结构非线性动力分析中地震动记录的选择和调整方法研究
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摘要
地震动输入的确定是开展结构动力反应分析的重要环节,如何有效地反映地震动对建筑结构地震反应及其破坏的影响,是开展结构非线性地震反应分析时面临的重要问题。随着基于性能的抗震设计理论的不断完善、结构动力分析软件的快速发展和计算机性能的不断提高,结构非线性动力分析逐渐成为结构抗震性能评估和重要工程抗震设计的主要方法。选择合适的地震动是有效地估计结构抗震性能的基础。尽管有关结构动力分析中地震动输入的研究迄今已有不少有价值的成果,各国抗震规范也对地震动记录的选取作了一些规定和要求,但由于地震动的随机性及其对工程结构破坏作用的复杂性,在选择及调整地震动输入时如何能有效地反映地震动的破坏作用还未能形成共识。深入研究地震动输入的选择方法和调整方法对基于性能的结构抗震设计及性能评估具有重要意义。
本论文以实际地震动记录为基础,围绕地震参数的有效性、地震动记录的调整方法、结构地震性能估计中地震动样本容量、基于设定地震的地震动选择方法及基于条件平均谱的地震动选择方法等相关问题开展研究。研究内容和研究成果如下：
一、开展了地震动参数的有效性研究。系统总结归纳了44种地震动参数,包括地震动幅值特征参数、地震动频谱特征参数、地震动持时特征参数以及其他由地震动幅值、频谱和持时组合而成的地震动参数。建立了具有不同周期和延性系数的弹塑性单自由度结构模型,通过分析地震动参数之间以及地震动参数与结构弹塑性位移反应之间的相关性,对这些地震动参数进行分类,探寻对结构地震反应有显著影响的地震动参数,研究不同地震动参数的有效性。结果表明：峰值加速度(PGA)类参数适用于表征短周期结构的地震影响；峰值速度(PGV)类参数适用于表征中等周期结构的地震影响；峰值位移(PGD)类参数适用于表征长周期结构的地震影响；对应于结构基本周期的反应谱值参数适用于表征短、中及长周期结构的地震影响,是比较理想的描述地震作用的参数。
二,开展了地震动的调整方法研究。建立了从低层到高层的六个钢筋混凝土框架模型,采用非线性动力分析方法计算结构的地震反应,通过结构地震反应与对应于不同周期的反应谱值的相关性分析,定量研究对结构反应起控制作用的地震动反应谱周期；对比分析了单周期点地震动调整、多周期点地震动调整和谱值匹配方法的适用性。研究表明：通过结构反应与不同周期对应的反应谱值的相关性分析,可以定量有效地给出对结构地震反应起主要控制作用的地震动反应谱周期。短周期结构的地震反应主要受控制于对应于结构基本周期(T1)的反应谱值；中长周期结构的地震反应主要受控制于0.2T1-2T1范围内的反应谱值。对于短周期结构或当地震动强度较低时,单周期点地震动调整法已具有较好的效果。对于中长周期结构和当地震动强度较高时,结构可能进入非线性阶段,应该充分考虑高阶振型和振动周期延长的影响,多周期点地震动调整方法和谱值匹配方法是比较有效地方法。
三、开展了基于可靠度的地震动样本容量研究。通过分析在大样本地震动作用下结构非线性地震反应的统计特征,研究了估计结构地震反应时,取样本最大值和平均值的差异,分析了结构地震反应的概率分布模型,提出基于可靠度的地震动样本容量的确定方法,并对比分析了不同地震动调整方法对样本容量需求的影响,为小样本地震动作用下对结构地震反应的有效估计提供依据。研究表明：1)在进行地震反应估计时,最大值法增大了计算结果的不确定性,并且结果偏于保守,建议采用平均值法来确定结构在小样本地震动作用下的地震反应估计值：2)通过假设检验,结构的地震反应最可接受对数极值分布的假设,也可接受对数正态分布假设,完全拒绝正态分布假设；3)提出了基于可靠度的地震动样本容量估计方法,可对结构反应估计值的可靠度和误差范围给出一个定量的判断；4)多周期点调整方法、谱值匹配法以及人工合成地震动能够有效地减少地震动样本容量的需求。
四、开展了基于设定地震的地震动选择方法研究。首先确定了设定地震对应的加速度反应谱,用来表征设定地震的强度水平,并将此作为地震动记录选取和调整的目标谱；然后针对地震特征参数(震级,距离,断层类型)和局部场地条件探讨了该目标谱的有效性,为地震动的选择提供了定量的参考。研究认为,以设定地震反应谱作为目标谱选择地震动时,应当充分考虑震级、距离、断层类型和场地条件的影响。当在地震动记录有限情况下,可以适当放宽对距离的限制。另外提出了能够有效考虑反应谱离散性和谱形的地震动选择和调整方法,保证了调整后的地震动记录与设定地震反应谱在统计意义上的一致性,克服了Greedy优化算法的局限性。
五、开展了基于条件平均谱的地震动选择方法研究。研究了标准差系数ε对反应谱谱形和结构非线性地震反应的影响。并详细介绍了条件平均谱的概念和计算方法。通过五种方法选取地震动记录,比较不同方法对应的结构地震反应分布特征,研究条件平均谱的有效性。分析表明：1)标准差系数￡与地震动记录的反应谱谱形有密切的关系,对结构的非线性地震反应有重要的影响；2)条件平均谱克服了一致概率反应谱过于保守的问题,利用条件平均谱选择地震动记录所计算的结构地震反应具有一定的无偏性,离散性也较小,可有效地估计结构的地震反应。
The ground motion input is one important part of structural dynamic analysis. The important issue for performing nonlinear dynamic analysis is to reflect the influence of ground motions for structural response and damage effectively. With the rapid development of the theory of performance-based seismic design, structural dynamic analysis software and computational facilities, nonlinear dynamic analysis is becoming more common in seismic analysis and design of numerous vital projects. Selecting the suitable ground motions is the basis of evaluate the anti-seismic performance. So far a lot of valuable results and regulations had been developed in many codes for seismic design of buildings; however, due to the stochastic of ground motions and the complexity of structure damage excited by ground motion, no consensus has been formed for selection and scaling ground motions. Thoroughly study on the methods of selection and scaling ground motions have significance value for performance-based seismic design and structural performance evaluation.
