桥梁抗震性能评价的静力非线性分析方法研究
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摘要
随着人类对桥梁震害的认识逐渐深入和计算机技术的不断发展,对桥梁的分析和计算已经由线性分析向非线性分析方向发展。非线性时程分析方法被认为是桥梁结构弹塑性分析的最准确的方法,但是由于其技术复杂、计算工作量大、结果处理繁杂,而且结果的准确性很大程度上依赖于输入的地面运动情况,因此在实际工程中并没有得到广泛的应用。而Pushover分析方法概念简单,计算简便,并能有效地评估结构的抗震性能,近年来逐渐被应用到桥梁结构的抗震性能评估中。但是由于传统的Pushover方法皆基于固定的侧向荷载分布模式,不能考虑高阶振型的影响以及结构屈服后振动特性的改变,因此只适用于桥墩高度较低的梁式桥,不能对高阶振型影响显著的高架桥和斜拉桥进行抗震性能评价。为了克服这些局限性,本文提出了几种改进方法,并提出了适用于斜拉桥的Pushover分析方法,主要研究内容如下:
1.在动力学理论的基础上,借鉴MPA法中对各阶振型完全解耦的思想,对ASPA法进行简化,提出了改进的适应谱Pushover方法(简称IASPA法)。并对典型地震动下改进的适应谱Pushover法、传统的Pushover分析方法、MPA法以及非线性时程分析方法进行对比研究。结果表明,由于改进的适应谱Pushover方法直接利用反应谱来定义加载特性,且考虑了高阶振型的影响以及结构屈服后振动特性的改变,因此比传统的Pushover方法和MPA法具有更高的精度;并且,由于改进的适应谱Pushover方法忽略了结构屈服后各振型之间的耦合作用,所以较ASPA法计算更加简便,更适用于工程实际。
2.利用改进的适应谱Pushover方法,对三个不同高度的桥墩进行推覆分析,考查高阶振型的影响,并将计算所得到的结果与非线性时程分析的结果进行对比。结果表明,对于中低高度的桥墩,高阶振型的影响较小,可以将桥墩简化成单自由度体系,利用传统的Pushover方法进行静力弹塑性分析。但是随着桥墩高度的增加,高阶振型对桥墩抗震性能的影响越来越显著,对于高度超过40m的高墩,忽略桥墩自身的惯性力以及高阶振型的贡献将会导致较大的误差。
3.传统的基于力的Pushover分析方法,侧向荷载分布模式的选取将直接影响到Pushover分析方法对结构整体抗震性能的评估结果,震害、实验和理论分析都表明,变形能力不足和耗能能力不足是结构在大震作用下倒塌的主要原因,结构构件在大震作用下的破坏程度与结构的位移响应和构件的变形能力有关,所以用位移控制结构在大震作用下的行为更为合理。本文利用直接基于位移的方法对一个6层框架进行推覆分析,并对结构在推覆过程中的振型参与系数及位移模式的变化进行分析研究,提出了基于位移的适应谱Pushover方法(简称DASPA法)。
4.利用DASPA法分别对两个不同高度的梁式桥进行Pushover分析,并将分析结果与非线性时程分析以及传统Pushover方法分析的结果进行比较。结果表明,由于DASPA法直接基于非弹性位移反应谱来定义加载位移模式,且考虑了高阶振型的影响及结构屈服后振动特性的改变,因此在评价结构的抗震性能时有着很高的精度,不仅适用于受基本振型控制的中低高度的桥梁,同时也适用于高阶振型影响显著的高架桥梁;由于DASPA法直接用位移来控制结构的加载模式,其每一步计算得到的结果直接是结构的变形,省略了基于力的Pushover分析方法中将结构的内力转化为变形来评估结构的抗震性能的步骤,并且当结构破坏达到一定程度时采用固定的位移加载模式,因此使得计算过程大为简化。
5.斜拉桥为复杂的多自由度结构体系,其在地震中的反应受高阶振型影响显著,等效地震力的分布模式非常复杂,传统的基于力的Pushover方法无法对斜拉桥进行静力弹塑性分析。而DASPA法直接基于位移来定义加载模式,且考虑了高阶振型的影响,因此可以用来对斜拉桥进行弹塑性分析。但是由于斜拉桥桥型的特殊性,使得DASPA法的计算结果依赖于侧向荷载的加载方向,这与实际不符。鉴于此,本文又提出了针对斜拉桥的修正的DASPA法,对斜拉桥屈服后的位移模式进行修正。将DASPA法和修正的DASPA法得到的计算结果分别与非线性时程分析得到的计算结果进行比较,结果表明,修正的DASPA法比DASPA法具有更高的精度,计算结果更接近结构的真实反应值。
With the deepening of understanding of seismic damage to bridges and the development of the computer technology, nonlinear analysis and calculation for bridges gradually replace linear analysis theory. Nonlinear time history analysis (RHA) is considered to be the most accurate method for bridges elasto-plastic analysis, but it isn't widely used because of its complex technology, complicated calculation and miscellaneous result processing, and the accuracy of RHA depends a great extent on the input ground motion. Recently, with the development of performance-based seismic design thought, pushover analysis procedure has been accepted and gradually used for estimating the seismic performance for bridges because of its simple concept and easy calculation. All the classic pushover analysis procedures are based on the invariant force distributions, but none of the invariant force distributions can account for the contributions of higher modes to response, or for a redistribution of inertia forces after structural yielding and the associated changes in the vibration properties of the structure. So the classic pushover analysis procedures are just suitable for the beam bridge with low piers, not for the beam bridge with high piers and not for cable-stayed bridge. To overcome these limitations, several improved pushover analysis procedures are proposed, and an improved pushover analysis procedure which is applicable to cable-stayed bridge is put forward. The main research work covers the following aspects:
