material modelling of reinforced concrete at elevated temperatures

124 Pages·2011·5.56 MB·English

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
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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
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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.
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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.
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