety factor of a slope is important in geotechnical engineering, and also involves a complex optimization problem. A novel mathematical model considering linear and nonlinear failure criteria is developed to locate the critical slip surface. And an improved whale optimization algorithm (IWOA), which employs a nonlinear adjustment parameter and Gaussian perturbation operator in whale optimization algorithm (WOA), is proposed to examine this model. The parameter of IWOA is determined by numerical experiments. The performance of IWOA, WOA, salp swarm algorithm (SSA), and cuckoo search algorithm (CS) is investigated. Statistical analyses of twelve benchmark functions show that the four algorithms with high to low performances are IWOA, WOA, SSA and CS. Two multimodal functions for analyzing slope stability show that IWOA outperforms ant colony optimization algorithm (ACO), and imperialistic competitive algorithm (ICA). The time computational complexity of IWOA is same as WOA. Case studies of homogeneous and multilayer soil slopes indicate that the failure criterion has a significant effect on the minimum safety factor and the critical slip surface, and that IWOA can show better performance than WOA, SSA and CS. This study develops an efficient method to locate critical slip surfaces of soil slopes for engineers.

在岩土工程中，确定关键的滑动面或计算边坡的最小安全系数很重要，并且还涉及一个复杂的优化问题。建立了考虑线性和非线性破坏准则的新型数学模型，以定位临界滑动面。提出了一种改进的鲸鱼优化算法（IWOA），该模型在鲸鱼优化算法（WOA）中采用了非线性调整参数和高斯摄动算子。IWOA的参数是通过数值实验确定的。研究了IWOA，WOA，salp swarm算法（SSA）和布谷鸟搜索算法（CS）的性能。对十二种基准函数的统计分析表明，四种性能从高到低的算法分别是IWOA，WOA，SSA和CS。两个用于分析边坡稳定性的多峰函数表明，IWOA优于蚁群优化算法（ACO）和帝国竞争算法（ICA）。IWOA的时间计算复杂度与WOA相同。均质和多层土质边坡的案例研究表明，破坏准则对最小安全系数和临界滑移面有重大影响，并且IWOA的性能优于WOA，SSA和CS。这项研究为工程师们开发了一种有效的方法来定位土质边坡的临界滑移面。均质和多层土质边坡的案例研究表明，破坏准则对最小安全系数和临界滑移面有重大影响，并且IWOA的性能优于WOA，SSA和CS。这项研究为工程师们开发了一种有效的方法来定位土质边坡的临界滑移面。均质和多层土质边坡的案例研究表明，破坏准则对最小安全系数和临界滑移面有重大影响，并且IWOA的性能优于WOA，SSA和CS。这项研究为工程师们开发了一种有效的方法来定位土质边坡的临界滑移面。