Keywords: RC shear walls, pushover analysis, time history analysis, finite elements, fiber model, shaking table tests.

The paper studies the capability of different modeling approaches, inserted within a displacement based design procedure based on a static pushover analysis, in prediciting the response to a strong earthquake of a new or existing RC structure. At the present state of the art the static push-over procedures are sufficiently well established, and are present in codes mainly devoted to new structures, as Eurocode 8, or to the assessment and rehabilitation of existing ones, as FEMA 356. A key point in their successful performance is the adoption of structural models more refined than those usually adopted in linear analyses, including a correct representation of the non-linear phenomena taking place during the seismic excitation. This results in an inter-dependence of modelling issues and analysis procedures.

The aim of this paper is to investigate the desirable features of a modelling approach for RC structures to be adopted in the procedure for displacement-based-design outlined in FEMA 356. To this purpose reference is made to the experimental results on one of the RC shear walls that were tested on a shaking table during the Camus project (Combescure & Sollogoub [1]). The wall was subjected to a series of seismic inputs, representative of both near and far field earthquakes, and having different peak ground accelerations. In this work the wall has been modelled at different levels of refinement, the meso-scale of the fibre models and the micro-scale of the finite element (FE) method. At the highest level of refinement the micro-scale of FE method is found, where the size of each 2D element is much smaller than the size of the structural element at study. The behaviour of the material is tracked locally, describing correctly not only the non-linear constitutive relations for concrete, steel and the bond between the two, but also the formation and diffusion of cracking [2]. At an intermediate level, within the meso-scale approach of the fibre models, 1D elements are adopted; they have the size of a structural element, but the material behaviour is still described locally on a series of points (fibres) at several cross-sections of the element [3]. Static non-linear analyses have been performed on both models, with different modelling options and by adopting both linear and constant load patterns. The displacement based approach has been subsequently adopted for the curves enveloping at best the dynamic experimental results. Finally, the model at meso scale has been adopted to perform a dynamic non linear analysis of the wall, making use of the seismic inputs that were applied at the base of the shaking table, to test the capability of this procedure in reproducing the effects of a sequence of several seismic events.

The results of the static non-linear analyses indicate that both the meso and micro-scale with a linear load distribution provide a good approximation of the skeleton curve enveloping the seismic cycles. The micro-scale approach is the best to capture the behaviour of the structure up to failure, considering the effects of details on the local behaviour, influencing the global response.

The displacement based approach following FEMA 356 with both the finite element and the fibre model gives a good approximation of global and local parameters of the response to the first three seismic events; hence the convenience of using the simpler meso-scale approach is highlighted. The experimental results for the fourth seismic event of the tests are underestimated by both models: this result shows the shortcomings of a displacement-based procedure applied to a virgin structure, when the actual situation is that of an already damaged building.

The results of the dynamic non-linear analysis at the meso-scale provide the best approximation of the test data, both as time history and envelope of maximum results, as a consequence of considering both the non-linearity of the response and the dynamic nature of the phenomena.

1

D. Combescure and P. Sollogoub, "Rapport DM2S (SEMT/EMSI/RT/02-047/C) IAEA CRP-NFE Camus Benchmark - Experimental results and specifications to the participants", CEA, Direction de l'Energie Nucléaire, February 2004.

2

M.G. Mulas, D. Coronelli, L. Martinelli, "Modeling of shear behavior in existing RC structures", submitted for possible publication to ACI Structural Journal, July 2004.

3

L. Martinelli, "The Behavior of Reinforced Concrete Piers Under Strong Seismic Actions", 12th World Conference on Earthquake Engineering, New Zealand, ID 1081, 2000.

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