A New Damage-Control Target Displacement Procedure for Direct Displacement-Based Design of Circular Reinforced Concrete Bridge Pier

A New Damage-Control Target Displacement Procedure for Direct Displacement-Based Design of Circular Reinforced Concrete Bridge Pier

Mohd Ritzman Abdul Karim  Zhaohui Huang

Department of Civil and Environmental Engineering, Brunel University, UK.

Available online: 
| Citation



In this paper, a new perspective procedure to determine the damage-control target displacement for circular reinforced concrete (RC) bridge pier is proposed by considering the new approach of damage-control limit states (DCLS). The new approach of DCLS is explored by integrating exist- ing damage-control concrete strain limit with recently proposed damage-control reinforcement strain limit. Modification of yield displacement and modified plastic-hinge along with new DCLS is used to estimate the damage-control target displacement for a circular RC bridge pier. Three-dimensional (3D) finite element (FE) model has been developed to validate the damage-control target displacement sub- ject to ground motion based on a nonlinear time-history (NLTH) analysis. The 3D FE model is updated to achieve a reasonable relationship between numerical, analytical, and outcomes found in the litera- ture. It is worth noting that the proposed procedure manages to estimate an improved damage-control target displacement for 7.0 m, 11.0 m and 13.0 m height of circular RC bridge pier. The influence of new reinforcement limit strain along with both modification of yield displacement and plastic-hinge contributes to providing better results. The result shows that new DCLS were efficient to predict dam- age-control target displacement, consistent with FE analysis result.


circular RC bridge pier, damage-control limit states, damage-control target displacement, plastic-hinge region, yield displacement.


[1] Sadan, O.B., Petrini, L. & Calvi, G.M., Direct displacement-based seismic assess- ment procedure for multi-span reinforced concrete bridges with single-column piers. Earthquake Engineering & Structural Dynamics, 42(7), pp. 1031–1051, 2013. https:// doi.org/10.1002/eqe.2257

[2] Kappos, A.J., Gidaris, I.G. & Gkatzogias, K.I., Problems associated with direct displacement-based design of concrete bridges with single-column piers, and some suggested improvements. Bulletin of Earthquake Engineering, 10(4), pp. 1237–1266, 2012. https://doi.org/10.1007/s10518-012-9354-y

[3] Reza, S.M., Alam, M.S. & Tesfamariam, S., Seismic performance comparison between direct displacement-based and force-based design of a multi-span continuous reinforced concrete bridge with irregular column heights. Canadian Journal of Civil Engineering, 41(5), pp. 440–449, 2014. https://doi.org/10.1139/cjce-2012-0278

[4] Calvi, G.M., Priestley, M.J.N. & Kowalsky, M.J., Displacement-based seismic design of bridges. Structural Engineering International: Journal of the International Association for Bridge and Structural Engineering (IABSE), 23(2), pp. 112–121, 2013. https://doi. org/10.2749/101686613x13439149157399

[5] Priestley, M.J.N., Calvi, G.M. & Kowalsky, M.J., Displacement-Based Seismic Design of Structures, Pavia, Italy: IUSS Press, 2007.

[6] Suarez, V.A., Implementation of Direct Displacement-Based Design for Highway Bridges, Ph.D. Thesis, North Carolina State University, 2008.

[7] Mackie, K.R., Wong, J.M. & Stojadinovic, B., Post-earthquake bridge repair cost and repair time estimation methodology. Earthquake Engineering & Structural Dynamics, 39, pp. 281–301, 2010. https://doi.org/10.1002/eqe.942

[8] Mander, J.B., Priestley, M.J.N. & Park, R., Theoretical stress-strain model for confined concrete. Journal of Structural Engineering, 114(8), pp. 1804–1826, 1988. https://doi. org/10.1061/(asce)0733-9445(1988)114:8(1804)

[9] Kowalsky, M.J., Deformation limit states for circular reinforced concrete bridge columns. Journal of Structural Engineering, 126(8), pp. 869–878, 2000. https://doi. org/10.1061/(asce)0733-9445(2000)126:8(869)

