A multi-model structural analysis of the vaults of Notre-Dame de Paris Cathedral after the 2019 fire and a proposal for a hybrid model merging continuum and discrete approaches

Abstract

After the Notre-Dame de Paris (NDP) Cathedral fire, a structural analysis was undertaken to provide decision support for architects in charge of diagnosis and repair operations. Due to the potential impact of the results on the renovation project, calculations on the vaults and walls of the monument were compared to increase their reliability. This article presents the 3 modelling strategies implemented: 2 discrete block-to-block 3D approaches (DEM and FEM) and 1 continuum 3D approach (FEM). The assumptions common to the 3 approaches are presented. They mainly concern the geometrical model, the thermal actions and a diagnosis methodology called the working point method, previously used by the authors on other Gothic vaults. Comparisons of the results with each other and with on-site deflection measurements should lead to validation of the calculation strategies. The analysis will highlight the strengths and weaknesses of the computational approaches and propose research perspectives. Future developments concern the determination of models of homogenized thermomechanical behaviour of masonry and the development of a new hybrid calculation tool taking advantage of the continuum and discontinuum approaches detailed in this article.