Abstract
The severe damage and collapse of many reinforced concrete (RC) wall buildings in the recent earthquakes of Chile (2010) and New Zealand (2011) have shown that RC walls did not perform as well as required by the modern codes of both countries. It seems therefore appropriate to intensify research efforts towards more accurate simulations of damage indicators, in particular local engineering demand parameters such as material strains, which are central to the application of performance-based earthquake engineering. Potential modelling improvements will necessarily build on a thorough assessment of the limitations of current state-of-the-practice simulation approaches for RC wall buildings. This work compares different response parameters obtained from monotonic analyses of RC walls using numerical tools that are commonly employed by researchers and specialized practitioners, namely: plastic hinge analyses, distributed plasticity models, and shell element models. It is shown that a multi-level assessment—wherein both the global and local levels of the response are jointly addressed during pre- and post-peak response—is fundamental to define the dependability of the results. The displacement demand up to which the wall response can be predicted is defined as the first occurrence between the attainment of material strain limits and numerical issues such as localization. The present work also presents evidence to discourage the application of performance-based assessment of RC walls relying on non-regularized strain EDPs.
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Notes
Proposals for plastic hinge analyses wherein shear displacements are accounted for will be analysed in the present document.
Due to numerical issues, the Basic model does not reach the steel MSL.
References
SEAOC (1959) Recommended lateral force requirements and commentary. Seismology Committee, Structural Engineers Association of California, First Edition
Bozorgnia Y, Bertero VV (2004) Earthquake engineering—from engineering seismology to performance-based engineering. CRC Press
SEAOC (1980) Recommended lateral force requirements and commentary. Seismology Committee, Structural Engineers Association of California, Fourth Edition Revised
ATC-3-06 (1978) Tentative provisions for the development of seismic regulations for buildings. Applied Technology Council, California
EN1998-3 (2005) Eurocode 8: design of structures for earthquake resistance. Part 3: Assessment and retrofitting of buildings. Doc CEN/TC250/SC8/N306
FEMA 356 (2000) Prestandard and commentary for the seismic rehabilitation of buildings. Federal Emergency Management Agency. California, USA
ATC-40 (1996) Seismic evaluation and retrofit of concrete buildings. Applied Technology Council. Redwood City, CA
SEAOC (1995) Vision 2000—performance based seismic engineering of buildings. Structural Engineers Association of California. Sacramento, California, USA
ASCE (2006) ASCE/SEI 41–06: seismic rehabilitation of existing buildings. ASCE, Reston
FEMA (2012) FEMA P-58-1: seismic performance assessment of buildings, vol. 1—Methodology. Prepared by the Applied Technology Council for the Federal Emergency Management Agency. USA
FEMA (2012) FEMA P-58-2: seismic performance assessment of buildings, vol. 2—Implementation guide. Prepared by the Applied Technology Council for the Federal Emergency Management Agency. USA
EN1998-1 (2004) Eurocode 8: design of structures for earthquake resistance. Part 1: general rules, seismic actions and rules for buildings. Doc CEN/TC250/SC8/N306
FEMA 368 (2001) NEHRP recommended provisions for seismic regulations for new buildings and other structures. Federal Emergency Management Agency. Washington D.C., USA
ASCE 7-02 (2002) Minimum design loads for buildings and other structures. American Society of Civil Engineers. Reston, VA, USA
Romão X, Delgado R, Costa A (2010) Practical aspects of demand and capacity evaluation of RC members in the context of EC8-3. Earthq Eng Struct Dyn 39:473–499
Whittaker A, Deierlein GG, Hooper J, Merovich A (2004) ATC-58 project task report: engineering demand parameters for structural framing systems. Prepared for the Applied Technology Council by the ATC-58 Structural Performance Products Team. USA
Computers and Structures Inc. (2013) Perform-3D: nonlinear analysis and performance assessment for 3D structures. Computers and Structures Inc., Berkeley
