Seismic Reliability of the Non-Code-Conforming RC Building Due to Vertical Mass Irregularity Effect

Document Type : Regular Paper


1 Assistant Professor of Earthquake Engineering, School of Civil Engineering, University of Bojnord, Bojnord, Iran

2 MSc. of Structural Engineering, University of Bojnord, Bojnord, Iran


Recent studies showed that the inelastic seismic response of irregular structures can significantly differ from regular structures. Irregular distribution of mass in elevation is regarded as a structural irregularity by which the modes with high energy levels are excited and occasionally prevents the structure from developing nonlinear deformations and causes some unpredictable damages in structural elements. In this study, seismic reliability and risk assessment of a non-code-conforming concrete building reinforced by plain bars is investigated with consideration of the vertical mass irregularity effect. The framework of this study is based on the determination of fragility via incremental dynamic analysis (IDA). The analyses are carried out on a reference 3-story multi-bay 3D structure modeled in Opensees software. Seismic risk assessment for the complete collapse limit state is evaluated by integrating the site hazard and the structural fragility curves. Also, a relatively simple and efficient nonlinear model based on the experimental behavior of substructures reinforced by plain bars is used to simulate pre- and post-elastic behavior buildings. The results indicated that the effects of vertical mass irregularity of the building have almost significant effects on the represented building's fragility curve parameters and seismic reliability of the represented buildings. Probabilities of occurrence for the irregular bottom and median story are about 1.51 and 1.6 times of the building with regular mass distribution.