1. The adaptive spectra-based pushover analysis (ASPA) procedure has been proposed by Gupta which accounts for the effect of higher modes and overcomes the shortcomings of the classic pushover analysis procedures. While it provides better estimates of seismic demands, it is conceptually complicated and computationally demanding for routine application in structural engineering practice. In this paper, an improved adaptive spectra-based pushover analysis (IASPA) procedure is proposed by using the thought of neglecting the coupling of the N modes in modal pushover analysis procedure (MPA). And the seismic performance determined by IASPA is compared with pushover analysis using two force distributions in FEMA-274 and nonlinear RHA procedures. The results indicate that IASPA procedure provides more superior accuracy in estimating seismic performance on bridge structures because that it accounts for the effect of higher modes and for a redistribution of inertia forces after structural yielding. And because of its neglecting the coupling of the N modes, it is more convenient for structural engineering practice than ASPA method.
2. Three piers in different height are investigated by the IASPA procedure and nonlinear RHA method. And the effects of higher modes to seismic performance of the piers in different height are studied. The results indicate that higher modes have little effects on medium or low piers but great effects on higher piers. The medium or low piers can be equivalent to single freedom systems and be estimated by the classic pushover analysis procedures. But neglecting the inertia force of pier body and the effects of higher modes will lead to big errors for piers higher than 40m.
3. The results of the classic pushover analysis procedure based on force for estimating the seismic performance of the bridge depend on the selection of the lateral load pattern. Earthquake damage, experiment and theoretical analysis all indicate that the deficiency of transfiguration capacity and capacity of energy dissipation is the main reason of structure collapse. The degree of damage of the structures in large earthquake relates to their displacement responses and deformability. So it is more reasonable to control structural behavior by displacement. By studying the change of mode participation coefficient and displacement pattern of a six-story-frame in pushover process, in this paper, an adaptive displacement-spectra-based pushover analysis procedure (DASPA) is put forward which accounts for the effect of higher modes and for a redistribution of inertia forces because of structural yielding and the associated changes in the vibration properties of the structure.
4. Pushover analysis is carried out for two bridges of different height by DASPA procedure and other two classic pushover methods. And the seismic performance determined by the three pushover analysis methods is compared with nonlinear RHA method. The results indicate that DASPA procedure provides more superior accuracy and reasonability than other two classic pushover methods. Because DASPA is based on displacement directly, and the behavior of the structure in the earthquake is controlled by displacement in the whole processing, it omits the process of transformation the internal force to deformation to estimate the seismic performance of the structure. So it has the simpler calculating process and computational attractiveness for routine application in structure engineering practice.
