Endurance time method

The endurance time (ET) method is a dynamic structural analysis procedure for seismic assessment of structures. In this procedure, an intensifying dynamic excitation is used as the loading function.^[1] Endurance time method is a time-history based dynamic analysis procedure. An estimate of the structural response at different equivalent seismic intensity levels is obtained in a single response history analysis.^[2] This method has applications in seismic assessment of various structural types and in different areas of earthquake engineering.^[3][4][5]

The concept of endurance time method

Endurance time (ET) method is a dynamic structural analysis procedure in which intensifying dynamic excitation is used as the loading function. An estimate of structural response and/or performance at the entire seismic intensity range of interest is obtained in each response history analysis. The concept of endurance time analysis is similar to the exercise test applied in medicine.^[6] Similar concept has also been extended to applications in the analysis of offshore platforms under water waves.^[7]

Development history

The basic concepts of the endurance time method were published in 2004.^[8] Application in linear seismic analysis appeared in 2007.^[2] ET was subsequently extended to nonlinear analysis of single degree of freedom (SDOF) and multi degree of freedom systems.^[9] Procedures for multi-component seismic analysis were subsequently developed.^{[10][11][12][13]}

ET excitation functions

ET excitation functions are generated by using numerical optimization methods.^[14][15] ET excitation functions are publicly available through internet websites.^[1][16] ET excitation functions can be categorized into five generations as follows:

1. First generation of ET excitation functions (ETEFs) are essentially a filtered and profiled white noise. These were used for demonstrating the concept of ET and have limited practical significance.^[8]
2. Second-generation ETEFs incorporate response spectrum matching. These ETEFs produce numerically significant analysis results.^[17]
3. Third-generation ETEFs are optimized in nonlinear range. These ETEFs deliver improved analysis performance.
4. Fourth-generation ETEFs are optimized to include duration consistency.^[18]
5. Fifth-generation ETEFs are optimized to include damage consistency.^[19]

Fig. 1. A typical endurance time excitation function (ETA20f03 record)

Application areas in earthquake engineering

Endurance time method has been applied in the following areas of earthquake engineering:

• Nonlinear dynamic analysis of structures^[20][21]
• Seismic evaluation of jacket-type offshore platforms ^[22]
• Optimal damper placement in framed buildings^[23][24]
• Optimal design of energy dissipation systems ^{[25][26][27][28]}
• Seismic assessment of structures^[9]
• Performance-based seismic design method ^{[29][30][31][32][33]}
• Collapse-based seismic design method ^[34]
• Value-based seismic design ^[35][36]
• Structural optimization^[37]
• Multi-component seismic analysis^[13]
• Soil–structure interaction^[38][39]
• soil-pile-superstructure interaction ^[22]
• Liquid–structure interaction^[40]
• Dam engineering^[41]
• Bridge engineering^[42][43][44]
• Seismic rehabilitation^[45]
• Collapse analysis^[46]

Structural type applications

ET method has been applied in seismic assessment of the following structural types:

• Single degree of freedom systems^{[citation needed]}
• Moment and braced steel frames^[13][47][48]
• Concrete frames
• Bridges^[49][50]
• Gravity dams^[41]
• Arch dams^[51]
• Shell structures^[52]
• Steel tanks^[40][53]
• Offshore structures^[22]

Advantages of ET method

Major advantages of the endurance time method are as follows:

• ET significantly reduces the computational demand required for performing a standard response history analysis of structures for seismic assessment, especially when response at multiple levels of intensity is to be considered.^[54]
• ET is applicable in a wide range of seismic assessment problems and provides a generic approach for the seismic analysis of a wide range of structural types.
• ET method is reasonably simple and sensible when a realistic dynamic analysis of a complex structure is required

Limitations of ET method

Major limitations of the endurance time method are as follows:

• ET is an approximate method for predicting the structural response.
• The production of usable ETEFs that are applicable in a particular situation can be complicated.
• The procedure is still under development and sufficient background information may not be available for specific applications.

