Advanced Modeling of a Historical Masonry Umbrella Vault: Settlement Analysis and Crack Tracking via Adaptive NURBS Kinematic Analysis

In this work, the study of a complex masonry umbrella vault located within Masegra Castle (Museum of Sondrio territory, Northern Italy) is presented. Built during the renewal of the castle in the 16th century, the umbrella vault of Masegra Castle is characterized by a total of eight sails, with four half-cross vaults added at the corners, supported by four walls, and resulting in a quadrangular horizontal plan. The observed crack pattern seems to derive from vertical settlement phenomena involving at least one of the supporting walls. A multidisciplinary approach based on innovative technologies for the geometric reconstruction, detailed analysis of the construction, the historical evolution, and its state of conservation, has been followed. Starting from dense laser scanner point clouds and photogrammetric surveys, historical building information modeling (HBIM) models have been created and allowed the generation of an accurate geometrical representation of the umbrella vault through nonuniform rational basis-splines (NURBS) surfaces. Starting from the NURBS-based model, an adaptive kinematic procedure is used to determine the failure behavior under settlements. A discretization through triangular NURBS elements, in which the real geometry remains unvaried, is adopted. Each element is idealized as a rigid block and jumps of displacement are allowed at the boundaries only. By applying the principle of virtual works, a discontinuous displacement field deriving from an imposed settlement is obtained. As a consequence of the reduced number of elements adopted, a metaheuristic mesh adaptation procedure is finally applied to find the correct disposition of fracture lines. Different settlement typologies are adopted in the analyses to reproduce the crack pattern observed on the umbrella vault. Finally, an inverse analysis is conducted to estimate the shape of the occurred settlements starting from the observed crack pattern.