桥梁结构抗震性能概率性分析方法研究
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摘要
目前,基于性能的抗震设计已逐步成为工程抗震领域的主要研究课题,无论在建筑工程还是桥梁工程界均受到广泛关注。考虑到地面运动的巨大不确定性和桥梁结构组成几何、材料的随机性,其地震响应和抗震能力均具有随机性的特点,因而桥梁结构基于性能的抗震设计应建立于概率方法之上。本文综合分析、评价了当前工程结构抗震和基于性能抗震设计方法的发展现状及未来发展趋势,考虑地面运动的随机性和结构特性的随机性,对桥梁结构抗震性能的概率性分析方法进行了较为系统的研究。主要对桥梁基于性能的抗震设防标准、钢筋混凝土延性构件抗震性能指标的概率特性、地震危险性曲线的建立、结构随机非弹性响应谱、静力弹塑性分析方法的改进、桥梁结构抗震性能可靠度的分析方法等方面进行了研究,所获得的主要研究成果如下：
1)对建立桥梁结构基于性能的抗震设防标准中需要考虑的几个问题进行了探讨,结合国内外各种抗震设计规范中关于抗震设防标准的规定,考虑我国的实际情况,对我国基于性能的抗震设防标准提出了建议,提出了桥梁结构设防地震水准、抗震性能水准、抗震重要性的划分标准及不同桥梁的抗震性能目标。
2)对钢筋混凝土延性构件提出了五种损伤状态、四种极限状态的性能水准定义,并从微观上给出各个极限状态的应变控制指标；然后以钢筋和混凝土的力学特性及其统计特性为基础,针对圆截面钢筋混凝土延性构件各个性能等级下的强度及界限变形特征进行概率分析,得到各个性能等级下构件界限性能指标的概率分布特征,提出了便于进行概率性抗震性能分析的构件各级性能指标的回归公式和概率分布模型。
3)以地震安全性评价的概率法为基础,利用现行《中国地震动参数区划图》的编图成果,根据地震烈度和地震加速度的统计概率分布公式,建立了一定年限内不同超越概率水平的地震烈度和地震动加速度与基本烈度和基本加速度之间的换算关系,从而获得以规范为基础的地震危险性曲线；同时,推导了以不同年限表达的地震危险性曲线之间的关系。
4)对人工合成地震波的方法进行了改进。首先采用精细积分法计算地震波的反应谱,提高了地震波在高频区段的拟合精度,然后采用高次多项式进行地震波的基线校正,使所合成的地震波有效消除了位移和速度的漂移现象。
5)以随机地震动模型为基础,确定了与现行《中国地震动参数区划图(GB18306-2001)》的基本加速度分档和场地类别及特征周期分组相容的随机地震动模型参数。进而基于随机振动理论得到与设计规范相容的基于随机地震动模型的随机弹性反应谱。
6)利用历次破坏性地震中所获得的1064条强震记录,根据我国的场地类别和设计特征周期分组进行分类,对单自由度弹塑性系统的非线性地震响应进行计算；基于Nassar&Krawinkler所提出的强度折减系数模型,对计算结果进行统计回归分析,获得了与我国设计规范相容的强度折减系数模型。根据所获得的强度折减系数模型对随机弹性反应谱进行折减,从而获得了各种随机非弹性反应谱。
7)以Chopra提出的模态Pushover方法为基础,基于地震荷载的Chopra分解和结构能量平衡方程,推得某阶模态荷载作用下结构系统所输入能量全部转化为该阶模态所吸收能量的结论,并推导了增量模态荷载作用下结构能量增量与谱位移增量和谱加速度增量之间的关系,在此基础上提出了基于能量的Pushover方法。采用所提出的方法对一座连续刚构桥进行了抗震性能分析,结果表明所提出的方法适应性较好,可以适用于较复杂结构的非线性抗震性能分析。
8)综合运用关于抗震性能划分标准、抗震性能变形控制指标的概率特性、地震危险性分析成果、随机非弹性地震响应的简化计算方法等的研究成果,建立了桥梁结构抗震性能的概率性分析方法。
9)以一座实际桥梁为工程背景,对该桥的抗震性能进行了概率性分析,分别计算了确定强度地震作用下和50年基准期内地震作用下各种极限状态的抗震可靠度。结果表明,所提出的方法计算简便,适应性强,避免了传统结构抗震可靠性分析中因需要进行大规模Monte Carlo模拟、计算量过大而导致分析难以进行的困难。所提出的方法可以用于基于变形破坏准则的大震下结构抗震性能的概率性分析。
Performance-based seismic design (PBSD) has become the main research subject in aseismic engineering and attracted a lot of research attention both in building engineering and bridge engineering. The seismic response and capacity of bridge are random because of the uncertainty of the ground motion and the geometry and material of the structure. Hence PBSD should be built on probability theory. In this paper, the probabilistic method for seismic performance analysis of bridge structures was studied systematically, including the criterion for PBSD of bridge, probability characteristics of the ductility-based seismic performance indices for reinforced concrete components, seismic hazard curve, stochastic inelastic seismic response spectra, improvement of modal pushover analysis method, and nonlinear seismic reliability analysis method for bridge under large earthquakes. The following major achievements were gained:
1) Some problems concerning the seismic fortification criterion of PBSD in bridge engineering were discussed. Based on the studying of guidelines concerning seismic fortification criterion in the seismic design codes of several countries, and considering the reality of China, some proposals were put forward for the seismic fortification criterion in PBSD of bridge engineering in China, including the fortification ground motion levels, seismic performance levels, seismic importance classification of bridge structures, as well as seismic fortification objectives for bridges of variant importance.
