A kinematic limit analysis approach for seismic retrofitting of masonry towers through steel tie-rods

The paper provides an insight into the seismic strengthening of masonry towers by means of horizontal and vertical steel tie-rods. The approach is based on the kinematic theorem of limit analysis with pre-assigned failure mechanisms. Among all the possible ones, five of them commonly observed during post-earthquake surveys are selected: (#1) vertical splitting; (#2) base rocking; (#3) Heyman's diagonal rocking; (#4) combination of splitting and diagonal rocking; (#5) base sliding.The aim is to put at disposal a procedure that can be used in any case of technical interest. To provide general output applicable in different contexts, towers are supposed isolated and idealized with a constant hollow square cross-section, without openings and any type of irregularity. Different mechanisms can be activated as a consequence of geometric features (base, height and thickness of the walls) and masonry mechanical properties, here assumed obeying a Mohr-Coulomb failure criterion.Thanks to the simplicity of the approach, comprehensive sensitivity analyses with different heights, base widths and wall thicknesses varying in the range of technical interest, as well as large scale Monte Carlo (MC) simulations with several geometries and three different sets of mechanical properties are carried out.The possible introduction of horizontal and vertical steel tie-rods is investigated in the same way, simply considering the contribution of the reinforcement in the internal dissipation in limit analysis computations. The results of the analyses show that, depending on the geometry of the tower and the mechanical properties of masonry, different mechanisms can be activated and therefore the choice of the reinforcement must be done on the basis of the expected failure mode. In addition, it is possible to predict the change in the active failure mechanism due to the introduction of reinforcement, as well as to evaluate the increase in the load carrying capacity