基于极限分析上限方法的海底斜坡稳定性评价

Stability of seafloor slopes based on upper bound approach of limit analysis

极限平衡法仍是当前海底斜坡稳定性的主要工程评价方法,但该法只能给出稳定性分析的近似解答。基于极限分析运动学定理,假定海底斜坡发生对数螺线型滑移破坏模式,将滑体有效自重和简化波浪力等以外荷载形式叠加引入到虚功率方程中,与潜在滑动面上由黏聚力产生的内能耗散率相平衡,建立考虑一阶简化波浪效应的海底斜坡上限解法;利用多变量无导数求极值的逐级迭代方法与最优化技术,结合抗剪强度折减思想,求解波浪加载下不同时刻的海底斜坡稳定性与相应的临界破坏机构,并针对典型算例开展有限元数值解的验证。进而联合采用数值法与上限解,探讨波高、波长、水深等波浪参数对海底斜坡稳定性与滑动机制的影响。结果表明,本文提出的上限解与数值解吻合较好,获得的安全系数与破坏模式等符合一般规律,为波浪作用下海底斜坡的稳定性评价提供了新的途径。

Currently, the limit equilibrium method （LEM） has been one of the most popular approaches to assess the seafloor stability. But still, the method has some limitations and only the approximate solutions can be obtained. To achieve the true solution, the upper bound approach based on kinematic theorem of limit analysis incorporating a log-spiral rotational failure mechanism, is established to solve the stability of submarine slopes, in which the simpli- fied linear wave loading is considered,and the external work rates produced by the effective self-gravity of sliding body and the wave-induced pressure on the seafloor slope are equal to the internal energy dissipation rates yielded by the cohesion along the critical sliding surface （CSS）. The safety factor （FS） and the corresponding CSS at dif- ferent time under waves are obtained by combining multivariate stepwise iterative method without derivative and the mathematically optimal technique with strength reduction method （SRM）. And, typical example is introduced to carry out the verification of the finite element numerical solution. On the basis of these, the effect of wave pa- rameters such as wave length, wave height and water depth on the slope stability and failure mechanism are dis- cussed. Calculation results show that the FSs and the corresponding CSSs obtained by the upper bound approach agreet well with the numerical solutions, and are also consistent with the general rules. The proposed approach provides a new path for the analysis of seafloor stability.