5. Cable-stayed bridge belongs to a typical multi-degree-of-freedom system which has complicated vibration characteristic. The seismic performance of the cable-stayed bridge can't be estimated by classic pushover analysis methods because of the great effects of higher modes on it. But DASPA procedure can be used to estimate the seismic performance for cable-stayed bridge because it considers the contributions of higher modes to response and the changes in the vibration properties of the structure after structural yielding. But seismic performance determined by DASPA for cable-stayed bridge depends on the loading direction because of the special bridge type for cable-stayed bridge. In this paper, a modified DASPA procedure (MDASPA) is put forward that the post-yield displacement pattern is modified to be close to practice. The seismic performance determined by DASPA and MDASPA is compared with nonlinear RHA procedure. The results indicate that the MDASPA procedure provides more superior accuracy in estimating seismic performance for structures compared with DASPA procedure.
1.在动力学理论的基础上,借鉴MPA法中对各阶振型完全解耦的思想,对ASPA法进行简化,提出了改进的适应谱Pushover方法(简称IASPA法)。并对典型地震动下改进的适应谱Pushover法、传统的Pushover分析方法、MPA法以及非线性时程分析方法进行对比研究。结果表明,由于改进的适应谱Pushover方法直接利用反应谱来定义加载特性,且考虑了高阶振型的影响以及结构屈服后振动特性的改变,因此比传统的Pushover方法和MPA法具有更高的精度;并且,由于改进的适应谱Pushover方法忽略了结构屈服后各振型之间的耦合作用,所以较ASPA法计算更加简便,更适用于工程实际。
2.利用改进的适应谱Pushover方法,对三个不同高度的桥墩进行推覆分析,考查高阶振型的影响,并将计算所得到的结果与非线性时程分析的结果进行对比。结果表明,对于中低高度的桥墩,高阶振型的影响较小,可以将桥墩简化成单自由度体系,利用传统的Pushover方法进行静力弹塑性分析。但是随着桥墩高度的增加,高阶振型对桥墩抗震性能的影响越来越显著,对于高度超过40m的高墩,忽略桥墩自身的惯性力以及高阶振型的贡献将会导致较大的误差。
3.传统的基于力的Pushover分析方法,侧向荷载分布模式的选取将直接影响到Pushover分析方法对结构整体抗震性能的评估结果,震害、实验和理论分析都表明,变形能力不足和耗能能力不足是结构在大震作用下倒塌的主要原因,结构构件在大震作用下的破坏程度与结构的位移响应和构件的变形能力有关,所以用位移控制结构在大震作用下的行为更为合理。本文利用直接基于位移的方法对一个6层框架进行推覆分析,并对结构在推覆过程中的振型参与系数及位移模式的变化进行分析研究,提出了基于位移的适应谱Pushover方法(简称DASPA法)。
4.利用DASPA法分别对两个不同高度的梁式桥进行Pushover分析,并将分析结果与非线性时程分析以及传统Pushover方法分析的结果进行比较。结果表明,由于DASPA法直接基于非弹性位移反应谱来定义加载位移模式,且考虑了高阶振型的影响及结构屈服后振动特性的改变,因此在评价结构的抗震性能时有着很高的精度,不仅适用于受基本振型控制的中低高度的桥梁,同时也适用于高阶振型影响显著的高架桥梁;由于DASPA法直接用位移来控制结构的加载模式,其每一步计算得到的结果直接是结构的变形,省略了基于力的Pushover分析方法中将结构的内力转化为变形来评估结构的抗震性能的步骤,并且当结构破坏达到一定程度时采用固定的位移加载模式,因此使得计算过程大为简化。
5.斜拉桥为复杂的多自由度结构体系,其在地震中的反应受高阶振型影响显著,等效地震力的分布模式非常复杂,传统的基于力的Pushover方法无法对斜拉桥进行静力弹塑性分析。而DASPA法直接基于位移来定义加载模式,且考虑了高阶振型的影响,因此可以用来对斜拉桥进行弹塑性分析。但是由于斜拉桥桥型的特殊性,使得DASPA法的计算结果依赖于侧向荷载的加载方向,这与实际不符。鉴于此,本文又提出了针对斜拉桥的修正的DASPA法,对斜拉桥屈服后的位移模式进行修正。将DASPA法和修正的DASPA法得到的计算结果分别与非线性时程分析得到的计算结果进行比较,结果表明,修正的DASPA法比DASPA法具有更高的精度,计算结果更接近结构的真实反应值。
With the deepening of understanding of seismic damage to bridges and the development of the computer technology, nonlinear analysis and calculation for bridges gradually replace linear analysis theory. Nonlinear time history analysis (RHA) is considered to be the most accurate method for bridges elasto-plastic analysis, but it isn't widely used because of its complex technology, complicated calculation and miscellaneous result processing, and the accuracy of RHA depends a great extent on the input ground motion. Recently, with the development of performance-based seismic design thought, pushover analysis procedure has been accepted and gradually used for estimating the seismic performance for bridges because of its simple concept and easy calculation. All the classic pushover analysis procedures are based on the invariant force distributions, but none of the invariant force distributions can account for the contributions of higher modes to response, or for a redistribution of inertia forces after structural yielding and the associated changes in the vibration properties of the structure. So the classic pushover analysis procedures are just suitable for the beam bridge with low piers, not for the beam bridge with high piers and not for cable-stayed bridge. To overcome these limitations, several improved pushover analysis procedures are proposed, and an improved pushover analysis procedure which is applicable to cable-stayed bridge is put forward. The main research work covers the following aspects:
