Nonlinear Wall Models for Earthquake Response Analysis

1. Introduction The use of nonlinear time history analysis for design of new buildings and for strength evaluation of the existing ones is allowed in the Eurocode8. Linear elastic analysis depends on few factors and gives more-or-less comparable results irrespective on the computer code used. The qualities of results obtained by the nonlinear analysis depend on many factors and the obtained results can have only a vague connection to the reality. Their quality, sometimes, questions the endeavor put into it. (If we know that we are going to be wrong we could be it the easy way). There are various numerical models available for the analysis of wall nonlinear response during earthquake excitation. They could be divided into two main groups: microelement- (nonlinear- FEM, micro-fiber, etc.) and macro element-models (beam-column, structural-wall, etc.) models. In this paper, we modeled two reinforced/concrete cantilever walls tested on the shaking table during two European experiments and compared the measured results with the results obtained by using various numerical models. The numerical models used are: micro fiber element model used in ZeusNL (Elnashai, 2004.), structural-wall element model with- and without shear spring used in Ruaumoko (Athol, 2003.) and one component beam-column (wall) element model used in LarzWD (Lopez, 1988.) with the modifications (Sigmund, 2000.). The quality of numerically calculated results have been verified against the measured ones in terms of the response waveforms, maximum displacements and base shears, inter-story drifts of the first story and stiffness degradation expressed as period elongation. 2. Experimental analysis Large-scale RC cantilever structural walls were studied in the frame of the CAMUS (Conception et Analyse des Murs sous Seisme) program on the shaking table at the CEA, Saclay in France. Within the CAMUS3 (Combescure, 2000.), the wall was designed according to the EC8 standard. The project was supported by international benchmark studies (blind analytical predictions and after test numerical simulation). Within the ECOLEADER Slo-wall test (Kante, 2005.) a shaking table test of a 1/3rd scaled specimen, representing relatively low, thin and lightly reinforced H-shaped structural wall with openings was performed. Seismic loading was applied in both horizontal directions at the same time. 3. Numerical models The performed analysis has been limited to the plane in the excitation direction and out-of-plane deformations were neglected. Models were fixed to the shaking table and its deformations were neglected in the calculations. Masses were concentrated at the floor levels and equivalent viscous damping was assumed to be 2%. Geometry of the sections and initial mechanical characteristics of 2 the materials were used the same in all models. The computer codes used were: Ruaumoko (Athol, 2003.) with the Structural-wall (R-wall) and Structural-wall with shear spring model (R-wall+spring), ZeusNonlinear (ZeusNL-wall, Elnashai, et all. 2004.) and LarzWD (LarzWD-wall, Lopez, et all. 1998.). Table 1. Measured and calculated characteristic values Camus III Ecoleader Slo-WALL Wall w+s Wall Wall Wall w+s Wall Wall Exsp R R Z L Exsp R R Z L dxr6 1 0.7 0.7 0.52 0.78 1.00 0.43 0.42 0.69 0.68 IDR23 1 0.64 0.65 0.54 0.73 1.00 0.28 0.26 0.55 0.54 Correlation BS 1 0.56 0.62 0.4 0.76 1.00 0.06 0.09 0.56 0.71 0.51 0.6 0.45 0.51 MDR 0.4 0.16 0.27 0.48 0.29 0.09 % -0.71 -0.25 -0.65 -0.77 -0.75 -0.21 -0.55 -0.52 -0.31 -0.11 IDR 0.87 0.1 0.28 0.45 0.6 0.33 0.12 0.20 0.12 0.06 % -0.5 -0.34 -0.18 -0.3 -0.34 -0.48 -0.27 -0.24 -0.13 -0.07 148.4 107.5 159.5 122.5 154.7 63.50 34.42 35.37 94.40 52.21 Max / Min values BS (kN) Max/Min -151.5 -66.81 -155.4 -158.9 -100.8 -80.15 -30.71 -41.13 -110.04 -70.88 T0 ( s ) 0.15 0.15 0.16 0.1 0.11 0.15 0.11 0.12 0.12 0.12 Period T1 ( s ) 0.22 0.31 0.33 0.24 0.2 0.23 0.42 0.41 0.11 0.16 4. Conclusion Though geometry, material characteristics, masses and input excitations were known before the calculations, different codes gave different quality of the calculated nonlinear response results. The general response values (maximum displacements and base-shear) were much better represented than local ones (inter-story drift). It seems that the first story waveforms are more sensitive to small differences in evaluated stiffness properties. Nonlinear response of r/c walls to earthquake excitation gives a clue on what the true response might be. It still does not fully represent the true wall behavior during earthquake and must be observed statistically. Microelement model (as used in ZeusNL) have no visible advantages over macro element model. Considering many uncertainties involved in establishing input design motion, material characteristics and member behavior, simple macro-element model gives a good idea of expected lateral drifts and maximal responses during inelastic earthquake response of structures and is justified for engineers’ usage. References [1] Athol, J.C., 2003. RUAUMOKO-2D Inelastic Dynamic Analysis, University of Canterbury, NZ [2] Combescure, D., and Chaudat, Th., 2000. ICONS European program seismic tests on r/c bearing walls, CAMUS 3 Specimen, CEA Report DMT, Saclay, France [3] Elnashai, A. et all, 2004. ZeusNL, University of Illinois at Urbana/Champaign, USA, 2004. [4] Lopez, R. and Sozen, M.A., 1988. A Guide to Data Preparation for LARZWD and LARZWS Computer Programs for Non-linear Analysis of Planar Reinforced Concrete Structures Incorporating Frame and Walls, University of Illinois, Urbana, IL. Vladimir Z. Sigmund, Ph.D., Tanja Kalman, MCE and Ivica Guljas, Ph.D. University of Osijek, Faculty of Civil Engineering, Drinska 16a, 31000 Osijek, Croatia, sigmund@gfos.hr