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基于极限分析上限法基本原理和强度折减技术,根据滑坡体处于极限状态时两功率相等(虚功率方程)条件,推导了带台阶的多级边坡整体失稳和可能出现的局部失稳安全系数计算公式。并以3级边坡为例,编制优化程序,采用序列二次规划迭代算法计算确定最危险滑动面的位置:即对多个可能的滑动面进行搜索,获得安全系数最小(也即稳定性最差)的面作为潜在最危险滑裂面。采用具体算例,对比分析了3级边坡的整体稳定性和可能出现的局部稳定性问题,并由此开展了参数分析。对比分析表明:获得的安全系数较已有方法略小,得到的最危险滑动面与已有结果颇为接近,可以验证其有效性和可行性;参数分析表明:对均质多级边坡,当某级边坡坡角过大时,边坡更易发生局部失稳;高边坡增设边坡台阶可以有效提高边坡稳定性并降低施工难度。
Based on the basic principle of upper bound method of limit analysis and the technology of strength reduction, according to the condition of equal power (virtual power equation) when the landslide body is in the limit state, the global instability of multi-stage slope with steps and the possible local instability safety Coefficient calculation formula. Taking the Grade 3 slope as an example, the optimization program is compiled, and the position of the most dangerous slip surface is calculated by using the sequential quadratic programming iterative algorithm. That is, the search for multiple possible slip surfaces yields the least safety factor (that is, the most stable Poor) face as the most potentially dangerous slip surface. The concrete example is used to analyze the overall stability of the grade 3 slope and the possible local stability problems. And then, the parameter analysis is carried out. The comparative analysis shows that the obtained safety factor is slightly smaller than the existing method and the most dangerous sliding surface obtained is quite close to the existing one, which can verify its effectiveness and feasibility. The parameter analysis shows that for the homogeneous multistage slope, When the slope angle of a certain slope is too large, the local instability of the slope is more likely to occur. Adding a slope step to a high slope can effectively improve the slope stability and reduce the construction difficulty.