基于高性能材料的千米级跨径混凝土斜拉桥力学性能研究
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摘要
本文基于RPC和CFRP材料的优越性能，依托国家自然科学基金资助项目“基于高性能材料的特大跨径混凝土斜拉桥的结构性能”，提出千米级CFRP索RPC梁混凝土斜拉桥方案，并从静力特性、动力特性、稳定性能、抗风以及抗震性能等方面探讨CFRP拉索超高性能混凝土特大跨径斜拉桥结构应用的可行性。主要的研究工作如下：
（1）以1090m主跨的钢索钢主梁普通混凝土索塔斜拉桥设计方案为例，拟定了一座同跨度的CFRP索RPC梁混凝土斜拉桥体系新方案。其中拉索采用等强度原则将原桥的钢索替换成CFRP索，主梁考虑截面刚度、抗剪、抗冲切、局部稳定和局部抗弯等要求将原桥的钢主梁替换成RPC主梁，主塔考虑强度和稳定需要将原桥的普通混凝土主塔替换成RPC主塔。
（2）采用有限元法分别对原方案和新方案在恒载、活载、温度荷载和静风荷载及各种荷载组合下的主梁挠度、索塔偏位、结构内力及应力等各项静力性能进行了对比分析，结果表明本文所提新方案具有良好的结构静力特性。相对于原方案，新方案在RPC主梁替换钢主梁后应力明显减少，且分布更均匀；在CFRP索替换钢索后，由于线膨胀系数不及钢材的1/10，在结构中所引起的温度变形很小，约为钢拉索的1/25。
（3）考虑几何非线性和材料非线性的双重影响，应用大型有限元通用程序ANSYS对两种方案结构的静力稳定和静风稳定性能进行分析。静力稳定分析结果表明两种方案各工况下弹性稳定安全系数和非线性稳定安全系数均满足规范要求，且新方案静力稳定安全系数较原方案有所增大。相对于原方案，新方案CFRP索由于较高的比刚度和比强度，分析时可不计入其几何非线性的影响；而RPC主塔替换后纵向刚度的改善，在一定程度上延缓了新方案结构失稳破坏。静风稳定分析结果表明，在0°风攻角下，原方案静风失稳临界风速为179m/s，新方案静风失稳临界风速为165m/s，失稳形态均为弯扭耦合屈曲失稳；相对于原方案，新方案主梁在替换后竖向刚度下降了38%、扭转刚度下降了57%，但CFRP索较高的比刚度和比强度对结构竖向刚度和扭转刚度的改善以及主梁自重的增加，使新方案失稳临界风速仅下降了8%左右。
（4）应用大型有限元程序MIDAS对两种方案进行了动力特性分析。结果表明，虽然新方案主梁替换后竖向刚度下降了38%，但CFRP索较高的比刚度和比强度改善了结构的竖向刚度，使新方案竖弯振型对应的频率下降不足20%；在RPC主塔替换普通混凝土主塔后，由于纵向刚度和横向刚度的改善，提高了新方案的基频，并延缓了主塔侧弯振型的出现。
（5）分别采用反应谱法和时程分析法对原方案和新方案进行了弹性地震响应分析，并对所提体系进行了抗震性能评价。结果表明新方案具有与原方案相近的抗震性能，且在恒载与地震力组合下新方案各部分的应力和位移均能满足正常使用要求。相对于原方案，新方案在主塔采用RPC材料后纵向刚度和横向刚度的提高，减少了地震荷载作用下主塔塔顶位移，增大了塔底弯矩，有效的发挥了RPC材料的高强性能；在拉索采用CFRP材料后比刚度和比强度的提高，改善了结构的竖向刚度，并在一定程度上弥补了RPC主梁替换钢主梁后竖向刚度下降的不足，使两种方案在地震荷载作用下主梁竖向位移基本一致，新方案略大于原方案。
（6）提出了RPC桥墩恢复力模型。以RPC箱型桥墩为研究对象，首先基于OPENSEES计算平台，选取Concrete02本构关系和Steel02本构关系，结合非线性梁柱单元，建立了RPC桥墩抗震分析模型，并通过3个常轴力RPC桥墩水平反复加载试验结果对数值分析模型进行了验证，在此基础上运用OPENSEES对RPC桥墩延性抗震性能进行了参数分析。然后基于数值分析结果和3个常轴力RPC箱型桥墩拟静力试验结果，考虑水平荷载作用方向对RPC箱型墩抗震性能的影响，建立了计入双轴水平力耦合效应的RPC箱型桥墩恢复力模型，并通过编制的双轴压弯构件非线性分析程序对恢复力模型进行了验证。
（7）基于编制的双轴压弯构件非线性分析程序对RPC桥墩塑性铰长度进行了探讨并提出了相应的塑性铰长度回归公式。结果表明，桥墩塑性铰长度随墩柱高度和截面短边尺寸的增加单调递增，随轴压比的增加单调递减，随水平加载角度和纵筋直径的增加呈先增大后减少的趋势；其中强轴塑性铰长度小于弱轴，斜向60°左右加载时塑性铰长度最大，而在高轴压比时塑性铰长度接近零。提出的塑性铰长度回归公式计算结果与数值结果对比表明，回归公式计算值能较好的吻合数值结果并限制过大的塑性铰长度。
（8）基于提出的RPC桥墩恢复力模型和塑性较长度回归公式，运用大型有限元程序Midas建立了新方案弹塑性地震响应分析模型并对其进行了延性分析。结果表明，通过修正Midas中已有的Takeda四直线恢复力模型能较好的拟合RPC桥墩恢复力模型；在E2地震作用下，主塔塔底虽已进入塑性阶段，但其塑性变形并未充分发挥，抗震设计时可适当减少其截面尺寸。最后为提高所提体系的抗震能力，基于建立的分析模型对粘滞阻尼器进行了阻尼系数和速度指数优化。结果表明，就本文所提体系而言，阻尼系数C取2000且速度指数α为0.4时，阻尼器减震效果最优，相应的塔顶纵向位移和塔底纵向弯矩最大值分别减少了35%和31%。
Based on the superior performances of RPC and CFRP materials, it is putforward for the scheme of super-long span concrete cable-stayed bridge with CFRPcables and RPC girder under the financial support of Program “Structural behaviors ofsuper-long span cable-stayed based on high performance materials”. The feasibilityof the new structure was discussed based on the results from static performances,dynamic performances, stability, wind resistance behavior and seismic resistancebehavior. This dissertation involves the following work:
(1) Taking a main span of1090m cable-stayed bridge with steel girder and steelcables as an example, a new cable-stayed bridge in the same span with RPC girder andCFRP cables was designed, in which the cable’s cross section was determined by theprinciple of equivalent cable capacity, the girder’s cross section was determined invirtual of its stiffness, shear capacity, punching capacity, local stability and localbending capacity, and the tower’s cross section was determined in virtual of itsstability and intensity.
(2) Based on the methods of finite element analysis, the comparative analysis ofthese two cable-stayed bridge schemes about static performances such as thedeflection of main girder, deviation of tower, force, and stress, etc. were carried outunder different load including dead load, vehicle load, temperature load and aerostaticload. The results show that the proposed scheme has good static performance.Compared with steel girder, The stress of RPC girder is reduced significantly, and thestress distribution is more uniform, because of the low linear expansion coefficient ofRPC which is just1/10of the steel material, the deformation of the new schemecaused by temperature effect is about1/25of the old scheme.
(3) Considering the influence of geometric nonlinearity and material nonlinearity,the static stability and the aerostatic stability of the two cable-stayed bridge schemeswere analyzed using large finite element program ANSYS. The results of staticstability analysis show that the elastic stability safety coefficient and nonlinearstability safety coefficient of these two schemes can meet the specificationrequirements, and the static stability safety coefficient of the new scheme is greaterthan that of the old scheme. Because of the higher specific stiffness and specificstrength of CFRP cables, the corresponding geometric nonlinearity could be ignored, and the buckling failure of the new scheme would be delayed with the longitudinalstiffness improvement of RPC tower. The results of aerostatic stability analysis showthat the critical wind speed of the old scheme and new scheme are179m/s and169m/sat the0degree wind attack angle, respectively, and the instability pattern of twocable-stayed bridge schemes are all bending-torsional coupling instability. Comparedwith steel girder, the vertical stiffness and the torsion stiffness of RPC girder arereduced by38%and57%, respectively, but the higher specific stiffness and specificstrength of CFRP cables and the increased dead weight of the girder would improvethe stiffness of the structure, so the critical wind speed of the new scheme is onlyreduced by about8%.