2) Five damage states with four limit states were defined for the seismic performance level of ductile reinforced concrete components, along with the strain limit definition for each limit state. Then, based on the mechanical characteristics and statistical characteristics of reinforcement and concrete, the strength and deformation characteristics of circular reinforced concrete ductile component were analyzed probabilistically for each performance level. Hereby the probabilistic distribution characteristics of the performance indices for each performance level were obtained for reinforced concrete ductile members, and the regression formula as well as probability distribution model for the performance index of each performance level were proposed, in convenient for the probabilistic analysis of seismic performance of bridge structures.
3) Based on the probabilistic method for seismic hazard evaluation, according to the achievements of Seismic ground motion parameter zonation map of China and the statistical probability distribution of seismic intensity and peak ground acceleration (PGA), the conversion relationship from the basic seismic intensity and basic PGA, i.e., those presented in the Seismic ground motion parameter zonation map of China, to the seismic intensity and PGA with variant probability of exceedance in certain considering years, was deduced. Hence the seismic hazard curve that is based on the currently in effect seismic specification was obtained. In addition, the conversion relationship between seismic hazard curves of different considering years was also presented.
4) The artificial seismic ground motion simulation method was improved in two aspects. Firstly, the precise integration method was adopted for the calculation of seismic response spectra of the seismic wave, which improves the calculation accuracy for high frequency domain. Then, a high order polynomial was adopted for the baseline correction of the simulated wave, which can effectively clear up the baseline-shift of the artificially simulated seismic ground motion.
5) Based on a proper stochastic earthquake ground motion model, the parameters of the model that are compatible with the PGA, site classification and characteristic period grouping specified in the currently in effect zonation map in China were determined. Further more, the stochastic elastic response spectra that are based on the stochastic earthquake ground motion model and compatible with the currently in effect seismic design code were obtained.
6) By utilizing the 1064 strong ground motion records obtained from the destructive events in the history, which are classified according to the site classification and characteristic period grouping specified in the design code of China, the inelastic response of SDOF systems with variant periods and ductility factors were analyzed. Then, based on the strength reduction factor model proposed by Nassar & Krawinkler, the calculation results were analyzed with statistical regression method. Thereby the strength reduction factor model that is compatible with the seismic design code of China was obtained. By the reduction of the stochastic elastic response spectra with the obtained strength reduction factor, the stochastic inelastic response spectra were obtained.
7) Based on the Modal Pushover Analysis (MPA) method proposed by Chopra and the decomposition of the seismic action, as well as the energy balance equation, it was deduced and concluded that the inputted energy by the modal load was completely converted to the absorbed energy by the corresponding mode. Then the relationship between the spectral displacement increment and the energy increment in the structure under the action of modal load was deduced, which brings on the proposal of an improved Modal Pushover Analysis method-Energy Based Modal Pushover Analysis method (EMPA). As an example, a continuous rigid frame bridge was analyzed with the proposed method to illustrate its adaptability for the nonlinear seismic analysis of complex bridge structures.
8) By making use of the achievements on the seismic performance level classification, probabilistic characteristics of the deformation-based performance indices for each performance level, seismic hazard curve, and simplified computation method for the stochastic inelastic seismic demand, the probabilistic method for seismic performance analysis of bridge structures was proposed.
