自锚式悬索桥静力可靠度研究
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摘要
自锚式悬索桥造型优美,适应于各种地质条件,是城市桥梁常用的桥型之一。二十一世纪来我国已建成和在建的自锚式悬索桥有20多座。迄今为止针对自锚式悬索桥的研究和分析工作大多停留在确定性分析方面,考虑其结构尺寸、材料特性和荷载的随机影响,开展其受力可靠度性能研究的工作很少。且作为高次超静定结构,自锚式悬索桥某一构件的破坏并不意味着整体结构的失效,其整个结构的体系可靠度问题是设计时的关键问题。基于此,本文针对大跨度自锚式悬索桥结构的静力可靠度问题开展了研究,主要完成了以下工作：
(1)针对复杂工程结构的极限状态方程为隐式的问题,提出了基于均匀设计和支持向量机的响应面法,采用网格搜索法、遗传算法和粒子群算法确定支持向量机模型参数,实现了基于均匀设计和支持向量机的响应面法在结构可靠度计算方面的应用,并编制相应程序,通过数值算例验证了所提出方法的正确性和有效性,大大提高了可靠度分析的计算效率。
(2)采用基于均匀设计和支持向量机的响应面法进行了猎德大桥和三汊矶大桥正常使用极限状态的可靠度分析。主跨满布汽车活载时,猎德大桥关于主梁最大挠度的可靠度指标为3.92,三汊矶大桥为3.94,在正常使用极限状态下两座桥的加劲梁均有较高的可靠度。通过结构几何形状、材料特性和外荷载等相关随机变量均值和变异系数对可靠度指标影响的分析,识别出主缆的弹性模量和面积,以及钢加劲梁的弹性模量和惯性矩是影响自锚式悬索桥关于加劲梁主梁最大挠度可靠度指标的主要随机变量。
(3)采用CR列式法,推导了平面梁与杆单元的材料刚度矩阵和几何刚度矩阵,基于位移法梁-柱单元考虑材料非线性的影响,推导了直接微分法计算结构响应梯度的公式,将非线性有限元法与一次可靠度方法结合,建立了杆系结构的非线性随机有限元可靠度分析方法,编制了基于直接微分法的随机有限元可靠度计算程序,并通过数值算例验证了所编程序的正确性和精度。
(4)采用编制的基于直接微分的杆系非线性随机有限元可靠度计算程序,考虑自锚式悬索桥主梁、主缆、索塔和吊索等各种构件可能的失效,对猎德大桥和三汉矶大桥进行了承载能力极限状态的体系可靠度评估,实现了基于直接微分的随机有限元计算结构体系可靠度的方法在大跨度自锚式悬索桥中的运用。计算表明,不同汽车活载下,猎德大桥进入失效历程第1阶段的都是主塔和主梁单元,当主跨均布汽车活载时,猎德大桥的1级体系可靠度指标是3.9439；三汊矶大桥进入失效历程第1阶段的是吊索单元,继续搜索到第2失效阶段,其2级体系可靠度指标是5.9170。这两座桥的承载能力极限状态具有较高的安全性。通过敏感性分析,得出单元截面的抗力对单元的可靠度指标影响最显著。恒载、活载和主梁的抗弯刚度对主梁、主缆和主塔的可靠度指标有较大影响。
(5)进行了猎德大桥贝壳索塔结构1：10模型试验和空间分析,通过模型试验和精细模型的理论计算均表明该索塔结构强度满足规范要求；在施工荷载和成桥荷载作用下,索塔处于安全状态。在超载作用下,索塔结构没有出现可见裂缝,表明该索塔结构具有较强的超载能力,具有较高的安全系数,检验了设计的可靠性。
(6)考虑索塔的几何和材料非线性,采用纤维模式的梁柱单元,建立了猎德大桥索塔弹塑性有限元分析模型,计算了其应力可靠度指标,并进行了敏感性分析。
Due to its aesthetic appearance and adaptability for poor foundation, self-anchored suspension bridge becomes one of the most widespread bridge types used in cities. From the beginning of the 21st century, more than 20 self-anchored suspension bridges have been built in China. So far the design of self-anchored suspension bridges are limited to deterministic analysis. However taking into account the stochastic variations of structural material parameters, geometry factors and external loadings, the reliability analysis of self-anchored suspension bridges are seldom investigated. As a highly indeterminate structure, the failure of some components of a self-anchored suspension bridge doesn't mean failure of the whole structure, system reliability is a key issue in the design and construction of self-anchored suspension bridges. In this dissertation the static reliability of long-span self-anchored suspension bridges was investigated and main results obtained are listed as follows:
(1) As the limit state functions of complex engineering structures are inexplicit, a uniform design method and support vector machines (UDM-SVM)-based approach was proposed, which is an improvement of the traditional response surface method.. Three algorithms, i.e. grid search, genetic algorithm and particle swarm optimization methods, were adopted to determine the parameters of the model of SVM. The proposed UDM-SVM response surface method was applied to the reliability analysis of the structure, and a relevant program was then developed. With several numerical examples, the proposed method and program were demonstrated to be accurate and effective, and the efficiency of computation could be greatly improved.
