Enhanced empirical models for predicting the drift capacity of less ductile RC columns with flexural, shear, or axial failure modes

Abstract

Capacity of components subjected to earthquake actions is still a widely interesting research topic. Hence, developing precise tools for predicting drift capacities of reinforced concrete (RC) columns is of great interest. RC columns are not only frequently constructed, but also their composite behavior makes the capacity prediction a task faced with many uncertainties. In the current article, novel empirical approaches are presented for predicting flexural, shear and axial failure modes in RC columns. To this aim, an extensive experimental database was created by collecting outcomes of previously conducted experimental tests since 1964, which are available in the literature. It serves as the basis for deriving the equations for predicting the drift capacity of RC columns by different regression analyses (both linear with different orders and nonlinear). Furthermore, fragility curves are determined for comparing the obtained results with the experimental results and with previously proposed models, like the ones of ASCE/SEI 41-13. It is demonstrated that the proposed equations predict drift capacities, which are in better agreement with experimental results than those computed by previously published models. In addition, the reliability of the proposed equations is higher from a probabilistic point of view.

Keywords

flexural-shear-axial failure / drift capacity / reinforced concrete columns / statistical analysis / fragility curves

References

[1] Allahvirdizadeh R, Rashetnia R, Dousti A, Shekarchi M. Application of polymer concrete in repair of concrete structures: A literature review. The 4th International Conference on Concrete Repair, Dresden, Germany, 2011

[2] Ellingwood B R. Earthquake risk assessment of building structures. Reliability Engineering & System Safety, 2001, 74(3): 251–262

[3] Chao S H, Goel S C, Lee S S. A seismic design lateral force distribution based on inelastic state of structures. Earthquake Spectra, 2007, 23(3): 547–569

[4] Allahvirdizadeh R, Khanmohammadi M, Marefat M S. Local and global design criteria in performance-based seismic design of new R.C buildings. The 4th International Conference on Seismic Retrofitting, Tabriz, Iran, 2013

[5] Allahvirdizadeh R, Khanmohammadi M, Marefat M S. Investigating effects of scaling and selecting earthquake ground motions on performance-based design of RC buildings. The 4th International Conference on Concrete & Development, Tehran, Iran, 2013

[6] Allahvirdizadeh R, Mohammadi M A. Upgrading equivalent static method of seismic designs to performance-based procedure. Journal of Earthquakes and Structures, 2016, 10(4): 849–865

[7] Azadi Kakavand M R, Neuner M, Schreter M, Hofstetter G. A 3D continuum FE-model for predicting the nonlinear response and failure modes of RC frames in pushover analyses. Bulletin of Earthquake Engineering, 2018, 16(10): 4893–4917

[8] Hamdia K M, Arafa M, Alqedra M. Structural damage assessment criteria for reinforced concrete buildings by using a Fuzzy Analytic Hierarchy Process. Underground Space, 2018, 3(3): 243–249

[9] Farahmand H, Kakavand M R A, Tafreshi S T, Hafiz P H. The effect of mechanical and geometric parameters on the shear and axial failures of columns in reinforced concrete frames. Journal of Ciencia & Natura, 2015, 37: 247–259

[10] Shirmohammadi F, Esmaeily A. Performance of reinforced concrete columns under bi-axial lateral force/displacement and axial load. Journal of Engineering Structures, 2015, 99: 63–77

[11] Choi K K, Truong G T, Kim J C. Seismic performance of lightly shear reinforced RC columns. Journal of Engineering Structures, 2016, 126: 490–504

[12] Weng J, Lee C K, Tan K H, Lim N S. Damage assessment for reinforced concrete frames subject to progressive collapse. Journal of Engineering Structures, 2017, 149: 147–160

[13] Witarto W, Lu L, Roberts R H, Mo Y L, Lu X. Shear-critical reinforced concrete columns under various loading rates. Frontiers of Structural and Civil Engineering, 2014, 8(4): 362–372

[14] Sharifi Y, Maghsoudi A A. An experimental study on the flexural behavior of heavily steel reinforced beams with high-strength concrete. Frontiers of Structural and Civil Engineering, 2014, 8(1): 46–56

