自锚式斜拉—悬索协作体系桥动力学问题研究
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摘要
自锚式斜拉—悬索协作体系桥作为一种新型的桥梁结构形式,具备了传统的斜拉—悬索协作体系桥的诸多优点,而且由于庞大锚碇的取消,更好的适应了深海软土地基的建设,在不良地质环境条件下具有强劲的竞争力,目前已被工程界采纳。但从已有的文献看,对这种桥型动力性能的研究颇为少见。本文结合以自锚式斜拉—悬索协作体系桥为研究主体的交通部西部交通建设科技项目“斜拉—悬索协作体系桥梁的研究”这一科研课题,以拟建的大连湾跨海大桥为工程背景,对该新型结构体系若干动力学问题进行了深入的研究,主要工作如下：
(1)基于大位移非线性弹性理论的广义变分原理,考虑了加劲梁的压弯耦合、剪切应变能和扭转应变能的影响,建立了三跨自锚式斜拉—悬索协作体系桥的空间耦合自由振动大位移不完全广义势能泛函,通过约束变分推导出自锚式斜拉—悬索协作体系桥的竖向挠曲振动、横向挠曲振动、纵向振动、扭转振动以及主塔纵向振动和横向振动的基础微分方程,忽略非线性项的影响,进而得到线性振动微分方程。以一座主跨100m的混凝土自锚式斜拉—悬索协作体系桥为例,求出了竖向振动方程自振频率的解析解,并与数值解作了比较,吻合较好,这一理论和方法为自锚式斜拉—悬索桥的固有振动特性分析提供可靠的理论依据。
(2)桩-土-结构相互作用使体系的动力特性和地震反应与刚性基础上的结构不同,主要表现为自振周期延长、阻尼增加、内力及位移反应改变等。考虑桩-土相互作用效应,分别建立了考虑实际桩长和等效嵌固桩长的群桩模型,对结构进行反应谱和时程分析,并与墩底固结模式下的地震响应进行比较,得到了加劲梁、主塔、边墩等控制截面的内力和位移响应,并对其影响规律进行了讨论。通过对比计算结果,群桩实际桩长与群桩等效嵌固桩长两种考虑桩-土效应模式下结构地震响应值较为接近,因此,在工程上,可以采用等效嵌固桩长来代替桩的实际桩长来模拟桩基础。
(3)考虑了几何非线性及材料非线性,采用纤维模型对自锚式斜拉—悬索协作体系桥进行了弹塑性时程分析,对比弹性时程分析的结果表明,结构进入弹塑性阶段,由于塑性铰的产生,使结构控制节点的位移有了明显的增大,同时弹塑性阶段的结构控制截面的内力均有较大幅度的降低,对于半漂浮体系的自锚式斜拉—悬索协作体系桥,塑性铰的产生增大了结构控制节点的纵向位移,主要表现在主塔塔顶及主梁跨中,
(4)基于弹塑性分析结果,引入粘滞阻尼器,考虑边界非线性,对结构进行了弹性与弹塑性阶段的耗能减震分析,分析结果表明,进入弹塑性阶段的结构,由于塑性铰耗散了一部分地震输入的能力,引入粘滞阻尼器后,对结构控制截面的内力改善较小但对结构控制节点的纵向位移有较大幅度的降低。
(5)利用铅芯橡胶支座叠层橡胶良好的剪切性能以及铅芯的阻尼特性,通过分析在边墩、主塔与加劲梁间设置铅芯橡胶支座的多种方案发现,设置了铅芯橡胶支座后的结构,在地震荷载作用时,由于减小了地震作用时输入到上部结构的能量,使得结构主要控制节点的位移和控制截面的内力都得到了降低。
(6)基于模糊决策理论,建立了自锚式斜拉—悬索协作体系桥多层多目标模糊优选模型,它将众多因素分层考虑,协调各因素之间的复杂关系,并应用模糊定权的方法来确定因素的权重,克服了目标函数中用线性评判指标来处理高度非线性多目标问题的不足与确定权重问题的不足。应用该模型对大连湾跨海大桥工程中所提出的动力模型方案进行优化选型,通过比较分析认为选择粘滞阻尼耗能较为合理。
As a new type of bridge, self-anchored cable-stayed suspension bridge has not only some advantages of traditional cable-stayed suspension bridge, but also is more adaptive to being built in deeper sea and soft soil base owing to canceling giant anchor block, so is highly competitive under bad geologic conditions and has been adopted by engineering filed so far. However, there is little research on dynamic behavior for the type of bridge from the documents that have existed. Combined the scientific research question, i.e. the study on cable-stayed suspension bridge-which is scientific and technological item of Ministry of Communciation for traffic construction of west region with the engineering background of Dalian bay across sea bridge, some dynamic problems such as pile-soil-structure interaction, ductility analysis are investigated in this dissertation, the main research work covers the following aspects:
(1) Based on Large-displacement Non-linear Elastic Generalized Variational Principle, coupling effect of axial and flexural action, shearing strain energy, torsional strain energy of stiffening girder being considered, the large-displacement incomplete generalized potential energy functional of space coupling free vibration of a three-span self-anchored cable-stayed suspension bridge is presented. By constraint variation, fundamental differential equations of vertical flexural vibration, lateral flexural vibration, longitudinal vibration and torisional vibration are formulated, also presented the equations for the main tower with respect to longitudinal and lateral vibration. The linear free vibration differential equation is obtained when the nonlinear items are discarded. In this paper, a self-anchored cable-stayed suspension bridge with the main of span 100m is an example for the analytic solution of frequency of vertical free vibration. Compared with numerical solution, the results inosculate well. This approach provides theoretical basis for analysis of natural vibration character of self-anchored cable-stayed suspension bridges.