(2) The reliability analysis of Liede Bridge and Sanchaji Bridge under serviceability limit-state was carried out with the proposed UDM-SVM response surface method. When the main span was fully occupied with traffic loads, the reliability index of maximum displacement of main girder of Liede Bridge and Sanchaji Bridge were 3.92 and 3.94 respectively, which showed that both the two bridges owned high reliability under serviceability limit-state. The impact of the mean and coefficient of variation of random variables on the reliability index were also analyzed. The results showed that the section areas and Young's modulus of main cables, Young's modulus and inertia moment of steel stiffening girder were the main influential factors on the maximum deflection of stiffening girder.
(3) With co-rotational formulation, the material and geometric stiffness matrix of a plane beam and bar element were deduced. The material nonlinearity of beam-column element was considered on the basis of the displacement method, from which the formula of response gradients in direct differentiation method was deduced. The nonlinear finite element method and first-order reliability method were combined, based on which the reliability approach was proposed and a program was developed, numerical examples were then computed to validate the accuracy and high efficiency of the proposed approach and program.
(4) The nonlinear static stochastic finite element analysis program was used to assess the reliability of Liede Bridge and Sanchaji Bridge under ultimate limit states, taking account of the possible failure of girder, main cable, cable tower and suspension cables. The stochastic finite element method based on direct differentiation method was directly applied in the system reliability of long-span self-anchored suspension bridge. The results showed that the main tower and main beam of Liede Bridge failed at level 1 under different traffic loads. When the main span was fully occupied with traffic loads, the system reliability index at level 1 was 3.9439. For Sanchaji Bridge, its suspension cables failed at level 1. When searching for level 2, the system reliability index at level 2 was 5.9170. The results showed that two bridges processed high security under ultimate limit states. The sensibility analysis showed that the resistance of element sections had the most remarkable impact on element reliability index. Dead loads, live loads and bending stiffness of main girder had large impact on reliability of main beam, main cables and main tower.
(5) A model test with 1:10 scale and spatial analysis were carried out on the shell shaped tower of Liede Bridge. The test and calculation indicated that strength of cable tower could meet the requirements of design specifications; the tower was safe under the construction load and operational load. And there was no visible crack under testing overloads. The results showed that the tower owned strong overload ability and high safety coefficient.
(6) The main tower of Liede Bridge was modeled with elastic-plastic fiber beam-column elements, taking the geometry and material nonlinearity into consideration. The stress reliability of the main tower was assessed and the sensitivity analysis was conducted.
(1)针对复杂工程结构的极限状态方程为隐式的问题,提出了基于均匀设计和支持向量机的响应面法,采用网格搜索法、遗传算法和粒子群算法确定支持向量机模型参数,实现了基于均匀设计和支持向量机的响应面法在结构可靠度计算方面的应用,并编制相应程序,通过数值算例验证了所提出方法的正确性和有效性,大大提高了可靠度分析的计算效率。
(2)采用基于均匀设计和支持向量机的响应面法进行了猎德大桥和三汊矶大桥正常使用极限状态的可靠度分析。主跨满布汽车活载时,猎德大桥关于主梁最大挠度的可靠度指标为3.92,三汊矶大桥为3.94,在正常使用极限状态下两座桥的加劲梁均有较高的可靠度。通过结构几何形状、材料特性和外荷载等相关随机变量均值和变异系数对可靠度指标影响的分析,识别出主缆的弹性模量和面积,以及钢加劲梁的弹性模量和惯性矩是影响自锚式悬索桥关于加劲梁主梁最大挠度可靠度指标的主要随机变量。
(3)采用CR列式法,推导了平面梁与杆单元的材料刚度矩阵和几何刚度矩阵,基于位移法梁-柱单元考虑材料非线性的影响,推导了直接微分法计算结构响应梯度的公式,将非线性有限元法与一次可靠度方法结合,建立了杆系结构的非线性随机有限元可靠度分析方法,编制了基于直接微分法的随机有限元可靠度计算程序,并通过数值算例验证了所编程序的正确性和精度。
(4)采用编制的基于直接微分的杆系非线性随机有限元可靠度计算程序,考虑自锚式悬索桥主梁、主缆、索塔和吊索等各种构件可能的失效,对猎德大桥和三汉矶大桥进行了承载能力极限状态的体系可靠度评估,实现了基于直接微分的随机有限元计算结构体系可靠度的方法在大跨度自锚式悬索桥中的运用。计算表明,不同汽车活载下,猎德大桥进入失效历程第1阶段的都是主塔和主梁单元,当主跨均布汽车活载时,猎德大桥的1级体系可靠度指标是3.9439；三汊矶大桥进入失效历程第1阶段的是吊索单元,继续搜索到第2失效阶段,其2级体系可靠度指标是5.9170。这两座桥的承载能力极限状态具有较高的安全性。通过敏感性分析,得出单元截面的抗力对单元的可靠度指标影响最显著。恒载、活载和主梁的抗弯刚度对主梁、主缆和主塔的可靠度指标有较大影响。
(5)进行了猎德大桥贝壳索塔结构1：10模型试验和空间分析,通过模型试验和精细模型的理论计算均表明该索塔结构强度满足规范要求；在施工荷载和成桥荷载作用下,索塔处于安全状态。在超载作用下,索塔结构没有出现可见裂缝,表明该索塔结构具有较强的超载能力,具有较高的安全系数,检验了设计的可靠性。
(6)考虑索塔的几何和材料非线性,采用纤维模式的梁柱单元,建立了猎德大桥索塔弹塑性有限元分析模型,计算了其应力可靠度指标,并进行了敏感性分析。