Computers and Structures Inc. (2013) ETABS 2013: integrated analysis, design and drafting of building systems. Computers and Structures Inc., Berkeley
SeismoSoft (2013) SeismoStruct—a computer program for static and dynamic nonlinear analysis of framed structures
OpenSees (2013) Open system for earthquake engineering simulation, version 2.4.3
Wong PS, Vecchio FJ, Trommels H (2014) VecTor2—software for nonlinear analysis of two-dimensional reinforced concrete membrane structures
Berry MP, Lehman DE, Lowes LN (2008) Lumped-plasticity models for performance simulation of bridge columns. ACI Struct J 105(3):270–279
Mackie K, Stojadinovic B (2001) Seismic demands for performance-based design of bridges. In: PEER annual meeting
Sritharan S, Beyer K, Henry RS, Chai YH, Kowalsky M, Bull D (2014) Understanding poor seismic performance of concrete walls and design implications. Earthq Spectra 30(1):307–334
Ile N, Reynouard JM (2005) Behaviour of U-shaped walls subjected to uniaxial and biaxial cyclic lateral loading. J Earthq Eng 9(1):67–94
Mazars J, Kotronis P, Ragueneau F, Casaux G (2006) Using multifiber beams to account for shear and torsion. Comput Methods Appl Mech Eng 195(52):7264–7281
Sittipunt C, Wood SL (1993) Finite element analysis of reinforced concrete shear walls. Report, University of Illinois, Urbana, Illinois
Palermo D, Vecchio FJ (2007) Simulation of cyclically loaded concrete structures based on the finite-element method. J Struct Eng 133(5):728–738
Beyer K, Simonini S, Constantin R, Rutenberg A (2014) Seismic shear distribution among interconnected cantilever walls of different lengths. Earthq Eng Struct Dyn 43(10):1423–1441
Orakcal K, Massone LM, Wallace JW (2006) Analytical modeling of reinforced concrete walls for predicting flexural and coupled shear–flexural responses. Report No. PEER 2006/07, PEER University of California at Berkeley, Los Angeles, California
Beyer K, Dazio A, Priestley MJN (2008) Seismic design of torsionally eccentric buildings with U-shaped RC walls, Pavia. Research Report ROSE School, Pavia
Beyer K, Dazio A, Priestley MJN (2008) Inelastic wide-column models for U-shaped reinforced concrete walls. J Earthq Eng 12(sup1):1–33
Miki T, Niwa J (2004) Nonlinear analysis of RC structural members using 3D lattice model. J Adv Concr Technol 2(3):343–358
Lu Y, Panagiotou M (2014) Three-dimensional cyclic beam-truss model for nonplanar reinforced concrete walls. J Struct Eng 140(3):1–11
Lu Y, Panagiotou M (2012) Three-dimensional nonlinear cyclic beam-truss model for non-planar reinforced concrete walls. Report No. UCB/SEMM-2012/01, Department of Civil and Environmental Engineering, University of California at Berkeley, Berkeley, USA
Belletti B, Damoni C, Gasperi A (2013) Modeling approaches suitable for pushover analyses of RC structural wall buildings. Eng Struct 57:327–338
Yazgan U, Dazio A (2011) Simulating maximum and residual displacements of RC structures: I Accuracy. Earthq Spectra 27(4):1187–1202
Hines EM (2002) Seismic performance of hollow rectangular reinforced concrete bridge piers with confined corner elements. Ph.D. Thesis, University of California
Paulay T, Priestley MJN (1992) Seismic design of reinforced concrete and masonry buildings. Wiley, New York
Priestley MJN, Calvi GM, Kowalsky MJ (2007) Displacement-based seismic design of structures. IUSS Press, Pavia
Arbulu AGB (2006) Plastic hinge length in high-rise concrete shear walls. M.Sc. University of British Columbia, Vancouver, Canada
Fardis MN (2009) Seismic design, assessment and retrofitting of concrete buildings. Springer, Dordrecht
Pam HJ, Ho JCM (2009) Length of critical region for confinement steel in limited ductility high-strength reinforced concrete columns. Eng Struct 31(12):2896–2908
Bae S, Bayrak O (2008) Plastic hinge length of reinforced concrete columns. ACI Struct J 105(3):290–300
Almeida JP, Das S, Pinho R (2012) Adaptive force-based frame element for regularized softening response. Comput Struct 102–103:1–13
NZS 3101 (2006). Concrete structures standard. Part 1 - The design of concrete structures. Standards Council. New Zealand
NZS 3101 (2006). Concrete structures standard. Part 2 - Commentary on the design of concrete structures. Standards Council. New Zealand
ACI 318 (2002) Building code requirements for structural concrete (ACI 318-02) and Commentary (ACI 318R-02). American Concrete Institute (ACI) Committee. USA
Coleman J, Spacone E (2001) Localization issues in force-based frame elements. J Struct Eng 127(11):1257–1265
