DEPARTAMENTO DE MECÁNICA DE MEDIOS CONTINUOS Y TEORÍA DE ESTRUCTURAS Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos Universidad Politécnica de Madrid NONLINEAR SEISMIC BEHAVIOUR OF CONCRETE ARCH BRIDGES Pedram Manouchehri In Partial Fulfilment of the Requirements for the Degree of: Máster Universitario en Ingeniería de las Estructuras, Cimentaciones y Materiales (Master of Science) Advisor: Prof. Dr. Miguel Ángel Astiz Suárez September 2015 Nonlinear seismic behaviour of concrete arch bridges Universidad Politécnica de Madrid Madrid, September 2015 La composición de este texto se ha realizado íntegramente en LATEX. Pedram Manouchehri Civil Engineer Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos Departamento de Mecánica de Medios Continuos y Teoría de Estructuras (Department of Continuum Mechanics and Theory of Structures) Universidad Politécnica de Madrid Profesor Aranguren s/n Madrid 28040 Teléfono: (+34) 91 336 66 59 Correo electronico: [email protected] Dedicated to my Parents For their endless support and encouragements Acknowledgement ThismasterthesishasbeencarriedoutattheDepartmentofContinuumMechanics and Theory of Structures, Universidad Politécnica de Madrid , in September 2015. A number of people deserve thanks for their support and help. It is therefore my greatest pleasure to express my gratitude to them all in this acknowledgement. First and foremost I offer my sincerest gratitude to my advisor, Prof. Miguel Ángel Astiz Suárez, who has supported me throughout my thesis with his patience andknowledge. IattributethelevelofmyMaster’sdegreetohisencouragementand effort and without him this thesis, too, would not have been completed or written. One simply could not wish for a better or friendlier supervisor. My sincere thanks also goes to my fellow lab mates in bridge department Sergio Blancas Saiz and Ángel Fernández Gómez for their companionship and helping me get through, also made many helpful suggestions. Last but not least, I would like to thank my friend Shadi Samavi for her helps in three dimensional models and graphical figures. Contents 1 Introduction 1 2 Modelling and assumptions 5 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Arch bridge description . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Geometric aspects . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Boundary condition . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.3 Deck connections . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Concrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.2 Reinforcement steel . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.3 Elastomer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.4 Finite element type . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Seismic analysis 17 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 The mathematical system of dynamics . . . . . . . . . . . . . . . . . 17 3.3 Elastic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3.1 Direct Response History Analysis: DRHA . . . . . . . . . . . 18 3.3.2 Modal Response History Analysis: MRHA . . . . . . . . . . . 19 3.3.3 Modal Response Spectrum Analysis: MRSA . . . . . . . . . . 21 3.4 Inelastic analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.4.1 Nonlinear Response History Analysis: NL-RHA . . . . . . . . 22 3.4.2 Modal Pushover Analysis: MPA . . . . . . . . . . . . . . . . 23 3.4.3 Extended Modal Pushover Analysis: EMPA . . . . . . . . . . 25 3.4.4 Coupled Nonlinear Static Pushover Analysis: CNSP . . . . . 28 4 The ground motion and discussion of results 31 4.1 Ground motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 4.2 Discussion of results . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.2.1 Result of Elastic procedures . . . . . . . . . . . . . . . . . . . 32 4.2.2 Results of Inelastic procedures . . . . . . . . . . . . . . . . . 32 4.3 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 A Description of pushover analyses 40 A.1 Modal Pushover Analysis: MPA . . . . . . . . . . . . . . . . . . . . . 40 A.2 Extended Modal Pushover Analysis: EMPA . . . . . . . . . . . . . . 42 A.3 Coupled Nonlinear Pushover Analysis: CNSP . . . . . . . . . . . . . 