钢筋混凝土框架结构的整体概率抗震能力分析
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摘要
21世纪初,美国太平洋地震工程研究中心(Pacific Earthquake Engineering Research Center, PEER)提出了新一代“基于性能的地震工程(Peformance-Based Earthquake Engineering, PBEE)”概率决策框架;与此同时,美国中部地震研究中心(Mid-American Earthquake Engineering, MAE)也提出了“基于后果的地震工程(Consequence-Based Earthquake Engineering, CBEE)”概率决策框架。由于这两个框架都是建立在地震风险分析的基础上,为此,本文初步提出了“基于风险的地震工程(Risk-Based Earthquake Engineering, RBEE)”概率决策框架。地震动(Earthquake Motion)、地震需求(Seimsic Demand)和抗震能力(Seimsic Capacity)以及它们之间的相互关系是PBEE、CBEE和RBEE所共同关心的三个核心问题。由于地震发生的随机性、地震动的随机过程性以及工程结构自身参数的随机性,因此结构的抗震能力本质上是随机的,研究结构地震需求与抗震能力之间概率关系的学科称为“概率抗震能力分析(Probabilsitic Seismic Capacity Analysis, PSCA)”。
工程结构的概率抗震能力分析是结构抗震可靠度分析、结构地震易损性分析以及结构地震风险分析的基础,同时,也是采用全概率方法进行结构概率抗震性能设计和概率抗震性能评定的重要组成部分;另外,概率抗震能力分析的结果也可以为地震损失估计和防震减灾决策提供科学的依据。由于结构整体抗震能力可以从宏观上刻画结构的抗震性能,因此,对重大土木工程结构和基础设施系统进行整体概率抗震能力分析,不仅具有重要的理论意义,而且具有重要的工程实用价值。
本文首先研究了复杂随机函数的统计矩分析方法,提出了基于Nataf变换的点估计法;通过对同一算例的计算,将点估计法同蒙特卡洛模拟法、数值积分法和平均值一次二阶矩法进行了比较;然后,将随机函数统计矩分析方法和Pushover分析结合起来,提出随机Pushover分析方法;以最大层间位移角(Inter-Storey Drift Angle, ISDA)作为结构整体能力参数,然后从随机Pushover分析和有限元可靠度分析两个角度,建立了钢筋混凝土框架结构的整体概率抗震能力模型;在此基础上,结合场地的地震危险性,对结构的整体概率抗震能力危险性和整体概率抗震能力易损性进行了系统深入的分析。得到以下结论:
(1)本文提出的改进的点估计法可以提高Zhao-Ono点估计法的精度;MVFOSM的效率最高,但精度较低,特别是当随机函数的非线性程度较高时;数值积分法的精度与点估计法相当,其效率高于点估计法。
(2)随机Pushover分析方法和有限元可靠度分析方法都可以用来计算结构整体能力的统计矩。随机Pushover分析方法将随机函数统计矩分析方法与传统的Pushover分析相结合,可以很好地解决结构整体能力统计分析中所遇到的隐式函数难以处理的困难;有限元可靠度分析方法将结构可靠度的近似解析法与有限元分析以及有限元反应灵敏度分析相结合,本质上是一种随机有限元方法,可以精细地模拟结构模型中的各种不确定性。
(3)结构整体抗震能力基于统计矩的概率模型和基于可靠度的回归模型,结果存在一定差异。前者基于结构能力参数服从对数正态分布假设,是一种具有“共性”的假设;后者基于有限元可靠度分析则是针对具体的结构形式,得到了“个性”的结果。“个性”的结果一定会体现“共性”的假设特征,但是,更多的体现的是结构个体的性质。
(4)结构的概率抗震能力模型只考虑结构自身参数的不确定性,而结构抗震能力的易损性模型则进一步考虑了地震动参数的随机性。显然,后者是对前者的进一步拓广。
(5)结构抗震能力的危险性是在结构抗震能力易损性分析基础上,考虑了场地的危险性。因此,结构的抗震能力危险性分析是对结构抗震能力分析的进一步拓广。
At the beginning of the twenty-first century, Pacific Earthquake Engineering Research Center (PEER) proposed a probabilistic decision-making framework for Performance-Based Earthquake Engineering (PBEE). At the same time, Mid-American Earthquake Engineering (MAE) proposed another probabilistic decision-making framework for Consequence-Based Earthquake Engineering (CBEE). Actually, the two frameworks both are based on seismic risk analysis, threrfore, the probabilistic decision-making framework of Risk-Based Earthquake Engineering is put forward in this thesis. Earthquake motion, seismic demand and seismic capacity as well as their relationships are central concerned problems in PBEE, CBEE and RBEE. Because of the randomness of seismic activity, the random process characteristics of earthquake motions and stochastic parameters of engineering structures, the seismic capacities of structures are random in nature. The subject which studies the probabilistic relationships between seismic capacity and seismic demand of structures is called as Probabilistic Seismic Capacity Analysis (PSCA).
