Optimal design of reinforcement of masonry arches = Progetto ottimo di rinforzi di archi in muratura

The preservation of Italian architectural heritage is of crucial importance and requires ongoing interventions to ensure its structural integrity. Masonry constructions are designed to withstand gravitational loads through their geometric configuration; however, they are susceptible to instabilities induced by slight changes of the loading distribution. The recent seismic events highlighted this weak mechanical behavior of masonry structures and thus the need for strengthening interventions. One of the commonly used methods for strengthening masonry structures is the application of tensile reinforcements, which constraint the kinematics of the masonry system and consequently increase the collapse load. Nevertheless, as evidenced by recent seismic events, current strengthening techniques have demonstrated ineffective in preserving masonry constructions and, in some cases, have even contributed to induce unpredicted collapse mechanisms. In order to bridge the gap between structural safety and preservation, innovative strengthening materials such as Fiber Reinforced Cementitious Matrix composites (FRCM), have been developed and are increasingly being used due to their greater compatibility with the substrates they are intended to reinforce. However, experimental results have demonstrated that the presence of reinforcement significantly modifies the structural behavior of masonry, leading to different collapse modes such as crushing or sliding between joints. Therefore, a key purpose of this thesis is to develop a design procedure for “optimal” reinforcement interventions for masonry arches that increase the collapse multiplier without excessively constraining the structural system. This approach allows for limiting the extent of strengthening interventions while preserving the typical mechanical behavior of masonry arches. In the framework of the non-standard limit analysis for dry masonry systems, an optimization algorithm is implemented to design the optimal reinforcement by defining the collapse load multiplier and the related mechanism. In particular, the limit analysis problem with a non-associative flow rule involves the solution of the nonlinear programming (NLP) as a sequence of linear programming problems (LP). Then, this algorithm is enhanced with additional constraint equations in the linear programming problem to take into account the inserted reinforcement. A first solution considered is the use of elastic reinforcements capable to limit the opening at the interface endpoints at the extrados or the intrados where the reinforcement is applied, inhibiting a hinge to occur on the opposite side of the interface. A second option is employing elastic perfectly plastic reinforcements that give the structure some degree of ductility, since after the yielding limit the reinforcement is capable to freely deform. The implemented algorithm is then validated through numerical simulations.