Ifsttar PhD subject

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Title : Homogenized Models with Flexible Supports for the Study of the Soil-Structure Interaction during the Assessment of the Seismic Vulnerability of Regular Buildings

Main host Laboratory - Referent Advisor GERS - SRO  -  CHESNAIS Céline      tél. : +33 181668378

Director of the main host Laboratory REIFFSTECK Philippe  -

PhD Speciality dynamique des sols et des structures

Axis of the performance contract 3 - COP2017 - Planning and protecting regions

Main location Marne-la-Vallée

Doctoral affiliation UNIVERSITE GUSTAVE EIFFEL

PhD school SCIENCES, INGENIERIE ET ENVIRONNEMENT (SIE)

Planned PhD supervisor BERTRAND Etienne  -  Université Gustave Eiffel  -  GERS - SRO

Planned financing Contrat doctoral  - Université Gustave Eiffel

Abstract

As the majority of existing constructions predate the application of earthquake regulations, the assessment of their vulnerability is a major issue for the prediction and reduction of the seismic risk. However, the calculation costs are important in dynamics and this limits the carrying out of specific studies for strategic structures. By retaining only the phenomena that have a significant influence on the structure's response, homogenization makes it possible to build simple and yet realistic models, well suited to the diagnosis of a large stock. The objectives of this thesis are to integrate the effects of the soil-structure interaction in this type of modelling in order to be able to describe the effects of this interaction on the seismic response of regular buildings and to propose a strategy for the model calibration using in situ measurements of ambient vibrations.

Problematic:
Since many buildings have a periodic structure consisting of the repetition of the same storey, it was proposed to study their dynamic behaviour by means of homogenized models. This consists in representing them by an equivalent beam model, i.e. a continuous and analytical 1D model. The model used can be classical or enriched according to the characteristics of the building and its constituent parameters obtained by means of a static analysis of the typical storey. The current homogenized model describes the vibrations of the structure in the plane and is a generalization of the Timoshenko beam model: in addition to the usual bending and shear mechanisms, it includes an internal deformation mechanism related to the bending of the walls which is a specificity of hollow structures [Hans 2008].
The work carried out until now in this field has only considered structures that are perfectly embedded at the bottom. However, real buildings are based on a soil whose flexibility can modify their dynamic response. On the one hand, the distribution of deformations between the structure and the soil depends on the stiffness contrasts and, on the other hand, the radiation of vibrations induces additional damping. Moreover, it is frequent that the structures are not entirely periodic because the lower storeys have a different plan to accommodate shops or car parks. The correct description of the behaviour of the homogenizable part of the structure therefore requires taking into account its environment by means of more realistic support conditions.
Since the equivalent beam model includes three mechanisms, it verifies three homogenized boundary conditions at each end. The flexibility of the supports must therefore be represented by three impedances: one impedance associated with the translational movement of the base of the structure, one associated with its overall rotation and one associated with its deformation under the effect of the bending of the walls. It should be noted that the flexibility of the foundation is rarely taken into account in the literature, although it has been observed experimentally in a building with shear walls [Hans 2002]. The analysis of the consequences of this flexibility is particularly interesting in the french context where this construction technique is frequently used.

Intended approach:
This original study of the soil-structure interaction with homogenized building models will be based on the case of a structure consisting of a pile of single frames laid on a homogenous (possibly laminated) soil via a shallow foundation. The great interest of this model is that it is both:
• simple enough to allow quasi-analytical developments that provide a good understanding of the physical phenomena and highlight the key parameters,
• rich enough to illustrate many situations and allow parametric studies.
Indeed, the homogenization technique has already been implemented on structures made up of single frames and all the analytical results are available [Hans 2008]. In particular, it has been shown that the modification of the stiffness contrast between walls and floors makes it possible to generate a large variety of behaviours and that the corresponding equivalent beam models also apply to more complex structures [Chesnais 2010, Franco 2019].
Concerning the soil, it is planned to calculate the foundation impedances analytically using the cone model where possible. For the soil characteristics where this model is unsuitable or for new kinematics, in particular the deformability of the foundation, numerical simulations can be carried out considering different soil classes. In the same way, the equivalent beam for a more complex building can be derived numerically using tools already developed in Cast3M.
This modelling strategy should allow:
• to relate the real boundary conditions of the structure to the homogenized boundary conditions verified by the equivalent beam,
• to analyse the edge effects caused by the loss of the periodicity,
• to carry out an in-depth study of the evolution of this system as a function of the contrast between the impedances of the soil and the rigidities of the mechanisms of the structure (expected beneficial effects),
• to propose enrichment functions for the analytical model to take into account flexible boundary conditions.