In this study, the effectiveness of ground motion parameters, scaling methods, sample size of ground motions, selection methods for scenario earthquake and conditional mean spectrum are developed base on the real earthquake ground motions.
The detail contents of research and conclusions are as follows:
1. Study on the effectiveness of ground motion parameters. Forty-four ground motion parameters have been summarized, including amplitude type, frequency type, duration type and combined parameters. The three hundred elastic-plastic single-degree-of-freedom (SDOF) systems with different natural vibration periods and ductility factors are created as the structural model. The correlation between different parameters and the correlation between elastic-plastic displacements and ground motion parameters have been analyzed to classify these parameters and seek for the suitable parameter which has an important impact on structural seismic response. The study shows that:the peak ground acceleration (PGA) type parameters are suited to represent the seismic influence for short period structures; the peak ground velocity (PGV) type parameters are suited to represent the seismic influence for medium period structures; the peak ground displacement (PGD) type parameters are suited to represent the seismic influence for long period structures; spectral acceleration at the first mode period of vibration of the structure(Sa(T1)) are suited to short, medium and long period structure, which are regard as the ideal parameter to describe seismic action.
2. Study on scaling methods of ground motions. Six reinforced concrete structure models with different height are created for nonlinear dynamic analysis. The correlation between structures' nonlinear dynamic response and spectral acceleration at different periods had been analyzed to quantitative research the period range which play main role in structural seismic response. Comparative analysis of single-period scaling method, multi-periods method and spectrum-matching method are done to research the applicability of each scaling methods. The study shows that:The analysis of correlation between structures' nonlinear dynamic response and spectral acceleration at different periods could quantitative seek the period range which play main role in structural seismic response. The short period structure's responses are controlled by spectral acceleration at the first mode period of vibration of the structure. The medium and long period structures' responses are controlled by spectral acceleration at one period range0.2T1～2T1. For the short period structure or low level earthquake intensity, the single-period method would have a good effect. For the medium and long period structure or high level earthquake intensity, the structure would be enter in the nonlinear stage, the effect of higher modes and vibration period extended should be fully considered, so the multi-periods method and spectrum-matching method are the better choices.
