PSI - Issue 44

Francesco Nigro et al. / Procedia Structural Integrity 44 (2023) 1704–1711 F. Nigro, R. Falcone, E. Martinelli/ Structural Integrity Procedia 00 (2022) 000–000

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1. Introduction The European Environmental Agency (2020) recently stated that Europe has the highest proportion of land use on the globe, with respect to the other continents. However, since land is a finite resource, Governments are strongly encouraging the upgrading and the reuse (rather than the demolition) of older structures. Moreover, recent estimates of Italian CNI (2012) outlined that huge investments are needed to enhance the safety of many existing Italian buildings, since only the 2% of them were built after the year 2000, when technical standards began to impose really restrictive criteria. In the most of cases, the required structural performance can be achieved by means of a combination of member level techniques (steel jacketing, FRP wrapping) and structure-level techniques (steel bracing, damper devices, shear walls), although it is really hard to find in the scientific literature any agreed design rules for such combination. Since the reduction of seismic vulnerability of RC structures is usually addressed relying upon the practitioners’ subjective skills, the design of the upgrading interventions is not usually regarded as an optimization problem, although many recently-developed Soft Computing techniques can be adapted to this kind of civil engineering problem, as highlighted by Falcone et al. (2020). In this respect, Di Trapani et al. (2022) faced the problem of optimizing retrofit intervention of non-conforming RC structures, even taking into account the influence of masonry infills on the structural response, formulating a Genetic Algorithm (GA) while Papavasileiou et al. (2020) -through a numerical optimization procedure- were able to compare the effectiveness of different retrofit techniques on frame structures provided with steel-concrete composite columns. Moreover, Falcone (2017) formulated an optimization procedure based on a Genetic Algorithm (GA) to determine the “optimal” solutions with respect to a previously defined criterion for the seismic retrofit of RC structures. By means of an iterative procedure, based on the application of the so called genetic operators, Falcone et al. (2019) showed that is possible to obtain different retrofit solution varying some relevant algorithm parameters, in order to support the engineering choice with a result that is based upon one or more objective criteria. In the proposed procedure, the main GA operators (namely, selection, crossover, and mutation) operate on the candidate retrofitting solutions, combining both member and structure-level techniques, until the (approximately) cheapest solution is found. Thus, it is possible to support the engineering choice with a result that is based upon one or multiple objective criteria previously defined by the engineer, folding together the variety of requirements coming from structural performance, sustainability criteria, durability and economy, as well. In the present paper, Section 2 offers a short overview of the main steps of the procedure and of its latest advancements, while Section 3 describes the main aspects concerning the analyses presented herein. The main results of the applications are summarized in Section 4. 2. Summary of the GA procedure A general optimization procedure based on a Genetic Algorithm (GA) relies on the definition of an objective function, usually named as f(x) , aimed at measuring the “fitness” of the chromosomes (namely, individuals), which represent the candidate solution of the problem. After the definition of the first population of chromosomes, at each “generation” of the procedure the seismic performance and the fitness of each chromosome are evaluated. Hence, the genetic operators are applied in order to increase the fitness of the population, with the aim of optimizing the objective function. 2.1. Definition of the chromosomes Each chromosome collects in its genes all the design variables which describe the candidate solution, as it indicates the elements that are subjected to a “local” (member-level) intervention and the bays where the “global” (structure level) are installed. Consequently, the number of design variables is given by the total number of columns (that can be interested by the presence of a local intervention) plus the number of bays (beams) of a single floor, since the bracing area at a certain level of the structure is proportional to the one at the bottom floor by means of a factor that takes into account the structure weight distribution in height. More specifically, each chromosome can be ideally divided in two parts: