The flexural toppling occurring in anti-dip layered slopes exhibits complex mechanical behaviours and poses a serious threat to human engineering practices. In this paper, a novel method for evaluating the stability of flexural toppling is proposed by combining analytical solution and numerical simulation. The anti-dip rock layers in the slope are regarded as inclined slabs, and the deflection equations of each rock slab are calculated when the slab at the basal plane is restrict and that at the top is free. Critical length of the rock slab is then determined with the energy conservation principle, and it can be employed to evaluate the stability of flexural toppling. Numerical simulations have been conducted to validate the present calculation method and explore the mechanisms of flexural toppling. The simulation results indicate that failure initially occurs at the slope toe due to strong stress concentration, subsequently triggering a domino effect with failures propagate to the upper rock slabs as a result of the loss of support from the lower ones. These simulation results also combined with the analytical solution enhance the calculation accuracy of the method. This innovative approach not only advances our understanding of flexural toppling mechanisms but also provides a method for practical stability assessments.

中文翻译：

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一种基于能量守恒原理和数值模拟的弯曲倾倒稳定性及机理评价新方法


防倾层状边坡中发生的弯曲倾倒表现出复杂的机械行为，对人类工程实践构成严重威胁。本文通过解析解和数值模拟相结合，提出了一种评价弯曲倾倒稳定性的新方法。将边坡中的抗倾岩层视为倾斜板，计算基底面板受约束而顶部板自由时各岩板的挠度方程。然后利用能量守恒原理确定岩板的临界长度，并可用于评估弯曲倾倒的稳定性。已经进行了数值模拟，以验证现有的计算方法并探索弯曲倾倒的机制。模拟结果表明，由于应力集中强烈，破坏最初发生在坡脚处，随后触发多米诺骨牌效应，由于下部岩板失去支撑，破坏传播到上部岩板。这些仿真结果还与解析解相结合，提高了该方法的计算精度。这种创新方法不仅促进了我们对弯曲倾倒机制的理解，还为实际的稳定性评估提供了一种方法。