自锚式悬索桥结构可靠性研究
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摘要
自锚式悬索桥以其造型美观、经济、适应性强等优点，越来越受到工程界的青睐，在国内外，已有多座自锚式悬索桥建成或建造中。随着自锚式悬索桥的迅速发展和被大量设计采用，人们已对自锚式悬索桥的设计理论、静力和动力特性方面以及极限跨度、极限承载力、施工控制等方面都进行深入的研究和探讨。以上这些关于自锚式悬索桥的分析研究大都是在确定性分析的基础之上。然而，确定性分析方法在许多方面难于像非确定性分析方法那样可以更深层次地揭示结构参数的变化对结构响应的影响程度。因此，引入可靠性理论，从概率论的角度出发研究探讨结构的各种参数(变量)对自锚式悬索桥的静力、动力响应的影响规律，进而研究各随机变量对自锚式悬索桥可靠度的影响程度，找到对可靠度影响较大的影响因素，为合理设计提供理论依据。本文的具体研究内容如下：
(1)对于大型复杂桥梁结构的极限功能函数不能用显式表达的可靠度评估问题，在已有的响应面法基础上，采取了一种自动调整样本点取值区间策略的改进响应面法求解真实极限状态曲面。通过算例表明，文中的改进响应面法可以提高计算效率与计算精度，在大型复杂的工程结构可靠度评估中尤为适用。最后，将MATLAB软件与结构分析软件ANSYS相结合，编制了可用于大型复杂桥梁结构在正常使用极限下的可靠度评估程序。
(2)考虑材料、几何尺寸、外部荷载等的变异，应用响应面法对自锚式悬索桥结构进行了随机静力分析。研究了各种随机因素变异时自锚式悬索桥结构响应的变化规律。使设计者清楚地了解各种随机因素对自锚式悬索桥结构响应的影响程度，为合理设计提供理论依据。最后应用自行编制的结构在正常使用极限状态下的可靠度评估程序对一座自锚式悬索桥加劲梁最大挠度的可靠度进行了评估。
(3)对自锚式悬索桥在承载能力极限状态下的系统可靠度进行了评估。应用全局b约界法搜索自锚式悬索桥的主要失效模式，采用微分等价递归算法确定自锚式悬索桥各个失效历程中阶段失效模式的等价安全裕量方程。通过计算验证了全局b约界法是识别系统主要失效模式的高效、精确的算法。最后，通过Ditlevsen上、下界理论确定了自锚式悬索桥结构的系统失效概率界限值。
(4)将虚拟激励法引入自锚式悬索桥结构抗震动力可靠度分析中，克服了以往随机振动计算方法计算量庞大的缺点，使随机振动理论应用于大型复杂桥梁结构的动力可靠度分析中成为可能。系统地研究了混凝土自锚式悬索桥在随机地震荷载作用下的主要抗震子系统中的各墩、塔控制截面的抗震动力可靠度。重点考察了地震动的空间效应、非平稳性以及阻尼比对各墩、塔控制截面的抗震动力可靠度的影响。
(5)对于加劲梁以混凝土为材料的自锚式悬索桥结构，不可避免要面临钢筋混凝土结构所共有的耐久性问题。文中在已有钢筋混凝土结构耐久性研究成果基础之上，尝试性采用一种基于等效抗力时变可靠度的耐久性设计方法。文中所采用的耐久性设计方法比传统设计方法增加了计算在使用期内时变可靠度指标一项，将其作为结构构件的截面配筋、混凝土强度等级以及混凝土保护层厚度的验算。
At present, self-anchored suspension bridges are greatly appreciated for their aestheticappearances, low costs and high adaptabilities. Many self-anchored suspension bridges havebeen constructed or are in construction now. This kind of bridge has its own features, which isgreatly different from the conventional suspension bridge both in construction and inmechanical performances. No matter in the theoretical research on static and dynamicmechanical performances or in the supervision of design and construction, the research on theconventional suspension bridges has been greatly developed with a large number of relatedpapers. With the rapid development and wide adoption of the self-anchored suspension bridge,the research on its design theory, static and dynamic mechanical performances, limit span,ultimate carrying capability and construction control has been carried out deeply. Based onthe structural reliability theory and combining engineering practice, this doctoral paper isfocused on the evaluation of reliability for self-anchored suspension bridges under servicelimit states and ultimate limit states, analyzing the dynamic reliability under seismicexcitations. Moreover, the durability design for concrete self-anchored suspension bridges isalso discussed in the paper. The main research involves the following:
(1) As for the problem of reliability evaluation that the limit state function of the large,complex bridge structures can not be expressed explicitly, an improved response surfacemethod (IRSM) is proposed based on the existing response surface method (RSM). It issuggested that the IRSM is highly efficient. And it can simulate the real limit state curvedsurface so that it will be helpful to improve the convergence of the existing RSM. At last,based on the large commercial software MATLAB and combining the general structuralanalysis software ANSYS with it, the program is established for any complex structuralreliability analysis under service limit states.
