【作者】 王建民；

【导师】 朱晞；

【作者基本信息】 北京交通大学 ， 桥梁与隧道工程， 2006， 博士

【摘要】 由于结构能力和地震作用下结构需求的不确定性，使得研究结构的抗震性能应当用概率的方法进行。在用概率方法研究地震作用下结构性能的进程中，美国太平洋地震工程研究中心（Pacific Earthquake Engineering Research，PEER）提出了基于性能的抗震设计和评估的概率法基本框架，该框架的目的是把基于性能地震工程这个复杂的问题，在全概率理论的基础上分割成为地震危险性分析、结构的地震响应分析、破坏分析和损失分析四个主要的步骤，并假设性能评估的构成能被当作在参数之间的条件概率是独立的和离散的Markov过程，使之能够在严格的和一致的状态中研究与求解，是一种有很好应用前景的基于性能地震工程方法。本文以PEER基于性能的抗震设计和评估基本框架为依托，重点研究了以概率为基础的桥梁结构的地震需求模型和能力模型以及桥梁结构的脆弱性分析方法，并在全概率理论的基础上研究了针对钢筋混凝土桥梁结构的地震危害性分析方法。主要的研究工作如下：一、研究了地面运动强度度量参数（Intensity Measure，IM）与双线性单自由度（Single Degree of Freedom，SDOF）结构系统的最大变形需求的相关性。在PEER基于性能的抗震设计和评估的框架中，地震危险性分析和结构的地震响应分析是通过中间变量IM来建立联系的，IM应当是与结构地震响应相关性强的参数。文中采用一组以LMSR_N表示的40条水平地面运动记录，通过非线性动力分析研究了工程中常用的单参数的IM与双线性SDOF结构系统变形需求的相关性，结果表明在结构基阶周期处的谱加速度S_a（T₁）与双线性SDOF结构系统的变形需求有着很强的相关性。二、分析了地面运动强度度量参数在估计结构地震响应时的有效性。建议了一个向量形式的IM，比较了建议的IM与标量的IM以及Jack W．BAKER采用的向量的IM在估计结构响应时的有效性，研究中采用了两种周期（T=0.3，1.2s）的双线性SDOF结构系统，分析结果表明，采用向量的IM较标量的IM可以有效的减小估计结构地震需求的标准离差，而本文建议的向量的IM较Jack W．BAKER采用的向量的IM又可以进一步减小标准离差，从而可以很大的减小计算的工作量。三、通过对圆截面钢筋混凝土桥墩的弯矩-曲率分析，本文研究了桥墩截面的无量纲屈服、服务和破坏控制曲率极限状态同轴压比、纵筋配筋率和配箍率的关系。研究中首先用直径为1.0m桥墩作为基准桥墩分析了无量纲曲率极限状态与上述桥墩设计参数的关系，然后通过回归分析建立了用于计算其它截面直径桥墩对应于不同极限状态的曲率延性的直径调整系数近似计算公式。四、研究了圆截面钢筋混凝土桥墩曲率极限状态和延性的概率特性。在PEER基于性能的抗震设计和评估的概率法基本框架中，结构的破坏分析是用在给定工程需求参数下（Engineering Demand Parameter，EDP）结构达到或超过指定极限状态的条件概率形式来计算的，因而需要从构件能力的不确定性方面来研究圆截面钢筋混凝土桥墩的极限状态。研究中把桥墩截面的材料参数和几何参数作为随机变量，采用拉丁超立方体抽样模拟（Latin Hypercube Sampling，LHS）方法，分析了在不同的轴压比、纵筋配筋率和配箍率下桥墩截面的无量纲屈服、服务和破坏控制曲率极限状态的概率特性。另外，还分析了服务性和破坏控制极限状态的曲率延性系数的概率分布特征值，通过回归分析提出了用桥墩设计参数计算圆截面钢筋混凝土桥墩的服务性和破坏控制曲率延性系数的特征值的近似计算公式。五、编制了用非线性静力分析（能力谱法）和非线性动力分析（全概率法）建立结构脆弱性曲线的程序，并以一个高架桥为例，分别用这两种程序建立了桥梁结构的脆弱性曲线。通过用这两种不同方法和程序所得到的脆弱性曲线的结果的比较表明：对于服务极限状态，两种分析结果的差别不大；但是对于破坏控制极限状态及倒塌极限状态，非线性静力分析方法所得到的脆弱性曲线偏右，说明非线性静力方法低估了结构在给定地面运动强度下达到或超过指定极限状态的概率。六、在全概率理论的基础上推导了结构在特定地震危险性水平下的年平均达到或超过指定极限状态的概率的解析表达式，并用此解析表达式对一个三跨连续刚构桥结构进行了在特定地震环境下的地震危害性研究。更多还原