(4) The dynamic characteristics of the two cable-stayed bridge schemes wereanalyzed using large finite element program MIDAS. The results show that, althoughthe vertical stiffness of the girder are reduced by38%after RPC girder replace steelgirder, the higher specific stiffness and specific strength of CFRP cables wouldimprove the stiffness of the structure, so the frequency of vertical bending vibrationmode for the new scheme is reduced by less20%. While the longitudinal stiffness andtransverse stiffness improvement of the main tower after RPC tower replace RC towerincrease the fundamental frequency of the new scheme, and delay the occurrence ofmain tower lateral bending vibration mode.
(5) The elastic earthquake responses of these two schemes were analyzed basedon response spectrum method and time history analysis method, respectively, andseismic performance of proposed scheme was evaluated. The results show seismicperformance of the new scheme is almost same with the old scheme, and the stressand displacement of the new scheme can be satisfied with the requirement ofserviceability under the combination of dead load and earthquake force. Comparedwith the old scheme, the improvements of the longitudinal stiffness and the transversestiffness decrease the displacement of the tower top, increase the moment of the towerbottom, and give full play the high performance of RPC material. Althouth thevertical stiffness of RPC girder is less than that of steel girder, the higher specificstiffness and specific strength of CFRP cables improve the vertical stiffness of thestructure, so the vertical displacements of steel gieder and RPC girder are almost thesame under the earthquake, and that of steel girder is a little less than RPC girder.
(6) Restoring force model of Reactive Power Concrete piers was put forward.Taking Reactive Power Concrete box piers as research object, the seismic analysismodels were built by choosing the material constitutive relation including Concrete02 and Steel02and element types including Beam-with-Hinges-Element in OPENSEES,and the comparison between the experimental results of three Reactive PowerConcrete piers samples under the invariable axial force and reversed horizontal loadand the computed results proved the accuracy of the model. At the same time, thefactors affecting the seismic behavior of RPC piers were analyzed on this basis of theseismic model. Then, basing on the results of numerical analysis and cyclic loadingtests of three Reactive Power Concrete box piers samples under the invariable axialforce and reversed horizontal load, those factors affecting the restoring force modelsof the samples were considered in order to establish restoring force model of ReactivePower Concrete box piers under biaxial horizontal load. In addition, the numericalsimulation analysis was performed with the program taking into account thesecond-order effects of the axial force and biaxial laods, and the results are in goodagreement with the experimental results.
(7) Based on the biaxial bending component nonlinear analysis program,parameters which effect RPC pier plastic hinge length were analyzed, and theregression formula of RPC pier plastic hinge length was put forward. The results showthat, the plastic hinge length monotonically increases with the increase of pier heightand section size of the short side, decreases with the increase axial compression ratio,and increases at first and then decreases with the increase of horizontal loading angleand longitudinal reinforcement diameter. The strong axis plastic hinge length is lessthan the weak axis, the maximum plastic hinge length can be obtained when the loaddirection inclined about60degrees, and the plastic hinge length almost closes to zeroat high axial compression ratio. Compared the numerical results with the calculationresults of RPC pier plastic hinge length regression formula, the calculation results ofthe corresponding regression formula are in good agreement with the numericalresults and limit too much plastic hinge length.
(8) Based on the proposed RPC restoring force model and RPC pier plastic hingelength regression formula, elastic-plastic seismic response analysis model of the newscheme was built by the finite element program Midas, and the ductility seismicresponse was analyzed. The results show that the restoring force model of RPC can bewell simulated by revising Takeda restoring force model in Midas. Although thebottom of the main tower has been in the plastic stage under the E2earthquake, theplastic deformation of the plastic hinge isn’t used adequately, so the section size ofRPC tower can be reduced appropriately from the point of seismic design. Finally, toimprove the seismic resistance of the proposed system, based on the elastic-plastic seismic response analysis model, the damping coefficient and the speed index of theviscous damper was optimized. The results show that, in terms of system is proposed,the damping coefficient C of2000and the velocity index α of0.4can help the damperachieving the best damping effect, meanwhile the maximal longitudinal displacementof the tower top and bending moment of the tower bottom are reduced by35%and40%, respectively.
