摘要
针对采用一次二阶矩法计算复杂、高度非线性功能函数的可靠指标时,求解功能函数对随机变量的偏导数极其困难,并且偏导数形式非常复杂等问题,提出用响应面函数代替原功能函数的方法,使其求导过程方便,并且使偏导数形式转化为随机变量的线性表达式,便于程序化求解。然后以计算三维Hoek-Brown强度准则的可靠度为例,确认响应面法在复杂、高度非线性功能函数可靠度计算中的可行性,并与变量代换法和复合函数求导法则的计算结果进行比较,说明利用响应面法计算的结果具有较高的精度。最后,用响应面法分析强度准则参数分布类型和岩体参数之间的相关性对三维Hoek-Brown准则可靠度的影响规律。研究结果表明:该方法具有较高精度;强度准则参数分布类型对可靠指标的敏感性较弱;岩体参数的负相关系数与可靠指标线性相关,对可靠指标的影响不大。
Considering that it is very difficult for the FOSM to solve partial derivatives of performance function because random variables and the forms of partial derivatives are very complex in calculating the reliability index of complex,high order nonlinear performance function, the response surface method which used the response surface function to replace the original function was proposed. The solving process of function＇s derivation was convenient and the form of the partial derivative was a linear expression of random variables. Based on the 3D Hoek Brown strength criterion for the limit state function, the response surface method was adopted to calculate the reliability index, which assured that this method was suitable for the complex and high-nonlinear performance function. Moreover, the variables replacing technique and the compound function method were employed as comparison. The results show that this method has higher accuracy, and the probability distribution of the basic random variables has less effect on the reliability index. The correlation of rock mass parameters and the relation between the reliability index and negative correlation coefficient of rock mass parameters is linear.
出处
《中南大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2017年第2期491-497,共7页
Journal of Central South University:Science and Technology
基金
国家重点基础研究发展计划(973计划)项目(2010CB732004)
国家自然科学基金资助项目(41272304,11472311)~~
关键词
HOEK-BROWN准则
响应面法
高度非线性的功能函数
偏导数
3D Hoek-Brown criterion
the response surface method
the high order nonlinear performance function
partial derivative
