基于地震能量输入历程的RC框架损伤研究
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摘要
性能化设计是目前工程设计领域的一个热点话题，在基于性能的抗震设计中，性能目标的确定是整个设计的基础与关键，即如何定义一组有限的破坏状态，而对结构的损伤提出一个可以量化的指标是实现这一基础与关键的前提。论文以国家自然科学基金项目“基于地震波非平稳能量特征的RC框架结构损伤量化研究”为依托，以地震波能量输入历程特征为依据，着重在以下几个方面进行研究工作：
1．地震波的复杂之处在于它的非平稳特性，而该特性可以被理解为地震动能量在频域和时域上的不均匀分布，不均匀分布中的能量集中对结构响应非常不利。小波分析由于其良好的局部化特性和弹性的时一频窗特点，被广泛应用于地震波模拟、工程振动的响应分析等领域中。本文从地震能量分析入手，阐述了应用小波工具计算地震波能量的方法，并提出了平均能量密度的概念。通过对台湾1999年集集地震中130条地震波的统计，得到了地震频带平均能量密度，有效持时等参数与场地土、震中距及分布时间的统计关系。
2．以瞬时输入能量在时间轴上的分布特征（瞬时输入能量时变特征）来描述地震能量输入历程的特点，提出了一种能够模拟瞬时输入能量时变特征的数学模型。建立了瞬时输入能量时变特征与结构总输入能、最大瞬时输入能及瞬时输入能反应持时三个参数的关系。通过数学推导得到了线性单自由度结构体系基于能量参数的结构位移历程求解方法。56条波算例对比分析表明该方法在模拟弹性结构的幅值反应和持时反应上具有较好的准确性，同时利用模拟的瞬时输入能时变特征也能延伸应用于多层弹性结构体系的分析。
3．以弹塑性结构体系为对象，讨论了单自由度结构延性系数及多自由度结构塑性发展程度对总输入能、最大瞬时输入能以及能量增长持时三个地震能量输入历程特征参数的影响。提出了根据结构弹性总输入能量谱、最大瞬时输入能量谱及弹性能量增长持时谱求得具有不同延性系数弹塑性结构三参数谱的方法。
4．根据以往结构损伤模型的优缺点，提出了一种既能够描述结构地震损伤位移首超破坏又能够描述结构累积损伤破坏的损伤模型。并采用统计学方法讨论了总输入能、最大瞬时输入能、能量增长持时、延性系数、名义强振次数以及最大瞬时输入能比6个参数与结构位移损伤、退化损伤、总损伤以及位移损伤比之间的相互关系。
5．基于本文提出的损伤模型并利用拟力法为工具，结构能量指标为桥梁提出了一种确定结构的局部损伤及整体损伤的估计方法。通过一个单层单跨的算例分析表明地震过程中形成的塑性铰损伤是框架结构地震损伤的根源，因此，控制塑性铰区域在地震往复作用下的强度衰减，减小塑性铰区域在震后的塑性转动量是控制钢筋混凝土框架结构地震损伤的关键。
6．以结构输入能历程特征的数学描述模式为基础，通过建立结构变形能耗散历程的简化描述模型，并基于该简化模型对结构进行往复推覆分析。分析表明基于变形能耗散历程的往复推覆分析方法在描述结构地震损伤主要参数时具有较好的准确性。通过对无损结构与已损结构分别进行单向推覆分析来替代结构动力时程分析，从而获得结构损伤求解的简化方法。
Performance-based seismic design of structures has been discussed as hotspottopic in engineering design area. The determination of seismic performance objectivesis the key to whole structure design on performance-based seismic design. Thequantitative index of damage model is the basic condition for it. In this dissertation,combined with the research project “quantitative analysis of seismic damage on RCframe structures based on the properties of non-stationarity of seismic wave energy”financially supported by National natural science foundation of china (NSFC), severalkey problems are studied according with the energy input course of seismic wave.
1． Non-stationarity is the complex characteristic of seismic waves. It can beinterpreted as the inhomogeneous distribution in time and frequency domains. Theinhomogeneous distribution of energy is harmful to structures. Wavelet analysis hasbeen widely applied in simulating earthquake motions and analysis of response toengineering vibration. By using the direct wavelet analysis method, the concept ofmean energy density is set up. Furthermore, the mean energy density and effectiveduration characteristics of ChiChi earthquake in1999for various site conditions andepicentral distances, time history are obtained.