Scott MH, Fenves GL (2006) Plastic hinge integration methods for force-based beam-column elements. J Struct Eng 132(2):244–252
Crisfield MA (1990) A consistent co-rotational formulation for non-linear, three-dimensional, beam-elements. Comput Methods Appl Mech Eng 81(2):131–150
Wong PS, Vecchio FJ, Trommels H (2013) VecTor2 & FormWorks User’s Manual. University of Toronto
Mander JB, Priestley MJN, Park R (1988) Theoretical stress–strain model for confined concrete. J Struct Eng 114(8):1804–1826
Biskinis D, Fardis MN (2010) Flexure-controlled ultimate deformations of members with continuous or lap-spliced bars. Struct Concr 11:93–108
Kowalsky MJ (2000) Deformation limit states for circular reinforced concrete bridge columns. J Struct Eng 126(8):869–878
Kazaz Í, Gulkan P, Yakut A (2012) Deformation limits for structural walls with confined boundaries. Earthq Spectra 28(3):1019–1046
Calabrese A, Almeida JP, Pinho R (2010) Numerical issues in distributed inelasticity modeling of RC frame elements for seismic analysis. J Earthq Eng 14(S1):38–68
Pugh JS, Lowes LN, Lehman DE (2014) Seismic design of concrete walled buildings. In: Second European conference on earthquake engineering and seismology. Istanbul
Beyer K, Dazio A, Priestley MJN (2011) Shear deformations of slender reinforced concrete walls under seismic loading. ACI Struct J 108(2):167–177
Lodhi MS, Sezen H (2012) Estimation of monotonic behavior of reinforced concrete columns considering shear–flexure–axial load interaction. Earthq Eng Struct Dyn 41:2159–2175
Dazio A, Beyer K, Bachmann H (2009) Quasi-static cyclic tests and plastic hinge analysis of RC structural walls. Eng Struct 31(7):1556–1571
Hines EM, Restrepo JI, Seible F (2004) Force–displacement characterization of well-confined bridge piers. ACI Struct J 101(4):537–548
Miranda PA, Calvi GM, Pinho R, Priestley MJN (2005) Displacement-based assessment of RC columns with limited shear resistance. IUSS Press, Pavia
Park R, Paulay T (1975) Reinforced concrete structures. Wiley, New York
Xu S, Zhang J (2011) Hysteretic shear–flexure interaction model of reinforced concrete columns for seismic response assessment of bridges. Earthq Eng Struct Dyn 40:315–337
Zhang J, Xu S, Tang Y (2011) Inelastic displacement demand of bridge columns considering shear–flexure interaction. Earthq Eng Struct Dyn 40:731–748
Guedes J, Pinto AV (1997) A numerical model for shear dominated bridge piers. In: 2nd Italy–Japan workshop on seismic design and retrofit of bridges. Tsukuba, Japan
Navarro Gregori J, Miguel Sosa P, Fernández Prada Ma, Filippou FC (2007) A 3D numerical model for reinforced and prestressed concrete elements subjected to combined axial, bending, shear and torsion loading. Eng Struct 29(12):3404–3419
Ceresa P, Petrini L, Pinho R, Sousa R (2009) A fibre flexure–shear model for seismic analysis of RC-framed structures. Earthq Eng Struct Dyn 38:565–586
Petrangeli M (1996) Modelli numerici per strutture monodimensionali in cemento armato. PhD Thesis
Remino M (2004) Shear modeling of RC concrete structures. Starrylink Editrice Collana Tesi e Ricerca. PhD Thesis
Marini A, Spacone E (2007) Analysis of reinforced concrete elements including shear effects. ACI Struct J 103(5):645–655
Petrangeli M, Pinto PE, Ciampi V (1999) Fiber element for cyclic bending and shear of RC structures. I: Theory. J Eng Mech 125(9):994–1001
Martinelli L (2002) Numerical simulation of cyclic tests of R/C shear walls. In: 12th European conference on earthquake engineering. London, United Kingdom
Ranzo G, Petrangeli M (1998) A fibre finite beam element with section shear modelling for seismic analysis of RC structures. J Earthq Eng 2(3):443–473
Mergos PE, Beyer K (2013) Modelling shear–flexure interaction in equivalent frame models of slender reinforced concrete walls. Struct Des Tall Spec Build Published Online First. doi:10.1002/tal
Correia AA, Almeida JP, Pinho R (2014) Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part I: Theory. Eng Struct (accepted for publication)
Almeida JP, Correia AA, Pinho R (2014) Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part II: Applications. Eng Struct (accepted for publication)
Vecchio FJ, Collins MP (1986) The modified compression-field theory for reinforced concrete elements subjected to shear. ACI J 83(2):219–231
Vecchio FJ (2000) Disturbed stress field model for reinforced concrete: formulation. J Struct Eng 126(9):1070–1489