[10] Goodnight, J.C., Kowalsky, M.J. & Nau, J.M., Strain limit states for circular RC bridge columns. Earthquake Spectra, 32(3), pp. 1627–1652, 2016. https://doi. org/10.1193/030315eqs036m

[11] Goodnight, J.C., Kowalsky, M.J. & Nau, J.M., Modified plastic-hinge method for circular rc bridge columns. Journal of Structural Engineering, 142(11), pp. 1–12, 2016. https://doi.org/10.1061/(asce)st.1943-541x.0001570

[12] Karim, M.R.A. & Huang, Z., Estimation of yield displacement for seismic based design of circular RC bridge piers. In 7th Asia Conference on Earthquake Engineering, 2018.

[13] Suarez, V.A. & Kowalsky, M.J., A stability-based target displacement for direct dis- placement-based design of bridge piers. Journal of Earthquake Engineering, 15(5), pp. 754–774, 2011. https://doi.org/10.1080/13632469.2010.534233

[14] Priestley, M.J.N., Seible, F. & Calvi, G.M., Seismic Design and Retrofit of Bridges, New York: John Wiley & Sons, 1996.

[15] Kong, C., Rapid Direct Displacement-Based Assessment Approach for Bridge Struc- tures, Ph.D. Thesis, North Carolina State University, 2017.

[16] Hernández-Montes, E. & Aschheim, M., An estimate of the yield displacement of coupled walls for seismic design. International Journal of Concrete Structures and Materials, 11(2), pp. 275–284, 2017. https://doi.org/10.1007/s40069-017-0188-5

[17] Priestley, M.J.N. & Kowalsky, M.J., Direct displacement-based seismic design of concrete buildings. Bulletin of the New Zealand National Society for Earthquake Engineering, 33(4), pp. 421–444, 2000.

[18] Sheikh, M.N., Tsang, H.H., McCarthy, T.J. & Lam, N.T.K., Yield curvature for seismic design of circular reinforced concrete columns. Magazine of Concrete Research, 62(10), pp. 741–748, 2010. https://doi.org/10.1680/macr.2010.62.10.741

[19] Dassault Systèmes Simulia Corp, Abaqus Analysis User’s Manual, Providence, RI, USA, 2016.

[20] Belarbi, A., Zhang, L.X. & Hsu, T.T.C., Constitutive laws of reinforced concrete mem- brane elements. In Eleventh World Conference on Earthquake Engineering, pp. 1–8, 1996.

[21] Cashell, K.A., Elghazouli, A.Y. & Izzuddin, B.A., Experimental and analytical assess- ment of ductility in lightly reinforced concrete members. Engineering Structures, 32(9), pp. 2729–2743, 2010. https://doi.org/10.1016/j.engstruct.2010.04.043

[22] CEN, Eurocode 2: Design of concrete structures (EN1992-1-1). Brussels, 2004.

[23] Lubliner, J., Oliver, J., Oller, S. & Oñate, E., A plastic-damage model for concrete. International Journal of Solids and Structures, 25(3), pp. 299–326, 1989. https://doi. org/10.1016/0020-7683(89)90050-4

[24] Lee, J. & Fenves, G.L., Plastic-damage model for cyclic loading of concrete structures. Journal of Engineering Mechanics, 124(8), pp. 892–900, 1998. https://doi.org/10.1061/ (asce)0733-9399(1998)124:8(892)

[25] Yahya, N.A., Strategies for Mitigation of the Failure of Concrete Pedestals Supporting

Bridge Girder Bearings, Ph.D. Queensland University of Technology, 2017.

[26] Jankowiak, T. & Lodygowski, T., Identification of parameters of concrete damage plasticity constitutive model. Foundations of Civil and Environmental Engineering, 6(1), pp. 53–69, 2005.

[27] Lehman, D., Moehle, J., Mahin, S., Calderone, A. & Harry, L., Experimental evalu- ation of the seismic performance of reinforced concrete bridge columns. Journal of Structural Engineering, 130(6), pp. 869–879, 2004. https://doi.org/10.1061/(asce)0733-9445(2004)130:6(869)

[28] CEN, Eurocode 8: Seismic Design of Buildings (EN1998-1). Brussels, 2004.