2．A mathematical model is carried out to reflect the time varying characteristic ofmomentary input energy. By established the relationship between the time varyingcharacteristic of momentary input energy and the input energy, the maximummomentary input energy, the duration of input energy process, a simplified procedureto develop the simulated deformation history of linear single degree offreedom(SDOF) system is proposed in this paper. The methodology proposed in thispaper is validated using the maximum deformation and cyclic demand spectrum oflinear system. It is found that the simulated deformation response can reflect the maxamplitude of actual deformation and the effect of duration of multi degree of freedomsystem(MDOF).
3．In this dissertation, total input energy, maximum momentary input energy andduration of input energy process are taken as three description parameters of inputenergy time histories. The influence of ductility factor of SDOF system and plasticitystatus of MDOF system on the three parameters is investigated according with56earthquake records of4site types and the V/A ratio of ground motions. Based on the three description parameters spectra and ductility factor of structures, a analyticalprocedure is developed for the elastic-plastic three description parameters spectra.
4．Based on existing damage models, a new structure seismic damage is definedwhich reflect first excursion failure and cumulative damage failure. Statistics weremade to analyze the association between the content of six parameters which namedinput energy, the maximal momentary input energy, energy growth duration, ductilityfactor, nominal strong vibration times, the ration of maximal momentary input energyand displacement damage, degradation damage on structures, total damage, the rationof displacement damage.
5．Using force analogy method, a process is obtained which can estimate the localdamage and the whole damage based on the damage model in this paper. A numericalexample of single-story and single-bay frames shows that injury of plastic hinge inthe course of seismic is the source of frame structure damage. Control of strengthdegradation in the time of reciprocating seismic and reducing the plastic rotationangels in the time of post-earthquake on plastic-hinge region are the keys ofseismic damage on frame structures.
6．Based on the mathematical model which reflect the time varying characteristicof momentary input energy, a simple analytical procedure which reflect the timevarying characteristic of dissipation on deformation energy is developed forpush-over analysis of frame structures. The correlation analysis showed that thepush-over analysis based on the time varying characteristic of dissipation ondeformation energy have good accuracy in described the injury three descriptionparameters. By push-over analysis the damage of frame structures can be obtainedinstead of complex dynamic time-history analysis.
1．地震波的复杂之处在于它的非平稳特性，而该特性可以被理解为地震动能量在频域和时域上的不均匀分布，不均匀分布中的能量集中对结构响应非常不利。小波分析由于其良好的局部化特性和弹性的时一频窗特点，被广泛应用于地震波模拟、工程振动的响应分析等领域中。本文从地震能量分析入手，阐述了应用小波工具计算地震波能量的方法，并提出了平均能量密度的概念。通过对台湾1999年集集地震中130条地震波的统计，得到了地震频带平均能量密度，有效持时等参数与场地土、震中距及分布时间的统计关系。
2．以瞬时输入能量在时间轴上的分布特征（瞬时输入能量时变特征）来描述地震能量输入历程的特点，提出了一种能够模拟瞬时输入能量时变特征的数学模型。建立了瞬时输入能量时变特征与结构总输入能、最大瞬时输入能及瞬时输入能反应持时三个参数的关系。通过数学推导得到了线性单自由度结构体系基于能量参数的结构位移历程求解方法。56条波算例对比分析表明该方法在模拟弹性结构的幅值反应和持时反应上具有较好的准确性，同时利用模拟的瞬时输入能时变特征也能延伸应用于多层弹性结构体系的分析。
3．以弹塑性结构体系为对象，讨论了单自由度结构延性系数及多自由度结构塑性发展程度对总输入能、最大瞬时输入能以及能量增长持时三个地震能量输入历程特征参数的影响。提出了根据结构弹性总输入能量谱、最大瞬时输入能量谱及弹性能量增长持时谱求得具有不同延性系数弹塑性结构三参数谱的方法。
4．根据以往结构损伤模型的优缺点，提出了一种既能够描述结构地震损伤位移首超破坏又能够描述结构累积损伤破坏的损伤模型。并采用统计学方法讨论了总输入能、最大瞬时输入能、能量增长持时、延性系数、名义强振次数以及最大瞬时输入能比6个参数与结构位移损伤、退化损伤、总损伤以及位移损伤比之间的相互关系。
5．基于本文提出的损伤模型并利用拟力法为工具，结构能量指标为桥梁提出了一种确定结构的局部损伤及整体损伤的估计方法。通过一个单层单跨的算例分析表明地震过程中形成的塑性铰损伤是框架结构地震损伤的根源，因此，控制塑性铰区域在地震往复作用下的强度衰减，减小塑性铰区域在震后的塑性转动量是控制钢筋混凝土框架结构地震损伤的关键。
6．以结构输入能历程特征的数学描述模式为基础，通过建立结构变形能耗散历程的简化描述模型，并基于该简化模型对结构进行往复推覆分析。分析表明基于变形能耗散历程的往复推覆分析方法在描述结构地震损伤主要参数时具有较好的准确性。通过对无损结构与已损结构分别进行单向推覆分析来替代结构动力时程分析，从而获得结构损伤求解的简化方法。