PSCA is the foundation of seismic reliability analysis, seismic vulnerability analysis and seismic risk analysis of engineering structures. Meanwhile, it is an important part of probabilistic performance-based seismic design and assessment by using full probability method. Moreover, the results of PSCA can also provide scientific support for earthquake loss evaluation and earthquake disaster mitigation decision-making. Since the global seismic capacity of structures can describe the seismic performance of structures from the macroscope viepoint, it is very important to study the theory and methodologies of global PSCA for key civil engineering structures and infrastructure systems.
In this thesis, an improved point estimation method (PEM) based on Nataf transformation is put forward to compute the statisticalal momens of complex stochastic functions, The proposed method is compared with crude Monte Carlo simulation method, numerical integration method and mean-value first order second moment (MVFOSM) by an detailed numerical example. Then the four stochastic analysis methods are then combined with pushover analysis (POA) method, which is named“random POA”to compute the statisticalal moments of the stochastic seismic capacity of structures. The inter-story drift angle (ISDA) is taken as the capacity parameter and the computation results of random POA method are compared with that by using two finite element reliability method based on MVFOSM and FORM. After constructing the global probabilistic seismic capacity models (PSCM) of R.C. frame structures, the global seismic capacity fragility and hazard are studied more deeply and systematically considering the seismic hazard of the site. The main conclusions are summarized as follows:
(1) The modified point estimation method probopsed by this thesis can improve the accuracy of Zhao-Ono method. Among the four methods to compute the statisticalal moments of a complex random function, the efficiency of the mean-value first order second moment (MVFOSM) method is the best, however, its accuracy is worse, especially in the condition of high nonlinearity of the random function. Numerical integraton method has the same accuracy as the point estimation method, and its efficiency is higher than the latter.
(2) Random pushover analysis (RPOA) method combines statisticalal moments analysis of random functions with pushover analysis. Because there are a lot of mathematics problems in implicit functions in structural analysis, this idea that combines finite Element analysis with mathematics method is so revealing for structural analysis.
(2) RPOA method and finite element reliability analysis (FERA) method can all be applied to compute the statisticalal moments of random functions. Combining statisticalal moments analysis of random functions with conventional pushover analysis, RPOA can overcome the difficulties of implicit performance functions in global capacity statisticalal analysis of structures. FERA method couples the approximate analytical methods in structural reliability theory with finite element analysis (FEA) and finite element response sensitivity analysis (FERSA) efficiently, therefore, it is a kind of stochastic finite element methods in ature. It can be used to more finely simulate the various uncerainties in structural model.
(3) There are some differences in the results of global probabilistic seismic capacity model based on statistical moments analysis and finite element reliability analysis. The former is built upon the“common”assumption that the global capacity of structures satisfies the log-normal model, which is based on a lot of experimental data. However, when the“individual”result that based on reliability analysis also is regressed by log-normal model on the basis of“common”assumptions, then the diversities would surely exist. Although the“individual”sample can reflect the“common”aspect of the population, it still would manifest its more specific characteristics.