The obtained results will be validated by comparing them with those of detailed finite element models of the soil-structure system and by confronting them with existing experimental data (in situ or geotechnical centrifuge modelling). Two case studies seem particularly interesting for this thesis:
• the Prefecture of Nice, a periodic structure located in a zone with a significant seismic risk, already instrumented by the RAP and whose modelling was carried out as part of a thesis at Cerema [Fernandez Lorenzo 2016].
• the building surveyed in [Hans 2002] for which the phenomenon of soil-structure interaction with flexibility of the foundation was observed. It is a residential building made of reinforced concrete from the 1970s, a very common type of construction in France, including in seismic zones.
The approach developed in this thesis can also be compared to the simplified methods used by design offices.

This work is in line with the research carried out by the SRO laboratory of the Université Gustave Eiffel on the seismic risk and the vulnerability of structures [Abboud 2017, Franco 2021]. It is proposed in collaboration with the CEREMA and the LMPS/ENS-Paris-Saclay.

References :

ABBOUD, Y. (2017). Développement d’un macroélément pour l’étude des fondations superficielles sous charge sismique. Thèse de doctorat, Ifsttar – Université Paris-Est.

CHESNAIS, C. (2010). Dynamique de milieux réticulés non contreventés – Application aux bâtiments. Thèse de doctorat, ENTPE - Ecole Centrale de Lyon.

FERNANDEZ LORENZO, G. (2016). From accelerometric records to the dynamic behavior of existing buildings. Thèse de doctorat, Université Côte d’Azur.

FRANCO, C., CHESNAIS, C., SEMBLAT, J.-F., DESPREZ, C. et GIRY, C. (2019). Une technique d’homogénéisation appliquée aux bâtiments périodiques multiportiques. 10e colloque national AFPS, Strasbourg, 24 au 27 septembre 2019.

FRANCO, C. (2021). Multiscale modeling of the seismic response of buildings: Coupling between Homogenization Method and Multifiber Element Method. Thèse de doctorat, Université Gustave Eiffel.

HANS, S. (2002). Auscultation dynamique de bâtiments et modélisation par homogénéisation – Contribution à l’analyse de la vulnérabilité sismique. Thèse de doctorat, ENTPE - INSA de Lyon.

HANS, S. et BOUTIN, C. (2008). Dynamics of discrete framed structures: A unified homogenized description. Journal of Mechanics of Materials and Structures, 3(9):1709-1739

Keywords : dynamics, soil-structure interaction, homogenization, generalized continua, seismic vulnerability, building

