Overturning of No-Tension Towers

Abstract

This study investigates the overturning behavior of leaning masonry towers on a rigid foundation. Unreinforced masonry is assumed to be incapable of withstanding tension, thus anticipating a progressive fracturing to occur outside the compressive zone of masonry towers as they incline under the force of self-weight alone. A theoretical model for the analysis of rectangular towers is extended to cylindrical towers, where overturning is assumed to occur when the fracture reaches through the entire width of the tower. The results of the theoretical model offer an approximate prediction for the critical angle of inclination that may be reached by a leaning no-tension cylindrical tower of variable slenderness and hollowness. A comparison of the predictions for each of the two tower geometries shows that the predicted critical angles of overturning are very close, while the cylinder is likely to begin cracking at lower inclinations compared to rectangular towers. The theoretical predictions for both rectangular and cylindrical towers are validated experimentally by tilting masonry model towers until failure. The experimental results are found to have reasonable agreement with the predictions, though overturning occurs earlier than predicted in all cases, which is attributed to imperfections in the models and scaling effects. As such, the theoretical predictions are unconservative for the critical angle of overturning of the models in the experiment. Furthermore, two case studies are conducted for existing leaning masonry towers in Italy, where theoretical predictions for their critical angles of overturning are put forth. The results of the case studies indicate that the Garisenda tower in Bologna is relatively close to its theoretical critical inclination, while the Leaning Tower of Pisa is not close. Both towers are found to be very close to their predicted angle of first cracking. However, the assumption of a rigid foundation does not account for the possibility of soil failure which remains a risk for leaning towers on compressible soils. Overall, the research guides further understanding of the failure conditions of masonry towers, which is useful in assessing their safety and preventing catastrophic collapses.