Nonlinear finite-element analysis of reinforced-concrete beams retrofitted with externally bonded fibre-reinforced polymers

Research output: ThesisDoctoral Thesis


Three dimensional (3D) nonlinear finite–element (FE) models have been developed within the FE code ABAQUS to simulate the loading–unloading–reloading behaviour of full–scale reinforced concrete (RC) beams externally retrofitted with carbon–fibre–reinforced polymers (CFRP) sheets and tested under four–point bending. Engineers embarking on such types of simulations still face considerable challenges, which include the computational cost of the analyses, the choice of an optimal solution scheme, the difficulties in achieving convergence with implicit solution schemes, the stability and accuracy of the solution with dynamic explicit solution schemes and the choice of optimal material models and finite–elements for concrete, steel rebars, CFRP and the steel–concrete and CFRP–concrete interfaces, the calibration of material constants and the validation of the modelling procedures. A critical analysis of the literature reveals the lack of comprehensive studies providing clear guidelines within this wide range of modelling strategies and options. Therefore, the main aim of this thesis is to critically evaluate the most adopted of these modelling options, focussing on cases where the widely used ‘concrete damaged–plasticity’ model (CDP) is used for concrete. The beams studied included two non–retrofitted RC control beams, which differed in length and cross–sectional areas, and two RC beams retrofitted in flexure with CFRP sheets. To validate the modelling procedures, numerical predictions were compared with experimental results previously obtained within the research group and available in the literature.

In terms of solution schemes, it was possible to achieve good agreement between numerical and experimental results, using both static implicit and dynamic explicit solution schemes but, both the explicit and implicit schemes required non–negligible amount of numerical damping, and possible reasons for this result were suggested. In the case of dynamic explicit procedures, particular attention needs to be paid to the loading variation with time and it is shown that time increments that ensure stability do not necessarily also lead to sufficient accuracy.

Comprehensive sensitivity analyses on the input parameters defining the CDP model were also conducted in order to provide guidance on their calibration. The CDP was defined based on both stress–displacement and stress–strain post–failure relationships of bi–linear, exponential and linear shapes. Using stress–displacement or stress–strain relationships does not normally lead to different results as long as the aspect ratio of the FE mesh is kept relatively close to one. This, however, is not always possible and can explain some differences obtained in the case of the retrofitted beams.

Steel reinforcement was modelled using truss or beam elements ‘embedded’ within the 3D mesh of concrete elements, and while they normally provide similar results, discrepancies were found, particularly in the post–yield phase, when using truss elements in a geometrically nonlinear analysis, which can be an important issue when studying cases of progressive collapse. The effect of using different types of elements and meshes for concrete was widely investigated, with particular regards to their effect on the predicted crack patterns.

Ultimately, through the results of this work, including but not limited to those highlighted above, a wide range of experimentally validated nonlinear modelling procedures and detailed guidelines on how to choose among the various options available have been produced. It is believed that these will be useful both to advanced engineering analysts (e.g. for forensic investigations, where computational cost may be justified) and to researchers. The latter can find numerical modelling as an effective way to replace significant part of experimental testing to appraise and guide new strengthening techniques or materials as well as to develop and preliminarily validate new design guidelines in codes of practice.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Brunel University
  • Alfano , Giulio, Supervisor, External person
  • Cashell, Katherine, Supervisor, External person
Thesis sponsors
Award date31 Jan 2017
Place of PublicationUxbridge
Publication statusPublished - 13 Feb 2017


  • Dynamic explicit
  • Static implicit
  • Damage-plasticity coupling
  • Perfect pond
  • Cohesive model


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