9) The probabilistic seismic performance of a realistic bridge was analyzed, by computing its determined-intensity-based aseismic reliability and 50-year-based aseismic reliability. This example illustrated the simplicity and adaptability of the proposed method for aseismic reliability analysis in the PBSD of bridge structures based on deformation-based failure criterion under large earthquake. Thus the difficulty of the conventional method for aseismic reliability analysis was avoided, which is generally performed by the huge computation of a lot of nonlinear time-history analysis by Monte Carlo simulation.
1)对建立桥梁结构基于性能的抗震设防标准中需要考虑的几个问题进行了探讨,结合国内外各种抗震设计规范中关于抗震设防标准的规定,考虑我国的实际情况,对我国基于性能的抗震设防标准提出了建议,提出了桥梁结构设防地震水准、抗震性能水准、抗震重要性的划分标准及不同桥梁的抗震性能目标。
2)对钢筋混凝土延性构件提出了五种损伤状态、四种极限状态的性能水准定义,并从微观上给出各个极限状态的应变控制指标；然后以钢筋和混凝土的力学特性及其统计特性为基础,针对圆截面钢筋混凝土延性构件各个性能等级下的强度及界限变形特征进行概率分析,得到各个性能等级下构件界限性能指标的概率分布特征,提出了便于进行概率性抗震性能分析的构件各级性能指标的回归公式和概率分布模型。
3)以地震安全性评价的概率法为基础,利用现行《中国地震动参数区划图》的编图成果,根据地震烈度和地震加速度的统计概率分布公式,建立了一定年限内不同超越概率水平的地震烈度和地震动加速度与基本烈度和基本加速度之间的换算关系,从而获得以规范为基础的地震危险性曲线；同时,推导了以不同年限表达的地震危险性曲线之间的关系。
4)对人工合成地震波的方法进行了改进。首先采用精细积分法计算地震波的反应谱,提高了地震波在高频区段的拟合精度,然后采用高次多项式进行地震波的基线校正,使所合成的地震波有效消除了位移和速度的漂移现象。
5)以随机地震动模型为基础,确定了与现行《中国地震动参数区划图(GB18306-2001)》的基本加速度分档和场地类别及特征周期分组相容的随机地震动模型参数。进而基于随机振动理论得到与设计规范相容的基于随机地震动模型的随机弹性反应谱。
6)利用历次破坏性地震中所获得的1064条强震记录,根据我国的场地类别和设计特征周期分组进行分类,对单自由度弹塑性系统的非线性地震响应进行计算；基于Nassar&Krawinkler所提出的强度折减系数模型,对计算结果进行统计回归分析,获得了与我国设计规范相容的强度折减系数模型。根据所获得的强度折减系数模型对随机弹性反应谱进行折减,从而获得了各种随机非弹性反应谱。
7)以Chopra提出的模态Pushover方法为基础,基于地震荷载的Chopra分解和结构能量平衡方程,推得某阶模态荷载作用下结构系统所输入能量全部转化为该阶模态所吸收能量的结论,并推导了增量模态荷载作用下结构能量增量与谱位移增量和谱加速度增量之间的关系,在此基础上提出了基于能量的Pushover方法。采用所提出的方法对一座连续刚构桥进行了抗震性能分析,结果表明所提出的方法适应性较好,可以适用于较复杂结构的非线性抗震性能分析。
8)综合运用关于抗震性能划分标准、抗震性能变形控制指标的概率特性、地震危险性分析成果、随机非弹性地震响应的简化计算方法等的研究成果,建立了桥梁结构抗震性能的概率性分析方法。
9)以一座实际桥梁为工程背景,对该桥的抗震性能进行了概率性分析,分别计算了确定强度地震作用下和50年基准期内地震作用下各种极限状态的抗震可靠度。结果表明,所提出的方法计算简便,适应性强,避免了传统结构抗震可靠性分析中因需要进行大规模Monte Carlo模拟、计算量过大而导致分析难以进行的困难。所提出的方法可以用于基于变形破坏准则的大震下结构抗震性能的概率性分析。
Performance-based seismic design (PBSD) has become the main research subject in aseismic engineering and attracted a lot of research attention both in building engineering and bridge engineering. The seismic response and capacity of bridge are random because of the uncertainty of the ground motion and the geometry and material of the structure. Hence PBSD should be built on probability theory. In this paper, the probabilistic method for seismic performance analysis of bridge structures was studied systematically, including the criterion for PBSD of bridge, probability characteristics of the ductility-based seismic performance indices for reinforced concrete components, seismic hazard curve, stochastic inelastic seismic response spectra, improvement of modal pushover analysis method, and nonlinear seismic reliability analysis method for bridge under large earthquakes. The following major achievements were gained:
1) Some problems concerning the seismic fortification criterion of PBSD in bridge engineering were discussed. Based on the studying of guidelines concerning seismic fortification criterion in the seismic design codes of several countries, and considering the reality of China, some proposals were put forward for the seismic fortification criterion in PBSD of bridge engineering in China, including the fortification ground motion levels, seismic performance levels, seismic importance classification of bridge structures, as well as seismic fortification objectives for bridges of variant importance.