Main Subjects

[1]     ASCE7-16., “Minimum design loads for buildings and other structures,” Am. Soc. Civ. Eng. Reston, Virginia. , 2017.
[2]     Standard.No.2800, “Iranian Code of Practice for Seismic Resistant Design of Buildings,” 4th Ed. Road, Hous. Urban Deve;opment Res. Center, Tehran, BHRC-PN S-253, 2014.
[3]     FEMA P-2012, “Assessing Seismic Performance of Buildings with Configuration Irregularities, Calibrating Current Standards and Practices,” 2018.
[4]     E. V Valmundsson and J. M. Nau, “Seismic response of building frames with vertical structural irregularities,” J. Struct. Eng., vol. 123, no. 1, pp. 30–41, 1997.
[5]     Al-Ali, K. A.A., and H. Krawinkler, “Effects of vertical irregularities on seismic behaviour of building structures. ,” Rep. No. 130. Dep. Civ. Environ. Eng. Stanford Univ. San Fr., 1998.
[6]     B. J. Choi, “Hysteretic energy response of steel moment‐resisting frames with vertical mass irregularities,” Struct. Des. Tall Spec. Build., vol. 13, no. 2, pp. 123–144, 2004.
[7]     M. DeStefano, E. M. Marino, and S. Viti, “Evaluation of second order effects on the seismic response of vertically irregular RC framed structures,” Proc. 4th Eur. Work. Seism. Behav. Irregul. complex Struct. Thessaloniki, Greece, 2005.
[8]     F. Michalis, V. Dimitrios, and P. Manolis, “Evaluation of the influence of vertical irregularities on the seismic performance of a nine‐storey steel frame,” Earthq. Eng. Struct. Dyn., vol. 35, no. 12, pp. 1489–1509, 2006.
[9]     T. L. Karavasilis, N. Bazeos, and D. E. Beskos, “Estimation of seismic inelastic deformation demands in plane steel MRF with vertical mass irregularities,” Eng. Struct., vol. 30, no. 11, pp. 3265–3275, 2008.
[10]   M. Pirizadeh and H. Shakib, “Probabilistic seismic performance evaluation of non-geometric vertically irregular steel buildings,” J. Constr. Steel Res., vol. 82, pp. 88–98, 2013.
[11]   A. Habibi and K. Asadi, “Seismic performance of RC frames irregular in elevation designed based on Iranian seismic code,” J. Rehabil. Civ. Eng., vol. 1, no. 2, pp. 40–55, 2013.
[12]   V. Mohsenian and A. Nikkhoo, “A study on the effects of vertical mass irregularity on seismic performance of tunnel-form structural system,” Adv. Concr. Constr., vol. 7, no. 3, pp. 131–141, 2019.
[13]   M. Amiri and M. Yakhchalian, “Performance of intensity measures for seismic collapse assessment of structures with vertical mass irregularity,” Structures, vol. 24, pp. 728–741, 2020.
[14]   A. Karami, S. Shahbazi, and M. Kioumarsi, “A study on the effects of vertical mass irregularity on seismic behavior of BRBFs and CBFs,” Appl. Sci., vol. 10, no. 23, p. 8314, 2020.
[15]   K. Ghimire and H. Chaulagain, “Influence of structural irregularities on seismic performance of RC frame buildings,” J. Eng. Issues Solut., vol. 1, no. 1, pp. 70–87, 2021.
[16]   Y. Bai, Y. Li, Z. Tang, M. Bittner, M. Broggi, and M. Beer, “Seismic collapse fragility of low-rise steel moment frames with mass irregularity based on shaking table test,” Bull. Earthq. Eng., vol. 19, no. 6, pp. 2457–2482, 2021.
[17]   L. Halder and S. Paul, “Seismic damage evaluation of gravity load designed low rise RC building using non-linear static method,” Procedia Eng., vol. 144, pp. 1373–1380, 2016.
[18]   K. K. Arani, M. S. Marefat, A. Amrollahi‐Biucky, and M. Khanmohammadi, “Experimental seismic evaluation of old concrete columns reinforced by plain bars,” Struct. Des. Tall Spec. Build., vol. 22, no. 3, pp. 267–290, 2013.
[19]   M. Adibi, M. S. Marefat, A. Esmaeily, K. K. Arani, and A. Esmaeily, “Seismic retrofit of external concrete beam-column joints reinforced by plain bars using steel angles prestressed by cross ties,” Eng. Struct., vol. 148, 2017, doi: 10.1016/j.engstruct.2017.07.014.
[20]   M. Adibi, M. S. Marefat, K. K. Arani, and H. Zare, “External retrofit of beam-column joints in old fashioned RC structures,” Earthq. Struct., vol. 12, no. 2, 2017, doi: 10.12989/eas.2017.12.2.237.
[21]   M. Adibi and R. Talebkhah, “Development of seismic fragility curves for the existing RC building with plain bars,” Eur. J. Environ. Civ. Eng., pp. 1–16, 2020.
[22]   M. Adibi, M. S. Marefat, and R. Allahvirdizadeh, “Nonlinear modeling of cyclic response of RC beam–column joints reinforced by plain bars,” Bull. Earthq. Eng., 2018, doi: 10.1007/s10518-018-0399-4.
[23]   D. Vamvatsikos and C. A. Cornell, “Incremental dynamic analysis,” Earthq. Eng. Struct. Dyn., vol. 31, no. 3, pp. 491–514, 2002, doi:
[24]   HAZUS-MH MR5, “Earthquake loss Estimation Methodology Model,” FEMA, Washington, D.C, 2005.
[25]   S. B. Kadam, Y. Singh, and L. Bing, “Seismic fragility reduction of an unreinforced masonry school building through retrofit using ferrocement overlay,” Earthq. Eng. Eng. Vib., vol. 19, pp. 397–412, 2020.
[26]   S. Ahmad, N. Kyriakides, K. Pilakoutas, K. Neocleous, and Q. uz Zaman, “Seismic fragility assessment of existing sub-standard low strength reinforced concrete structures,” Earthq. Eng. Eng. Vib., vol. 14, no. 3, pp. 439–452, 2015.
[27]   R. K. L. Su and C.-L. Lee, “Development of seismic fragility curves for low-rise masonry infilled reinforced concrete buildings by a coefficient-based method,” Earthq. Eng. Eng. Vib., vol. 12, no. 2, pp. 319–332, 2013.