44 B Ground motion definition 48 Contents vii Bibliography 51 Chapter 1 Introduction Arch bridge structural solution has been known for centuries, in fact the simple nature of arch that require low tension and shear strength was an advantage as the simple materials like stone and brick were the only option back in ancient centuries. By the pass of time especially after industrial revolution, the new materials were adopted in construction of arch bridges to reach longer spans. Nowadays one long spanarchbridgeismadeofsteel, concreteorcombinationofthesetwoas"CFST"1, astheresultofusingthesehighstrengthmaterials, verylongspanscanbeachieved. The current record for longest arch belongs to Chaotianmen bridge over Yangtze riverinChinawith552metersspanmadeofsteelandthelongestreinforcedconcrete type is Wanxian bridge which also cross the Yangtze river through a 420 meters span (see figure 1.1). Today the designer is no longer limited by span length as long Figure 1.1: Wanxian Bridge: The current longest RC arch bridge with 420m span. Photograph by [Glabb 2012] 1CFST stands for Concrete Filled Steel Tubular 2 as arch bridge is the most applicable solution among other approaches, i.e. cable stayed and suspended bridges are more reasonable if very long span is desired (A comparison between largest spans of every type is presented in figure 1.3). Like Akashi Kaikyō Bridge Great Belt Fixed Link East Bridge Chaotianmen BridgeSydney Harbour BridgeRussky Bridge Millau Viaduct Airbus A380 0 100 m © 2015CMG Lee 0 300 ft Golden Gate Bridge (USA, 1932-37) Rialto Bridge (Italy, 1588-91) Tower Bridge (England, 1886-94) Forth Bridge (Scotland, 1882-90) RMS Titanic Figure 1.2: A comparison of famous long span bridges. Figure by [Cmglee 2015] any super structure, the economical and architectural aspects in construction of a bridge is extremely important, in other words, as a narrower bridge has better appearance, it also require smaller volume of material which make the design more economical. Design of such bridge, beside the high strength materials, requires precise structural analysis approaches capable of integrating the combination of material behaviour and complex geometry of structure and various types of loads whichmaybeappliedtobridgeduringitsservicelife. Dependonthedesignstrategy, analysis may only evaluates the linear elastic behaviour of structure or consider the nonlinear properties as well. Although most of structures in the past were designed to act in their elastic range, the rapid increase in computational capacity allow us to consider different sources of nonlinearities in order to achieve a more realisticevaluationswherethedynamicbehaviourofbridgeisimportantespeciallyin seismiczoneswherelargemovementsmayoccurorstructureexperienceP−∆effect during the earthquake. The above mentioned type of analysis is computationally expensive and very time consuming. In recent years, several methods were proposed inordertoresolvethisproblem. Discussionofrecentdevelopmentsonthesemethods and their application on long span concrete arch bridges is the main goal of this research. Accordingly available long span concrete arch bridges have been studied to gather the critical information about their geometrical aspects and properties of their materials. Based on concluded information, several concrete arch bridges were designed for further studies. The main span of these bridges range from 100 to 400 meters. The Structural analysis methods implemented in in this study are as following: Elastic Analysis: Direct Response History Analysis (DRHA): This method solves the direct equation of motion over time history of applied acceleration or imposed load in linear elastic range. Modal Response History Analysis (MRHA): Similar to DRHA, this method is also based on time history, but the equation of motion is simplified to 3 Figure 1.3: The arch of Almonte railway bridge during construction. Personal photograph by Pedram Manouchehri. 25 Mar 2015. single degree of freedom system and calculates the response of each mode independently. Performing this analysis require less time than DRHA. Modal Response Spectrum Analysis (MRSA): Asitisobviousfromitsname, this method calculates the peak response of structure for each mode and com- bine them using modal combination rules based on the introduced spectra of ground motion. This method is expected to be fastest among Elastic analysis. Inelastic Analysis: Nonlinear Response History Analysis (NL-RHA): The most accurate strat- egy to address significant nonlinearities in structural dynamics is undoubtedly thenonlinearresponsehistoryanalysiswhichissimilartoDRHAbutextended to inelastic range by updating the stiffness matrix for every iteration. This oneroustask, clearlyincreasethecomputationalcostespeciallyforunsymmet- rical buildings that requires to be analyzed in a full 3D model for taking the torsional effects in to consideration. Modal Pushover Analysis (MPA): The Modal Pushover Analysis is basically the MRHA but extended to inelastic stage. After all, the MRHA cannot solve the system of dynamics because the resisting force f (u,u˙) is unknown for s inelastic stage. The solution of MPA for this obstacle is using the previously recorded f to evaluate system of dynamics. s