Optimal disposition of tie rods in masonry historical buildings through computerized upper bound limit analysis combined with genetic algorithm or surrogate model

Abstract Tie rods are effective in masonry seismic upgrading because they can change considerably the collapse mechanism triggered, thus increasing the load carrying capacity. In this context, two fast algorithms for the optimal placement of tie rods in historical masonry buildings subjected to seismic loads are proposed. They are coupled with an upper bound finite element limit analysis code where masonry is discretized with infinitely resistant hexahedron elements connected by quadrilateral interfaces where all internal dissipation takes place. Rods are modelled by means of rigid plastic trusses, whose extremes are joined to hexahedron centroids. Assuming a certain number of rods to use, their optimal disposition can be determined with a direct combinatorial approach, taken as reference for the algorithms proposed. First two subsets of elements, one for the heads and the other for the tails, are selected in the mesh to define rod domain of installation. Then all possible permutations for rod layout are computed taking in input the two subsets separately. Clearly, such direct procedure is computationally very demanding and would need parallelization. In alternative, the paper proposes both a Genetic Algorithm and a Surrogate model to converge more rapidly to the most suitable geometric configuration that secures the maximization of the load carrying capacity. The proposed methodology is applied to the church of San Martino dei Gualdesi, a representative historical church located in central Italy. The results show that both the Genetic Algorithm and the Surrogate Model can identify optimal tie-rod configurations reducing the computational burden associated with the combinatorial approach.