Substructure Analyses of the Baptistery of Pisa as a Method to Address Uncertainties on Materials and Construction Phases of Monumental Structures

The study of monumental structures is a challenging task due to various factors. This includes the difficulty of gathering information for their mechanical characterization and the high variability of non-standard materials and employed construction techniques. Besides, the knowledge of the construction sequence is often partial, despite its significance in identifying potential past intermediate stages when the structure withstood precarious equilibrium conditions potentially leading to crack and deformation patterns. In this context, material uncertainties play a significant role in determining the performance of masonry historical structures. This paper applies probabilistic methodologies to evaluate the static behavior of a relevant case, notably a substructure of the Baptistery of Pisa that includes a dodecahedral dome resting on an arched drum supported by 12 pillars. Mazars’ material damage law is used to simulate the non-linear behavior of masonry, and uncertainty affecting masonry mechanical properties is considered by appointing suitable density functions according to prior engineering expertise. The uncertainties propagation is based upon general Polynomial Chaos Expansion (gPCE) response surfaces, which remarkably reduces the computational burden in the forward problem-solving of the non-linear FE model. The sensitivity of the response in terms of crack propagation is assessed through Sobol’ indices, which identify the most relevant input parameters and, thus worthy of careful consideration. This work significantly contributes to the comprehension of the construction sequence of the Baptistery, thus paving the way for further evaluations entailing staged construction analyses of the entire monumental structure.