基于极限分析上限原理的简化毕肖普法分析

A simplified Bishop method based on the upper bound limit theory

运用极限分析原理探讨简化毕肖普条分法的精度问题.通过将极限分析上限定理引入简化毕肖普条分法中,采用强度折减法推导出边坡临界破坏状态下的安全系数Fs上限解的计算公式以及速度场计算方法.通过算例将该方法与瑞典圆弧条分法、简化毕肖普条分法、有限元计算的结果进行比较.结果表明,条分法不计土条间的相互作用,使计算的安全系数存在较大误差(16.2%);极限分析上限定理从边坡的极限状态开始研究,可获得严格的理论解,误差仅2.8%.

In order to explore the accuracy of a simplified Bishop slice method,the principle of limit analysis was used in this paper.By introducing the upper bound theorem of limit analysis into the simplified Bishop slice method and adopting the strength reduction method,the upper bound solution formula of safety factor Fsand the calculation method of velocity field under a critical failure state of slope were derived.The results showed that the slice method did not consider the interaction between soil strips,and the error was 16.2%.The upper limit theorem of limit analysis was studied from the limit state of slope,which could obtain a very strict theoretical solution,with the error being only 2.8%.