土坡稳定分析圆弧法的解析解及应用

Analytical solution of circle sliced method and its application in slope stability assessment

土坡稳定性分析的圆弧条分法的原理简单 ,公式简洁 ,至今仍被工程界广泛应用。但该方法的具体计算过程烦琐 ,在搜索最危险滑动面时 ,每给定一个滑动面 ,都要重新确定分条的边界、高度、宽度和分条数目等参数 ;而且要反复试算 ,存在着不确定性。为此 ,笔者曾提出了搜索最危险滑动面的一种方法 ,本文结合该方法对圆弧法作了进一步推导。首先是将地面线用分段直线方程表示 ,将滑动面用一圆弧方程表示 ,这样可以将原公式中的求和部分化为积分式 ,从而推导出了求解稳定系数的解析式 ,进一步推导出用于具有后缘拉裂的边坡稳定性计算式。

Circle sliced method,with its simple principle and brief formula,is complex in calculation process,the searching of potential slip surface also has uncertainty.So the authors have proposed a method of searching the most possible slip surface. Further more, an analytical solution of Fellenius method was also produced. On the other wise, in consider of many sliding surfaces with high back cliff and nearly circle in the lower potion, the authors made some revisions for the analytical formula to suitable for the situation. The method is used to calculated the factor of safety of a high loess slope of a coal mine in Binxian County ,Shaanxi Province, China.The results are more close to the actual situation than with circle sliced method.