（1）以1090m主跨的钢索钢主梁普通混凝土索塔斜拉桥设计方案为例，拟定了一座同跨度的CFRP索RPC梁混凝土斜拉桥体系新方案。其中拉索采用等强度原则将原桥的钢索替换成CFRP索，主梁考虑截面刚度、抗剪、抗冲切、局部稳定和局部抗弯等要求将原桥的钢主梁替换成RPC主梁，主塔考虑强度和稳定需要将原桥的普通混凝土主塔替换成RPC主塔。
（2）采用有限元法分别对原方案和新方案在恒载、活载、温度荷载和静风荷载及各种荷载组合下的主梁挠度、索塔偏位、结构内力及应力等各项静力性能进行了对比分析，结果表明本文所提新方案具有良好的结构静力特性。相对于原方案，新方案在RPC主梁替换钢主梁后应力明显减少，且分布更均匀；在CFRP索替换钢索后，由于线膨胀系数不及钢材的1/10，在结构中所引起的温度变形很小，约为钢拉索的1/25。
（3）考虑几何非线性和材料非线性的双重影响，应用大型有限元通用程序ANSYS对两种方案结构的静力稳定和静风稳定性能进行分析。静力稳定分析结果表明两种方案各工况下弹性稳定安全系数和非线性稳定安全系数均满足规范要求，且新方案静力稳定安全系数较原方案有所增大。相对于原方案，新方案CFRP索由于较高的比刚度和比强度，分析时可不计入其几何非线性的影响；而RPC主塔替换后纵向刚度的改善，在一定程度上延缓了新方案结构失稳破坏。静风稳定分析结果表明，在0°风攻角下，原方案静风失稳临界风速为179m/s，新方案静风失稳临界风速为165m/s，失稳形态均为弯扭耦合屈曲失稳；相对于原方案，新方案主梁在替换后竖向刚度下降了38%、扭转刚度下降了57%，但CFRP索较高的比刚度和比强度对结构竖向刚度和扭转刚度的改善以及主梁自重的增加，使新方案失稳临界风速仅下降了8%左右。
（4）应用大型有限元程序MIDAS对两种方案进行了动力特性分析。结果表明，虽然新方案主梁替换后竖向刚度下降了38%，但CFRP索较高的比刚度和比强度改善了结构的竖向刚度，使新方案竖弯振型对应的频率下降不足20%；在RPC主塔替换普通混凝土主塔后，由于纵向刚度和横向刚度的改善，提高了新方案的基频，并延缓了主塔侧弯振型的出现。
（5）分别采用反应谱法和时程分析法对原方案和新方案进行了弹性地震响应分析，并对所提体系进行了抗震性能评价。结果表明新方案具有与原方案相近的抗震性能，且在恒载与地震力组合下新方案各部分的应力和位移均能满足正常使用要求。相对于原方案，新方案在主塔采用RPC材料后纵向刚度和横向刚度的提高，减少了地震荷载作用下主塔塔顶位移，增大了塔底弯矩，有效的发挥了RPC材料的高强性能；在拉索采用CFRP材料后比刚度和比强度的提高，改善了结构的竖向刚度，并在一定程度上弥补了RPC主梁替换钢主梁后竖向刚度下降的不足，使两种方案在地震荷载作用下主梁竖向位移基本一致，新方案略大于原方案。
（6）提出了RPC桥墩恢复力模型。以RPC箱型桥墩为研究对象，首先基于OPENSEES计算平台，选取Concrete02本构关系和Steel02本构关系，结合非线性梁柱单元，建立了RPC桥墩抗震分析模型，并通过3个常轴力RPC桥墩水平反复加载试验结果对数值分析模型进行了验证，在此基础上运用OPENSEES对RPC桥墩延性抗震性能进行了参数分析。然后基于数值分析结果和3个常轴力RPC箱型桥墩拟静力试验结果，考虑水平荷载作用方向对RPC箱型墩抗震性能的影响，建立了计入双轴水平力耦合效应的RPC箱型桥墩恢复力模型，并通过编制的双轴压弯构件非线性分析程序对恢复力模型进行了验证。
（7）基于编制的双轴压弯构件非线性分析程序对RPC桥墩塑性铰长度进行了探讨并提出了相应的塑性铰长度回归公式。结果表明，桥墩塑性铰长度随墩柱高度和截面短边尺寸的增加单调递增，随轴压比的增加单调递减，随水平加载角度和纵筋直径的增加呈先增大后减少的趋势；其中强轴塑性铰长度小于弱轴，斜向60°左右加载时塑性铰长度最大，而在高轴压比时塑性铰长度接近零。提出的塑性铰长度回归公式计算结果与数值结果对比表明，回归公式计算值能较好的吻合数值结果并限制过大的塑性铰长度。
（8）基于提出的RPC桥墩恢复力模型和塑性较长度回归公式，运用大型有限元程序Midas建立了新方案弹塑性地震响应分析模型并对其进行了延性分析。结果表明，通过修正Midas中已有的Takeda四直线恢复力模型能较好的拟合RPC桥墩恢复力模型；在E2地震作用下，主塔塔底虽已进入塑性阶段，但其塑性变形并未充分发挥，抗震设计时可适当减少其截面尺寸。最后为提高所提体系的抗震能力，基于建立的分析模型对粘滞阻尼器进行了阻尼系数和速度指数优化。结果表明，就本文所提体系而言，阻尼系数C取2000且速度指数α为0.4时，阻尼器减震效果最优，相应的塔顶纵向位移和塔底纵向弯矩最大值分别减少了35%和31%。
Based on the superior performances of RPC and CFRP materials, it is putforward for the scheme of super-long span concrete cable-stayed bridge with CFRPcables and RPC girder under the financial support of Program “Structural behaviors ofsuper-long span cable-stayed based on high performance materials”. The feasibilityof the new structure was discussed based on the results from static performances,dynamic performances, stability, wind resistance behavior and seismic resistancebehavior. This dissertation involves the following work:
(1) Taking a main span of1090m cable-stayed bridge with steel girder and steelcables as an example, a new cable-stayed bridge in the same span with RPC girder andCFRP cables was designed, in which the cable’s cross section was determined by theprinciple of equivalent cable capacity, the girder’s cross section was determined invirtual of its stiffness, shear capacity, punching capacity, local stability and localbending capacity, and the tower’s cross section was determined in virtual of itsstability and intensity.
(2) Based on the methods of finite element analysis, the comparative analysis ofthese two cable-stayed bridge schemes about static performances such as thedeflection of main girder, deviation of tower, force, and stress, etc. were carried outunder different load including dead load, vehicle load, temperature load and aerostaticload. The results show that the proposed scheme has good static performance.Compared with steel girder, The stress of RPC girder is reduced significantly, and thestress distribution is more uniform, because of the low linear expansion coefficient ofRPC which is just1/10of the steel material, the deformation of the new schemecaused by temperature effect is about1/25of the old scheme.
(3) Considering the influence of geometric nonlinearity and material nonlinearity,the static stability and the aerostatic stability of the two cable-stayed bridge schemeswere analyzed using large finite element program ANSYS. The results of staticstability analysis show that the elastic stability safety coefficient and nonlinearstability safety coefficient of these two schemes can meet the specificationrequirements, and the static stability safety coefficient of the new scheme is greaterthan that of the old scheme. Because of the higher specific stiffness and specificstrength of CFRP cables, the corresponding geometric nonlinearity could be ignored, and the buckling failure of the new scheme would be delayed with the longitudinalstiffness improvement of RPC tower. The results of aerostatic stability analysis showthat the critical wind speed of the old scheme and new scheme are179m/s and169m/sat the0degree wind attack angle, respectively, and the instability pattern of twocable-stayed bridge schemes are all bending-torsional coupling instability. Comparedwith steel girder, the vertical stiffness and the torsion stiffness of RPC girder arereduced by38%and57%, respectively, but the higher specific stiffness and specificstrength of CFRP cables and the increased dead weight of the girder would improvethe stiffness of the structure, so the critical wind speed of the new scheme is onlyreduced by about8%.