1. The adaptive spectra-based pushover analysis (ASPA) procedure has been proposed by Gupta which accounts for the effect of higher modes and overcomes the shortcomings of the classic pushover analysis procedures. While it provides better estimates of seismic demands, it is conceptually complicated and computationally demanding for routine application in structural engineering practice. In this paper, an improved adaptive spectra-based pushover analysis (IASPA) procedure is proposed by using the thought of neglecting the coupling of the N modes in modal pushover analysis procedure (MPA). And the seismic performance determined by IASPA is compared with pushover analysis using two force distributions in FEMA-274 and nonlinear RHA procedures. The results indicate that IASPA procedure provides more superior accuracy in estimating seismic performance on bridge structures because that it accounts for the effect of higher modes and for a redistribution of inertia forces after structural yielding. And because of its neglecting the coupling of the N modes, it is more convenient for structural engineering practice than ASPA method.
2. Three piers in different height are investigated by the IASPA procedure and nonlinear RHA method. And the effects of higher modes to seismic performance of the piers in different height are studied. The results indicate that higher modes have little effects on medium or low piers but great effects on higher piers. The medium or low piers can be equivalent to single freedom systems and be estimated by the classic pushover analysis procedures. But neglecting the inertia force of pier body and the effects of higher modes will lead to big errors for piers higher than 40m.
3. The results of the classic pushover analysis procedure based on force for estimating the seismic performance of the bridge depend on the selection of the lateral load pattern. Earthquake damage, experiment and theoretical analysis all indicate that the deficiency of transfiguration capacity and capacity of energy dissipation is the main reason of structure collapse. The degree of damage of the structures in large earthquake relates to their displacement responses and deformability. So it is more reasonable to control structural behavior by displacement. By studying the change of mode participation coefficient and displacement pattern of a six-story-frame in pushover process, in this paper, an adaptive displacement-spectra-based pushover analysis procedure (DASPA) is put forward which accounts for the effect of higher modes and for a redistribution of inertia forces because of structural yielding and the associated changes in the vibration properties of the structure.
4. Pushover analysis is carried out for two bridges of different height by DASPA procedure and other two classic pushover methods. And the seismic performance determined by the three pushover analysis methods is compared with nonlinear RHA method. The results indicate that DASPA procedure provides more superior accuracy and reasonability than other two classic pushover methods. Because DASPA is based on displacement directly, and the behavior of the structure in the earthquake is controlled by displacement in the whole processing, it omits the process of transformation the internal force to deformation to estimate the seismic performance of the structure. So it has the simpler calculating process and computational attractiveness for routine application in structure engineering practice.
5. Cable-stayed bridge belongs to a typical multi-degree-of-freedom system which has complicated vibration characteristic. The seismic performance of the cable-stayed bridge can't be estimated by classic pushover analysis methods because of the great effects of higher modes on it. But DASPA procedure can be used to estimate the seismic performance for cable-stayed bridge because it considers the contributions of higher modes to response and the changes in the vibration properties of the structure after structural yielding. But seismic performance determined by DASPA for cable-stayed bridge depends on the loading direction because of the special bridge type for cable-stayed bridge. In this paper, a modified DASPA procedure (MDASPA) is put forward that the post-yield displacement pattern is modified to be close to practice. The seismic performance determined by DASPA and MDASPA is compared with nonlinear RHA procedure. The results indicate that the MDASPA procedure provides more superior accuracy in estimating seismic performance for structures compared with DASPA procedure.
引文
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