(4) The probabilistic seismic capacity model of structures can only consider the randomness in structure itself, while the vulnerability model of seismic capacity of structures can further include the variations in earthquake motion’s parameters. Obviously, the latter is the generalization of the former.
(5) Based on probabilistic seismic capacity fragility analysis of sructures, the hazard analysis of seismic capacity of structures further considers the hazard of the site, so the seismic capacity hazard analysis is the generalization of the probabilistic seismic capacity analysis.
工程结构的概率抗震能力分析是结构抗震可靠度分析、结构地震易损性分析以及结构地震风险分析的基础,同时,也是采用全概率方法进行结构概率抗震性能设计和概率抗震性能评定的重要组成部分;另外,概率抗震能力分析的结果也可以为地震损失估计和防震减灾决策提供科学的依据。由于结构整体抗震能力可以从宏观上刻画结构的抗震性能,因此,对重大土木工程结构和基础设施系统进行整体概率抗震能力分析,不仅具有重要的理论意义,而且具有重要的工程实用价值。
本文首先研究了复杂随机函数的统计矩分析方法,提出了基于Nataf变换的点估计法;通过对同一算例的计算,将点估计法同蒙特卡洛模拟法、数值积分法和平均值一次二阶矩法进行了比较;然后,将随机函数统计矩分析方法和Pushover分析结合起来,提出随机Pushover分析方法;以最大层间位移角(Inter-Storey Drift Angle, ISDA)作为结构整体能力参数,然后从随机Pushover分析和有限元可靠度分析两个角度,建立了钢筋混凝土框架结构的整体概率抗震能力模型;在此基础上,结合场地的地震危险性,对结构的整体概率抗震能力危险性和整体概率抗震能力易损性进行了系统深入的分析。得到以下结论:
(1)本文提出的改进的点估计法可以提高Zhao-Ono点估计法的精度;MVFOSM的效率最高,但精度较低,特别是当随机函数的非线性程度较高时;数值积分法的精度与点估计法相当,其效率高于点估计法。
(2)随机Pushover分析方法和有限元可靠度分析方法都可以用来计算结构整体能力的统计矩。随机Pushover分析方法将随机函数统计矩分析方法与传统的Pushover分析相结合,可以很好地解决结构整体能力统计分析中所遇到的隐式函数难以处理的困难;有限元可靠度分析方法将结构可靠度的近似解析法与有限元分析以及有限元反应灵敏度分析相结合,本质上是一种随机有限元方法,可以精细地模拟结构模型中的各种不确定性。
(3)结构整体抗震能力基于统计矩的概率模型和基于可靠度的回归模型,结果存在一定差异。前者基于结构能力参数服从对数正态分布假设,是一种具有“共性”的假设;后者基于有限元可靠度分析则是针对具体的结构形式,得到了“个性”的结果。“个性”的结果一定会体现“共性”的假设特征,但是,更多的体现的是结构个体的性质。
(4)结构的概率抗震能力模型只考虑结构自身参数的不确定性,而结构抗震能力的易损性模型则进一步考虑了地震动参数的随机性。显然,后者是对前者的进一步拓广。
(5)结构抗震能力的危险性是在结构抗震能力易损性分析基础上,考虑了场地的危险性。因此,结构的抗震能力危险性分析是对结构抗震能力分析的进一步拓广。
At the beginning of the twenty-first century, Pacific Earthquake Engineering Research Center (PEER) proposed a probabilistic decision-making framework for Performance-Based Earthquake Engineering (PBEE). At the same time, Mid-American Earthquake Engineering (MAE) proposed another probabilistic decision-making framework for Consequence-Based Earthquake Engineering (CBEE). Actually, the two frameworks both are based on seismic risk analysis, threrfore, the probabilistic decision-making framework of Risk-Based Earthquake Engineering is put forward in this thesis. Earthquake motion, seismic demand and seismic capacity as well as their relationships are central concerned problems in PBEE, CBEE and RBEE. Because of the randomness of seismic activity, the random process characteristics of earthquake motions and stochastic parameters of engineering structures, the seismic capacities of structures are random in nature. The subject which studies the probabilistic relationships between seismic capacity and seismic demand of structures is called as Probabilistic Seismic Capacity Analysis (PSCA).