[15] Marí A, Cladera A, Bairán J, Oller E, Ribas C. Shear-flexural strength mechanical model for the design and assessment of reinforced concrete beams subjected to point or distributed loads. Frontiers of Structural and Civil Engineering, 2014, 8(4): 337–353

[16] Adibi M, Marefat M S, Allahvirdizadeh R. Nonlinear modeling of cyclic response of RC beam-column joints reinforced by plain bars. Bulletin of Earthquake Engineering, 2018, 16(11): 5529–5556

[17] Shing P B, Spencer B. Modeling of shear behavior of RC bridge structures. In: Modeling of Inelastic Behavior of RC Structures Under Seismic Load. American Society of Civil Engineers, 2001, 315–333

[18] Ozbolt J, Mayer U, Vocke H. Smeared fracture FE-analysis of reinforced concrete structures – theory and examples. In: Modeling of Inelastic Behavior of RC Structures Under Seismic Load. American Society of Civil Engineers, 2001, 234–256

[19] Kaneko Y, Mihashi H, Ishihara S. Entire load-displacement characteristics for direct shear failure of concrete. In: Modeling of Inelastic Behavior of RC Structures Under Seismic Load. American Society of Civil Engineers, 2001, 175–192

[20] Kato D, Ohnishi K. Axial load carrying capacity of reinforced concrete columns under lateral load reversals. In: Proceedings of the Third US-Japan Workshop on Performance-Based Earthquake Engineering Methodology for Reinforced Concrete Building Structures, 2002, 247–255

[21] Sezen H. Seismic Response and Modeling of Reinforced Concrete Building Columns. Dissertation for the Doctoral Degree. Berkeley: University of California, 2002

[22] Pujol S, Ramirez J A, Sozen M A. Drift capacity of reinforced concrete columns subjected to cyclic shear reversals. Seismic response of concrete bridges, Special Publication. American Concrete Institute, 1999, 187: 255–274

[23] Pujol S, Sozen M, Ramírez J A. Transverse reinforcement for columns of frames to resist earthquakes. Journal of Structural Engineering, 2000, 126(4): 461–466

[24] Pincheira J A, Dotiwala F S, D’Souza J T. Seismic analysis of older reinforced concrete columns. Earthquake Spectra, 1999, 15(2): 245–272

[25] Elwood K J. Shake table tests and analytical studies on the gravity load collapse of reinforced concrete frames. Dissertation for the Doctoral Degree. Berkeley: University of California, 2002

[26] Zhu L, Elwood K J, Haukaas T. Classification and seismic safety evaluation of existing reinforced concrete columns. Journal of Structural Engineering, 2007, 133(9): 1316–1330

[27] ASCE/SEI 41. Seismic Rehabilitation of Existing Buildings. American Society of Civil Engineers, Reston, Virginia, USA, 2013

[28] Thanh Ngoc Tran C, Li B. Ultimate displacement of reinforced concrete columns with light transverse reinforcement. Journal of Earthquake Engineering, 2013, 17(2): 282–300

[29] Aboutaha R S, Engelhardt M D, Jirsa J O, Kreger M E. Rehabilitation of shear critical concrete columns by use of rectangular steel jackets. ACI Structural Journal, 1999, 90(1): 68–78

[30] Arakawa T, Arai Y, Mizoguchi M, Yoshida M. Shear resisting behavior of short reinforced concrete columns under biaxial bending-shear and varying axial load. Transactions of the Japan Concrete Institute, 1990, 12: 347–354

[31] Atalay M B, Penzien J. The seismic behavior of critical regions of reinforced concrete components as influenced by moment, shear and axial force. University of California, Berkeley, California, 1975

[32] Azizinamini A, Johal L S, Hanson N W, Corley W G. Effects of transverse reinforcement on seismic performance of columns – A partial parametric investigation. Project No. CR-9617, Construction Technology Laboratories, Skokie, Illinois, 1988

[33] Bayrak O, Sheikh S. Design of rectangular HSC columns for ductility. Special Publication, American Concrete Institute, 2003, 61–82