Performance-based seismic design of structures has been discussed as hotspottopic in engineering design area. The determination of seismic performance objectivesis the key to whole structure design on performance-based seismic design. Thequantitative index of damage model is the basic condition for it. In this dissertation,combined with the research project “quantitative analysis of seismic damage on RCframe structures based on the properties of non-stationarity of seismic wave energy”financially supported by National natural science foundation of china (NSFC), severalkey problems are studied according with the energy input course of seismic wave.
1． Non-stationarity is the complex characteristic of seismic waves. It can beinterpreted as the inhomogeneous distribution in time and frequency domains. Theinhomogeneous distribution of energy is harmful to structures. Wavelet analysis hasbeen widely applied in simulating earthquake motions and analysis of response toengineering vibration. By using the direct wavelet analysis method, the concept ofmean energy density is set up. Furthermore, the mean energy density and effectiveduration characteristics of ChiChi earthquake in1999for various site conditions andepicentral distances, time history are obtained.
2．A mathematical model is carried out to reflect the time varying characteristic ofmomentary input energy. By established the relationship between the time varyingcharacteristic of momentary input energy and the input energy, the maximummomentary input energy, the duration of input energy process, a simplified procedureto develop the simulated deformation history of linear single degree offreedom(SDOF) system is proposed in this paper. The methodology proposed in thispaper is validated using the maximum deformation and cyclic demand spectrum oflinear system. It is found that the simulated deformation response can reflect the maxamplitude of actual deformation and the effect of duration of multi degree of freedomsystem(MDOF).
3．In this dissertation, total input energy, maximum momentary input energy andduration of input energy process are taken as three description parameters of inputenergy time histories. The influence of ductility factor of SDOF system and plasticitystatus of MDOF system on the three parameters is investigated according with56earthquake records of4site types and the V/A ratio of ground motions. Based on the three description parameters spectra and ductility factor of structures, a analyticalprocedure is developed for the elastic-plastic three description parameters spectra.
4．Based on existing damage models, a new structure seismic damage is definedwhich reflect first excursion failure and cumulative damage failure. Statistics weremade to analyze the association between the content of six parameters which namedinput energy, the maximal momentary input energy, energy growth duration, ductilityfactor, nominal strong vibration times, the ration of maximal momentary input energyand displacement damage, degradation damage on structures, total damage, the rationof displacement damage.
5．Using force analogy method, a process is obtained which can estimate the localdamage and the whole damage based on the damage model in this paper. A numericalexample of single-story and single-bay frames shows that injury of plastic hinge inthe course of seismic is the source of frame structure damage. Control of strengthdegradation in the time of reciprocating seismic and reducing the plastic rotationangels in the time of post-earthquake on plastic-hinge region are the keys ofseismic damage on frame structures.
6．Based on the mathematical model which reflect the time varying characteristicof momentary input energy, a simple analytical procedure which reflect the timevarying characteristic of dissipation on deformation energy is developed forpush-over analysis of frame structures. The correlation analysis showed that thepush-over analysis based on the time varying characteristic of dissipation ondeformation energy have good accuracy in described the injury three descriptionparameters. By push-over analysis the damage of frame structures can be obtainedinstead of complex dynamic time-history analysis.
引文
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