【Abstract】 The uncertainty of structural capacity and seismic demand make it necessary to consider the seismic performance of structure from the probabilistic points. Ongoing this progress, the Pacific Earthquake Engineering Research Center （PEER） is developing a probabilistic framework for performance-based design and evaluation. The goal of the framework is to utilize the Total Probability Theorem to de-aggregate the complicated PBEE problem into decouple the complicated PBEE problem into four stages: hazard analysis, structural analysis, damage analysis, and loss analysis. And the framework assume that these stages are independent and discrete Markov process, where the conditional probabilities between parameters are independent, which making it as robust methodology for performance-based earthquake engineering to research and resolve the logical elements of process in a rigorous and consistent manner. In this paper, it is focused on the investigations of seismic hazard analysis methods with total probability theory and fragility analysis methods for reinforced concrete bridge structure, in which seismic demand model and seismic capacity model are mainly involved. The major studies and creative intents are as follows:1. The correlation between ground motion intensity measures （IM） and bilinear single-degree—of-freedom （SDOF） structure systems deformation demand is studied. In the Pacific Earthquake Research Center’s probabilistic performance-based design and evaluation framework, the structure seismic response analysis and the ground motion predictions are related by an interface variable referred as the ground motion intensity measure （IM）, IM should be correlated strongly to the seismic demand placed on the structure. In this paper, using a suit of 40 horizontal ground motions records referred to as LMSR_N, the correlation between the common IMs used in engineering practice and bilinear SDOF structure systems deformation demand is studied through nonlinear dynamic analysis. The numerical results obtained by nonlinear dynamic analyses have shown good correlation between S_a（T₁）（the spectral acceleration for the fundamental period of the structure） and bilinear SDOF structure systems deformation demand.2. The effect of adopted IM on structural responses is investigated through dynamic nonlinear analysis for several SDOF systems with different periods and different strength reduction factors. It was shown that the vector IM is more efficiency than scalar IM, and the proposed IM is the most efficiency of the three IMs adopted in this study. Moreover, by performing the analyses of prediction of structures response conditional IM, using the proposed vector IM only need one regression analysis as opposed to the vector IM proposed by Jack W. BAKER, which will reduce computational effort.3. Through the use of moment-curvature analysis of circular bridge columns, dimensionless serviceability and damage control curvature are investigated for different values of the axial load ratio, longitudinal reinforcement ratio and percentage of confinement. A constant value of section diameter 1.0m was used as reference column to study dimensionless curvatures. Furthermore, diameter modified factor to estimate dimensionless curvatures for other section dimensions are developed by regression analysis.4. The probabilistic dimensionless serviceability and damage control curvature limit state of circular reinforced concrete bridge column are investigated. Material and geometric parameters are modeled as random variables, using the LHS simulation, the probabilistic parameters of the two levels of curvature limit states are calculated for different values of the axial load ratio, longitudinal reinforcement ratio and transverse reinforcement ratio. Furthermore, the characteristic values of the curvature ductility factors for serviceability and damage control limit states are obtained respectively. Finally, two equations to estimate the curvature ductility factors are developed through the use of regression analysis.5. The programs of generate fragility curves for bridges through nonlinear static analysis （capacity spectra method） and nonlinear dynamic RHA （total probability theorem method） is developed. And the fragility curves of viaduct structure are developed by capacity spectra method and nonlinear dynamic RHA method, respectively. The results from structural fragility curves computed by two methods are shown that there’s no big difference between two analysis methods for the serviceability limit state, and the rightward excursion of the fragility curve developed by nonlinear static analysis because of the damage control and collapse limit states, which reveals that nonlinear static analysis underestimates the probability of the specific damage state that structure reaches under a given ground motion intensity.6. The structural seismic risk analysis method based on probability is investigated systematically for the uncertainty of structural capacity and seismic demand. A procedure is provided to separate the structural seismic risk analysis logically into two stages, seismic hazard analysis and structural fragility analysis, with parameters of ground motion intensity measure as interim variables. An analytical expression is presented based on total probability theory to describe the mean annual rate of structural performance level reaching or exceeding a specific limit state, and the analytical solutions are adopted to analyze the seismic risk of a three-span rigid-frame bridge in a specific hazard environment.更多还原