3. Study on the sample size of ground motion based on reliability. By analyzing the statistical characteristics of the structural seismic response subject to large samples of ground motions, the difference between maximum and average value of structural seismic response is investigated and the probability distribution models of structural response are analyzed. Method for determining the sample size of ground motion is proposed based on reliability. The effect of ground motion adjustment methods on the sample size demand is analyzed, providing the basis for estimates of structural response by using small sample of ground motions. The studies show that:1) maximum value method increases the uncertainty in the estimation of structural response, and the results are too conservative. Mean value method is more appropriate to estimate the structural response when using small sample of ground motions.2) as seen through hypothesis testing, extreme value distribution is the most acceptable probability distribution model of seismic response, lognormal assumption is acceptable and normal distribution assumption is completely rejected.3) reliability-based method to determine the sample size of ground motions is proposed, which can give a quantitative judgment on confidence level and margin of error to the estimated structural response.4) multi-periods adjustment method, spectral-matching method as well as synthetic ground motion can effectively reduce the demand of ground motion sample size.
4. Study on the scenario earthquake based ground motion selection method. Firstly, the demand spectrum is determined to characterize the seismic intensity level of the scenario earthquake. And this demand spectrum is set as the target spectrum to select and adjust ground motion records. Then the validity of the demand spectrum is investigate in terms of the seismic parameters (magnitude, distance, fault type) and local site conditions, providing a quantitative reference to ground motions selection. The studies shows that, magnitude, distance, fault type and site conditions should be fully considered when selecting ground motions based on the demand spectrum of the scenario earthquake. The restriction on distance can be appropriately relaxed when the number of record is not sufficient. The ground motion selection and adjustment method is proposed by effectively considering the variability of response spectra and spectral shape, ensuring that the adjusted ground motion records consistent with the demand spectrum in the statistical sense, and overcoming the limitations of Greedy Algorithm.
5. Study on conditional mean spectrum based ground motion selection method. The impact of standard deviation factor ε on spectral shape and structural nonlinear dynamic response has been investigated. Then the concept and algorithmic method of conditional mean spectrum are introduced in detail. Five different ground motion selection methods are compared to research the effective of conditional mean spectrum. The study shows that:1) The standard deviation factor ε has close ties to the spectral shape and has an important impact on structural nonlinear dynamic response.2) The conditional mean spectrum overcome the conservative of uniform hazard spectrum. Structural responses from ground motions matching the conditional mean spectrum have lower bias from record scaling and smaller dispersion.
