Fracturing and collapse behavior of masonry vaulted structures: a lattice-discrete approach

This study presents a novel meso-scale approach to investigate the fracturing and collapse behaviors of unreinforced masonry vaulted structures induced by spreading supports. Traditionally, the behavior of masonry vaulted structures is investigated by resorting on limit analysis method, that is a limited approach as: (i) it tackles just the failure condition of the arched structural configuration as it assumes the simultaneous formation of hinges once the thrust line reaches the edge of the masonry structure, (ii) it completely ignores the damage propagation phenomenon, starting from the trigger of the first fracture up to the complete structural failure condition. The comprehension of this fracturing process is fundamental aiming to analyze intermediate damage states for the check of serviceability limit states and to individuate a more realistic structural crack distribution in ultimate conditions. This paper proposes a thorough understanding of the fracturing behavior of masonry vaults based on non-linear fracture mechanics concepts. For this purpose, the Lattice Discrete Particle Model (LDPM) is adopted to simulate a variety of stone masonry vaulted structures up to their collapse. LDPM simulates the behavior of masonry at the stone level. The interaction between stones that are bounded by weak layers of mortar is governed by specific constitutive equations describing tensile fracturing with strain-softening, cohesive and frictional shearing, and compressive response with strain-hardening. The formation of hinges, the activation of the mechanism and the kinematic mechanism are analyzed for three different types of vaults, namely groin, barrel and depressed vaults, and for six different slenderness. The first conclusion of this study is that LDPM can be used as an alternative tool to perform typical limit analysis for the assessment of safety of arches and vaults in ultimate conditions. Most importantly, LDPM is able to show that the fracturing process is a progressive phenomenon, the cracked surfaces are never strictly symmetric respect to the vertical axis and do not appear simultaneously. In particular, the features of non simultaneity and asymmetry of the cracks increases as the distance between the crown of the vault and the imposts increases, i.e. going from depressed vaults to groin vaults. Finally, the evolution of the fracturing process occurs more progressively and exhibits less pronounced asymmetry in the case of depressed vaults as compared to groin vaults for which, in turn, the damage appears to be more brittle and characterized by asymmetry in the cracks distribution.