Structural Response of the Dome of Pisa Cathedral: Challenges Between Geometric Irregularities and Different Modelling Techniques

This article aims to discuss the reliability of the structural analysis of monumental masonry structures with reference to two different factors: an accurate description of the geometric characteristics of the structure and the constitutive law of the material. To this aim, a particularly interesting case study is chosen, i.e. the dome of the Pisa Cathedral, characterized by a pointed profile and an oval plan. First, the study compares the results obtained from analyses conducted with the Abaqus CAE software using two different models: one based on a precise geometry derived from an accurate laser scanner survey; the other based on an idealized geometry resulting from the analytical expressions of the surfaces of the intrados and extrados of the dome. Second, it contrasts the Abaqus finite element results, assuming a non-linear constitutive law incorporating plasticity and damage, with those of a recent formulation of the funicular approach to limit analysis, based on the force density concept and multi-constrained optimization, and adopting the Heyman’s assumptions. The different theoretical backgrounds of these methods are discussed, in relation to the results. The finite element analyses show that ignoring imperfections in real domes can provide inaccurate results when using oversimplified, idealized geometries. Additionally, the funicular approach proves to be a powerful numerical method, providing results as accurate as the FEM to assess the safety of the dome under gravitational loads, despite the simplifying assumptions on the mechanical behaviour of masonry. This allows for a reduction in computational costs compared to finite element analyses. Finally, preliminary results on the seismic behaviour of the dome are commented, with reference to both methods.