PSCA is the foundation of seismic reliability analysis, seismic vulnerability analysis and seismic risk analysis of engineering structures. Meanwhile, it is an important part of probabilistic performance-based seismic design and assessment by using full probability method. Moreover, the results of PSCA can also provide scientific support for earthquake loss evaluation and earthquake disaster mitigation decision-making. Since the global seismic capacity of structures can describe the seismic performance of structures from the macroscope viepoint, it is very important to study the theory and methodologies of global PSCA for key civil engineering structures and infrastructure systems.
In this thesis, an improved point estimation method (PEM) based on Nataf transformation is put forward to compute the statisticalal momens of complex stochastic functions, The proposed method is compared with crude Monte Carlo simulation method, numerical integration method and mean-value first order second moment (MVFOSM) by an detailed numerical example. Then the four stochastic analysis methods are then combined with pushover analysis (POA) method, which is named“random POA”to compute the statisticalal moments of the stochastic seismic capacity of structures. The inter-story drift angle (ISDA) is taken as the capacity parameter and the computation results of random POA method are compared with that by using two finite element reliability method based on MVFOSM and FORM. After constructing the global probabilistic seismic capacity models (PSCM) of R.C. frame structures, the global seismic capacity fragility and hazard are studied more deeply and systematically considering the seismic hazard of the site. The main conclusions are summarized as follows:
(1) The modified point estimation method probopsed by this thesis can improve the accuracy of Zhao-Ono method. Among the four methods to compute the statisticalal moments of a complex random function, the efficiency of the mean-value first order second moment (MVFOSM) method is the best, however, its accuracy is worse, especially in the condition of high nonlinearity of the random function. Numerical integraton method has the same accuracy as the point estimation method, and its efficiency is higher than the latter.
(2) Random pushover analysis (RPOA) method combines statisticalal moments analysis of random functions with pushover analysis. Because there are a lot of mathematics problems in implicit functions in structural analysis, this idea that combines finite Element analysis with mathematics method is so revealing for structural analysis.
(2) RPOA method and finite element reliability analysis (FERA) method can all be applied to compute the statisticalal moments of random functions. Combining statisticalal moments analysis of random functions with conventional pushover analysis, RPOA can overcome the difficulties of implicit performance functions in global capacity statisticalal analysis of structures. FERA method couples the approximate analytical methods in structural reliability theory with finite element analysis (FEA) and finite element response sensitivity analysis (FERSA) efficiently, therefore, it is a kind of stochastic finite element methods in ature. It can be used to more finely simulate the various uncerainties in structural model.
(3) There are some differences in the results of global probabilistic seismic capacity model based on statistical moments analysis and finite element reliability analysis. The former is built upon the“common”assumption that the global capacity of structures satisfies the log-normal model, which is based on a lot of experimental data. However, when the“individual”result that based on reliability analysis also is regressed by log-normal model on the basis of“common”assumptions, then the diversities would surely exist. Although the“individual”sample can reflect the“common”aspect of the population, it still would manifest its more specific characteristics.
(4) The probabilistic seismic capacity model of structures can only consider the randomness in structure itself, while the vulnerability model of seismic capacity of structures can further include the variations in earthquake motion’s parameters. Obviously, the latter is the generalization of the former.
(5) Based on probabilistic seismic capacity fragility analysis of sructures, the hazard analysis of seismic capacity of structures further considers the hazard of the site, so the seismic capacity hazard analysis is the generalization of the probabilistic seismic capacity analysis.
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