MATERIAL MODELLING OF REINFORCED CONCRETE AT ELEVATED TEMPERATURES Master Thesis February 2011 Fire Safety, Section for Building Design, Department of Civil Engineering, the Technical University of Denmark Josephine Voigt Carstensen, s052204 Material Modelling of Reinforced Concrete at Elevated Temperatures M.Sc. inCivilEngineering-MasterThesiscreditedwith30ECTSpoints ProjectPeriod: 2010.09.13-2011.02.11 Language: English FireSafetyattheSectionforBuildingDesign DepartmentofCivilEngineering TechnicalUniversityofDenmark In collaboration with: BRECentreforFireSafetyEngineering TheUniveristyofEdinburgh Supervisor: External Supervisor: Dr. Grunde Jomaas Dr. Pankaj Pankaj Assistant Professor Senior Lecturer Department of Civil Engineering School of Engineering Technical University of Denmark The University of Edinburgh Handed in 2011.02.11 by: Josephine Voigt Carstensen, s052204 i Abstract Previous disasters have elucidated that accurate and realistic modelling of concrete behaviour at elevated temperatures is fundamental for the safe design of, for example, nuclear and struc- tures exposed to fire. However, when the same model is evaluated with different mesh sizes, the existing models for the behaviour of concrete at elevated temperatures are subject to problems withconvergenceofresultsintheFiniteElement(FE)analysis. Theseproblemsariseasaresult oftheproblemoflocalizationofdeformationsassociatedwiththepost-peakresponseofconcrete. This current research focuses on the modelling of the uniaxial behaviours of reinforced concrete at elevated temperatures and in particular on the key issues associated with the post-peak be- haviour. It is generally recognized that in order to obtain mesh independent results of models of rein- forced concrete in FE-analysis at ambient conditions, a fracture energy based material model must be adopted. In tension, such models are widely used and in most FE-codes, for example ABAQUS, it is possible to define the tensile post-peak behaviour in three ways; either through an element size dependent stress-strain relation, through a stress-displacement formulation or by giving the tensile fracture energy and letting ABAQUS define the behaviour. However, if reinforcedconcreteistobeconsidered,thetensiledefinitionmustaccountforthetensionstiffen- ing effect that gradually shifts the load-bearing capacity from the concrete to the reinforcement as the cracking progresses. This issue can be tackled by defining an element size dependent interactionstresscontributionthatiscombinedwiththeconcretecontributionforthedefinition ofthepost-peakbehaviour. Incompressionthefractureenergybasedbehaviourmodelsareless used and the compressive fracture energy is, for example, not discussed in any current codes and it is generally examined by very few. To apply a fracture energy based compressive model in a FE-analysis, an element size dependent stress-strain formulation must be used. In this current research, the existing models for the ambient condition have been extended to elevated temperatures, largely by applying the material properties at a given elevated temper- ature to the current formulation. Therefore, the existing models have been evaluated prior to the extension and it has been found necessary to express limits for their application. It is well established that a limit on the maximum element size exists. However, herein it has been found that restrictions on the minimum element size and, if modelling the tension stiffening through the definition of an interaction stress contribution, on the minimum level of reinforcement ad- missible also apply. As experimental data is currently not available on the evolution of the compressive and the tensile fracture energy with temperature, the fracture energies inherent in the existing elevated temperature models have been examined. It has been found that the tensile fracture energy inherent in the currently available model follows the decay function for material strength. The iii compressive fracture energy has been based on the models by four current compressive models where two considers solely the instantaneous stress-related strain and two includes the effects of the LITS. It has been established that the current compressive elevated temperature models does not agree on the post-peak behaviour and that the LITS does not seem to have an effect on the post-peak response. The limits of application are extended to elevated temperatures by expressing a validity range for the element sizes and a minimum reinforcement ratio. It has been found that up to about 500◦C, the maximum element size is typically governed by the tensile properties after which the compressive parameters are governing. Once the compressive model becomes governing, it only provides meaningful results within a very limited range of mesh-sizes. This range should be considered the new validity domain of the model. Thisnovelmodelfortheuniaxialbehavioursofreinforcedconcreteatelevatedtemperaturescan readily be applied for FE analysis, for example in ABAQUS, and, if the modelling is performed within the limits of application, it is possible to get mesh independent results of the analyses with different mesh configurations. Preface This project is a M.Sc. thesis of 30 ECTS points created in the period September 13th 2010 to February 11th 2011. A M.Sc. thesis is a compulsary project in order to fulfill the requirements for the M.Sc. programme in Civil Engineering at the Technical University of Denmark, (DTU). The project has been carried out for the Fire Safety Group at the Section for Building Design, Department of Civil Engineering at the Technical University of Denmark in collaboration with at the BRE Centre for Fire Safety at the University of Edinburgh. TheinternalsupervisoroftheprojecthasbeenDr. GrundeJomaas(AssistantProfessor, DTU) and the external supervisor has been Dr. Pankaj Pankaj (Senior Lecturer, Edinburgh). The work presented in the thesis was conducted at the University of Edinburgh. v Acknowledgements First, a great amount of appreciation must be given to the BRE Center for Fire Safety En- gineering at the University of Edinburgh and especially to the students and staff in the John Muir Building for creating a welcoming and inspiring research environment. My visit there has proved to be a highly educative experience, thanks both to the academic and the non-academic support received at the premises. A special expression of gratitude is given to Prof. José L. Torero for setting up the practical framework, without which this project would not have been accomplished. A very special thanks is directed to Dr. Pankaj Pankaj for all his guidance and encouragement. I have immensely appreciated that he has always taken time to patiently explain the arisen problems - no matter the magnitude. His ability to make even the most complex problems understandable is something I profoundly admired. On this note appreciation is also dedicated to Prof. Kristian D. Hertz (DTU) and Dr. Martin Gillie for their clarifications of puzzling definitions. Will Kingston is to be deeply thanked for the helpful discussions and useful hints throughout the project period. Especially his calm introduction to ABAQUS modelling at the project start and his patient answers to emerging ABAQUS related questions have been beyond compare. On this note Adam Ervine, Kate Andersson and Joanne Knox must also be recognized along with Rory Hadden, Cristián Maluk, Nicolas Bal, Steffen Kahrmann and Dr. Francesco Colella. Further, a particularly gratefulness is given to Dr. Grunde Jomaas (DTU) for his friendly ap- proach and guidance. He must be recognized for creating the contact between the collaborators of the project and for being an tremendous source of inspiration. His mentoring and guidance through the project planning and execution, as well as through decision making about further professional career, have had great effects on both the project at hand and on future choice of occupation. LærkeMikkelsen(DTU)andMikiKobayashi(DTU)areacknowledgedforhelpingwithretriev- ing literature and Mads Mønster Jensen (DTU) for his clarification of the mysteries of concrete technology. Last but not least, gratitude is directed to the OTICON Foundation, Reinholdt W. Jorck’s Foundation, KAB’s studielegat, the Department of Civil Engineering at the Technical Univer- sity of Denmark and BRE Center for Fire Safety Engineering at the University of Edinburgh for the received financial support. vii