基于MATLAB的边坡稳定性极限上限分析程序开发

Program development for slope stability using MATLAB software and upper bound limit analysis

基于系统能耗最小原理的极限分析上限定理,利用MATLAB强大的数据处理功能,对边坡稳定系数Ncr采用序列二次规划法(SQP)进行优化计算,并与枚举法相结合,从而解决SQP算法求解优化解容易陷入局部最优解的问题。同时开发了一款简单实用的边坡稳定性分析软件,实现了计算结果与临界滑裂破坏面图形的可视化输出。与经典算例对比分析,计算结果具有较好的一致性,表明了程序的可靠性。分析了内摩擦角、边坡倾斜角、3个参数对边坡稳定系数Ncr的影响。计算结果表明:边坡稳定性系数Ncr对、较为敏感,而对的敏感次之。其次,当、比较接近或在小范围内波动时,对稳定性系数Ncr的影响特别敏感;当、值较小时,滑动面通过坡趾下方,而当值比较大时,滑动面通过坡趾。

Based on the upper bound limit analysis,the functional program about the slope stability problem was developed by MATLAB.The stability factor（Ncr） and graph of critical slip surface can be visually shown in the program window.The solutions of stability factor（Ncr） were obtained through the calculation results of nonlinear and sequential quadratic programs（SQP）,combined with the method of exhaustion to avoid sticking at the local optimization.The results demonstrated the effectiveness of the program.The influence on the stability of slope was evaluated by analyzing the factors in terms of the internal frictional angle,slope angles and.The calculation results show that the stability factor（Ncr） is more sensitive to the frictional angles and than.In addition,if the frictional angles and are close to each other and the values of and fluctuate in the narrow range,the slope stability is sensitive to the stability factor（Ncr）.In other words,when the low values of and are inputted in the program,the slip surface would cross below the slope toe,while the slip surface would intersect at the slope toe for the case of steep slope.