(2) The stochastic static analysis method for the self-anchored suspension bridges isestablished through applying the RSM, in which the variation of material, geometricdimension and external loads are taken into account. The response law is studied for theself-anchored suspension bridges with variation of the diversified stochastic factors. Then it iseasily seen how the diversified stochastic factors affect the self-anchored suspension bridges.The reliability for self-anchored suspension bridge is evaluated under service limit state bythe IRSM.
(3) The system reliability method is established for the self-anchored suspension bridgesunder ultimate limit states. The globalβ-unzipping method and the different equivalentrecursion algorithm are adopted to recognize the significant failure models and equivalent limit state functions. The results show that the globalβ-unzipping method is highly efficientand accurate in recognizing the main failure models of structural system. The bond of failureprobability of the self-anchored suspension bridge system is calculated by the Ditlevsen'stheory.
(4) The pseudo excitation method is introduced in the structural dynamic reliabilityanalysis, which overcomes the shortcoming of time consuming of the random vibrationapproach and makes it possible to apply the random vibration approach for large and complexbridge structures. In the paper, the reliability of important structural component, piers andtowers used as resist the seismic action, is analyzied in detail. It is special considered that thespace effect, non-stationary and damping ratio can impact on the dynamic reliability.
(5) The girder of the suspension bridge is made of concrete material, which makes itinevitable to face the common durability problem as the reinforced concrete structures do. Inthis paper, a new equivalent resistance durability design method is introduced based on theexisting durability researches. In the method, calculating the time dependant reliability indexis used as the item to check the reinforcement calculation, concrete grade and cover thicknessare meet the requirement or not.
(1)对于大型复杂桥梁结构的极限功能函数不能用显式表达的可靠度评估问题，在已有的响应面法基础上，采取了一种自动调整样本点取值区间策略的改进响应面法求解真实极限状态曲面。通过算例表明，文中的改进响应面法可以提高计算效率与计算精度，在大型复杂的工程结构可靠度评估中尤为适用。最后，将MATLAB软件与结构分析软件ANSYS相结合，编制了可用于大型复杂桥梁结构在正常使用极限下的可靠度评估程序。
(2)考虑材料、几何尺寸、外部荷载等的变异，应用响应面法对自锚式悬索桥结构进行了随机静力分析。研究了各种随机因素变异时自锚式悬索桥结构响应的变化规律。使设计者清楚地了解各种随机因素对自锚式悬索桥结构响应的影响程度，为合理设计提供理论依据。最后应用自行编制的结构在正常使用极限状态下的可靠度评估程序对一座自锚式悬索桥加劲梁最大挠度的可靠度进行了评估。
(3)对自锚式悬索桥在承载能力极限状态下的系统可靠度进行了评估。应用全局b约界法搜索自锚式悬索桥的主要失效模式，采用微分等价递归算法确定自锚式悬索桥各个失效历程中阶段失效模式的等价安全裕量方程。通过计算验证了全局b约界法是识别系统主要失效模式的高效、精确的算法。最后，通过Ditlevsen上、下界理论确定了自锚式悬索桥结构的系统失效概率界限值。
(4)将虚拟激励法引入自锚式悬索桥结构抗震动力可靠度分析中，克服了以往随机振动计算方法计算量庞大的缺点，使随机振动理论应用于大型复杂桥梁结构的动力可靠度分析中成为可能。系统地研究了混凝土自锚式悬索桥在随机地震荷载作用下的主要抗震子系统中的各墩、塔控制截面的抗震动力可靠度。重点考察了地震动的空间效应、非平稳性以及阻尼比对各墩、塔控制截面的抗震动力可靠度的影响。
(5)对于加劲梁以混凝土为材料的自锚式悬索桥结构，不可避免要面临钢筋混凝土结构所共有的耐久性问题。文中在已有钢筋混凝土结构耐久性研究成果基础之上，尝试性采用一种基于等效抗力时变可靠度的耐久性设计方法。文中所采用的耐久性设计方法比传统设计方法增加了计算在使用期内时变可靠度指标一项，将其作为结构构件的截面配筋、混凝土强度等级以及混凝土保护层厚度的验算。
At present, self-anchored suspension bridges are greatly appreciated for their aestheticappearances, low costs and high adaptabilities. Many self-anchored suspension bridges havebeen constructed or are in construction now. This kind of bridge has its own features, which isgreatly different from the conventional suspension bridge both in construction and inmechanical performances. No matter in the theoretical research on static and dynamicmechanical performances or in the supervision of design and construction, the research on theconventional suspension bridges has been