基于响应面法的三维H-B强度准则可靠度的研究

发布时间：2018-07-04 09:11

本文选题：Hoek-Brown准则 + 响应面法　；参考：《中南大学学报(自然科学版)》2017年02期

【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。
[Abstract]:When the first order second moment method is used to calculate the reliability index of complex and highly nonlinear function, it is very difficult to solve the partial derivative of function to random variable, and the form of partial derivative is very complex. The method of replacing the original function with response surface function is put forward, which makes the derivation process convenient and the partial derivative form transformed into the linear expression of random variable, which is easy to solve programmatically. Then, taking the reliability of the 3-D Hoek-Brown strength criterion as an example, the feasibility of the response surface method in the reliability calculation of complex and highly nonlinear functional functions is confirmed, and the results are compared with the results of the variable substitution method and the complex function derivation rule. The results obtained by response surface method are proved to be of high accuracy. Finally, the response surface method is used to analyze the relationship between the distribution types of strength criterion parameters and rock mass parameters, which affects the reliability of the 3-D Hoek-Brown criterion. The results show that the method has higher accuracy, the distribution type of strength criterion parameters is less sensitive to the reliability index, and the negative correlation coefficient of rock mass parameters is linearly related to the reliability index, but has little effect on the reliability index.
【作者单位】：中南大学资源与安全工程学院;
【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)~~
【分类号】：TU45

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