[34] Bechtoula H, Kono S, Watanabe F. Experimental and analytical investigations of seismic performance of cantilever reinforced concrete columns under varying transverse and axial loads. Journal of Asian Architecture and Building Engineering, 2005, 4(2): 467–474

[35] Esaki F. Reinforcing effect of steel plate hoops on ductility of reinforced concrete square column. In: The 11th World Conference on Earthquake Engineering, Pergamon, Turkey, 1996

[36] Henkhaus K W. Axial failure of vulnerable reinforced concrete columns damaged by shear reversals. Dissertation for the Doctoral Degree. Indiana: Purdue University, 2010

[37] Ikeda A. Experimental Studies on Load-Deflection Characteristics of Reinforced Concrete Columns Subjected to Alternate Loading. Report of the Training Institute for Engineering Teachers, Yokohama National University, Kanagawa, Japan, 1968

[38] Imai H S, Yamamoto Y A. Study on causes of earthquake damage of Izumi high school due to Miyagi-Ken-Oki earthquake in 1978. Transactions of the Japan Concrete Institute, 1986, 8: 405–418

[39] Iwasaki T, Kawasima K, Hagiwara R, Koyama T, Yoshida T. Experimental investigation on hysteretic behavior of reinforce concrete bridge pier columns. In: The 17th Joint Meeting of U.S.-Japan Panel on Wing and Seismic Effects, Public Works Research Institute, Ministry of Construction, Japan, 1985

[40] Kabeyasawa T, Tasai A, Igarashi S. Test and analysis of reinforced concrete columns strengthened with polyester sheet. In: 13th World Conference on Earthquake Engineering, Vancouver, British Columbia, Canada, 2004

[41] Kanda M, Shirai N, Adachi H, Sato T. Analytical study on elasto-plastic hysteretic behaviors of reinforced concrete members. Transactions of the Japan Concrete Institute, 1988, 10: 257–264

[42] Kokusho S. A List of Past Experimental Results of Reinforced Concrete Columns. Building Research Institute, Ministry of Construction, 1964

[43] Kokusho S, Fukuhara M. A List of Past Experimental Results of Reinforced Concrete Columns. Building Research Institute, Ministry of Construction, 1965

[44] Li X, Park R, Tanaka H. Effects of variations in axial load level on the strength and ductility of reinforced concrete columns. In: Pacific Conference on Earthquake Engineering, Auckland, New Zealand, 1991

[45] Lynn A C. Seismic evaluation of existing reinforced concrete building columns. Dissertation for the Doctoral Degree. Berkeley: University of California, 2001

[46] Matamoros A B. Study of drift limits for high-strength concrete columns. Dissertation for the Doctoral Degree. Illinois: University of Illinois at Urbana-Champaign, 1999

[47] Matchulat L. Mitigation of collapse risk in vulnerable concrete buildings. Thesis for the Master’s Degree. Kansas: University of Kansas, 2008

[48] Mo Y, Wang S J. Seismic behavior of RC columns with various tie configurations. Journal of Structural Engineering, 2000, 126(10): 1122–1130

[49] Nagasaka T. Effectiveness of steel fiber as web reinforcement in reinforced concrete columns. Transactions of the Japan Concrete Institute, 1982, 4: 493–500

[50] Nakamura T, Yoshimura M. Gravity load collapse of reinforced concrete columns with brittle failure modes. Journal of Asian Architecture and Building Engineering, 2002, 1(1): 21–27

[51] Nakamura T, Yoshimura M. Simulation of old reinforced concrete column collapse by pseudo-dynamic test method. In: The 15th World Conference on Earthquake Engineering, Lisbon, Portugal, 2012

[52] Ohno T, Nishioka T. An experimental study on energy absorption capacity of columns in reinforced concrete structures. Japan Society of Civil Engineers, 1984, 1(2): 137–147

[53] Ohue M, Morimoto H, Fujii S, Morita S. The behavior of R.C. short columns failing in splitting bond-shear under dynamic lateral loading. Transactions of the Japan Concrete Institute, 1985, 7: 293–300