greatly developed with a large number of relatedpapers. With the rapid development and wide adoption of the self-anchored suspension bridge,the research on its design theory, static and dynamic mechanical performances, limit span,ultimate carrying capability and construction control has been carried out deeply. Based onthe structural reliability theory and combining engineering practice, this doctoral paper isfocused on the evaluation of reliability for self-anchored suspension bridges under servicelimit states and ultimate limit states, analyzing the dynamic reliability under seismicexcitations. Moreover, the durability design for concrete self-anchored suspension bridges isalso discussed in the paper. The main research involves the following:
(1) As for the problem of reliability evaluation that the limit state function of the large,complex bridge structures can not be expressed explicitly, an improved response surfacemethod (IRSM) is proposed based on the existing response surface method (RSM). It issuggested that the IRSM is highly efficient. And it can simulate the real limit state curvedsurface so that it will be helpful to improve the convergence of the existing RSM. At last,based on the large commercial software MATLAB and combining the general structuralanalysis software ANSYS with it, the program is established for any complex structuralreliability analysis under service limit states.
(2) The stochastic static analysis method for the self-anchored suspension bridges isestablished through applying the RSM, in which the variation of material, geometricdimension and external loads are taken into account. The response law is studied for theself-anchored suspension bridges with variation of the diversified stochastic factors. Then it iseasily seen how the diversified stochastic factors affect the self-anchored suspension bridges.The reliability for self-anchored suspension bridge is evaluated under service limit state bythe IRSM.
(3) The system reliability method is established for the self-anchored suspension bridgesunder ultimate limit states. The globalβ-unzipping method and the different equivalentrecursion algorithm are adopted to recognize the significant failure models and equivalent limit state functions. The results show that the globalβ-unzipping method is highly efficientand accurate in recognizing the main failure models of structural system. The bond of failureprobability of the self-anchored suspension bridge system is calculated by the Ditlevsen'stheory.
(4) The pseudo excitation method is introduced in the structural dynamic reliabilityanalysis, which overcomes the shortcoming of time consuming of the random vibrationapproach and makes it possible to apply the random vibration approach for large and complexbridge structures. In the paper, the reliability of important structural component, piers andtowers used as resist the seismic action, is analyzied in detail. It is special considered that thespace effect, non-stationary and damping ratio can impact on the dynamic reliability.
(5) The girder of the suspension bridge is made of concrete material, which makes itinevitable to face the common durability problem as the reinforced concrete structures do. Inthis paper, a new equivalent resistance durability design method is introduced based on theexisting durability researches. In the method, calculating the time dependant reliability indexis used as the item to check the reinforcement calculation, concrete grade and cover thicknessare meet the requirement or not.
引文
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