2) Five damage states with four limit states were defined for the seismic performance level of ductile reinforced concrete components, along with the strain limit definition for each limit state. Then, based on the mechanical characteristics and statistical characteristics of reinforcement and concrete, the strength and deformation characteristics of circular reinforced concrete ductile component were analyzed probabilistically for each performance level. Hereby the probabilistic distribution characteristics of the performance indices for each performance level were obtained for reinforced concrete ductile members, and the regression formula as well as probability distribution model for the performance index of each performance level were proposed, in convenient for the probabilistic analysis of seismic performance of bridge structures.
3) Based on the probabilistic method for seismic hazard evaluation, according to the achievements of Seismic ground motion parameter zonation map of China and the statistical probability distribution of seismic intensity and peak ground acceleration (PGA), the conversion relationship from the basic seismic intensity and basic PGA, i.e., those presented in the Seismic ground motion parameter zonation map of China, to the seismic intensity and PGA with variant probability of exceedance in certain considering years, was deduced. Hence the seismic hazard curve that is based on the currently in effect seismic specification was obtained. In addition, the conversion relationship between seismic hazard curves of different considering years was also presented.
4) The artificial seismic ground motion simulation method was improved in two aspects. Firstly, the precise integration method was adopted for the calculation of seismic response spectra of the seismic wave, which improves the calculation accuracy for high frequency domain. Then, a high order polynomial was adopted for the baseline correction of the simulated wave, which can effectively clear up the baseline-shift of the artificially simulated seismic ground motion.
5) Based on a proper stochastic earthquake ground motion model, the parameters of the model that are compatible with the PGA, site classification and characteristic period grouping specified in the currently in effect zonation map in China were determined. Further more, the stochastic elastic response spectra that are based on the stochastic earthquake ground motion model and compatible with the currently in effect seismic design code were obtained.
6) By utilizing the 1064 strong ground motion records obtained from the destructive events in the history, which are classified according to the site classification and characteristic period grouping specified in the design code of China, the inelastic response of SDOF systems with variant periods and ductility factors were analyzed. Then, based on the strength reduction factor model proposed by Nassar & Krawinkler, the calculation results were analyzed with statistical regression method. Thereby the strength reduction factor model that is compatible with the seismic design code of China was obtained. By the reduction of the stochastic elastic response spectra with the obtained strength reduction factor, the stochastic inelastic response spectra were obtained.
7) Based on the Modal Pushover Analysis (MPA) method proposed by Chopra and the decomposition of the seismic action, as well as the energy balance equation, it was deduced and concluded that the inputted energy by the modal load was completely converted to the absorbed energy by the corresponding mode. Then the relationship between the spectral displacement increment and the energy increment in the structure under the action of modal load was deduced, which brings on the proposal of an improved Modal Pushover Analysis method-Energy Based Modal Pushover Analysis method (EMPA). As an example, a continuous rigid frame bridge was analyzed with the proposed method to illustrate its adaptability for the nonlinear seismic analysis of complex bridge structures.
8) By making use of the achievements on the seismic performance level classification, probabilistic characteristics of the deformation-based performance indices for each performance level, seismic hazard curve, and simplified computation method for the stochastic inelastic seismic demand, the probabilistic method for seismic performance analysis of bridge structures was proposed.
9) The probabilistic seismic performance of a realistic bridge was analyzed, by computing its determined-intensity-based aseismic reliability and 50-year-based aseismic reliability. This example illustrated the simplicity and adaptability of the proposed method for aseismic reliability analysis in the PBSD of bridge structures based on deformation-based failure criterion under large earthquake. Thus the difficulty of the conventional method for aseismic reliability analysis was avoided, which is generally performed by the huge computation of a lot of nonlinear time-history analysis by Monte Carlo simulation.
引文
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