基于耐震时程法的重力坝失效概率密度演化分析
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摘要
混凝土重力坝在强地震动作用下的响应,对结构的安全评价及损伤破坏模式有着深远的影响。采用耐震时程分析(ETA)法生成耐震时程加速度曲线(ETAs),获取Koyna混凝土重力坝在地震作用下的动力响应,得出结构在不同损伤评价指标下的概率密度演化过程及失效概率时程曲线。建立Koyna混凝土重力坝有限元模型,模拟坝体在ETA时程下(对应均匀增加的峰值加速度)的动力响应及损伤过程;采用塑性耗散能、损伤耗散能、损伤体积及基准损伤体积作为损伤评价指标,基于概率密度演化(PDE)理论,建立其概率密度演化模型,利用概率密度演化法计算不同损伤评价指标下的概率密度曲线随ETA时程的演化过程;选取2个典型破坏状态分别作为中等破坏、严重破坏的评价标准,结合概率密度曲线与失效概率的关系,分析并比较不同损伤评价指标、不同评价标准下的失效概率时程曲线,实现了坝体在不同峰值加速度地震动下的失效概率分析评价。对于以往的研究结果,损伤评价指标服从正态分布只是一种假定,并没有详细的依据,从本文的分析结果可以看出:损伤评价指标的概率密度分布结果只是近似于正态分布的形式,用PDE法得到的损伤评价指标的概率分布结果与正态分布的形式有一定的偏差;基于耐震时程加速度曲线下的概率密度演化过程具有较高的计算效率及精度,与正态分布假定相比具有明显的偏峰,更趋近于真实的概率分布;选取塑性耗散能、损伤耗散能作为损伤评价指标可以更保守地表征坝体在不同地震动强度下的失效概率。
Concrete gravity dam response under strong ground motions has a profound impact on the safety assessment and damage failure mode of structures. In this paper, the endurance time analysis(ETA) method was used to generate endurance time accelerations(ETAs), calculate and analyze the probability density evolution process and failure probability of damage evaluation factors subjected by the Koyna ground motion ETAs. The Koyna gravity dam finite element model was established, and the dynamic response and damage process of dam under ETAs was simulated. The plastic dissipation energy, damage dissipation energy, damage volume and normalized damage volume as damage evaluation factors were used. Based on the probability density evolution theory, the generalized probability density evolution model was set. The probability density curves varied with ETA history under different damage evaluation factors were calculated. Selecting two typical moments as moderate damage and severe damage evaluation criterion and combining probability density curves with failure probability, probability curves under different damage evaluation factors and different damage evaluation criterion were compared to realize failure probability analysis and evaluation of dam under different peak ground acceleration. Previous studies showed that damage evaluation index obeys the normal distribution which is just a kind of assumption and no detailed basis. According to the present research, the probability density distribution of damage evaluation index results is similar to normal distribution and has certain deviation compared with PDE method. The studies shows that probability density evolution process based on ETAs has high computation efficiency and precision. Compared with the results of normal distribution, the results of PDE are closer to the true probability distribution. It can be more conservative to represent failure probability of dam when using plastic dissipation energy and damage dissipation energy as damage factors under different ground motion intensity.
Concrete gravity dam response under strong ground motions has a profound impact on the safety assessment and damage failure mode of structures. In this paper, the endurance time analysis(ETA) method was used to generate endurance time accelerations(ETAs), calculate and analyze the probability density evolution process and failure probability of damage evaluation factors subjected by the Koyna ground motion ETAs. The Koyna gravity dam finite element model was established, and the dynamic response and damage process of dam under ETAs was simulated. The plastic dissipation energy, damage dissipation energy, damage volume and normalized damage volume as damage evaluation factors were used. Based on the probability density evolution theory, the generalized probability density evolution model was set. The probability density curves varied with ETA history under different damage evaluation factors were calculated. Selecting two typical moments as moderate damage and severe damage evaluation criterion and combining probability density curves with failure probability, probability curves under different damage evaluation factors and different damage evaluation criterion were compared to realize failure probability analysis and evaluation of dam under different peak ground acceleration. Previous studies showed that damage evaluation index obeys the normal distribution which is just a kind of assumption and no detailed basis. According to the present research, the probability density distribution of damage evaluation index results is similar to normal distribution and has certain deviation compared with PDE method. The studies shows that probability density evolution process based on ETAs has high computation efficiency and precision. Compared with the results of normal distribution, the results of PDE are closer to the true probability distribution. It can be more conservative to represent failure probability of dam when using plastic dissipation energy and damage dissipation energy as damage factors under different ground motion intensity.
