土坡稳定Hasofer-Lind可靠度指标的计算方法

工程中较为常用的是Hasofer和Lind提出的不变二阶矩可靠度指标,可采用正交变换法、MonteCarlo法、优化等方法求解β值。使用优化方法求解Hasofer-Lind可靠度指标,避免了相关变量的独立变换以及求极限状态函数对基本变量的偏导数这两个问题。本文明确了Hasofer-Lind可靠度指标的物理意义,提出了Hasofer-Lind可靠度指标在Fortran语言中的优化求解方法,通过与Excel规划求解器计算结果对比,表明本方法计算结果可靠,多变量情况下可靠度指标能够迅速收敛。该方法直接在基本变量空间求解,与已有的利用Fortran语言编制的边坡稳定程序无缝连接,除了可以用于求解边坡稳定分析中c和φ相关问题之外,还可以计算考虑土工参数空间变异情况下的土坡可靠度指标。

The method for Hasofer-Lind reliability index resolution of soil slope stability

The non-variable second moment reliability index presented by Hasofer and Lind is commonly used in engineering.Orthogonal transformation method,MonteCarlo method,and optimal method can be employed to solve for theβvalue in the index.By using the optimal method,the orthogonal transformation for correlation variables and the partial derivatives of the limit state function with respect to the original variables are avoided.EXCEL solver is commonly used for optimization.In this paper,the physical meanings of Hasofer-Lind reliability index was made clear and the optimal method by Fortran Language was presented. By comparing the result from Excel solver,the precision has been verified,and the computation is able to converge promptly under the condition of several variables.The present method can obtain the solution directly in the original variables space,and can be embedded in the existed slope stability program seamlessly.Besides the problem about c andφcorrelation,the method also can be used to get the soil slope reliability index considering the spatial variation of soil parameters.