本论文以实际地震动记录为基础,围绕地震参数的有效性、地震动记录的调整方法、结构地震性能估计中地震动样本容量、基于设定地震的地震动选择方法及基于条件平均谱的地震动选择方法等相关问题开展研究。研究内容和研究成果如下：
一、开展了地震动参数的有效性研究。系统总结归纳了44种地震动参数,包括地震动幅值特征参数、地震动频谱特征参数、地震动持时特征参数以及其他由地震动幅值、频谱和持时组合而成的地震动参数。建立了具有不同周期和延性系数的弹塑性单自由度结构模型,通过分析地震动参数之间以及地震动参数与结构弹塑性位移反应之间的相关性,对这些地震动参数进行分类,探寻对结构地震反应有显著影响的地震动参数,研究不同地震动参数的有效性。结果表明：峰值加速度(PGA)类参数适用于表征短周期结构的地震影响；峰值速度(PGV)类参数适用于表征中等周期结构的地震影响；峰值位移(PGD)类参数适用于表征长周期结构的地震影响；对应于结构基本周期的反应谱值参数适用于表征短、中及长周期结构的地震影响,是比较理想的描述地震作用的参数。
二,开展了地震动的调整方法研究。建立了从低层到高层的六个钢筋混凝土框架模型,采用非线性动力分析方法计算结构的地震反应,通过结构地震反应与对应于不同周期的反应谱值的相关性分析,定量研究对结构反应起控制作用的地震动反应谱周期；对比分析了单周期点地震动调整、多周期点地震动调整和谱值匹配方法的适用性。研究表明：通过结构反应与不同周期对应的反应谱值的相关性分析,可以定量有效地给出对结构地震反应起主要控制作用的地震动反应谱周期。短周期结构的地震反应主要受控制于对应于结构基本周期(T1)的反应谱值；中长周期结构的地震反应主要受控制于0.2T1-2T1范围内的反应谱值。对于短周期结构或当地震动强度较低时,单周期点地震动调整法已具有较好的效果。对于中长周期结构和当地震动强度较高时,结构可能进入非线性阶段,应该充分考虑高阶振型和振动周期延长的影响,多周期点地震动调整方法和谱值匹配方法是比较有效地方法。
三、开展了基于可靠度的地震动样本容量研究。通过分析在大样本地震动作用下结构非线性地震反应的统计特征,研究了估计结构地震反应时,取样本最大值和平均值的差异,分析了结构地震反应的概率分布模型,提出基于可靠度的地震动样本容量的确定方法,并对比分析了不同地震动调整方法对样本容量需求的影响,为小样本地震动作用下对结构地震反应的有效估计提供依据。研究表明：1)在进行地震反应估计时,最大值法增大了计算结果的不确定性,并且结果偏于保守,建议采用平均值法来确定结构在小样本地震动作用下的地震反应估计值：2)通过假设检验,结构的地震反应最可接受对数极值分布的假设,也可接受对数正态分布假设,完全拒绝正态分布假设；3)提出了基于可靠度的地震动样本容量估计方法,可对结构反应估计值的可靠度和误差范围给出一个定量的判断；4)多周期点调整方法、谱值匹配法以及人工合成地震动能够有效地减少地震动样本容量的需求。
四、开展了基于设定地震的地震动选择方法研究。首先确定了设定地震对应的加速度反应谱,用来表征设定地震的强度水平,并将此作为地震动记录选取和调整的目标谱；然后针对地震特征参数(震级,距离,断层类型)和局部场地条件探讨了该目标谱的有效性,为地震动的选择提供了定量的参考。研究认为,以设定地震反应谱作为目标谱选择地震动时,应当充分考虑震级、距离、断层类型和场地条件的影响。当在地震动记录有限情况下,可以适当放宽对距离的限制。另外提出了能够有效考虑反应谱离散性和谱形的地震动选择和调整方法,保证了调整后的地震动记录与设定地震反应谱在统计意义上的一致性,克服了Greedy优化算法的局限性。
五、开展了基于条件平均谱的地震动选择方法研究。研究了标准差系数ε对反应谱谱形和结构非线性地震反应的影响。并详细介绍了条件平均谱的概念和计算方法。通过五种方法选取地震动记录,比较不同方法对应的结构地震反应分布特征,研究条件平均谱的有效性。分析表明：1)标准差系数￡与地震动记录的反应谱谱形有密切的关系,对结构的非线性地震反应有重要的影响；2)条件平均谱克服了一致概率反应谱过于保守的问题,利用条件平均谱选择地震动记录所计算的结构地震反应具有一定的无偏性,离散性也较小,可有效地估计结构的地震反应。
The ground motion input is one important part of structural dynamic analysis. The important issue for performing nonlinear dynamic analysis is to reflect the influence of ground motions for structural response and damage effectively. With the rapid development of the theory of performance-based seismic design, structural dynamic analysis software and computational facilities, nonlinear dynamic analysis is becoming more common in seismic analysis and design of numerous vital projects. Selecting the suitable ground motions is the basis of evaluate the anti-seismic performance. So far a lot of valuable results and regulations had been developed in many codes for seismic design of buildings; however, due to the stochastic of ground motions and the complexity of structure damage excited by ground motion, no consensus has been formed for selection and scaling ground motions. Thoroughly study on the methods of selection and scaling ground motions have significance value for performance-based seismic design and structural performance evaluation.
In this study, the effectiveness of ground motion parameters, scaling methods, sample size of ground motions, selection methods for scenario earthquake and conditional mean spectrum are developed base on the real earthquake ground motions.
