Seismic upgrading of RC frames as a constrained optimisation problem: a rational solution based on Genetic Algorithms

Seismic assessment and retrofitting of existing RC structures is one of the most timely and tasks for modern structural engineers all over the World. As a matter of fact, the majority of existing structures have been realised in the past decades and designed either according to old seismic codes or only taking into consideration gravitational loads. Therefore, because of the current seismic safety standards, they do no conform to the current codes and need to be upgraded, their “capacity” is generally lower than the corresponding seismic “demand” in a performance-based design framework. Several techniques are currently utilised to either enhance capacity in under designed members: they are generally referred to as “member-level” techniques. On the other hand, other techniques rather aim at reducing demand on the structural as a whole by adding substructures to the existing one: they are generally referred to as “structure-level” techniques. Although these two classes of techniques are often considered as part of alternative approaches for seismic upgrading of existing structures, several studies have demonstrated the potential of combining member- and structure-level techniques, whose synergistic effect can lead to a more efficient design. In this light, seismic upgrading of RC structures can be regarded as a constrained minimisation problem, where a given objective functions (e.g. the intervention cost or other global parameters related, for instance, to its environmental impact) has to be minimised under the constraint that the seismic performance (at all the relevant Limit States) conforms to the requested seismic safety standards. Since the number of potential combinations of member- and structure-level interventions is very wide, Genetic Algorithms (GAs) can be fruitfully employed in determining their “optimal” combination. This paper will outline recent advancements in the in-house implementation of a GA-based Python code, combining member- and structure-level intervention techniques, in order to catch “the most feasible” upgrading solution according to a previouslydefined optimization criterion. Particular consideration will be given to how the choice of different objective functions can drive the results deriving from the optimization procedure, taking into account not only the economical, but also the ecological cost associated with the interventions needed to achieve the desired seismic performance.