基于Neumann展开随机有限元的混凝土重力坝结构可靠度分析
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摘要
针对混凝土重力坝等大体积混凝土结构中,受原材料、混凝土拌合过程以及浇筑施工影响而产生的材料特性空间分布的随机性问题,采用平稳随机场局部平均法离散理论,推导了基于Neumann展开随机有限元的重力坝结构随机响应计算公式,提出了重力坝可靠度计算方法,并开发了相应Matlab计算程序。通过悬臂梁算例对该方法进行验证,并运用该方法研究了随机场离散单元尺寸及相关偏度对结构可靠度的影响,进而计算了典型重力坝坝踵抗拉可靠度。结果表明,相关偏度取值对大坝的可靠度影响显著,可靠度随相关偏度的减小而增大,仅将坝体弹性模量视为单一随机变量时所得可靠度较实际值低;随机场离散单元尺寸应依据相关偏度确定且不宜过大,建议取值不大于相关偏度的1/10～1/8。
For massive concrete structures such as concrete gravity dams, the materials have random spatial distribution properties due to the influences of raw materials and their mixing, as well as the pouring construction. Using the discretization theory of the local average method for a stationary random field, a computational formula of the structural random response for gravity dams is derived based on Neumann expansion stochastic finite element. Corresponding calculation method for the reliability of gravity dams is proposed together with a programmed Matlab code. A cantilever beam is given for the validation of the method and the influence of element size and fluctuation scale of the random field on structural reliability is discussed. The tensile strength reliability of the dam heel is also calculated. The results show that the reliability of a dam can be influenced significantly by the fluctuation scale. Reliability increases with a decreasing fluctuation scale, and it is undervalued if the elastic modulus is considered as a single random variable. In addition, the discretized element size of the random field should be determined by the fluctuation scale and it should not be too large. The suggested element size is less than 1/10～1/8 of the fluctuation scale.
For massive concrete structures such as concrete gravity dams, the materials have random spatial distribution properties due to the influences of raw materials and their mixing, as well as the pouring construction. Using the discretization theory of the local average method for a stationary random field, a computational formula of the structural random response for gravity dams is derived based on Neumann expansion stochastic finite element. Corresponding calculation method for the reliability of gravity dams is proposed together with a programmed Matlab code. A cantilever beam is given for the validation of the method and the influence of element size and fluctuation scale of the random field on structural reliability is discussed. The tensile strength reliability of the dam heel is also calculated. The results show that the reliability of a dam can be influenced significantly by the fluctuation scale. Reliability increases with a decreasing fluctuation scale, and it is undervalued if the elastic modulus is considered as a single random variable. In addition, the discretized element size of the random field should be determined by the fluctuation scale and it should not be too large. The suggested element size is less than 1/10～1/8 of the fluctuation scale.
引文
[1]武清玺.结构可靠度理论、方法及应用[M].北京:机械工业出版社,2016.
[2]孙伟,何蕴龙,袁帅,等.考虑材料非均质性的胶凝砂砾石坝随机有限元分析[J].水利学报,2014,45(7):828-836.(SUN Wei,HE Yunlong,YUAN Shuai,et al.Stochastic finite element analysis of Hardfill dam with considering the material heterogeneity influence[J].Journal of Hydraulic Engineering,2014,45(7):828-836.(in Chinese))
[3]陈桂香,崔晨星,付志永,等.基于Monte-Carlo随机有限元法的地下筒仓可靠性灵敏度研究[J].河南工业大学学报(自然科学版),2017,38(4):86-90.(CHEN Guixiang,CUI Chenxing,FU Zhiyong,et al.Reliability sensitivity analysis of underground silo based on Monte-Carlo stochastic finite element method[J].Journal of Henan University of Technology(Natural Science Edition),2017,38(4):86-90.(in Chinese))
[4]刘宁,郑建青.工程随机力学及可靠性理论中的若干问题(上)[J].河海大学学报(自然科学版),1999,27(5):1-7.(LIU Ning,ZHENG Jianqing.Stochastic mechanics and reliability theory in engineering:part-1[J].Journal of Hohai University(Natural Sciences),1999,27(5):1-7.(in Chinese))
[5]SHINOZUKA M.Monte Carlo solution of structural dynamics[J].Computers and Structure,1972,2(5/6):855-874.
[6]DENDROU B A,HOUSTIS E N.An inference finite element model for field applications[J].Applied Mathematical Modelling,1978,3(1):49-55.
[7]HISADA T,NAKAGIRI S.Stochastic finite element method developed for structural safety and reliability[C]//Proceedings of the 3rd International Conference on Safety and Reliability.Trondheim:[s.n.],1981:395-408.
