COMBINED GENETIC ALGORITHM AND LIMIT ANALYSIS APPROACH FOR THE OPTIMAL DESIGN OF TIE RODS IN HISTORICAL MASONRY STRUCTURES

Seismic strengthening is essential for preserving many historical masonry structures, especially in southern Europe. Among all possibilities, tie rods are probably the most interesting for effectiveness, feasibility, and cost efficiency, at the same time exhibiting minimal architectural impact. In this paper, an automatic optimal design - in terms of number and position of strengthening elements - of tie rods used for the seismic retrofitting of existing masonry structures is presented. It relies on the utilization of a code based on Limit Analysis LA combined with an optimizer of the position of the rods based on a Genetic Algorithm. The LA approach consists of a discretization of the structure with infinitely resistant hexahedron elements and quadrilateral rigid-plastic interfaces, the latter characterized by a Mohr-Coulomb behavior where non-linearity is lumped. Different distributions of horizontal loads can be applied, which include user defined directions of the seismic action and a variety of profiles along the height. The best tie rod design, which provides the maximum structural performance of the intervention, is identified by the genetic algorithm. Some constraints are introduced in the genetic algorithm to find structurally meaningful solutions, such as a preliminary assessment of the feasible domain where tie rods can be installed, a minimum and maximum number of tie rods, and their orientation. The procedure is benchmarked for an existing single-nave church with an embedded bell tower.