基于突变理论的边坡安全系数自动搜索方法及应用分析

为解决搜寻强度折减系数与边坡位移关系曲线突变点数值计算量大、主观性较强等问题,基于尖点突变理论,提出边坡安全系数自动搜索方法,以Fortran语言和FLAC 3D数值计算软件为平台,开发了适用于自动搜索边坡安全系数的计算程序。将该方法应用于边坡实例的稳定性研究,讨论了各种评判标准所得安全系数的大小差别,并与极限平衡法计算的安全系数进行对比分析。结果表明:自动搜索边坡安全系数的计算程序能快速定量找到边坡临界稳定的突变点,提高了边坡稳定性分析的准确性和计算工作效率;计算结果与边坡规范推荐的极限平衡法所得的结果对比误差较小,并且对于未知滑动面边坡,极限平衡法得出的滑动面位置与该方法所得安全系数下对应的塑性区贯通区域基本一致。文中方法为边坡稳定性评价提供了有益借鉴。

Catastrophe theory-based automatic search method for slope safety factor and analysis on its application

In order to solve the problems of large amount and strong subjectivity of the numerical calculation on searching the catastrophe point of the relationship curve between the strength reduction factor and the slope displacement，an automatic search method for the slope safety factor is proposed herein based on the cusp catastrophe theory，and then the calculation program suitable for the automatic search of slope safety factor is developed by taking Fortran language and the numerical calculation software of FLAC 3D as the platform. This method is applied to the study on the stabilities of the actual cases，in which the differences among the safety factors obtained from all the judging criteria concerned are discussed，while an analytical comparison is made with the safety factor calculated by limit equilibrium method. The result shows that the calculation program for the automatic search of slope safety factor can quickly and quantitively find out the catastrophe point of the critical stability of slope，thus enhances the correctness and calculation efficiency of the slope stability analysis，from which the error of the calculation result is less in the comparison with that obtained from the limit equilibrium method recommended by the relevant slope engineering criteria，while the location of the sliding plane obtained from limit equilibrium method is basically coincided with the corresponding plastic penetrated area under the safety factor got from that method. The method proposed herein provides a beneficial reference for the qualitative evaluation of slope stability.