Nonlinear Analysis of Squat RC Walls Using Three-Dimensional Continuum Finite Element Models

J. Murcia-Delso1; R. S. Dunham2; D. R. Parker3; and R. J. James4

1Tecnalia, Parque Científico y Tecnológico de Bizkaia, Edificio 700, Derio 48160, Spain. E-mail: juan.murcia@tecnalia.com 2ANATECH Corp., 5435 Oberlin Dr., San Diego, CA 92121. E-mail: bob.dunham@anatech.com 3ANATECH Corp., 5435 Oberlin Dr., San Diego, CA 92121. E-mail: dan.parker@anatech.com 4ANATECH Corp., 5435 Oberlin Dr., San Diego, CA 92121. E-mail: randy.james@anatech.com Abstract This paper presents the three-dimensional finite element analysis of squat RC walls using a continuum constitutive model for concrete developed at ANATECH. The concrete model is based on the smeared-cracking concept and an elastic-plastic formulation that permits the simulation of cracking and other particular response characteristics of concrete. The laws governing the normal and tangential stresses on a crack are suitable for the simulation of shear failures and crack closing and re-opening under load reversals. Finite element models have been developed to reproduce experiments on squat walls found in the literature. These tests were conducted on walls with rectangular and non-rectangular sections subjected to cyclic lateral loading. The finite element models provide a good representation of the nonlinear response and shear failure of these walls. Results of a blind simulation of a five-story shear wall building tested on a shake-table, in which a diagonal shear failure was well predicted, are also presented. INTRODUCTION Reinforced concrete (RC) shear walls are commonly used as lateral-force resisting systems in buildings. RC walls can have a flexural-dominated or shear-dominated behavior depending on their aspect ratio, axial load, and reinforcement characteristics. Squat walls with low aspect ratio (height-to-length ratio less than 2), high axial loads, and heavily reinforced in flexure tend to behave in shear. These walls may experience diagonal tension failure when there is not sufficient horizontal shear reinforcement. When adequately reinforced to constraint the opening of diagonal cracks, failure may occur by crushing of the concrete due to diagonal

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compression forces or sliding shear. Even though ductile design principles and practices are intended to ensure flexural behavior of these elements, it is difficult to preclude the shear-dominated behavior of squat walls in short buildings and squat wall segments in taller buildings for walls with strong coupling effects or openings. In addition, existing buildings constructed before ductile design practices were implemented are likely to have shear-critical walls. Performance-based seismic design and assessment of buildings relies on the use of analytical models that can accurately predict their structural response. Modeling the nonlinear behavior of squat walls is a challenging task because of their shear-dominated behavior. Diagonal and sliding shear-resisting mechanisms in RC walls are commonly represented by approximate phenomenological models derived from experimental data. For example, ASCE 41-13 (ASCE 2013) provides lateral force – deformation backbone curves for shear-critical wall segments and coupling beams. However, these curves have been calibrated with limited test data. The use of high-fidelity finite element models that capture the mechanics of shear failures in RC structures are a versatile and more realistic alternative to phenomenological models. They are also an inexpensive complement to the laboratory tests allowed by ASCE 41 to derive case-specific backbone curves for the application of this standard. This paper presents the three-dimensional nonlinear analysis of RC shear walls using an advanced constitutive model for concrete developed at ANATECH. The salient features of the constitutive model and the results of finite element analyses of laboratory tests on RC walls are presented. The tests analyzed include rectangular and non-rectangular walls subjected to quasi-static cyclic loading which failed in shear, and a five-story shear wall building tested on a shake-table. CONCRETE CONSTITUTIVE MODEL The behavior of concrete is highly nonlinear with small tensile strengths, shear stiffness and strength that depend on crack widths, and compressive capacity degradation after the compressive strength is reached. Modeling concrete, especially under conditions where extensive damage can develop, requires advanced and detailed constitutive models. In response to this need, ANATECH has developed and refined over the past decades a constitutive model that is based on the pioneering work on smeared-crack models by Rashid (1968). This concrete model has been extensively used to predict the nonlinear behavior of RC structures in nuclear facilities and critical civil infrastructure, and has been validated with data from large-scale tests (e.g., Rashid et al. 2001). The main features of the constitutive model are presented in the following. In compression, concrete has an elastic-plastic behavior. The uniaxial stress-strain behavior obtained from material test data is generalized to multi-axial behavior with an isotropic-hardening plasticity formulation, using a Drucker-Prager surface to represent the yield condition. A non-associated plastic flow rule is defined to control

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CONCLUSION Performance-based analysis of shear-dominated RC walls often relies on phenomenological models derived from limited experimental data. High-fidelity mechanics-based finite element models can be a more versatile alternative to predict the behavior of these walls. They can also be used as a support for the calibration of phenomenological models. A three-dimensional constitutive model for concrete capable of predicting the shear behavior of RC walls has been presented in this paper. The model uses a smeared-cracking approach, and includes shear retention and shear shedding capabilities that allow a correct characterization of shear stresses across cracks. Nonlinear finite element analyses using this model have predicted with reasonably good accuracy the lateral strength, stiffness, deformation capacity, and hysteretic energy dissipation capacity of squat walls tested under cyclic loading. The models have also reproduced the shear failures observed in the tests, which included diagonal cracking and concrete crushing. REFERENCES

Al-Mahaidi, R.S.H. (1979), Nonlinear Finite Element Analysis of Reinforced Concrete Deep Members, Rep 79-1, Cornell University, Structural Engineering Department.

ASCE (2013), Seismic Evaluation and Retrofit of Existing Buildings (ASCE 41-13), Reston, Virginia.

Commissariat a l’Energie Atomique (1997), Mock-up and Loading Characteristic Specifications for the Participants Report, Report 1, CAMUS International Benchmark, France.

Dassault Systemes. (2014), Abaqus Version 6.14, Providence, RI.

Dowel, R.K., Zhang, L. (1998), Prediction Analysis of a 1/3-Scale Reinforced Building, Report to CAMUS International Benchmark, ANATECH Report ANA-98-0234.

Elwood, K.J., Matamoros, A.B., Wallace, J.W., Lehman, D.E., Heintz, J.A., Mitchell, A.D., Moore, M.A., Valley, M.T., Lowes, L.N., Comartin, C.D., Moehle, J.P. (2007), “Update to ASCE/SEI 41 Concrete Provisions,” Earthquake Spectra, 23 (3), 493-523.

Hidalgo, P.A., Ledezma, C.A., and Jordan, R.M. (2002), “Seismic Behavior of Squat Reinforced Concrete Shear Walls.” Earthquake Spectra, 18 (2), 287-308.

Orakcal, K., Massone, L.M., Wallace, J.W. (2009), “Shear Strength of Lightly Reinforced Wall Piers and Spandrels.” ACI Structural Journal, 106 (4), 455-465.

Palermo, D., Vecchio, F.J. (2002), “Behavior of Three-Dimensional Reinforced Concrete Shear Walls.” ACI Structural Journal, 99 (1), 81-89.

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Rashid, Y.R. (1968), “Ultimate Strength Analysis of Prestressed Concrete Pressure Vessels,” Nuclear Engineering and Design, 7, pp. 334-344.

Rashid, J.Y.R., Dameron, R.A., Dunham, R.S. (2001), “Finite Element Analysis of Reinforced Concrete in Bridge Seismic Design Practice,” Modeling of Inelastic Behavior of RC Structures Under Seismic Loads, edited by P. Benson Shing and Tada-aki Tanabe, ASCE, 217-233.

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