PhD topic (civil engineering) Multiscale modelling of the seismic response of buildings: coupling of homogenization and multifiber elements
The assessment of the seismic vulnerability of existing structures is a major issue in civil engineering. Having efficient modelling tools is necessary but is not enough to deal with this problem. The definition of robust damage indicators is a prerequisite for a reliable assessment.
To achieve this objective, the proposed PhD is based on the coupling of advanced modelling tools partly developed in the SV (Earthquakes and Vibrations) and SDOA (Safety and Durability of Structures) laboratories of Ifsttar (French Institute of Science and Technology for Transport, Development and Networks).
Issue: During the dynamic analysis of a structure, the displacement at the top and the inter-storey displacement are two frequently used indicators. They present the advantage of being easy to read but they lead to conclusions which are sometimes in contradiction with the damage level determined through local damage indicators (strain, stress, damage variable,...). The likelihood of this kind of inconsistency is particularly high for reinforced structures. As the global damage indicators were initially built using the study of typologies of structures, it is not possible at present to capture correctly the effect of the various sorts of reinforcement with this approach.
On the contrary, the global indicators are useful because they constitute a preferred tool for the conventional design offices in relation to the managers and the decision-makers. An important part of the solution of this problem lies in the definition of global damage indicators which are built using some local information.
Selected tools: The selected strategy to build such criteria is based on the coupling of numerical tools adapted to each of the two scales.
- Numerical modelling by homogenization The modelling of a regular building by homogenization consists in replacing it by an equivalent beam in order to compute its global response to an external load. The used beam model can be classic or not depending on the characteristics of the building and the parameters of the beam are obtained through a static analysis of a representative storey. Because of the small computational resource needed by this approach, it is particularly appropriate for a large-scale vulnerability analysis and the study of global damage indicators.
- Numerical modelling by multifiber finite elements On the contrary, the computation of the local damage indicators requires to finely represent the geometry of the building. Usually, the structural elements (walls, columns,...) are described either with three-dimensional finite elements leading to a great number of degrees of freedom or with beam elements. Halfway between this two approaches, the multifiber finite elements make it possible to describe the three-dimensional behaviour of a structure and to obtain some local information with a reasonable computational cost.
Case study: The work will be based on the case of the town hall of Grenoble which was already modelled with multifiber elements in the Cast3m code. The interest of this structure is also the existence of a continuous recording of ambient vibration which is processed by the ISTERRE laboratory of Grenoble. This kind of measure is a tool for the assessment of the state of damage of a structure or for the monitoring of its evolution during successive loadings.
Intended approach and expected results: The first step of this PhD will consist in validating the analysis of real buildings by homogenization. This kind of modelling gave excellent results for simple frame structures which must be confirmed for more complex geometries. This will require to program specific numerical tools.
The second step will consist in the coupling between the modelling by homogenization and the modelling by multifiber finite elements:
A homogenized model of the studied building will be established. The parameters of this idealized beam will be determined using the numerical multifiber model of the structure.
The response of the homogenized model to reference dynamic loadings will be studied in relation to global damage indicators.
Knowing the generalized forces, a return to the local scale on the multifiber model will be realised in order to determine the state of damage at the local scale.
On the basis of the coupling, the third step will consist in the development of a new vulnerability indicator which ensures the compatibility between the global scale and the local scale.
Finally, the validation of the proposed indicator will include the using of experimental results and the processing of in situ measurements.
Université Paris-Est, IFSTTAR
GERS-SV et MAST-SDOA
14-20 Boulevard Newton
Cité Descartes, Champs sur Marne
F-77447 Marne la Vallée Cedex 2
Supervisor : Jean-François SEMBLAT
Advisors: Céline CHESNAIS (
) Cédric DESPREZ (
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