[28]   A. Abo-El-Ezz, M.-J. Nollet, and M. Nastev, “Seismic fragility assessment of low-rise stone masonry buildings,” Earthq. Eng. Eng. Vib., vol. 12, no. 1, pp. 87–97, 2013.
[29]   J. Ren, J. Song, and B. R. Ellingwood, “Reliability assessment framework of deteriorating reinforced concrete bridges subjected to earthquake and pier scour,” Eng. Struct., vol. 239, p. 112363, 2021.
[30]   F. Di Trapani, V. Bolis, F. Basone, and M. Preti, “Seismic reliability and loss assessment of RC frame structures with traditional and innovative masonry infills,” Eng. Struct., vol. 208, p. 110306, 2020.
[31]   F. W. Taylor, S. E. Thompson, and E. Smulski, “Concrete, Plain and Reinforced,” J. Wiley sons, Inc., vol. 4, 1925.
[32]   C. W. Duhman, “The theory and practice of reinforced concrete,” McGraw-Hill, New York, 1953.
[33]   P. Pernot, “Le béton armé,” JB Baillière, 1954.
[34]   A. Guerrin, “Traite De Beton Arme,” Dunod, Paris, 1959.
[35]   J. A. Barker, “Reinforced concrete detailing,” Oxford Univ. Press. London (1st Print. 1967), vol. vol Second, 1979.
[36]   N. J. Edvard and J. L. Tanner, “Theory and problems of reinforced concrete design,” Schaum Publ. co., New York, 1996.
[37]   Opensees, “Open system for earthquke engineering simulation, Pacific Earthquake Engineering Research Center, University of Califonia, Brekely Ca,,” 2016.
[38]   L. Petrini, C. Maggi, M. J. N. Priestley, and G. M. Calvi, “Experimental verification of viscous damping modeling for inelastic time history analyzes,” J. Earthq. Eng., vol. 12, no. S1, pp. 125–145, 2008, doi:
[39]   J. F. Hall, “Problems encountered from the use (or misuse) of Rayleigh damping,” Earthq. Eng. Struct. Dyn., vol. 35, no. 5, pp. 525–545, 2006, doi:
[40]   M. Adibi, R. Talebkhaha, and A. Yahyaabadib, “Simulation of cyclic response of precast concrete beam-column joints,” Comput. Concr., vol. 24, no. 3, 2019, doi: 10.12989/cac.2019.24.3.223.
[41]   M. Adibi, R. Talebkhah, and A. Yahyaabadi, “Nonlinear modeling of exterior beam-column joints in precast concrete buildings,” J. Struct. Constr. Eng., 2020.
[42]   M. Adibi, J. Shafaei, and F. Aliakbari, “Experimental evaluation of external beam-column joints reinforced by deformed and plain bar,” EARTHQUAKES Struct., vol. 18, no. 1, pp. 113–127, 2020.
[43]   D. Vamvatsikos and C. A. Cornell, “The incremental dynamic analysis and its application to performance-based earthquake engineering,” Proc. 12th Eur. Conf. Earthq. Eng., 2002.
[44]   D. Vamvatsikos and A. Cornell, “Incremental dynamic analysis with two components of motion for a 3D steel structure,” 2006.
[45]   M. Javanmard and A. Yahyaabadi, “Assessment of Structure-Specific Intensity Measures for the Probabilistic Seismic Demand Analysis of Steel Moment Frames,” Arab. J. Sci. Eng., vol. 44, no. 5, pp. 4885–4894, 2019.
[46]   FEMA P695, “Quantification of building seismic performance factors,” Fed. Emerg. Manag. Agency, Washington, D.C, 2009.
[47]   M. Onvani and A. Yahyaabadi, “Probabilistic seismic demand analysis of steel moment frames by utilising Bayesian statistics,” Eur. J. Environ. Civ. Eng., pp. 1–17, 2018.
[48]   N. Shome, C. A. Cornell, P. Bazzurro, and J. E. Carballo, “Earthquakes, records, and nonlinear responses,” Earthq. Spectra, vol. 14, no. 3, pp. 469–500, 1998.
[49]   L. Ye, Q. Ma, Z. Miao, H. Guan, and Y. Zhuge, “Numerical and comparative study of earthquake intensity indices in seismic analysis,” Struct. Des. Tall Spec. Build., vol. 22, no. 4, pp. 362–381, 2013.
[50]   F. Izanlu and A. Yahyaabadi, “Determination of structural fragility curves of various building types for seismic vulnerability assessment in the Sarpol-e Zahab City,” J. Seismol. Earthq. Eng., vol. 20, no. 3, pp. 93–107, 2019.
[51]   A. E. Özel and E. M. Güneyisi, “Effects of eccentric steel bracing systems on seismic fragility curves of mid-rise R/C buildings: A case study,” Struct. Saf., vol. 33, no. 1, pp. 82–95, 2011.
[52]   H. L. Sadraddin, X. Shao, and Y. Hu, “Fragility assessment of high‐rise reinforced concrete buildings considering the effects of shear wall contributions,” Struct. Des. Tall Spec. Build., vol. 25, no. 18, pp. 1089–1102, 2016.
[53]   R. Talebkhah, A. A. Yahyaabadi, and M. Adibi, “Development of fragility curves for precast concrete frames comparing the methods of static pushover and incremental dynamic analysis,” Sharif J. Civ. Eng., vol. 36.2, no. 2.1, pp. 129–140, 2020, [Online]. Available:
[54]   M. Adibi, A. Yahyaabadi, and R. Talebkhah, “Seismic behavior assessment of RC precast frame damaged in Bojnord Earthquake 2017 considering soil-structure interaction effects,” Amirkabir J. Civ. Eng., vol. 53, no. 7, p. 19, 2021.
[55]   M. Rahimi and A. Yahyaabadi, “Bayesian probabilistic seismic hazard analysis with respect to near-fault effects,” Asian J. Civ. Eng., vol. 20, no. 3, pp. 341–349, 2019.
[56]   F. Nodehi and A. Yahyaabadi, “Probabilistic seismic hazard analysis of Bojnord region by considering near-fault effects,” Pap. Present. 6th Int. Conf. Earthq. Struct. Kerman, Iran, 2015.
  • Receive Date: 08 June 2021
  • Revise Date: 13 December 2021
  • Accept Date: 17 December 2021
  • First Publish Date: 17 December 2021