[54] Ono A, Shirai N, Adachi H, Sakamaki Y. Elasto-plastic behavior of reinforced concrete column with fluctuating axial force. Transactions of the Japan Concrete Institute, 1989, 11: 239–246

[55] Ousalem H, Kabeyasawa T, Tasai A. Evaluation of ultimate deformation capacity at axial load collapse of reinforced concrete columns. In: The 13th World Conference on Earthquake Engineering,Vancouver, Canada, 2004

[56] Priestley M J N, Verma R, Xiao Y. Seismic shear strength of reinforced concrete columns. Journal of Structural Engineering, 1994, 120(8): 2310–2329

[57] Ramirez H, Jirsa J O. Effect of Axial Load on Shear Behavior of Short RC Columns Under Cyclic Lateral Deformations. Report on a Research Project, Department of Civil Engineering, University of Texas at Austin, Austin, Texas, 1980

[58] Saatcioglu M, Grira M. Confinement of reinforced concrete columns with welded reinforcement grids. ACI Structural Journal, 1999, 96(1): 29–39

[59] Saatcioglu M, Ozcebe G. Response of reinforced concrete columns to simulated seismic loading. ACI Structural Journal, 1989, 86(1): 3–12

[60] Soesianawati M T. Limited ductility design of reinforced concrete columns. Thesis for the Master’s Degree. Christchurch: University of Canterbury, 1986

[61] Takemura H, Kawashima K. Effect of loading hysteresis on ductility capacity of bridge piers. Journal of Structural Engineering, 1997, 43: 849–858

[62] Tanaka H. Effect of lateral confining reinforcement on the ductile behavior of reinforced concrete columns. Dissertation for the Doctoral Degree. Christchurch: University of Canterbury, 1990

[63] Umehara H, Jirsa J O. Shear Strength and Deterioration of Short Reinforced Concrete Columns Under Cyclic Deformations. Report on a Research Project, Department of Civil Engineering, University of Texas at Austin, Austin, Texas, 1982

[64] Umemura H, Endo T. A List of Past Experimental Results of Reinforced Concrete Columns. Building Research Institute, Ministry of Construction. Japan, 1970

[65] Watson S. Design of reinforced concrete frames of limited ductility. Dissertation for the Doctoral Degree. Christchurch: University of Canterbury, 1989

[66] Wehbe N, Saiidi M S, Sanders D. Confinement of rectangular bridge columns for moderate seismic areas. National Center for Earthquake Engineering Research (NCEER), 1998, 12(1): 397–406

[67] Wibowo A, Wilson J L, Lam N T K, Gad E F, Fardipour M, Rodsin K, Lukkunaprasit P. Drift capacity of lightly reinforced concrete columns. Australian Earthquake Engineering Society Conference, Perth, Western Australia, 2010

[68] Wight J K, Sozen M A. Shear Strength Decay in Reinforced Concrete Columns Subjected to Large Deflection Reversals. Technical Report, University of Illinois, Urbana, Champaign, 1973

[69] Yalcin C. Seismic Evaluation and retrofitting of existing reinforced concrete bridge columns. Dissertation for the Doctoral Degree. Ontario: University of Ottawa, Ottawa, 1997

[70] Yoshimura M, Takaine Y, Nakamura T. Axial collapse of reinforced concrete columns. In: The 13th World Conference on Earthquake Engineering, Vancouver, British Columbia, Canada, 2004

[71] Zahn F A. Design of reinforced bridge columns for strength and ductility. Dissertation for the Doctoral Degree. Christchurch: University of Canterbury, 1985

[72] Zhou X S, Satoh T, Jiang W S, Ono A, Shimizu Y. Behavior of reinforced concrete short column under high axial load. Transactions of the Japan Concrete Institute, 1987, 9: 541–548

[73] Pujol S. Drift capacity of reinforced concrete columns subjected to displacement reversals. Dissertation for the Doctoral Degree. Indiana: Purdue University, 2002

[74] SPSS. IBM SPSS Statistics for Windows. Version 24.0. Armonk, NY: IBM Corp, 2016

[75] MATLAB and Statistics Toolbox Release. Natick, Massachusetts: The MathWorks, Inc., 2018

