Probabilistic estimation of repair cost for Performance assessment of concrete special moment frames

Document Type : Original Research

Authors
S. Abbasgholinia 1
H. Khosravi 2
S. Vaseghiamiri 3
1 M.Sc. in Structural Engineering, Babol Noshirvani University of Technology
2 Faculty Member of Babol Noshirvani University of Technology
3 Ph.D. of Structural Engineering, Sharif University of Technology, Tehran, Iran
Abstract
Nowadays, the seismic performance-based design of structures has been widely noticed by the engineering community. So, different methods for performance-based design have been presented by different researchers. This attitude has been included in the design code and regulations for seismic design of new buildings and retrofit of existing buildings. The FEMA P-58 performance-based design method presented by the Pacific Earthquake Engineering Research (PEER) can quantify the consequences related to the seismic response of buildings. Therefore, using this method, the seismic performance of buildings can be directly evaluated. In addition, this performance-based design method can define simpler criteria such as repair cost, repair time, and casualties for seismic evaluation and decision-making process. The method is based on considering different sources of uncertainty in earthquake input and its intensity, structural response, associated damage, and repair cost, using the concepts of conditional probability and total probability theorem. In this method, the building is designed in such a way that it meets the expected and predetermined performance level in a specific level of seismic excitation. Since the performance levels of the building are determined based on the amount of damage caused to structural and non-structural members, one of the practical and effective ways to evaluate performance is to estimate the building repair cost. In the approach presented in FEMA P-58, the repair cost is defined in a probabilistic approach, as the cost needed to restore the damaged parts to their original state in the form of expected annual loss. In this research, first, three 4-, 12-, and 20-story office buildings with the lateral force resisting system of reinforced concrete special moment frames were selected in a high seismic risk area. Then, the nonlinear model of structures was provided in OpenSEES software. In order to reduce the computational cost and analysis time, the single-bay Substitute Frame model was used to simplify the multi-bay reinforced concrete moment frames. All four structures were subjected to Incremental Dynamic Analysis (IDA) for 30 earthquake records. A probabilistic relationship between the spectral acceleration of the earthquake and the main damage parameter (i.e. the inter-story drift), as well as the collapse fragility curve, was obtained. Then, the repair cost including the cost of repairing structural members as well as beams and columns, the cost of repairing non-structural members as well as partition and curtain walls, and the cost of replacing collapsed structures was calculated as expected annual loss. The results show that the repair costs at the Design-Based Earthquake (DBE) for 4-, 12-, and 20-story buildings are 3%, 2.5%, and 10% of the building replacement cost and at Maximum Credible Earthquake (MCE) are 22%, 23%, and 38% of the building replacement cost, respectively. In addition, in short buildings, most of the cost is caused by repairing structural and non-structural members, and in tall buildings, most of the cost is caused by replacing collapsed or severely damaged structures. Considering two nonstructural elements (i.e. partition and curtain walls) in repair cost, the analysis results show that the cost of repairing structural elements is more than the cost of repairing non-structural elements.

