多阶多层复杂边坡稳定性的通用上限方法

极限分析上限方法在边坡稳定性评价中受到了广泛关注，但当前所取得的解析成果尚不能直接应用于解决任意多土层分布、多台阶的广义复杂层状边坡。基于组合对数螺线的旋转破坏机制，推导了具有任意坡面几何特征、任意多土层（含非水平土/岩层）边坡的外功率统一积分表达式及相应的虚功率方程，提出了多阶多层复杂边坡稳定性的通用极限分析上限方法；为克服积分式的复杂解析计算，引入了数值积分技术。在此基础上，结合最优化方法和强度折减技术，优化求解了复杂边坡的全局稳定性安全系数及相应的临界滑动面。通过多个典型算例的验证与对比分析，表明该方法具有较高的精度和广泛适用性。最后，针对典型多阶多层边坡实例，开展了上限法的深度拓展与应用研究，其结果为广义复杂层状边坡的稳定性评价提供了新思路。

A generalized upper-bound limit analysis approach for stability analysis of complex multistep and multilayer slopes

Although the upper bound approach of limit analysis has attracted extensive attention in the slope stability analysis, its derived analytical solutions have not been directly applied to the stability analysis of the slopes with arbitrary complicated multistep and multilayer. Adopting the rigid body assumption and the combined log-spiral rotational failure mechanism, we derive a unified integral expression for the external work rate and the related virtual work equation for slopes with arbitrary surface geometry and multiple soil layers. A generalized upper bound approach of limit analysis is proposed, by which the overall stability of complex multistep and multilayer slopes can be achieved. To overcome the difficulty in calculating integral formulations, the numerical integration technique is introduced. Based on this, the global factors of safety (FSs) and the corresponding CSSs of complex layered slopes are obtained by using the strength reduction technique combined with an optimization method. Several representative examples are employed to validate the analytical solutions and comparisons of the FSs and the corresponding CSSs obtained by various methods are also conducted. The results show that the proposed approach can yield the high-accuracy solutions and is widely applicable to the stability analysis of complex layered slopes. The new approach is applied to a typical multistep and multilayer slope case.