Calibration of Numerical Models to Support Shm: The Consoli Palace of Gubbio, Italy

Abstract

Historical masonry structures constitute a fundamental part of the built cultural heritage but are characterized by an intrinsic vulnerability to ageing and natural hazards, in particular to earthquakes. The related need to assess their current health condition and to ensure their future conservation is giving rise to increasing efforts in scientific research. The combined employment of health monitoring systems and structural modelling is widely adopted in this field, either to better interpret the effects of age-related degradation or to reliably predict the structural response to earthquakes. Both scenarios can leverage experimental measurements for the model calibration, thus reducing epistemic and aleatory uncertainties in the assessment phase. Among the available modelling strategies, refined Finite Element (FE) models represent the most common choice in the SHM perspective for monumental URM structures. Nonetheless, the computational effort required by the assessments in the nonlinear fieldunavoidable in seismic evaluationsis often unfeasible, especially in practice engineering. In the case of palaces, an alternative is the employment of more computationally efficient formulations such as Equivalent Frame (EF) models. Within this framework, the paper firstly deals with the equivalent-frame modelling and model updating of the Consoli Palace, a historic masonry building in Gubbio (Italy) investigated through ambient vibration tests. The peculiar aspects of the buildinge.g. the unusually high inter-storey height, the presence of vaulted floors, the irregular distribution of the openingsmake the equivalent-frame idealization a challenging task. The comparison with a detailed finite element model developed in previous research points out the differences and limits of the two approaches, providing some suggestions to benefit from their integrated use.

An Equivalent Frame Digital Twin for the Seismic Monitoring of Historic Structures: A Case Study on the Consoli Palace in Gubbio, Italy

“…In accordance with the satisfying results previously obtained in the dynamic calibration of the EF model of the palace [88,93], only a few parameters are chosen for the continuous updating, in particular, those governing the stiffness of the palace and of the bell tower along each of the two main structural directions x and y. It is assumed that structural masses are quantified up to a satisfactory level of accuracy, whereas the elastic properties of the building material remain affected by a higher degree of uncertainty-no experimental test is available to characterize precisely the mechanical properties of masonry panels.…”

“…The alteration of the original mesh made the height of the piers more representative of the expected deformable portion of the walls, reducing at the same time the excessive dimensions of rigid nodes, which may otherwise produce an overestimation of the overall stiffness. The development of the model, the optimization of the mesh, and the first dynamic calibration of the model based on the extended AVT campaign of May 2021 (Section 3.1) are described in detail in [88]. The EF model here presented has been recalibrated according to the new updating scheme presented in Section 4.2, which considers just four predefined regions and four updating variables, namely, the regions' Young moduli.…”

“…Keeping the two directions independent from each other has a twofold objective, aimed at achieving a successful updating phase and a reliable damage localization. First, as discussed in [88], this expedient overcomes some limitations in the modeling of the out-of-plane stiffness of masonry elements in the assumed EF formulation, whose effect is significant due to the large thickness of the palace masonry walls. Second, from the point of view of structural analysis and seismic damage assessment, the choice of analyzing independently the two main directions is a common choice for masonry buildings-in which directional earthquake-resistant systems are easily identified from the architectonic configuration-allowing a more accurate interpretation of the response to earthquake actions and damage proneness of each resisting subsystem.…”

“…Second, from the point of view of structural analysis and seismic damage assessment, the choice of analyzing independently the two main directions is a common choice for masonry buildings-in which directional earthquake-resistant systems are easily identified from the architectonic configuration-allowing a more accurate interpretation of the response to earthquake actions and damage proneness of each resisting subsystem. Other uncertain parameters, such as masonry mass density and the in-plane shear stiffness of vaults, are fixed according to the results obtained in previous calibrations (see [88]).…”

Analytical identification of dynamic structural models: Mass matrix of an isospectral lumped mass model

“…In general, model representativeness is commonly achieved through accurate calibrations based on experimental measurements. A typical example is defining an objective function weighting spectral differences, which is minimized with iterative numerical techniques 21–24 . A reasonable alternative is to search for a synthetic but representative mechanical description, that is, a lighter (low‐order) model that can still capture the essential dynamical traits of the structural system but trades simulation accuracy for computational efficiency.…”