Due to its aesthetic appearance and adaptability for poor foundation, self-anchored suspension bridge becomes one of the most widespread bridge types used in cities. From the beginning of the 21st century, more than 20 self-anchored suspension bridges have been built in China. So far the design of self-anchored suspension bridges are limited to deterministic analysis. However taking into account the stochastic variations of structural material parameters, geometry factors and external loadings, the reliability analysis of self-anchored suspension bridges are seldom investigated. As a highly indeterminate structure, the failure of some components of a self-anchored suspension bridge doesn't mean failure of the whole structure, system reliability is a key issue in the design and construction of self-anchored suspension bridges. In this dissertation the static reliability of long-span self-anchored suspension bridges was investigated and main results obtained are listed as follows:
(1) As the limit state functions of complex engineering structures are inexplicit, a uniform design method and support vector machines (UDM-SVM)-based approach was proposed, which is an improvement of the traditional response surface method.. Three algorithms, i.e. grid search, genetic algorithm and particle swarm optimization methods, were adopted to determine the parameters of the model of SVM. The proposed UDM-SVM response surface method was applied to the reliability analysis of the structure, and a relevant program was then developed. With several numerical examples, the proposed method and program were demonstrated to be accurate and effective, and the efficiency of computation could be greatly improved.
(2) The reliability analysis of Liede Bridge and Sanchaji Bridge under serviceability limit-state was carried out with the proposed UDM-SVM response surface method. When the main span was fully occupied with traffic loads, the reliability index of maximum displacement of main girder of Liede Bridge and Sanchaji Bridge were 3.92 and 3.94 respectively, which showed that both the two bridges owned high reliability under serviceability limit-state. The impact of the mean and coefficient of variation of random variables on the reliability index were also analyzed. The results showed that the section areas and Young's modulus of main cables, Young's modulus and inertia moment of steel stiffening girder were the main influential factors on the maximum deflection of stiffening girder.
(3) With co-rotational formulation, the material and geometric stiffness matrix of a plane beam and bar element were deduced. The material nonlinearity of beam-column element was considered on the basis of the displacement method, from which the formula of response gradients in direct differentiation method was deduced. The nonlinear finite element method and first-order reliability method were combined, based on which the reliability approach was proposed and a program was developed, numerical examples were then computed to validate the accuracy and high efficiency of the proposed approach and program.
(4) The nonlinear static stochastic finite element analysis program was used to assess the reliability of Liede Bridge and Sanchaji Bridge under ultimate limit states, taking account of the possible failure of girder, main cable, cable tower and suspension cables. The stochastic finite element method based on direct differentiation method was directly applied in the system reliability of long-span self-anchored suspension bridge. The results showed that the main tower and main beam of Liede Bridge failed at level 1 under different traffic loads. When the main span was fully occupied with traffic loads, the system reliability index at level 1 was 3.9439. For Sanchaji Bridge, its suspension cables failed at level 1. When searching for level 2, the system reliability index at level 2 was 5.9170. The results showed that two bridges processed high security under ultimate limit states. The sensibility analysis showed that the resistance of element sections had the most remarkable impact on element reliability index. Dead loads, live loads and bending stiffness of main girder had large impact on reliability of main beam, main cables and main tower.
(5) A model test with 1:10 scale and spatial analysis were carried out on the shell shaped tower of Liede Bridge. The test and calculation indicated that strength of cable tower could meet the requirements of design specifications; the tower was safe under the construction load and operational load. And there was no visible crack under testing overloads. The results showed that the tower owned strong overload ability and high safety coefficient.
(6) The main tower of Liede Bridge was modeled with elastic-plastic fiber beam-column elements, taking the geometry and material nonlinearity into consideration. The stress reliability of the main tower was assessed and the sensitivity analysis was conducted.
引文
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