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                <title xml:lang="en">Numerical modelling of the old masonry tunnels of the Paris subway system</title>
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                <term xml:lang="fr">METHODE DES ELEMENTS FINIS</term>
                <term xml:lang="fr">CESAR LCPC (LOGICIEL)</term>
                <term xml:lang="fr">ENDOMMAGEMENT</term>
                <term xml:lang="fr">METRO</term>
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              <p>The Paris subway system was mainly constructed with a masonry vault as a definitivestructure of the tunnel. Almost 85% of the underground assets administrated by the Régie 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.</p>
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              <p>La plupart des tunnels du métro de Paris comportent une voute en maçonnerie. Près de 85% des ouvrages du patrimoine géré par la RATP est constitué de maçonnerie et certains de ces ouvrages ont plus de 100 ans. La connaissance de leur état structurel actuel est une priorité pour la RATP, pour assurer la continuité du service et pour prédire les effets de travaux projetés à proximité des tunnels qui pourraient compromettre leur stabilité. Pour élargir la connaissance sur le comportement de la maçonnerie, nous avons entrepris de développer un modèle spécifique dans le code de calcul CESAR-LCPC. Une technique d'homogénéisation sera utilisée en combinaison avec un modèle d'endommagement, pour décrire l'évolution des propriétés de la voute. L'endommagement est évalué localement pour chaque composant (considéré comme isotrope), et une technique appropriée de changement d'échelle permet de simuler le comportement global anisotrope de la voute. Le but est d'identifier les zones de fissuration potentielle et les déformations résultant d'un chargement donné.</p>
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