桥梁结构非线性地震反应研究（支座摩擦·限位装置·基础非线性）
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摘要
桥梁非线性地震反应研究对于提高桥梁结构抗震分析、设计水平具有重要的意义。强震作用下,桥梁结构可能发生不同部位的破坏,相应地非线性地震反应分析方法和模型也不同。受各种非线性的影响,精确分析桥梁结构的地震响应是非常复杂的,一般利用合理的简化分析模型进行分析。本文在继承和发展国内外研究成果的基础上,针对强震下桥梁结构中存在的非线性问题、非线性地震反应分析方法、非线性有限单元及非线性有限元模型进行了研究,并对各种非线性特性对桥梁整体抗震性能的影响进行了参数分析,主要研究内容如下：
(1)总结了桥梁结构的非线性计算模型、材料的常用本构关系、非线性动力方程及其求解方法,介绍了弹塑性梁单元的三种不同模型及考虑塑性铰长度的弹塑性梁单元的单元柔度矩阵,介绍了钢筋混凝土桥墩常用的弯矩-曲率滞回模型。编写了截面弯矩-曲率关系的全过程分析程序,并介绍了弯矩-曲率关系曲线的线性化方法。
(2)建立了可以考虑支座水平摩擦和竖向地震动作用的接触摩擦单元,并利用接触摩擦单元建立了连续梁全桥模型。分别针对普通固定支座桥梁和滑动隔震支座桥梁,分析了滑动支座摩擦力及竖向地震动对桥梁结构地震反应的影响。并对支座的摩擦系数、初始刚度对不同桥梁结构的地震反应影响进行了参数分析。根据分析结果,给出了需要考虑活动支座摩擦力和竖向地震动影响的建议。
(3)提出了可以综合考虑活动支座摩擦非线性和限位装置接触及材料非线性的有限单元的刚度及滞回曲线。建立了可以综合考虑支座非线性、限位装置接触及材料非线性、墩身弹塑性的桥梁结构有限元模型。对限位装置的初始刚度及初始间隙对桥梁结构地震反应的影响进行了研究,并对活动支座摩擦力、限位装置、桥墩弹塑性各种非线性之间的相互影响进行了综合分析,探讨了可以降低固定墩地震反应的有效措施。
(4)改进了无拉力非线性Winkler地基弹簧的有限元模型,给出了其滞回规律,主要改进点为该无拉力土弹簧可以同时考虑桩双侧土的接触及材料非线性,可以模拟地震中往复振动下桩和土之间产生的裂缝。在总结目前桩基础桥梁的抗震计算模型的基础上,提出了改进的桩基础桥梁的非线性抗震分析计算模型,主要改进点是基础部分综合考虑了桩侧土的水平接触及材料非线性作用、土与桩基础间的竖向非线性摩擦作用、桩尖土的非线性压入和提离作用,并可以考虑墩与桩的弹塑性。对该非线性分析模型进行了循环荷载下的静力推倒分析,并通过与静力推倒试验结果的对比验证了此模型的合理性。
(5)以实际工程为背景,建立了桩基础桥墩分布弹簧非线性分析的有限元模型,探讨了该模型时程反应分析的可行性。根据时程分析结果,分析了地基非线性对桥墩和桩弹塑性地震反应的影响。时程分析结果表明,承台底水平剪力-水平位移、承台底弯矩-转角曲线呈纺锤状。利用实例验证了利用Clough集中支撑弹簧模型来模拟桩-土相互作用对桥梁上部结构地震反应影响的可行性,并建议了利用静力推倒分析骨架曲线进行简化分析模型参数取值的计算方法。
(6)对于在地震中薄弱环节不明显、各构件均有可能出现破坏的混合破坏型桥梁,提出了考虑桩-土-结构相互作用的桥梁结构整体非线性分析有限元模型,该模型综合考虑了支座、桥墩、桩基础、地基的非线性。通过工程实例,探讨了整体非线性模型时程分析的可行性。根据分析结果初步探讨了桥梁各部分构件之间的非线性地震反应的相互影响,、分析了不同非线性模型的墩底弯矩及曲率、承台底转角及水平位移、梁体位移等结构地震反应。
The research on the nonlinear seismic response is of great significance to the seismic analysis and design of the bridge structures. The bridge structure can be destroyed at different locations under the strong earthquake. Correspondingly, the analysis method and model are also different. Precise analysis of nonlinear seismic response of bridge structure is quite complicated because of various nonlinearities. So, the simplified mathematical model is usually adopted for the nonlinear analysis. Based on the research results obtained by others, some key technical issues on nonlinear analysis of bridge structures under strong motion are comprehensive analyzed. The corresponding finite elements and nonlinear finite model are put forward, which are used in the analysis of the effect of the nonlinearity on the integral seismic-resistant performance of the bridge structure. The studies and results in this dissertation are summarized as follows:
(1) The nonlinear computing model for the bridge structure, the general constitutive relationship, and the nonlinear dynamic equations and its solutions are summarized. Three models for elastic-plastic beam element are discussed. And the element flexibility matrix considering the length of plastic hinge for the elastic-plastic beam element is also introduced. The moment-curvature hysteretic model for the reinforced concrete pier is presented. A computer program is compiled and a linear method is also introduced to analyze the moment-curvature curve.