[8]杨杰,陈虬.Neumann随机有限元的一种推广形式[J].计算力学学报,2005,22(6):681-684.(YANG Jie,CHEN Qiu.A extended form of Neumann stochastic finite element method[J].Chinese Journal of Computational Mechanics,2005,22(6):681-684.(in Chinese))
[9]李典庆,蒋水华,周创兵,等.考虑参数空间变异性的边坡可靠度分析非侵入式随机有限元法[J].岩土工程学报,2013,35(8):1413-1422.(LI Dianqing,JIANG Shuihua,ZHOU Chuangbing,et al.Reliability analysis of slopes considering spatial variability of soil parameters using non-intrusive stochastic finite element method[J].Chinese Journal of Geotechnical Engineering,2013,35(8):1413-1422.(in Chinese))
[10]祁小辉,李典庆,周创兵,等.考虑土体空间变异性的边坡最危险滑动面随机分析方法[J].岩土工程学报,2013,35(4):745-753.(QI Xiaohui,LI Dianqing,ZHOU Chuangbing,et al.Stochastic analysis method of critical slip surfaces in soil slopes considering spatial variability[J].Chinese Journal of Geotechnical Engineering,2013,35(4):745-753.(in Chinese))
[11]裴亮,代萍,何坤,等.高碾压混凝土拱坝温控可靠性分析[J].水利水电科技进展,2016,36(1):90-94.(PEI Liang,DAI Ping,HE Kun,et al.Reliability analysis of temperature of high RCC arch dam[J].Adavances in Science and Technology of Water Resources,2016,36(1):90-94.(in Chinese))
[12]杜永恩,王生楠,闫晓中.基于Neumann展开的MonteCarlo随机扩展有限元法[J].西北工业大学学报,2013,31(3):413-416.(DU Yong’en,WANGShengnan,YAN Xiaozhong.Stochastically extended finite element method based on neumann expansion[J].Journal of Northwestern Polytechnical University,2013,31(3):413-416.(in Chinese))
[13]陈虬,刘先斌.随机有限元法及其工程应用[M].成都:西南交通大学出版社,1993.
[14]ARREGUI-MENA J D,MARGETTS L,MUMMERY PM.Practical application of the stochastic finite element method[J].Archives of Computational Methods in Engineering,2016,23(1):171-190.
[2]孙伟,何蕴龙,袁帅,等.考虑材料非均质性的胶凝砂砾石坝随机有限元分析[J].水利学报,2014,45(7):828-836.(SUN Wei,HE Yunlong,YUAN Shuai,et al.Stochastic finite element analysis of Hardfill dam with considering the material heterogeneity influence[J].Journal of Hydraulic Engineering,2014,45(7):828-836.(in Chinese))
[3]陈桂香,崔晨星,付志永,等.基于Monte-Carlo随机有限元法的地下筒仓可靠性灵敏度研究[J].河南工业大学学报(自然科学版),2017,38(4):86-90.(CHEN Guixiang,CUI Chenxing,FU Zhiyong,et al.Reliability sensitivity analysis of underground silo based on Monte-Carlo stochastic finite element method[J].Journal of Henan University of Technology(Natural Science Edition),2017,38(4):86-90.(in Chinese))
[4]刘宁,郑建青.工程随机力学及可靠性理论中的若干问题(上)[J].河海大学学报(自然科学版),1999,27(5):1-7.(LIU Ning,ZHENG Jianqing.Stochastic mechanics and reliability theory in engineering:part-1[J].Journal of Hohai University(Natural Sciences),1999,27(5):1-7.(in Chinese))
[5]SHINOZUKA M.Monte Carlo solution of structural dynamics[J].Computers and Structure,1972,2(5/6):855-874.
[6]DENDROU B A,HOUSTIS E N.An inference finite element model for field applications[J].Applied Mathematical Modelling,1978,3(1):49-55.
[7]HISADA T,NAKAGIRI S.Stochastic finite element method developed for structural safety and reliability[C]//Proceedings of the 3rd International Conference on Safety and Reliability.Trondheim:[s.n.],1981:395-408.
[8]杨杰,陈虬.Neumann随机有限元的一种推广形式[J].计算力学学报,2005,22(6):681-684.(YANG Jie,CHEN Qiu.A extended form of Neumann stochastic finite element method[J].Chinese Journal of Computational Mechanics,2005,22(6):681-684.(in Chinese))
[9]李典庆,蒋水华,周创兵,等.考虑参数空间变异性的边坡可靠度分析非侵入式随机有限元法[J].岩土工程学报,2013,35(8):1413-1422.(LI Dianqing,JIANG Shuihua,ZHOU Chuangbing,et al.Reliability analysis of slopes considering spatial variability of soil parameters using non-intrusive stochastic finite element method[J].Chinese Journal of Geotechnical Engineering,2013,35(8):1413-1422.(in Chinese))
[10]祁小辉,李典庆,周创兵,等.考虑土体空间变异性的边坡最危险滑动面随机分析方法[J].岩土工程学报,2013,35(4):745-753.(QI Xiaohui,LI Dianqing,ZHOU Chuangbing,et al.Stochastic analysis method of critical slip surfaces in soil slopes considering spatial variability[J].Chinese Journal of Geotechnical Engineering,2013,35(4):745-753.(in Chinese))
[11]裴亮,代萍,何坤,等.高碾压混凝土拱坝温控可靠性分析[J].水利水电科技进展,2016,36(1):90-94.(PEI Liang,DAI Ping,HE Kun,et al.Reliability analysis of temperature of high RCC arch dam[J].Adavances in Science and Technology of Water Resources,2016,36(1):90-94.(in Chinese))
[12]杜永恩,王生楠,闫晓中.基于Neumann展开的MonteCarlo随机扩展有限元法[J].西北工业大学学报,2013,31(3):413-416.(DU Yong’en,WANGShengnan,YAN Xiaozhong.Stochastically extended finite element method based on neumann expansion[J].Journal of Northwestern Polytechnical University,2013,31(3):413-416.(in Chinese))
[13]陈虬,刘先斌.随机有限元法及其工程应用[M].成都:西南交通大学出版社,1993.
[14]ARREGUI-MENA J D,MARGETTS L,MUMMERY PM.Practical application of the stochastic finite element method[J].Archives of Computational Methods in Engineering,2016,23(1):171-190.