Abstract The out-of-plane (OOP) seismic vulnerability of unreinforced masonry (URM) walls remains a critical concern, as highlighted by recent earthquakes. Full-length injected tie-rods (FIT) have emerged as a promising strengthening technique due to their feasibility and minimal visual impact on heritage masonry structures. This study investigates the OOP behavior of U-shaped URM walls retrofitted with FIT through validated finite element (FE) modeling, extensive parametric analyses, and a design-oriented kinematic approach. The FE models accurately reproduced the structural responses of URM walls and the bond mechanism of injected rods when compared with literature experimental data. Two modeling strategies, solid-element and truss-element representations, provided similar accuracy, with the latter offering substantial simplification for large-scale analyses. Parametric results indicated that while FIT retrofitting did not markedly change the initial stiffness, it significantly improved OOP capacity and post-peak stiffness, with multiple tie-rods at two different heights and larger rod diameters proving most effective, although benefits diminished beyond a threshold diameter. Dynamic simulations confirmed improved drift control and delayed failure across various excitations. A modified kinematic analysis method was proposed, incorporating deformation-dependent steel contribution and, for the strengthened configuration, considering only the OOP-loaded front-wall rods in line with FE evidence of preserved corner integrity and negligible mobilisation of transverse-wall rods, which closely matched FE predictions with an average error of ~ 7%. These findings provide both a reliable numerical framework and a practical analytical tool for designing FIT-retrofitted masonry walls.
Gokhan Yucel (Sun,) studied this question.