(2) A "friction and contact" element for the support is introduced to take into account the effect of the friction force at movable supports and the influence of the bearing dynamic vertical resistance force on the bearing horizontal friction force. A finite element model for a continuous bridge with "friction and contact" elements is created. With this model, the effects of the friction force at movable supports and vertical excitation on seismic-resistant performance of continuous bridges are analyzed. And the effects of the supports parameters such as friction coefficient and initial stiffness, etc on the seismic response are also discussed according to the finite element analysis results. It shows that the friction force at the movable supports and vertical excitation needs to be taken into account for the study of the seismic-resistance performance of continuous bridges in some cases.
(3) The finite element that considering the friction nonlinearity at the movable support and the contact and material nonlinearity at the restrainer is put forward. And its stiffness and hysteretic curve are also derived. The finite element model considering the nonlinearity of the supports and restrainer and pier is established to study the nonlinear seismic response of the bridge structure. The study on the interaction among the friction force at movable supports and contact and material nonlinearity at restrainer, and elasto-plasticity at pier is performed. The effect of initial gap and stiffness of the restrainer on the nonlinear seismic response is also discussed. And the effective methods to reduce the seismic response of the fixed pier are discussed.
(4) The nonlinear Winkler soil spring model is improved and the hysteretic features for the nonlinear compression soil spring are presented. The improved model takes into account the contact and material nonlinearity of soil around piles. Based on the current finite element models for the pile foundation bridges, an improved nonlinear finite model for the seismic analysis of pile foundation bridges is put forward, which include the horizontal contact and material nonlinearity of the soil on each side of the pile, the vertical friction nonlinearity between the soil and piles, and the nonlinear compression and uplift features of the soil at pile bottom. This model also takes the elasto-plastic characteristics of piers and piles into account. The static pushover experiment under cyclic loads for a pile foundation pier approved that results of this model match that of the experiment.
(5) The improved distributed spring finite element model of the pile foundation pier is used in a bridge project. The feasibility of the time-history analysis is discussed. And the nonlinear effect of pile foundation on the seismic response of the pier and pile is analyzed. The hysteric curves of the horizontal shear force-linear displacement and that of the moment-angular displacement at the bottom of pile cap are summarized. The results show that the curve is spindle-shaped or pinched spindle-shaped. The simplified centralized spring model is put forward in which the Clough spring model is used to simulate the influence of the soil-pile interaction on the superstructure. The comparison results indicate that the results of the simplified centralized Clough spring model and the distributed spring model are similar.