引文
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[13]Chen Jianbing,Li Jie.Probability density evolution analysis for stochastic seismic response of nonlinear structures[J].Journal of Wuhan University of Technology,2010,32(9):6-10.[陈建兵,李杰.非线性随机地震响应的概率密度演化分析[J].武汉理工大学学报,2010,32(9):6-10.]
[14]Liu Zhangjun,Chen Jianbing,Li Jie.Probability density evolution method-based nonlinear random seismic response analysis of structures[J].Chinese Journal of Solid Mechanics,2009,30(5):489-495.[刘章军,陈建兵,李杰.结构非线性随机地震反应的概率密度演化方法[J].固体力学学报,2009,30(5):489-495.]
[15]Nozari A,Estekanchi H E.Optimization of endurance time acceleration functions for seismic assessment of structures[J].Iran University of Science&Technology,2011,1(2):257-277.
[16]Skeel R D,Berzins M.A method for the spatial discretization of parabolic equations in one space variable[J].SIAMJournal on Scientific and Statistical Computing,1990,11(1):1-32.
[17]Sarkar R,Paul D K,Stempniewski L.Influence of reservoir and foundation on the nonlinear dynamic response of concrete gravity dams[J].ISET Journal of Earthquake Technology,2007,44(2):377-389.
[18]Guo Shengshan,Chen Houqun,Li Deyu,et al.Seismic damage and failure analysis of gravity dam and foundation system[J].Journal of Hydraulic Engineering,2013,44(11):1352-1358.[郭胜山,陈厚群,李德玉,等.重力坝与坝基体系地震损伤破坏分析[J].水利学报,2013,44(11):1352-1358.]
[19]Liu Zhangjun,Zeng Bo,Zhou Yihong,et al.Probabilistic model of ground motion processes and seismic dynamic reliability analysis of the gravity dam[J].Journal of Hydraulic Engineering,2014,45(9):1066-1074.[刘章军,曾波,周宜红,等.地震动过程的概率模型及在重力坝抗震可靠度分析中的应用[J].水利学报,2014,45(9):1066-1074.]
[20]Wang J T,Jin A Y,Du X L,et al.Scatter of dynamic response and damage of an arch dam subjected to artificial earthquake accelerograms[J].Soil Dynamics&Earthquake Engineering,2016,87:93-100.
[21]Fan Shuli,Chen Mingyang,Chen Jianyun,et al.Seismic damage analysis of a concrete gravity dam based on energy dissipation[J].Journal of Vibration and Shock,2011,30(4):271-275.[范书立,陈明阳,陈健云,等.基于能量耗散碾压混凝土重力坝地震损伤分析[J].振动与冲击,2011,30(4):271-275.]
[22]Chen Jianbing,Li Jie.Reliability analysis of stochastic structures based on probability density evolution method[J].Chinese Journal of Computational Mechanics,2004,21(3):285-290.[陈建兵,李杰.基于概率密度演化方法的随机结构可靠度分析[J].计算力学学报,2004,21(3):285-290.]
[2]Chen Houqun,Guo Shengshan.Seismic damage analysis of high concrete dam-foundation system[J].Journal of Hydraulic Engineering,2012,43(Supp1):2-7.[陈厚群,郭胜山.混凝土高坝-地基体系的地震损伤分析[J].水利学报,2012,43(增刊1):2-7.]
[3]水电工程水工建筑物抗震设计规范:NB35047-2015[S].北京:中国电力出版社,2015.
[4]Estekanchi H E,Vafai A,Sadeghazar M.Endurance time method for seismic analysis and design of structures[J].Scientia Iranica,2004,11(4):361-370.
[5]Hariri-Ardebili M A,Mirzabozorg H.Estimation of probable damages in arch dams subjected to strong ground motions using endurance time acceleration functions[J].KSCEJournal of Civil Engineering,2014,18(2):574-586.
[6]Valamanesh V,Estekanchi H E,Vafai A,et al.Application of the endurance time method in seismic analysis of concrete gravity dams[J].Scientia Iranica,2011,18(3):326-337.
[7]Hariri-Ardebili M A,Zarringhalam Y,Estekanchi H E,et al.Nonlinear seismic assessment of steel moment frames using time-history,incremental dynamic,and endurance time analysis methods[J].Scientia Iranica,2013,20(3):431-444.