Main host Laboratory - Referent Advisor	GERS - SRO - CHESNAIS Céline tél. : +33 181668378
Director of the main host Laboratory	REIFFSTECK Philippe -
PhD Speciality	dynamique des sols et des structures
Axis of the performance contract	3 - COP2017 - Planning and protecting regions
Main location	Marne-la-Vallée
Doctoral affiliation	UNIVERSITE GUSTAVE EIFFEL
PhD school	SCIENCES, INGENIERIE ET ENVIRONNEMENT (SIE)
Planned PhD supervisor	BERTRAND Etienne - Université Gustave Eiffel - GERS - SRO
Planned financing	Contrat doctoral - Université Gustave Eiffel
Abstract As the majority of existing constructions predate the application of earthquake regulations, the assessment of their vulnerability is a major issue for the prediction and reduction of the seismic risk. However, the calculation costs are important in dynamics and this limits the carrying out of specific studies for strategic structures. By retaining only the phenomena that have a significant influence on the structure's response, homogenization makes it possible to build simple and yet realistic models, well suited to the diagnosis of a large stock. The objectives of this thesis are to integrate the effects of the soil-structure interaction in this type of modelling in order to be able to describe the effects of this interaction on the seismic response of regular buildings and to propose a strategy for the model calibration using in situ measurements of ambient vibrations. Problematic: Since many buildings have a periodic structure consisting of the repetition of the same storey, it was proposed to study their dynamic behaviour by means of homogenized models. This consists in representing them by an equivalent beam model, i.e. a continuous and analytical 1D model. The model used can be classical or enriched according to the characteristics of the building and its constituent parameters obtained by means of a static analysis of the typical storey. The current homogenized model describes the vibrations of the structure in the plane and is a generalization of the Timoshenko beam model: in addition to the usual bending and shear mechanisms, it includes an internal deformation mechanism related to the bending of the walls which is a specificity of hollow structures [Hans 2008]. The work carried out until now in this field has only considered structures that are perfectly embedded at the bottom. However, real buildings are based on a soil whose flexibility can modify their dynamic response. On the one hand, the distribution of deformations between the structure and the soil depends on the stiffness contrasts and, on the other hand, the radiation of vibrations induces additional damping. Moreover, it is frequent that the structures are not entirely periodic because the lower storeys have a different plan to accommodate shops or car parks. The correct description of the behaviour of the homogenizable part of the structure therefore requires taking into account its environment by means of more realistic support conditions. Since the equivalent beam model includes three mechanisms, it verifies three homogenized boundary conditions at each end. The flexibility of the supports must therefore be represented by three impedances: one impedance associated with the translational movement of the base of the structure, one associated with its overall rotation and one associated with its deformation under the effect of the bending of the walls. It should be noted that the flexibility of the foundation is rarely taken into account in the literature, although it has been observed experimentally in a building with shear walls [Hans 2002]. The analysis of the consequences of this flexibility is particularly interesting in the french context where this construction technique is frequently used. Intended approach: This original study of the soil-structure interaction with homogenized building models will be based on the case of a structure consisting of a pile of single frames laid on a homogenous (possibly laminated) soil via a shallow foundation. The great interest of this model is that it is both: • simple enough to allow quasi-analytical developments that provide a good understanding of the physical phenomena and highlight the key parameters, • rich enough to illustrate many situations and allow parametric studies. Indeed, the homogenization technique has already been implemented on structures made up of single frames and all the analytical results are available [Hans 2008]. In particular, it has been shown that the modification of the stiffness contrast between walls and floors makes it possible to generate a large variety of behaviours and that the corresponding equivalent beam models also apply to more complex structures [Chesnais 2010, Franco 2019]. Concerning the soil, it is planned to calculate the foundation impedances analytically using the cone model where possible. For the soil characteristics where this model is unsuitable or for new kinematics, in particular the deformability of the foundation, numerical simulations can be carried out considering different soil classes. In the same way, the equivalent beam for a more complex building can be derived numerically using tools already developed in Cast3M. This modelling strategy should allow: • to relate the real boundary conditions of the structure to the homogenized boundary conditions verified by the equivalent beam, • to analyse the edge effects caused by the loss of the periodicity, • to carry out an in-depth study of the evolution of this system as a function of the contrast between the impedances of the soil and the rigidities of the mechanisms of the structure (expected beneficial effects), • to propose enrichment functions for the analytical model to take into account flexible boundary conditions. The obtained results will be validated by comparing them with those of detailed finite element models of the soil-structure system and by confronting them with existing experimental data (in situ or geotechnical centrifuge modelling). Two case studies seem particularly interesting for this thesis: • the Prefecture of Nice, a periodic structure located in a zone with a significant seismic risk, already instrumented by the RAP and whose modelling was carried out as part of a thesis at Cerema [Fernandez Lorenzo 2016]. • the building surveyed in [Hans 2002] for which the phenomenon of soil-structure interaction with flexibility of the foundation was observed. It is a residential building made of reinforced concrete from the 1970s, a very common type of construction in France, including in seismic zones. The approach developed in this thesis can also be compared to the simplified methods used by design offices. This work is in line with the research carried out by the SRO laboratory of the Université Gustave Eiffel on the seismic risk and the vulnerability of structures [Abboud 2017, Franco 2021]. It is proposed in collaboration with the CEREMA and the LMPS/ENS-Paris-Saclay. References : ABBOUD, Y. (2017). Développement d’un macroélément pour l’étude des fondations superficielles sous charge sismique. Thèse de doctorat, Ifsttar – Université Paris-Est. CHESNAIS, C. (2010). Dynamique de milieux réticulés non contreventés – Application aux bâtiments. Thèse de doctorat, ENTPE - Ecole Centrale de Lyon. FERNANDEZ LORENZO, G. (2016). From accelerometric records to the dynamic behavior of existing buildings. Thèse de doctorat, Université Côte d’Azur. FRANCO, C., CHESNAIS, C., SEMBLAT, J.-F., DESPREZ, C. et GIRY, C. (2019). Une technique d’homogénéisation appliquée aux bâtiments périodiques multiportiques. 10e colloque national AFPS, Strasbourg, 24 au 27 septembre 2019. FRANCO, C. (2021). Multiscale modeling of the seismic response of buildings: Coupling between Homogenization Method and Multifiber Element Method. Thèse de doctorat, Université Gustave Eiffel. HANS, S. (2002). Auscultation dynamique de bâtiments et modélisation par homogénéisation – Contribution à l’analyse de la vulnérabilité sismique. Thèse de doctorat, ENTPE - INSA de Lyon. HANS, S. et BOUTIN, C. (2008). Dynamics of discrete framed structures: A unified homogenized description. Journal of Mechanics of Materials and Structures, 3(9):1709-1739
Keywords :	dynamics, soil-structure interaction, homogenization, generalized continua, seismic vulnerability, building

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