基于Morgenstern-Price法和改进径向移动算法的边坡稳定性分析

为了能够准确确定边坡的非圆弧临界滑动面位置及其相应的安全系数，采用一种新的启发式优化算法——径向移动算法，对边坡进行稳定性分析。通过调整原算法中的数据结构，增强粒子的自反馈能力，提出改进径向移动算法（IRMO）。安全系数的求解采用严格的Morgenstern-Price法，应用Newton-Raphson法，建立了满足条间力平衡与力矩平衡的Morgenstern-Price法中安全系数F和条间力参数λ的迭代计算公式。基于Morgenstern-Price法，采用IRMO算法对边坡稳定性进行分析，通过2个典型边坡算例和1个复杂海堤边坡实例，从稳定性、精确性、计算效率等多个角度将IRMO算法与未改进的径向移动算法进行对比论证，同时将IRMO算法与粒子群算法、改进粒子群算法等其他算法进行对比分析。结果表明：相比未改进的径向移动算法，IRMO算法连续搜索20次临界滑动面的结果重叠度更高，证明IRMO算法稳定性更强，IRMO算法的安全系数值随代数收敛的速度更快，证明IRMO算法的计算效率更高；与粒子群算法、改进粒子群算法等启发式算法相比，IRMO算法搜索到的临界滑动面位置与其他算法一致，安全系数计算结果更接近裁判答案，标准差也最小，证明IRMO算法在边坡稳定性分析问题上更具可行性与优越性；通过海堤边坡实例的分析，IRMO算法得到了该边坡合理的安全系数值和临界滑动面位置，表明该算法能够正确评估边坡稳定程度，可以应用于实际工程中。

Slope Stability Analysis Based on Morgenstern-Price Method and Improved Radial Movement Optimization Algorithm

In order to accurately determine the critical non-circular slip surface location of slope and its corresponding safety factor, a new heuristic optimization algorithm, namely, radial movement optimization algorithm was used to analyze the stability of slope. By adjusting the data structure of the original algorithm and enhancing the self-feedback ability of particles, an improved radial movement algorithm (IRMO) was proposed. The safety factor was solved by dint of the strict Morgenstern-Price method. Newton-Raphson method was deployed to obtain the iterative calculation formula of the safety factor F and the parameter of the inter-slice force λ for Morgenstern-Price Method under the force balance and moment balance. Based on the Morgenstern-Price method, IRMO was used to analyze the slope stability. Through two typical slope examples and a complex example of seawall slope, IRMO was compared with the unmodified radial movement algorithm from the aspects of stability, accuracy and computational efficiency. At the same time, IRMO was compared with other algorithms such as particle swarm optimization, improved particle swarm optimization and so on. The results show that compared with the unmodified radial movement algorithm, results of critical slip surface based on IRMO by continuously searching for 20 times overlap in some degree. It proves that IRMO is more stable. The safety factor of IRMO converges faster with generation, which proves that the computational efficiency of IRMO is higher. Compared with particle swarm optimization and improved particle swarm optimization, the critical slip surface of IRMO is consistent with that of other algorithms. The result of safety factor is closer to the referee's answer, and the standard deviation reaches the smallest. The feasibility and superiority of IRMO in slope stability analysis are proved. Through the example of a complex seawall slope, the reasonable result of safety factor and the critical slip surface position of the slope are obtained by IRMO. It shows that this algorithm can correctly evaluate the slope stability, and can be applied in the actual project.