(6) For bridges whose weak points are not apparent and every part can be destroyed in the strong earthquake, an integral nonlinear finite element model, which takes the nonlinear pile-soil-structure interaction into account, is put forward. The model includes the nonlinearity of the supports, piers, piles and soil. The nonlinear interaction among different parts is discussed based on the results. The nonlinear seismic response of the moment-curvatures at the pier bottom and the linear and angular displacement at the bottom of the pile cap, and beam displacement are also studied.
(1)总结了桥梁结构的非线性计算模型、材料的常用本构关系、非线性动力方程及其求解方法,介绍了弹塑性梁单元的三种不同模型及考虑塑性铰长度的弹塑性梁单元的单元柔度矩阵,介绍了钢筋混凝土桥墩常用的弯矩-曲率滞回模型。编写了截面弯矩-曲率关系的全过程分析程序,并介绍了弯矩-曲率关系曲线的线性化方法。
(2)建立了可以考虑支座水平摩擦和竖向地震动作用的接触摩擦单元,并利用接触摩擦单元建立了连续梁全桥模型。分别针对普通固定支座桥梁和滑动隔震支座桥梁,分析了滑动支座摩擦力及竖向地震动对桥梁结构地震反应的影响。并对支座的摩擦系数、初始刚度对不同桥梁结构的地震反应影响进行了参数分析。根据分析结果,给出了需要考虑活动支座摩擦力和竖向地震动影响的建议。
(3)提出了可以综合考虑活动支座摩擦非线性和限位装置接触及材料非线性的有限单元的刚度及滞回曲线。建立了可以综合考虑支座非线性、限位装置接触及材料非线性、墩身弹塑性的桥梁结构有限元模型。对限位装置的初始刚度及初始间隙对桥梁结构地震反应的影响进行了研究,并对活动支座摩擦力、限位装置、桥墩弹塑性各种非线性之间的相互影响进行了综合分析,探讨了可以降低固定墩地震反应的有效措施。
(4)改进了无拉力非线性Winkler地基弹簧的有限元模型,给出了其滞回规律,主要改进点为该无拉力土弹簧可以同时考虑桩双侧土的接触及材料非线性,可以模拟地震中往复振动下桩和土之间产生的裂缝。在总结目前桩基础桥梁的抗震计算模型的基础上,提出了改进的桩基础桥梁的非线性抗震分析计算模型,主要改进点是基础部分综合考虑了桩侧土的水平接触及材料非线性作用、土与桩基础间的竖向非线性摩擦作用、桩尖土的非线性压入和提离作用,并可以考虑墩与桩的弹塑性。对该非线性分析模型进行了循环荷载下的静力推倒分析,并通过与静力推倒试验结果的对比验证了此模型的合理性。
(5)以实际工程为背景,建立了桩基础桥墩分布弹簧非线性分析的有限元模型,探讨了该模型时程反应分析的可行性。根据时程分析结果,分析了地基非线性对桥墩和桩弹塑性地震反应的影响。时程分析结果表明,承台底水平剪力-水平位移、承台底弯矩-转角曲线呈纺锤状。利用实例验证了利用Clough集中支撑弹簧模型来模拟桩-土相互作用对桥梁上部结构地震反应影响的可行性,并建议了利用静力推倒分析骨架曲线进行简化分析模型参数取值的计算方法。
(6)对于在地震中薄弱环节不明显、各构件均有可能出现破坏的混合破坏型桥梁,提出了考虑桩-土-结构相互作用的桥梁结构整体非线性分析有限元模型,该模型综合考虑了支座、桥墩、桩基础、地基的非线性。通过工程实例,探讨了整体非线性模型时程分析的可行性。根据分析结果初步探讨了桥梁各部分构件之间的非线性地震反应的相互影响,、分析了不同非线性模型的墩底弯矩及曲率、承台底转角及水平位移、梁体位移等结构地震反应。
The research on the nonlinear seismic response is of great significance to the seismic analysis and design of the bridge structures. The bridge structure can be destroyed at different locations under the strong earthquake. Correspondingly, the analysis method and model are also different. Precise analysis of nonlinear seismic response of bridge structure is quite complicated because of various nonlinearities. So, the simplified mathematical model is usually adopted for the nonlinear analysis. Based on the research results obtained by others, some key technical issues on nonlinear analysis of bridge structures under strong motion are comprehensive analyzed. The corresponding finite elements and nonlinear finite model are put forward, which are used in the analysis of the effect of the nonlinearity on the integral seismic-resistant performance of the bridge structure. The studies and results in this dissertation are summarized as follows:
(1) The nonlinear computing model for the bridge structure, the general constitutive relationship, and the nonlinear dynamic equations and its solutions are summarized. Three models for elastic-plastic beam element are discussed. And the element flexibility matrix considering the length of plastic hinge for the elastic-plastic beam element is also introduced. The moment-curvature hysteretic model for the reinforced concrete pier is presented. A computer program is compiled and a linear method is also introduced to analyze the moment-curvature curve.
