Uncertainty propagation of relevant soil and masonry parameters to design a SHM for the Baptistery of Pisa

Historic constructions are affected by several uncertainties, among which those on mechanical parameters of masonry, because of reduced knowledge given by the limitation imposed on performing extensive destructive tests not to jeopardize the structural integrity. Besides, uncertainties on soil characterization can play a significant role in the evaluation of structural response, however is often neglected. Finite Element Models (FEM) often represent a good compromise given the possibility of reproducing the complex geometry of historical structures while requiring relatively limited material parameters from experimental tests (to feed models). However, the computational burden can become prohibitive when the evaluation of the effects of the variation of input mechanical properties for the assessment of the current behavior of the structure and potential design of adequate interventions and definition of monitoring systems requires running several analyses. In this work, modal analyses of a monumental Medieval construction such as the Baptistery of Pisa are carried out within a probabilistic framework including material uncertainties on both mechanical parameters of soil and masonry, which are assigned suitable probability distributions based on the limited data from in-situ campaigns combined with engineering judgment. A gPCE-based surrogate model is employed to transform the onerous numerical runs into speeded-up analytical evaluations for the computation of Sobol’ indices to assess the influence of input variability on the first ten natural frequencies of the monument at issue. The method leads to the identification of the most relevant soil and masonry parameters and highlights which frequencies are primarily controlled by either the stiffness of the soil or that of the aboveground historical structure. In this sense, this work provides a first clue for designing a SHM of the Baptistery of Pisa with a view to assessing minimum detectable parameter change while monitoring natural frequencies.