Multi‐scale modelling approach for the pushover analysis of existing RC shear walls—Part I: Model formulation

Abstract

This work focuses on the modelling issues related to the adoption of the pushover analysis for the seismic assessment of existing reinforced concrete (RC) structures. To this purpose a prototype reference structure, one of the RC shear walls designed according to the multi-fuse concept and tested on shaking table for the CAMUS project, is modelled at different levels of refinement. The meso-scale of a stiffness-based fibre element and the micro-scale of the finite element (FE) method are herein adopted; in the latter separate elements are adopted for the concrete, the steel and the steel-concrete interface. This first of the two companion papers presents in detail the wall under study, illustrating the design philosophy, the geometry of the wall, the instrumentation set-up and the test programme. The two modelling approaches are then described; the most important points in terms of element formulation and constitutive relations for materials are presented and discussed for each approach, in the light of the particular design of the wall and of its experimental behaviour. fact: the necessity to assess both the effectiveness of the new seismic design codes and the performance of many existing structures, designed according to seismic provisions that have been judged insufficient. In both cases a challenging task must be faced: experimental and numerical simulations of the structural response in the non-linear dynamic/cyclic range are often necessary, since a direct study of earthquake excited structures is seldom possible. Experimental tests, however, are quite costly and often limited to structural components; they should provide the calibration of non-linear models to be adopted in numerical analyses. Highly refined models are needed to fully reproduce the complex degradation phenomena in the non-linear range, while simple models, a compromise between accuracy and simplicity, are necessary if a whole structure must be analysed under the effect of several earthquakes.Moreover, the philosophy of seismic design itself is at the moment under review. Recent earthquakes (Northridge 1994, Hanshin-Awaji-Kobe 1995 have shown that the level of damage to structures and the consequent economic losses have been unexpectedly high, even though buildings designed according to recent codes have performed well from the point of view of the safety of human lives. This fact has given rise to some criticism on the conventional methods of seismic design, aiming to fulfil the no-collapse requirement and based on limits on stresses and member forces resulting from a prescribed set of lateral forces or a design spectrum. The presence of many uncertainties about both the seismic demand and the seismic capacity of the structure in fact makes it difficult to assess the level of performance guaranteed with a specific design for earthquakes of different intensities. A more general design philosophy, the performance-based design, has thus been proposed, 'in which the design criteria are expressed in terms of achieving stated performance object...

Multi‐scale modelling approach for the pushover analysis of existing RC shear walls—Part II: Experimental verification

“…The bond parameters are calibrated in relation to the confinement situation and the surface characteristics of the bars in the CAMUS I wall, described in the companion paper [2]. The bond model parameters, determined according to the values provided by the MC90 [4], are detailed in Table I.…”

“…At the meso-scale a single model, depicted in Figure 1(c), has been analysed with the computer code NONDA [2]. A 2-node linear elastic beam element describes the basement of the wall; its cross-sectional properties are computed from the gross area and Young's modulus E = 30.0 GPa.…”

“…Due to the way the truss mechanism is modelled at the cross-sectional level [2], it is not necessary to explicitly define the area of concrete of the diagonal springs of this mechanism but only the mechanical properties of the concrete material and the geometrical ratio of the shear reinforcement. This value does not vary along the height of the wall and has been computed considering the rectangular hoop at the centre of the section.…”

“…These are given, due to the seismic nature of the load, by the inertia forces acting at each floor (where practically all the masses in the mock-up were located), computed as the product of the floor mass and absolute horizontal acceleration. The time history of the latter is recorded by the accelerometers placed on each floor as part of the instrumentation [2]. Damping forces acting on the structure, assumed to be mainly of hysteretic type, do not contribute to the reaction force at the base.…”

“…The main features of the two modelling approaches have been shown in a companion paper [2], together with a description of the structure under study and of the experimental programme. The structural models developed for the numerical analyses are described in this second paper; the results of the static pushover analysis, both with the FE and the fibre model, are presented in terms of global and local response and compared to the experimental results.…”