(2) A "friction and contact" element for the support is introduced to take into account the effect of the friction force at movable supports and the influence of the bearing dynamic vertical resistance force on the bearing horizontal friction force. A finite element model for a continuous bridge with "friction and contact" elements is created. With this model, the effects of the friction force at movable supports and vertical excitation on seismic-resistant performance of continuous bridges are analyzed. And the effects of the supports parameters such as friction coefficient and initial stiffness, etc on the seismic response are also discussed according to the finite element analysis results. It shows that the friction force at the movable supports and vertical excitation needs to be taken into account for the study of the seismic-resistance performance of continuous bridges in some cases.
(3) The finite element that considering the friction nonlinearity at the movable support and the contact and material nonlinearity at the restrainer is put forward. And its stiffness and hysteretic curve are also derived. The finite element model considering the nonlinearity of the supports and restrainer and pier is established to study the nonlinear seismic response of the bridge structure. The study on the interaction among the friction force at movable supports and contact and material nonlinearity at restrainer, and elasto-plasticity at pier is performed. The effect of initial gap and stiffness of the restrainer on the nonlinear seismic response is also discussed. And the effective methods to reduce the seismic response of the fixed pier are discussed.
(4) The nonlinear Winkler soil spring model is improved and the hysteretic features for the nonlinear compression soil spring are presented. The improved model takes into account the contact and material nonlinearity of soil around piles. Based on the current finite element models for the pile foundation bridges, an improved nonlinear finite model for the seismic analysis of pile foundation bridges is put forward, which include the horizontal contact and material nonlinearity of the soil on each side of the pile, the vertical friction nonlinearity between the soil and piles, and the nonlinear compression and uplift features of the soil at pile bottom. This model also takes the elasto-plastic characteristics of piers and piles into account. The static pushover experiment under cyclic loads for a pile foundation pier approved that results of this model match that of the experiment.
(5) The improved distributed spring finite element model of the pile foundation pier is used in a bridge project. The feasibility of the time-history analysis is discussed. And the nonlinear effect of pile foundation on the seismic response of the pier and pile is analyzed. The hysteric curves of the horizontal shear force-linear displacement and that of the moment-angular displacement at the bottom of pile cap are summarized. The results show that the curve is spindle-shaped or pinched spindle-shaped. The simplified centralized spring model is put forward in which the Clough spring model is used to simulate the influence of the soil-pile interaction on the superstructure. The comparison results indicate that the results of the simplified centralized Clough spring model and the distributed spring model are similar.
(6) For bridges whose weak points are not apparent and every part can be destroyed in the strong earthquake, an integral nonlinear finite element model, which takes the nonlinear pile-soil-structure interaction into account, is put forward. The model includes the nonlinearity of the supports, piers, piles and soil. The nonlinear interaction among different parts is discussed based on the results. The nonlinear seismic response of the moment-curvatures at the pier bottom and the linear and angular displacement at the bottom of the pile cap, and beam displacement are also studied.
引文
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