Richart FE, Brandtzaeg A, Brown RL (1928) A study of the failure of concrete under combined compressive stresses. Univ Illinois Bull XXVI(12)
Imran I, Pantazopoulou SJ (1996) Experimental study of plain concrete under triaxial stress. ACI Struct J 93(6):589–601
Samani AK, Attard MM (2012) A stress–strain model for uniaxial and confined concrete under compression. Eng Struct 41:335–349
Cusson D, Paultre P (1995) Stress–strain model for confined high-strength concrete. J Struct Eng 121(3):468–477
Willam KJ, Warnke EP (1974) Constitutive model for the triaxial behaviour of concrete. In: Seminar on “Concrete Structures Subjected fo Triaxial Stresses”. Bergamo, Italy
Cusson D, Paultre P (1994) High-strength concrete columns confined by rectangular ties. J Struct Eng 120(3):783–804
Légeron F, Paultre P (2003) Uniaxial confinement model for normal- and high-strength concrete columns. J Struct Eng 129(2):241–252
Sheikh SA, Uzumeri SM (1982) Analytical model for concrete confinement in tied columns. J Struct Div 108(ST12):2703–2722
Tarquini D (2014) Modelling approaches for inelastic behaviour of RC walls: multi-level assessment and dependability of results. M.Sc. Thesis, ROSE Master Program, Istituto Universitario di Studi Superiori, Pavia, Italy
Priestley MJN, Seible F, Calvi GM (1996) Seismic design and retrofit of bridges. Wiley, New York
Lin C-S, Scordelis AC (1975) Nonlinear analysis of RC shells of general form. J Struct Div 101(3):523–538
Popovics S (1973) A numerical approach to the complete stress–strain curve of concrete. Cem Concr Res 3(5):583–599
Hagsten LG, Hestbech L, Fisker J (2011) Energiprincipper—del 3: Betonkonstruktioner. Teori, lecture notes
Hannewald P (2013) Seismic behavior of poorly detailed RC bridge piers. Ph.D. Thesis, Thesis No. 5894:183, École polytechnique fédérale de Lausanne, Lausanne, Switzerland
Neuenhofer A, Filippou FC (1997) Evaluation of nonlinear frame finite-element models. J Struct Eng 123(7):958–966
Menegotto M, Pinto PE (1973) Method of analysis for cyclically loaded RC plane frames including changes in geometry and non-elastic behaviour of elements under combined normal force and bending. In: IABSE Symposium on resistance and ultimate deformability of structures acted on by well defined repeated loads—Final Report
Filippou FC, Popov EP, Bertero VV (1983) Effects of bond deterioration on hysteretic behavior of reinforced concrete joints. University of California, Berkeley
De Veubeke BF (1965) Displacement and equilibrium models in the finite element method. In: Stress analysis. Wiley, New York, pp 145–197
Bazant ZP (1976) Instability, ductility and size effect in strain-softening concrete. J Eng Mech Div 102(2):331–344
Bazant ZP, Pan J, Pijaudier-Cabot G (1987) Softening in reinforced concrete beams and frames. J Struct Eng 113(12):2333–2347
De Borst R, Sluys LJ, Muhlhaus H-B, Pamin J (1993) Fundamental issues in finite element analyses of localization of deformation. Eng Comput 10(2):99–121
Kupfer H, Hilsdorf HK, Rusch H (1969) Behavior of concrete under biaxial stresses. ACI J 66(8):656–666
Hsieh SS, Ting EC, Chen W-F (1979) An elastic-fracture model for concrete. In: 3rd ASCE/EMD Specialty Conference, Austin, Texas, pp 437–440
Ottosen NS (1977) A failure criterion for concrete. ASCE J Eng Mech Div 103(4):527–535
Acknowledgments
The work was financially supported by the Stiftung zur Förderung der Denkmalpflege in the framework of the project ‘Erbebenverhalten von bestehenden Stahlbetongebäuden mit dünnen Wänden’. The authors would like to thank the invaluable support provided by Prof. Frank Vecchio, from the University of Toronto, regarding the use of software VecTor2. The suggestions given by Prof. Rui Pinho, who thoroughly reviewed the manuscript, and by Prof. Sri Sritharan, are also kindly acknowledged. Finally, a word of gratitude goes to Hugues Vincent for the work carried out during his internship at the Earthquake Engineering and Structural Dynamics Laboratory, in École Polytechnique Fédérale de Lausanne.
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Almeida, J.P., Tarquini, D. & Beyer, K. Modelling Approaches for Inelastic Behaviour of RC Walls: Multi-level Assessment and Dependability of Results. Arch Computat Methods Eng 23, 69–100 (2016). https://doi.org/10.1007/s11831-014-9131-y
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DOI: https://doi.org/10.1007/s11831-014-9131-y