The detail contents of research and conclusions are as follows:
1. Study on the effectiveness of ground motion parameters. Forty-four ground motion parameters have been summarized, including amplitude type, frequency type, duration type and combined parameters. The three hundred elastic-plastic single-degree-of-freedom (SDOF) systems with different natural vibration periods and ductility factors are created as the structural model. The correlation between different parameters and the correlation between elastic-plastic displacements and ground motion parameters have been analyzed to classify these parameters and seek for the suitable parameter which has an important impact on structural seismic response. The study shows that:the peak ground acceleration (PGA) type parameters are suited to represent the seismic influence for short period structures; the peak ground velocity (PGV) type parameters are suited to represent the seismic influence for medium period structures; the peak ground displacement (PGD) type parameters are suited to represent the seismic influence for long period structures; spectral acceleration at the first mode period of vibration of the structure(Sa(T1)) are suited to short, medium and long period structure, which are regard as the ideal parameter to describe seismic action.
2. Study on scaling methods of ground motions. Six reinforced concrete structure models with different height are created for nonlinear dynamic analysis. The correlation between structures' nonlinear dynamic response and spectral acceleration at different periods had been analyzed to quantitative research the period range which play main role in structural seismic response. Comparative analysis of single-period scaling method, multi-periods method and spectrum-matching method are done to research the applicability of each scaling methods. The study shows that:The analysis of correlation between structures' nonlinear dynamic response and spectral acceleration at different periods could quantitative seek the period range which play main role in structural seismic response. The short period structure's responses are controlled by spectral acceleration at the first mode period of vibration of the structure. The medium and long period structures' responses are controlled by spectral acceleration at one period range0.2T1～2T1. For the short period structure or low level earthquake intensity, the single-period method would have a good effect. For the medium and long period structure or high level earthquake intensity, the structure would be enter in the nonlinear stage, the effect of higher modes and vibration period extended should be fully considered, so the multi-periods method and spectrum-matching method are the better choices.
3. Study on the sample size of ground motion based on reliability. By analyzing the statistical characteristics of the structural seismic response subject to large samples of ground motions, the difference between maximum and average value of structural seismic response is investigated and the probability distribution models of structural response are analyzed. Method for determining the sample size of ground motion is proposed based on reliability. The effect of ground motion adjustment methods on the sample size demand is analyzed, providing the basis for estimates of structural response by using small sample of ground motions. The studies show that:1) maximum value method increases the uncertainty in the estimation of structural response, and the results are too conservative. Mean value method is more appropriate to estimate the structural response when using small sample of ground motions.2) as seen through hypothesis testing, extreme value distribution is the most acceptable probability distribution model of seismic response, lognormal assumption is acceptable and normal distribution assumption is completely rejected.3) reliability-based method to determine the sample size of ground motions is proposed, which can give a quantitative judgment on confidence level and margin of error to the estimated structural response.4) multi-periods adjustment method, spectral-matching method as well as synthetic ground motion can effectively reduce the demand of ground motion sample size.
4. Study on the scenario earthquake based ground motion selection method. Firstly, the demand spectrum is determined to characterize the seismic intensity level of the scenario earthquake. And this demand spectrum is set as the target spectrum to select and adjust ground motion records. Then the validity of the demand spectrum is investigate in terms of the seismic parameters (magnitude, distance, fault type) and local site conditions, providing a quantitative reference to ground motions selection. The studies shows that, magnitude, distance, fault type and site conditions should be fully considered when selecting ground motions based on the demand spectrum of the scenario earthquake. The restriction on distance can be appropriately relaxed when the number of record is not sufficient. The ground motion selection and adjustment method is proposed by effectively considering the variability of response spectra and spectral shape, ensuring that the adjusted ground motion records consistent with the demand spectrum in the statistical sense, and overcoming the limitations of Greedy Algorithm.
5. Study on conditional mean spectrum based ground motion selection method. The impact of standard deviation factor ε on spectral shape and structural nonlinear dynamic response has been investigated. Then the concept and algorithmic method of conditional mean spectrum are introduced in detail. Five different ground motion selection methods are compared to research the effective of conditional mean spectrum. The study shows that:1) The standard deviation factor ε has close ties to the spectral shape and has an important impact on structural nonlinear dynamic response.2) The conditional mean spectrum overcome the conservative of uniform hazard spectrum. Structural responses from ground motions matching the conditional mean spectrum have lower bias from record scaling and smaller dispersion.
引文
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