(2) The system's dynamic characteristics and seismic response based on rigid foundation is different from under pile-soil-structure interaction which mainly to extend nature vibration period, increases damping and changes internal forces and displacement. Consider the pile-soil interaction effects, pile groups model is established with actual length and equivalent embedded length separately, compared the seismic response result to the consolidation model from response spectrum and time-history analysis, the force and displacement response on controlling section of stiffening girder, main tower and piers were obtained and effect rules were discussed. Seismic response value of structure is close between the mode with actual length and equivalent embedded length by compared the results, therefore, pile foundation could be simulated by equivalent embedded length in place of actual length in engineering.
(3) Considering geometric nonlinearity and material nonlinearity, the elastic-plastic time-history analysis had been done for self-anchored cable-stayed suspension bridge by using fiber model. Compared to the results of elastic time-history analysis showed that in elastic-plastic stage, the displacement of controlling node had a obviously increase because of the generation of plastic hinge, meanwhile, the internal force of controlling section were reduced significantly, for semi-floating self-anchored cable-stayed suspension bridge, the longitudinal displacement of controlling node may be increasing by generation of plastic hinge, mainly appeared on top of tower and main span of stiffening girder.
(4) Based on the results of elastic-plastic analysis, introduced viscous-damper, Analysis of passive energy dissipation for structure had been done by considering boundary non-linear in elastic and elastic-plastic stage. Results showed that the force of controlling had slightly changing, but the longitudinal displacement of controlling node had obviously reduced by considering viscous-damper. The reason of this condition was that plastic hinge had dissipated some energy from earthquake input in elastic-plastic stage.
(5) The lead-rubber bearing has favorable shearing property of rubber and damping characteristics of lead. From analyzing some plans with setting lead-rubber bearing among side pier, tower and stiffening girder showed that the displacement of controlling node and force of controlling section have been reduced, because of energy that inputted to superstructure decreased under earthquake.
(6) The multi-level and multi-objective fuzzy optimization model of self-anchored cable-stayed suspension bridge selection is built based on fuzzy decision theory, which combines binary comparison method. The model coordinates the complex relationship among the factors, which are divided into several levels. Fuzzy method is adapted to calculate the weight vector, which can overcome the limitation of linear method. Base on the analysis of the model, energy dissipation by viscous-damper is the most suitable type for dynamic caculation.
(1)基于大位移非线性弹性理论的广义变分原理,考虑了加劲梁的压弯耦合、剪切应变能和扭转应变能的影响,建立了三跨自锚式斜拉—悬索协作体系桥的空间耦合自由振动大位移不完全广义势能泛函,通过约束变分推导出自锚式斜拉—悬索协作体系桥的竖向挠曲振动、横向挠曲振动、纵向振动、扭转振动以及主塔纵向振动和横向振动的基础微分方程,忽略非线性项的影响,进而得到线性振动微分方程。以一座主跨100m的混凝土自锚式斜拉—悬索协作体系桥为例,求出了竖向振动方程自振频率的解析解,并与数值解作了比较,吻合较好,这一理论和方法为自锚式斜拉—悬索桥的固有振动特性分析提供可靠的理论依据。
(2)桩-土-结构相互作用使体系的动力特性和地震反应与刚性基础上的结构不同,主要表现为自振周期延长、阻尼增加、内力及位移反应改变等。考虑桩-土相互作用效应,分别建立了考虑实际桩长和等效嵌固桩长的群桩模型,对结构进行反应谱和时程分析,并与墩底固结模式下的地震响应进行比较,得到了加劲梁、主塔、边墩等控制截面的内力和位移响应,并对其影响规律进行了讨论。通过对比计算结果,群桩实际桩长与群桩等效嵌固桩长两种考虑桩-土效应模式下结构地震响应值较为接近,因此,在工程上,可以采用等效嵌固桩长来代替桩的实际桩长来模拟桩基础。
(3)考虑了几何非线性及材料非线性,采用纤维模型对自锚式斜拉—悬索协作体系桥进行了弹塑性时程分析,对比弹性时程分析的结果表明,结构进入弹塑性阶段,由于塑性铰的产生,使结构控制节点的位移有了明显的增大,同时弹塑性阶段的结构控制截面的内力均有较大幅度的降低,对于半漂浮体系的自锚式斜拉—悬索协作体系桥,塑性铰的产生增大了结构控制节点的纵向位移,主要表现在主塔塔顶及主梁跨中,
(4)基于弹塑性分析结果,引入粘滞阻尼器,考虑边界非线性,对结构进行了弹性与弹塑性阶段的耗能减震分析,分析结果表明,进入弹塑性阶段的结构,由于塑性铰耗散了一部分地震输入的能力,引入粘滞阻尼器后,对结构控制截面的内力改善较小但对结构控制节点的纵向位移有较大幅度的降低。
(5)利用铅芯橡胶支座叠层橡胶良好的剪切性能以及铅芯的阻尼特性,通过分析在边墩、主塔与加劲梁间设置铅芯橡胶支座的多种方案发现,设置了铅芯橡胶支座后的结构,在地震荷载作用时,由于减小了地震作用时输入到上部结构的能量,使得结构主要控制节点的位移和控制截面的内力都得到了降低。
(6)基于模糊决策理论,建立了自锚式斜拉—悬索协作体系桥多层多目标模糊优选模型,它将众多因素分层考虑,协调各因素之间的复杂关系,并应用模糊定权的方法来确定因素的权重,克服了目标函数中用线性评判指标来处理高度非线性多目标问题的不足与确定权重问题的不足。应用该模型对大连湾跨海大桥工程中所提出的动力模型方案进行优化选型,通过比较分析认为选择粘滞阻尼耗能较为合理。
As a new type of bridge, self-anchored cable-stayed suspension bridge has not only some advantages of traditional cable-stayed suspension bridge, but also is more adaptive to being built in deeper sea and soft soil base owing to canceling giant anchor block, so is highly competitive under bad geologic conditions and has been adopted by engineering filed so far. However, there is little research on dynamic behavior for the type of bridge from the documents that have existed. Combined the scientific research question, i.e. the study on cable-stayed suspension bridge-which is scientific and technological item of Ministry of Communciation for traffic construction of west region with the engineering background of Dalian bay across sea bridge, some dynamic problems such as pile-soil-structure interaction, ductility analysis are investigated in this dissertation, the main research work covers the following aspects:
(1) Based on Large-displacement Non-linear Elastic Generalized Variational Principle, coupling effect of axial and flexural action, shearing strain energy, torsional strain energy of stiffening girder being considered, the large-displacement incomplete generalized potential energy functional of space coupling free vibration of a three-span self-anchored cable-stayed suspension bridge is presented. By constraint variation, fundamental differential equations of vertical flexural vibration, lateral flexural vibration, longitudinal vibration and torisional vibration are formulated, also presented the equations for the main tower with respect to longitudinal and lateral vibration. The linear free vibration differential equation is obtained when the nonlinear items are discarded. In this paper, a self-anchored cable-stayed suspension bridge with the main of span 100m is an example for the analytic solution of frequency of vertical free vibration. Compared with numerical solution, the results inosculate well. This approach provides theoretical basis for analysis of natural vibration character of self-anchored cable-stayed suspension bridges.
(2) The system's dynamic characteristics and seismic response based on rigid foundation is different from under pile-soil-structure interaction which mainly to extend nature vibration period, increases damping and changes internal forces and displacement. Consider the pile-soil interaction effects, pile groups model is established with actual length and equivalent embedded length separately, compared the seismic response result to the consolidation model from response spectrum and time-history analysis, the force and displacement response on controlling section of stiffening girder, main tower and piers were obtained and effect rules were discussed. Seismic response value of structure is close between the mode with actual length and equivalent embedded length by compared the results, therefore, pile foundation could be simulated by equivalent embedded length in place of actual length in engineering.
(3) Considering geometric nonlinearity and material nonlinearity, the elastic-plastic time-history analysis had been done for self-anchored cable-stayed suspension bridge by using fiber model. Compared to the results of elastic time-history analysis showed that in elastic-plastic stage, the displacement of controlling node had a obviously increase because of the generation of plastic hinge, meanwhile, the internal force of controlling section were reduced significantly, for semi-floating self-anchored cable-stayed suspension bridge, the longitudinal displacement of controlling node may be increasing by generation of plastic hinge, mainly appeared on top of tower and main span of stiffening girder.
(4) Based on the results of elastic-plastic analysis, introduced viscous-damper, Analysis of passive energy dissipation for structure had been done by considering boundary non-linear in elastic and elastic-plastic stage. Results showed that the force of controlling had slightly changing, but the longitudinal displacement of controlling node had obviously reduced by considering viscous-damper. The reason of this condition was that plastic hinge had dissipated some energy from earthquake input in elastic-plastic stage.
(5) The lead-rubber bearing has favorable shearing property of rubber and damping characteristics of lead. From analyzing some plans with setting lead-rubber bearing among side pier, tower and stiffening girder showed that the displacement of controlling node and force of controlling section have been reduced, because of energy that inputted to superstructure decreased under earthquake.
(6) The multi-level and multi-objective fuzzy optimization model of self-anchored cable-stayed suspension bridge selection is built based on fuzzy decision theory, which combines binary comparison method. The model coordinates the complex relationship among the factors, which are divided into several levels. Fuzzy method is adapted to calculate the weight vector, which can overcome the limitation of linear method. Base on the analysis of the model, energy dissipation by viscous-damper is the most suitable type for dynamic caculation.
引文
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