摘要
Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.
Based on Bishop＇s model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method The result shows its absolute error is only 0.78% as compared with accurate solution.
基金
Project(50378036) supported by the National Natural Science Foundation of China
Project(200503) supported by Foundation of Communications Department of Hunan Province, China
关键词
斜坡
力学模型
失效概率
平均偏差法
Bishop mechanical model
failure probability of slope
mean deviation method
implicit function
Taylor series
dump of open-pit
