Panagiotis Kotronis

Simplified modelling strategies to simulate the dynamic behaviour of R/C walls

A continuous damage model and different simplified numerical strategies are proposed to simulate the behaviour of reinforced concrete (R/C) walls subjected to earthquake ground motions. For 2D modelling of R/C walls controlled primarily by bending, an Euler multilayered beam element is adopted. For 3D problems, a multifibre Timoshenko beam element having higher order interpolation functions has been developed. Finally, for walls with a small slenderness ratio we use the Equivalent Reinforced Concrete model. For each case, comparison with experimental results of R/C walls tested on shaking table or reaction wall shows the advantages but also the limitations of the approach.

The equivalent reinforced concrete model for simulating the behavior of walls under dynamic shear loading

In order to have a simplified model useful for dynamic shear loading analysis the equivalent reinforced concrete model (ERC) has been proposed. The ERC model is derived from the framework method and uses lattice meshes for concrete and reinforcement bars, and uniaxial constitutive laws based on continuum damage mechanics and plasticity. After describing the basis of the model, results showing its capacity to analyze shear walls tested in the framework of the SAFE program are presented. The use of the ERC model should reduce the computational time and allow parametrical studies. In this respect the performance of such a model is demonstrated. However it is shown that for low reinforcement ratios results are sensitive to the angle formed by the diagonals of the concrete lattice and the horizontal bars. Specific attention must be paid in this case.

Shaking Table Tests of Lightly RC Walls: Numerical Simulations

In the framework of the European consortium ECOLEADER, a seismic research project has been performed on specimens tested on a shaking table. The specimens were representative of reinforced concrete buildings with bearing walls. The mock-up studied in particular in this article is composed of two parallel walls linked with a perpendicular one that has openings. The walls are reinforced according to the current design practice in France with a small amount of reinforcement. Two kinds of finite element simulations have been performed: a refined one using a detailed 3D description of the specimen and a simplified one, based on multifiber beams. The comparison between the experimental and numerical results not only demonstrates the accuracy of the time-history analysis models, but also allows obtaining more detailed information about the behavior of the specimen for more complex seismic excitations. It is shown that both models are able to describe quantitatively the global and qualitatively the local behavior of the structure. The simplified model is furthermore used to investigate the behavior of the specimen under a 3D earthquake loading.

Local Second Gradient Models and Damage Mechanics: 1D Post-Localization Studies in Concrete Specimens

Continuum damage mechanics is often used as a framework for describing the variations of the elastic properties of due to micro-structural degradations. Experimentally, concrete specimens exhibit a network of microscopic cracks that nucleate sub-parallel to the axis of loading. Due to the presence of heterogeneities in the material (aggregates surrounded by a cement matrix), tensile transverse strains generate a self-equilibrated stress field orthogonal to the loading direction, a pure mode I (extension) is thus considered to describe the behaviour even in compression. This rupture mode must be reproduced numerically. This is the reason why the failure criterion of the chosen constitutive law is expressed in terms of the principal extensions and that a tension test is modelled at the end of this paper. The influence of micro-cracking due to the external loads is introduced via damage variables, ranging from 0 for the undamaged material to 1 for a completely damaged material.

The Seismic Behavior of Reinforced Concrete Structural Walls: Experiments and Modeling

Many European buildings are situated in seismic regions of low or moderate seismicity. Among these, a large part is not designed under parasismic regulations. Within this context the evaluation of the vulnerability of existing structures is an important issue. In the framework of the European Community Ecoleader programme, a seismic research project has been performed around shaking table tests on mock-ups representing parts of reinforced concrete buildings, the structure of which is based on structural walls. The program concerns two mock-ups: a Slovenian one and a French one (Fig. 1), the tests being performed at the laboratory LNEC in Lisbon. This work is related to the analysis of the response of the French mock-up. The structure is characteristic of a typical building met in France designed according to the European regulation EC8-1 with the French appendix. It is composed of two parallel walls linked with a perpendicular one that has openings. All the walls are designed for the seismic level prescribed for a typical seismic region in France. Two orthogonal directions of loading have been considered, X (parallel to the main walls) and Y (parallel to the wall connecting the main ones). Natural accelerograms at different levels have been used (PGA = from 0.3 g to 0.85 g for direction X and from 0.14 g to 0.50 g for direction Y) and various data have been collected from the different tests (strain on reinforcements, displacements, accelerations. . .). In order to follow the evolution of the stiffness, the apparent mode has been measured after each test. Two kinds of modeling are performed hereafter: a simplified one using multifiber beams and a refined one, based on a 3D finite element description of the mock-up.

