Numerical modelling of the old masonry tunnels of the Paris subway system

The Paris subway system was mainly constructed with a masonry vault as a definitive structure of the tunnel. Almost 85% of the underground assets administrated by the Regie Autonome des Transports Parisiens (RATP) are masonry made and some parts of it are more than 100 years old. Knowing the present structural state of these tunnels is a key priority to the RATP, in order to ensure the continuity of the metro service and also to model and predict the effects of some proposed engineering works in the tunnel itself or in its vicinity (for example, a new building on the surface, excavations near the tunnel or a new adjacent tunnel) that might compromise the safety of the existing structure. Searching to broaden the knowledge of the behaviour of the masonry tunnels, we aim to develop a specific model for the masonry lining which will be implemented in the finite element code CESAR-LCPC. An analytical homogenization technique will be utilized along with a damage model, as a means to describe the evolution of the properties of the vault. Damage is applied locally to each component of the masonry, described by means of an isotropic law, and an appropriate technique linking the micro and macro levels simulates the global anisotropic behaviour across the vault. Geometrical considerations are taken into account to assess the directions of the anisotropy. The goal is to identify potential cracking areas in the tunnel as well as its deformation resulting from a given load case.