Limit analysis of dry-masonry blocks structures: experimental and numerical investigation

Within the theoretical framework of limit analysis, this thesis examines some problems arising in the assessment of the collapse mechanisms of historical masonry structures, featured by dry mortar joints. The attention is focused on the constitutive laws that govern the frictional contact behaviour, taking into account both associative and nonassociative flow laws. Under the classical Heyman assumptions, the response of vaulted systems on spreading supports is investigated. Applying the lower-bound theorem of the limit analysis, the minimum thrust state in the undeformed configuration is determined. In large displacements, an original algorithm is proposed to evaluate vaulted structures capacity in terms of collapse displacement and associated thrust. The compatible bi- and three-dimensional mechanisms and the corresponding well-known crack patterns are analysed and discussed. The influence of the main geometric parameters on the minimum required thickness and on the different possible collapse mechanisms is examined and discussed as well. Three types of masonry arch are analysed: round, elliptical, and parabolic arch. Adopting the sliced model, the same approach is extended to the cases of rounded and parabolic cross vaults. The interesting case study of the unbuilt Musmeci vault, originally in reinforced concrete, is presented in the novel perspective of a dry-masonry structure. The thrust line analysis is conducted with the aim of evaluating the design thickness of the masonry vault, and the results show the feasibility of the new project. For a better insight into the frictional behaviour of interface, an extensive experimental campaign has been conducted on two dry-jointed tuff blocks subjected to different loading scenarios implying interactions among shear, torsion and bending moments. Observing the pure shear tests, not enough dilatancy to verify the normality condition has been detected. Moreover, the results of the laboratory tests have been compared with those obtained by a non-linear numerical model based on the assumptions of rigid blocks and notensional frictional interfaces. From the comparison with the predicted three-dimensional yield domains, it has resulted that the actual contact area is a parameter that should be considered in the model, in particular for its relevant role on the limiting torsion moment of the interface. Finally, considering Coulomb friction interfaces with no-dilatancy, the non-associative limit analysis of bi-dimensional structures has been formulated as a Mixed Complementarity Problem. Using variational arguments, it is proven that a solution can be constructed by considering a fixed-point problem, which is suitably stabilized and solved by a derivative-free algorithm. The resulting variational-based fixed-point algorithm succeeds to construct a non-associative limit analysis solution by iteratively addressing straightforward associative limit analysis problems. Numerical simulations show that the proposed algorithm is able to predict collapse multipliers of large masonry block structures with accuracy, robustness and effectiveness.