Numerical Analysis of Mechanical Damage in Ribbed Masonry Vaults under Differential Settlements

The present study takes advantage of a parametric model, which allows one to create automatically complex structural models of ribbed masonry vaults. Two numerical modelling strategies are discussed: a 3D continuum and a 3D contact-based model. The effects of settlements are studied by imposing vertical displacement at the vault supports up to collapse. Predictions of each modelling strategy are compared with actual damage observation. A representative square vault of Milan Cathedral is studied here, aiming to understand the causes of the damage documented through the years. The structure is noted to have suffered structural damage in the vaulting system due to a long history of soil settlements. The geometry is based on a photogrammetric scanning, and the three-dimensional solid models are created through parametric reconstruction procedures, including details such as springing, arch, ribs, web, and rubble-fill. Both modelling strategies allow to highlight the vulnerability of masonry vaults due to settlements. Significant differences in prediction capabilities are noted when large displacements and separation of elements are involved. The simulations show the possibility of predicting and interpreting different complex damage phenomena as arch block damage or sliding, and web–arch detachment, which is frequently observed in historical structures