Masonry vaulted structures under spreading supports: Analyses of fracturing behavior and size effect

This paper deals with the fracturing behavior of unreinforced masonry arches and vaults induced by spreading supports. The traditional method of limit analysis is limited in understanding the actual failure of arches, as it assumes the simultaneous formation of hinges once the thrust line reaches the edge of the masonry structure. The damage propagation phenomenon, starting from the trigger of the fracture up to the complete structural failure is thus ignored. Moreover, limit analysis does not capture the effect of structural size on the nominal strength due to strain-softening and damage localization. This manuscript proposes a thorough understanding of the fracturing behavior and size-effect of arches and vaults based on computational modeling and 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. 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 slendernesses. The effect of arch size on structural strength is then analyzed using LDPM, by simulating self-similar arches of five different sizes and of three different slenderness ratios. The numerical data of size-effect is also analyzed using a newly developed analytical formula based on non-linear fracture mechanics theory and taking into account self-weight, whose effect is of paramount importance in arches and vaults under spreading supports. Results show a strong reduction of structural strength as the size increases, as a matter of fact stronger than the typically observed reduction due to energetical size-effect. The difference is due to self-weight, one of the main driving forces in the collapse of thrusting arches. This might explain the reason why in some seismic locations, small sized vaulted structures remain almost undamaged whereas larger ones often collapse.