Optimal design of FRP retrofitting for seismic resistant RC frames

In earthquake-prone areas, in Italy and Europe, a great number of residential, commercial and public buildings is made of reinforced concrete (RC). Many of them were designed according to standards which did not take into account properly earthquake-induced effects on the structure, and thus may turn out to be particularly vulnerable. Recent catastrophic seismic events (L’Aquila, 2009; Emilia, 2012; Amatrice, 2016) have shown that RC structures, if not correctly designed, may suffer from substantial damage in case of strong earthquakes. Thus, one of the most pressing issues in structural engineering is the assessment and the strengthening of existing heritage. While under gravitational loading the columns are mainly subjected to axial forces, the horizontal forces acting during earthquakes induce strong bending moments which may lead the structure to brittle collapse and undesired failure mechanisms. The use of Fibre-Reinforced Polymers (FRP) jackets has proved to be particularly effective thanks to the enhancement in strength and ductility it can provide to the unreinforced columns, and limited invasiveness of the technique. Over the last years several researchers investigated the structural behaviour of RC reinforced elements and assemblies, aiming at improving the accuracy of the design. Zou et al (2007) showed that the seismic response of a FRP-retrofitted RC frame can be efficiently optimized assuming the thicknesses of the FRP jackets as the major design variables, and solving the optimization problem by using the principle of virtual work and the Taylor series approximation. The cited work shows the advantages of the FRP; however, this approach presents some drawbacks. Firstly, in order to have tractable analytical expressions for the objective function, simplified assumptions are to be considered, e.g. bilinear moment-rotation curve for the plastic hinges, without proper consideration of strength degradation in the constitutive relationship. Secondly, even though improvements in strength, ductility and collapse mechanism are observed, they are not made explicit in the optimization analysis, formulated simply as to minimize the FRP weight while satisfying interstorey drift code prescriptions. In this paper, based on the work developed in (Chisari and Bedon, 2016). it is shown that remarkable improvement in the formulation of the problem may be achieved if a more general approach is utilised. In particular, multi-objective optimization by means of Genetic Algorithms (GA) is used for the design of FRP jackets. To show the feasibility of the proposed approach, a reference case study is investigated. The goals of the multi-objective optimization analysis are then given by (i) maximization of the RC frame ductility and (ii) minimization of the volume (hence the cost) of FRP jackets, while satisfying the current provisions of the seismic design standards in use for concrete structures.