Simple limit analysis approach for the optimal strengthening of existing masonry towers

The paper provides an insight into the seismic strengthening of masonry towers with horizontal and vertical steel rods by means of a limit analysis approach. The kinematic theorem of limit analysis with five pre-assigned failure mechanisms, observed during post-earthquake surveys, has been implemented for different geometries of idealized towers, aimed to cover a wide range of real masonry towers. Different mechanisms can activate as a consequence of the geometric features in combination with masonry mechanical properties. The possible introduction of horizontal and vertical steel rods is investigated in the same way, simply considering in limit analysis computations the contribution of the reinforcement in the internal dissipation. Thanks to the simplicity of the limit analysis approach, large scale Monte Carlo (MC) simulations with several geometries are carried out. Results show that, depending on the geometry of the tower and the mechanical properties of masonry, different mechanisms can be active and therefore the choice of the reinforcement must be done basing on the expected failure mode. Furthermore, it is possible to evaluate the increase in the load carrying capacity of the tower and to observe any change in the active failure mechanism due to the introduction of reinforcement.