[8]Riahi H T,Estekanchi H E,Boroujeni S S.Application of endurance time method in nonlinear seismic analysis of steel frames[J].Procedia Engineering,2011,14:3237-3244.
[9]Bai Jiulin,Yang Le,Ou Jinping.The endurance time method for seismic response analyses of building structures[J].Earthquake Engineering and Engineering Dynamics,2014,34(1):8-18.[白久林,杨乐,欧进萍.结构抗震分析的耐震时程方法[J].地震工程与工程振动,2014,34(1):8-18.]
[10]Li J,Chen J.The principle of preservation of probability and the generalized density evolution equation[J].Structural Safety,2008,30(1):65-77.
[11]Yang Junyi,Chen Jianbing,Li Jie.Probability density evolution analysis of nonlinear seismic response of structures with random parameters following different distributions[J].Journal of Southwest Jiaotong University,2015,50(6):1047-1054.[杨俊毅,陈建兵,李杰.不同分布随机参数结构非线性地震反应的概率密度演化[J].西南交通大学学报,2015,50(6):1047-1054.]
[12]Chen Jianbing,Li Jie.Probability density evolution method for stochastic seismic response and reliability of structures[J].Engineering Mechanics,2014,31(4):1-10.[陈建兵,李杰.结构随机地震反应与可靠度的概率密度演化分析研究进展[J].工程力学,2014,31(4):1-10.]
[13]Chen Jianbing,Li Jie.Probability density evolution analysis for stochastic seismic response of nonlinear structures[J].Journal of Wuhan University of Technology,2010,32(9):6-10.[陈建兵,李杰.非线性随机地震响应的概率密度演化分析[J].武汉理工大学学报,2010,32(9):6-10.]
[14]Liu Zhangjun,Chen Jianbing,Li Jie.Probability density evolution method-based nonlinear random seismic response analysis of structures[J].Chinese Journal of Solid Mechanics,2009,30(5):489-495.[刘章军,陈建兵,李杰.结构非线性随机地震反应的概率密度演化方法[J].固体力学学报,2009,30(5):489-495.]
[15]Nozari A,Estekanchi H E.Optimization of endurance time acceleration functions for seismic assessment of structures[J].Iran University of Science&Technology,2011,1(2):257-277.
[16]Skeel R D,Berzins M.A method for the spatial discretization of parabolic equations in one space variable[J].SIAMJournal on Scientific and Statistical Computing,1990,11(1):1-32.
[17]Sarkar R,Paul D K,Stempniewski L.Influence of reservoir and foundation on the nonlinear dynamic response of concrete gravity dams[J].ISET Journal of Earthquake Technology,2007,44(2):377-389.
[18]Guo Shengshan,Chen Houqun,Li Deyu,et al.Seismic damage and failure analysis of gravity dam and foundation system[J].Journal of Hydraulic Engineering,2013,44(11):1352-1358.[郭胜山,陈厚群,李德玉,等.重力坝与坝基体系地震损伤破坏分析[J].水利学报,2013,44(11):1352-1358.]
[19]Liu Zhangjun,Zeng Bo,Zhou Yihong,et al.Probabilistic model of ground motion processes and seismic dynamic reliability analysis of the gravity dam[J].Journal of Hydraulic Engineering,2014,45(9):1066-1074.[刘章军,曾波,周宜红,等.地震动过程的概率模型及在重力坝抗震可靠度分析中的应用[J].水利学报,2014,45(9):1066-1074.]
[20]Wang J T,Jin A Y,Du X L,et al.Scatter of dynamic response and damage of an arch dam subjected to artificial earthquake accelerograms[J].Soil Dynamics&Earthquake Engineering,2016,87:93-100.
[21]Fan Shuli,Chen Mingyang,Chen Jianyun,et al.Seismic damage analysis of a concrete gravity dam based on energy dissipation[J].Journal of Vibration and Shock,2011,30(4):271-275.[范书立,陈明阳,陈健云,等.基于能量耗散碾压混凝土重力坝地震损伤分析[J].振动与冲击,2011,30(4):271-275.]
[22]Chen Jianbing,Li Jie.Reliability analysis of stochastic structures based on probability density evolution method[J].Chinese Journal of Computational Mechanics,2004,21(3):285-290.[陈建兵,李杰.基于概率密度演化方法的随机结构可靠度分析[J].计算力学学报,2004,21(3):285-290.]
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