(4) The dynamic characteristics of the two cable-stayed bridge schemes wereanalyzed using large finite element program MIDAS. The results show that, althoughthe vertical stiffness of the girder are reduced by38%after RPC girder replace steelgirder, the higher specific stiffness and specific strength of CFRP cables wouldimprove the stiffness of the structure, so the frequency of vertical bending vibrationmode for the new scheme is reduced by less20%. While the longitudinal stiffness andtransverse stiffness improvement of the main tower after RPC tower replace RC towerincrease the fundamental frequency of the new scheme, and delay the occurrence ofmain tower lateral bending vibration mode.
(5) The elastic earthquake responses of these two schemes were analyzed basedon response spectrum method and time history analysis method, respectively, andseismic performance of proposed scheme was evaluated. The results show seismicperformance of the new scheme is almost same with the old scheme, and the stressand displacement of the new scheme can be satisfied with the requirement ofserviceability under the combination of dead load and earthquake force. Comparedwith the old scheme, the improvements of the longitudinal stiffness and the transversestiffness decrease the displacement of the tower top, increase the moment of the towerbottom, and give full play the high performance of RPC material. Althouth thevertical stiffness of RPC girder is less than that of steel girder, the higher specificstiffness and specific strength of CFRP cables improve the vertical stiffness of thestructure, so the vertical displacements of steel gieder and RPC girder are almost thesame under the earthquake, and that of steel girder is a little less than RPC girder.
(6) Restoring force model of Reactive Power Concrete piers was put forward.Taking Reactive Power Concrete box piers as research object, the seismic analysismodels were built by choosing the material constitutive relation including Concrete02 and Steel02and element types including Beam-with-Hinges-Element in OPENSEES,and the comparison between the experimental results of three Reactive PowerConcrete piers samples under the invariable axial force and reversed horizontal loadand the computed results proved the accuracy of the model. At the same time, thefactors affecting the seismic behavior of RPC piers were analyzed on this basis of theseismic model. Then, basing on the results of numerical analysis and cyclic loadingtests of three Reactive Power Concrete box piers samples under the invariable axialforce and reversed horizontal load, those factors affecting the restoring force modelsof the samples were considered in order to establish restoring force model of ReactivePower Concrete box piers under biaxial horizontal load. In addition, the numericalsimulation analysis was performed with the program taking into account thesecond-order effects of the axial force and biaxial laods, and the results are in goodagreement with the experimental results.
(7) Based on the biaxial bending component nonlinear analysis program,parameters which effect RPC pier plastic hinge length were analyzed, and theregression formula of RPC pier plastic hinge length was put forward. The results showthat, the plastic hinge length monotonically increases with the increase of pier heightand section size of the short side, decreases with the increase axial compression ratio,and increases at first and then decreases with the increase of horizontal loading angleand longitudinal reinforcement diameter. The strong axis plastic hinge length is lessthan the weak axis, the maximum plastic hinge length can be obtained when the loaddirection inclined about60degrees, and the plastic hinge length almost closes to zeroat high axial compression ratio. Compared the numerical results with the calculationresults of RPC pier plastic hinge length regression formula, the calculation results ofthe corresponding regression formula are in good agreement with the numericalresults and limit too much plastic hinge length.
(8) Based on the proposed RPC restoring force model and RPC pier plastic hingelength regression formula, elastic-plastic seismic response analysis model of the newscheme was built by the finite element program Midas, and the ductility seismicresponse was analyzed. The results show that the restoring force model of RPC can bewell simulated by revising Takeda restoring force model in Midas. Although thebottom of the main tower has been in the plastic stage under the E2earthquake, theplastic deformation of the plastic hinge isn’t used adequately, so the section size ofRPC tower can be reduced appropriately from the point of seismic design. Finally, toimprove the seismic resistance of the proposed system, based on the elastic-plastic seismic response analysis model, the damping coefficient and the speed index of theviscous damper was optimized. The results show that, in terms of system is proposed,the damping coefficient C of2000and the velocity index α of0.4can help the damperachieving the best damping effect, meanwhile the maximal longitudinal displacementof the tower top and bending moment of the tower bottom are reduced by35%and40%, respectively.
引文
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