[76] Badawy M F, Msekh M A, Hamdia K M, Steiner M K, Lahmer T, Rabczuk T. Hybrid nonlinear surrogate models for fracture behavior of polymeric nanocomposites. Probabilistic Engineering Mechanics, 2017, 50: 64–75

[77] Hamdia K M, Ghasemi H, Zhuang X, Alajlan N, Rabczuk T. Sensitivity and uncertainty analysis for flexoelectric nanostructures. Computer Methods in Applied Mechanics and Engineering, 2018, 337: 95–109

[78] Hamdia K M, Silani M, Zhuang X, He P, Rabczuk T. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227

[79] Vu-Bac N, Lahmer T, Keitel H, Zhao J, Zhuang X, Rabczuk T. Stochastic predictions of bulk properties of amorphous polyethylene based on molecular dynamics simulations. Mechanics of Materials, 2014, 68: 70–84

[80] Vu-Bac N, Lahmer T, Zhang Y, Zhuang X, Rabczuk T. Stochastic predictions of interfacial characteristic of polymeric nanocomposites (PNCs). Composites. Part B, Engineering, 2014, 59: 80–95

[81] Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31

[82] Vu-Bac N, Silani M, Lahmer T, Zhuang X, Rabczuk T. A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites. Computational Materials Science, 2015, 96: 520–535

[83] Vu-Bac N, Rafiee R, Zhuang X, Lahmer T, Rabczuk T. Uncertainty quantification for multiscale modeling of polymer nanocomposites with correlated parameters. Composites. Part B, Engineering, 2015, 68: 446–464

[84] Kim J H, Mander J B. Truss Modeling of Reinforced Concrete Shear-Flexure Behavior. Multidisciplinary Center for Earthquake Engineering Research, University of Buffalo, Buffalo, New York, 1999

[85] Nowak A S, Collins K R. Reliability of Structures. London: CRC Press, 2012

[86] Mai C, Konakli K, Sudret B. Seismic fragility curves for structures using non-parametric representations. Frontiers of Structural and Civil Engineering, 2017, 11(2): 169–186

[87] Allahvirdizadeh R, Gholipour Y. Reliability evaluation of predicted structural performances using nonlinear static analysis. Bulletin of Earthquake Engineering, 2017, 15(5): 2129–2148

[88] Allahvirdizadeh R, Khanmohammadi M, Marefat M S. Probabilistic comparative investigation on introduced performance-based seismic design and assessment criteria. Engineering Structures, 2017, 151: 206–220

[89] Sucuoğlu H. The Turkish seismic rehabilitation code. In: Proceedings of the 1st European Conference on Earthquake Engineering and Seismology, Geneva, Switzerland, 2006, 1699–1708

[90] Wu C L, Kuo W W, Yang Y S, Hwang S J, Elwood K J, Loh C H, Moehle J P. Collapse of a nonductile concrete frame: Shaking table tests. Earthquake Engineering & Structural Dynamics, 2009, 38(2): 205–224

[91] Yavari S. Shaking table tests on the response of reinforced concrete frames with non-seismic detailing. Dissertation for the Doctoral Degree. Vancouver: University of British Columbia, 2011

[92] McKenna F, Fenves G L, Scott M H. Open system for earthquake engineering simulation. Berkeley: University of California, 2002

[93] Azadi Kakavand M R. Limit state material manual. 2012

[94] FEMA (Federal Emergency Management Agency). Quantification of Building Seismic Performance Factors, FEMA P695. 2009

[95] Azadi Kakavand M R, Khanmohammadi M. Seismic Fragility assessment of local and global failures in low-rise non-ductile existing RC buildings: Empirical shear-axial modelling vs. ASCE/SEI 41 approach. Journal of Computational Engineering and Physical Modeling, 2018, 1(1): 38–57

Open Access

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Electronic Supplementary Material Supplementary material is available in the online version of this article at https://doi.org/10.1007/s11709-019-0554-2 and is accessible for authorized users.

RIGHTS & PERMISSIONS

2019 The Author(s) 2019. This article is published with open access at link.springer.com and journal.hep.com.cn