Poutre multifibre Timoshenko pour la modélisation de structures en béton armé: Théorie et applications numériques

ABSTRACT The equations of a 3D multifiber Timoshenko beam element and its use for modeling the non linear behavior of reinforced concrete structures are presented hereafter. The originality of the element is that it has two nodes and higher order interpolation functions in order to deal with shear locking phenomena. Numerical applications and comparisons with experimental results show the well funding of the approach.

Modélisation simplifiée 3D du comportement dynamique de structures en béton armé

ABSTRACT In the framework of the ECOLEADER program dynamic tests have been performed on the seismic table at the laboratory LNEC in Lisbon. The structure tested is a five floor building composed of two parallel walls linked with a perpendicular one that has openings. The scope of the experimental program is to evaluate the behaviour of this structure under bi-directional loading. Multifiber beams are used for the numerical model of the structure. Constitutive laws are based on plasticity for steel and damage mechanics for concrete. Comparison of the numerical and the experimental results shows the performance of the approach.

Seismic vulnerability assessment of a RC structure before and after FRP retrofitting

In earthquake engineering, reliable vulnerability assessment tools suitable to existing reinforced concrete structures are necessary in order to mitigate the seismic risk. Furthermore, amongst the wide range of technical solutions available for structural upgrading, external reinforcement by fiber reinforced polymer (FRP) is often an interesting option. Nevertheless, the use of FRP is limited, one of the reasons being the lack of predictive numerical tools allowing for vulnerability assessment. Based on a case study, this article presents a simplified modeling strategy to assess the seismic vulnerability of an existing reinforced concrete building before and after FRP retrofitting. The structure is simulated using multifiber beam elements and constitutive laws based on damage mechanics and plasticity, while the dynamic characteristics of the numerical model are validated using in-situ ambient vibration records. Nonlinear transient dynamic analysis studies are performed using a synthetic earthquake signal compatible with the Eurocode 8 spectra. Local indicators are adopted to quantify the damage level in the structure before and after FRP retrofitting, in correspondence with the European Macroseismic Scale 98. One of the main conclusions of this study is that the use of local indicators can lead to contradictory assessment results with the evaluations based on global indicators as adopted in HAZUS or Risk-UE.

Simplified modelling strategies for reinforced concrete structures

ABSTRACT Three simplified modelling strategies are proposed to simulate the non linear behaviour of reinforced concrete (RC) structures submitted to severe loadings. The Equivalent Reinforced Concrete model (ERC) is suitable for very squat RC walls and it is based on the Framework method coupled with damage mechanics and plasticity constitutive laws. The multifiber Timoshenko beam can be used for slender or squat structures submitted to severe shear or torsion. Finally, the SSI macro-element coupled with the multifiber beam is able to reproduce soil structure interaction phenomena on the foundation and the structure.

A comparison of displacement-based Timoshenko multi-fiber beams finite element formulations and elasto-plastic applications

Various formulations of displacement-based Timoshenko multi-fiber beams are compared in this article. After a short literature review, the presentation of the shape functions leading to the stiffness matrices and the consistent nodal forces relative to each formulation are presented and their performances are studied using elastic or elastic perfectly plastic constitutive laws and simple to complex static loadings. The advantages and disadvantages of each formulation are highlighted and general conclusions are drawn on the use of displacement-based Timoshenko multi-fiber beams in engineering. An innovative solution is finally proposed to improve the performance for the case of axial-bending interactions.