Keywords

Subjects

[1] Moehle, J. and Deierlein, G.G., 2004, August. A framework methodology for performance-based earthquake engineering. In 13th world conference on earthquake engineering (Vol. 679, p. 12). WCEE Vancouver.
[2] Mitrani-Reiser, J., Haselton, C., Goulet, C., Porter, K., Beck, J. and Deierlein, G., 2006, April. Evaluation of the seismic performance of a code-conforming reinforced-concrete frame building-Part II: Loss estimation. In 8th National Conference on Earthquake Engineering (100th Anniversary Earthquake Conference) (pp. 18-22).
[3] Fischinger, M. ed., 2014. Performance-based seismic engineering: Vision for an earthquake resilient society (Vol. 32). Dordrecht, The Netherlands: Springer.
[4] Mitrani-Resier, J., Wu, S. and Beck, J.L., 2016. Virtual Inspector and its application to immediate pre-event and post-event earthquake loss and safety assessment of buildings. Natural hazards, 81, pp.1861-1878. doi: 10.1007/s11069-016-2159-6.
[5] Habibi, M., Kermanshachi, S. and Safapour, E., 2018, April. Engineering, procurement, and construction cost and schedule performance leading indicators: State-of-the-art review. In Construction Research Congress 2018 (pp. 378-388). doi: 10.1061/9780784481271.037.
[6] Miranda, E. and Aslani, H., 2003. Probabilistic response assessment for building-specific loss estimation. Pacific Earthquake Engineering Research Center.
[7] Ramirez, C.M., Liel, A.B., Mitrani‐Reiser, J., Haselton, C.B., Spear, A.D., Steiner, J., Deierlein, G.G. and Miranda, E., 2012. Expected earthquake damage and repair costs in reinforced concrete frame buildings. Earthquake Engineering & Structural Dynamics, 41(11), pp.1455-1475. doi: 10.1002/eqe.2216.
[8] Ramirez, C.M. and Miranda, E., 2012. Significance of residual drifts in building earthquake loss estimation. Earthquake Engineering & Structural Dynamics, 41(11), pp.1477-1493. doi: 10.1002/eqe.2217.
[9] Harle, S.M., Sagane, S., Zanjad, N., Bhadauria, P.K.S. and Nistane, H.P., 2024. Advancing seismic resilience: Focus on building design techniques. In Structures (Vol. 66, p. 106432).
[10] FEMA P-58, 2018 “Seismic performance assessment of buildings, volume 1 - methodology”, p. 340.
[11] Hwang, S.H. and Lignos, D.G., 2017. Earthquake‐induced loss assessment of steel frame buildings with special moment frames designed in highly seismic regions. Earthquake Engineering & Structural Dynamics, 46(13), pp.2141-2162. doi: 10.1002/eqe.2898.
[12] Joyner, M.D. and Sasani, M., 2020. Building performance for earthquake resilience. Engineering Structures, 210, p.110371. doi: 10.1016/j.engstruct.2020.110371.
[13] Soleimani, R., Khosravi, H. and Hamidi, H., 2019. Substitute Frame and adapted Fish-Bone model: Two simplified frames representative of RC moment resisting frames. Engineering Structures, 185, pp.68-89. doi: 10.1016/j.engstruct.2019.01.127.
[14] Soleimani, R., Hamidi, H. and Khosravi, H., 2022. On advantages of the “Substitute Frame” model for incremental dynamic analysis: Integration of speed and accuracy. In Structures (Vol. 39, pp. 266-277).
[15] Li, Z., Lu, J. and Teng, J., 2024. Seismic performance loss evaluation of reinforced concrete frame structure based on updatable damage model. Earthquake Engineering and Resilience, 3(1), pp.152-173.
[16] Fema, “Seismic Performance Assessment of Buildings Volume 2 – Implementation Guide,” Fema P-58-2, vol. 11, no. 10, p. 440, 2021, doi: 10.3390/buildings11100440.
[17] FEMA, “Seismic performance assessment of buildings Volume 3 – Supporting Electronic Materials,” FEMA P-58-3, vol. 1, no. December, p. 3, 2018.
[18] C. B. Haselton, “Assessing Seismic Collapse Safety of Modern Reinforced Concrete Moment-Frame Buildings Assessing Seismic Collapse Safety of Modern Reinforced Concrete Moment-Frame Buildings,” no. February, 2008.
[19] C. B. Haselton, A. B. Liel, S. T. Lange, and S. T. Lange, “Beam-Column Element Model Calibrated for Predicting Flexural Response Leading to Global Collapse of RC Frame Buildings Beam-Column Element Model Calibrated for Predicting Flexural Response Leading to Global Collapse of RC Frame Buildings,” no. maY, 2008.
[20] S. Mazzoni, F. McKenna, M. H. Scott, and G. L. Fenves, “Open System for Earthquake Engineering Simulation (OpenSees),” Pacific Earthq. Eng. Res. Cent., p. 465, 2006.
[21] Ibarra, L.F., Medina, R.A. and Krawinkler, H., 2005. Hysteretic models that incorporate strength and stiffness deterioration. Earthquake engineering & structural dynamics, 34(12), pp.1489-1511. doi: 10.1002/eqe.495.
[22] J. R. Harris et al., “Quantification of Building Seismic Performance Factors,” Fema P695, no. June, p. 421, 2009.
[23] Gokkaya, B.U., Baker, J.W. and Deierlein, G.G., 2016. Quantifying the impacts of modeling uncertainties on the seismic drift demands and collapse risk of buildings with implications on seismic design checks. Earthquake Engineering & Structural Dynamics, 45(10), pp.1661-1683. doi: 10.1002/eqe.2740.
[24] Baker, J.W., 2015. Efficient analytical fragility function fitting using dynamic structural analysis. Earthquake Spectra, 31(1), pp.579-599. doi: 10.1193/021113EQS025M.
[25] M. D. Petersen et al., “Documentation for the 2008 update of the united states national seismic hazard maps,” Earthq. Res. Backgr. Sel. Reports, pp. 107–234, 2010.
Modares Civil Engineering journal
Volume 25, Issue 6 - Serial Number 86
September and October 2025