Structural assessment of Historical Monuments subjected to fire, towards an optimal use of the FEM and the DEM – DEMMEFI

The proposed methodology aims to analyze the mechanical behavior of a nave span of Notre-Dame Cathedral and implements a multidisciplinary approach. The main scientific issue of the DEMMEFI project has been done in WP1: The hybrid model has been developed and validated. It consists of the implementation of an orthotropic damage model in the discrete element calculation software LMGC90. In parallel, a collection of data relating to the Cathedral of Notre-Dame (architectural data, data on the materials used, data on the history of the constructions) then relating more specifically to the fire of the Cathedral (determination thermal actions on the structure during the fire) was carried out in WP2. The data collected will allow on the one hand the development of homogeneous and heterogeneous geometric models (block by block) of a span of the structure (WP3) and on the other hand the implementation of an experimental campaign of determination thermomechanical properties on equivalent materials (WP4).
All the work carried out in the previous WPs will be used in WP5 which will consist of a structural evaluation of the cathedral with the continuous MEF approach on the basis of a masonry material homogenized thanks to the hybrid tool and with the hybrid MED-MEF approach first on the structural elements of a common span of the nave then on the span in its entirety. This methodology will invite the comparison of the results obtained by the MEF and by the hybrid method MED-MEF in order to make the results obtained by the two methods more reliable and the methodology for discretizing the structure. Finally, a summary of the results and a generalization to other case studies will be proposed in WP6 through the establishment of a global methodology for the evaluation of historic structures subjected to fire events.

The development of the hybrid tool is finalized (task WP1). The first test cases reveal a good cohabitation of the damage model in the discrete element calculation engine LMGC90. The first calculations at the substructure scale are in progress. The test cases are written and the user manual is being finalized.
The collection of data (WP2 task) on the cathedral was carried out by I2M and LMDC through 3 M2R internships. The data was collected on site and via archive research from documents whose obtaining was facilitated through the CNRS/MC Notre Dame scientific project. This task is complete.
The continuous and discrete geometric models (task WP3) of a common span of the cathedral were delivered by the subcontractor company STONO, and are accompanied by a report presenting the method for producing the meshes. This task is complete.
Concerning the WP4 task relating to the mechanical characterization, the thermomechanical tests carried out in Alès (LMGC) on the constituent materials are taking place within the time limits.

The next steps of the project consist in finalizing the thermomechanical characterization campaign on limestone, lime mortar and composite samples. Then, the phase of homogenization of the masonry using the hybrid tool will be carried out. Finally, the calculations at the scale of the substructure of the cathedral then at the scale of an entire span will be carried out with the finite element method and then with the hybrid model in order to obtain stability indicators for the cathedral.
Note that, today, the main highlight lies in the successful implementation of the damage model in the LMGC90 computer code. The resulting new hybrid model will undoubtedly be the subject of communications and offers many perspectives in the modeling of multi-scale and heterogeneous structures in both the scientific and industrial communities.

Today, the first elements of enhancement of the program include:
• 4 scientific articles submitted to journals being reviewed (3 to Journal of Cultural Heritage and 1 to Academic Journal of Civil Engineering)
• 1 international communication planned soon in Italy (ANIDIS XIX & ASSISi XVII – 2022, Torino)
• 2 national conferences by invitation
• 2 national conferences
Overall, this scientific production concerns the general presentation of the DEMMEFI project, the development of the hybrid tool and the estimation of thermal actions at Notre Dame.

The French territory presents many old historical constructions classified as building open to the public (ERP). However, this architectural heritage in masonry is fragile regarding the fire risk as the disaster that occurred on April 15 at Notre-Dame Cathedral in Paris. After a fire, the heritage value of these ERP implies that, if a doubt of structural stability exists, the question of their demolition is generally ruled out, unlike contemporary constructions without architectural value. Moreover, when these buildings are classified as Historic Monuments (HM), they must be restored and, or at least be rebuilt as it was. In any case, the question of the structure stability subjected to fire remains. However, today, knowledge and tools to assess the post-fire structural stability of a masonry building are still missing.
The DEMMEFI project proposes to respond to this problem by carrying out a post-fire structural assessment methodology for complex 3D masonry structures. This methodology will first be applied to a common span of the nave of Notre-Dame cathedral and then generalized to similar masonry historic buildings with high heritage value. The methodology developed will be based on the combined and optimized use of the two main existing numerical methods: the finite element method (FEM) and the discrete element method (DEM). A so-called hybrid FEM-DEM method will be proposed in order to combine the advantages of the FEM and DEM methods in order to simulate the mechanical behavior of masonry material. The problem of mechanical stability subjected to fire action (during fire and post-fire) will be provided by a thermo-mechanical characterization of equivalent materials (limestone and lime mortar) and assemblies. Moreover, an estimation of the spatio-temporal fire action on the vault extrados will be studied. The modeling strategy will be based on a multi-scale approach using the hybrid method from the material to the structure. Finally, the relevance of stability indicators in terms of limit thrusts, limit displacements or limit stresses will be studied for each type of sub-structure of the cathedral in order to propose practical verification methods contributing to the structural assessment of these complex heterogeneous structures.