References

1. Endurance Time Method website[Online]. https://sites.google.com/site/etmethod/
2. Estekanchi, H.E., Valamanesh, V. and Vafai, A. (2007), Application of Endurance Time Method in Linear Seismic Analysis, Engineering Structures, v29, n10, p2551-2562, doi:10.1016/j.engstruct.2007.01.009
3. Estekanchi, H. E., Mashayekhi, M., Vafai, H., Ahmadi, G., Mirfarhadi, S. A., & Harati, M. (2020, October). A state-of-knowledge review on the Endurance Time Method. In Structures (Vol. 27, pp. 2288-2299). Elsevier. https://doi.org/10.1016/j.istruc.2020.07.062
4. Estekanchi, H., & Vafai, H. (2018). Seismic analysis and design using the endurance time method, Volume I: Concepts and development. Momentum Press.
5. Estekanchi, H., & Vafai, H. (2018). Seismic analysis and design using the endurance time method, Volume II: Advanced topics and application. Momentum Press.
6. Estekanchi, H. E.; Riahi, H. T. and Vafai, A. (2009), Endurance Time Method: Exercise Test as Applied to Structures, Asian Journal of Civil Engineering, v10, n5, p559-577, Link
7. Zeinoddini, M., Nikoo, H. M. and Estekanchi H.E. (2012), "Endurance Wave Analysis (EWA) and its application for assessment of offshore structures under extreme waves", Applied Ocean Research, v37, p98-110, doi: 10.1016/j.apor.2012.04.003
8. Estekanchi, H. E., A. Vafai and M. Sadeghazar (2004), Endurance Time method for seismic analysis and design of structures, Scientia Iranica, v11, n4, p361-370, Link
9. Riahi, H. T. and Estekanchi, H. E, (2010), "Seismic Assessment of Steel Frames with Endurance Time Method", Journal of Constructional Steel Research, v66, n6, p780-792, doi:10.1016/j.jcsr.2009.12.001
10. Valamanesh, V and Estekanchi, H. E. (2010),"A Study of Endurance Time Method in the Analysis of Elastic Moment Frames under Three-Directional Seismic Loading ", Asian Journal of Civil Engineering, v11, n5, p543-562, Link
11. Valamanesh, V and Estekanchi, H. E. (2010), "Compatibility of the endurance time method with codified seismic analysis approaches on three-dimensional analysis of steel frames ", The Structural Design of Tall and Special Buildings, doi:10.1002/tal.666
12. Valamanesh, V and Estekanchi, H. E. (2011), "Endurance time method for multi-component analysis of steel elastic moment frames", Scientia Iranica, v18, n2, p139-142, doi:10.1016/j.scient.2011.03.024
13. Valamanesh V. and Estekanchi H. E. (2012), "Nonlinear Seismic Assessment of Steel Moment Frames under Bi-Directional Loading via Endurance Time Method", The Structural Design of Tall and Special Buildings, doi: 10.1002/tal.1054
14. Valamanesh, V; Estekanchi, H. E. and Vafai, A. (2010), Characteristics of Second Generation Endurance Time Accelerograms, Scientia Iranica, v17, n1, p53-61, Link
15. Kaveh A., Mahdavi V., "Generation of Endurance Time Acceleration Functions Using the Wavelet Transform". Iran University of Science & Technology. 2012; 2 (2) :203–219,Link
16. Estekanchi HE. 2012. Website of the Endurance Time method. [Online]. http://sharif.edu/~stkanchi/ET
17. Mashayekhi, M. and Estekanchi, H.E. (2012), "Significance of effective number of cycles in Endurance Time analysis", Asian Journal of Civil Engineering, v13, n5, p647-657, Link
18. Mashayekhi, M., Estekanchi, H. E., Vafai, A., & Mirfarhadi, S. A. (2018). Simulation of cumulative absolute velocity consistent endurance time excitations. Journal of Earthquake Engineering, 1-26. https://doi.org/10.1080/13632469.2018.1540371
19. Mashayekhi, M., Estekanchi, H. E., Vafai, H., & Mirfarhadi, S. A. (2018). Development of hysteretic energy compatible endurance time excitations and its application. Engineering Structures, 177, 753-769. https://doi.org/10.1016/j.engstruct.2018.09.089
20. Estekanchi, H. E., Arjomandi, K and Vafai, A. (2008), Estimating Structural Damage of Steel Moment Frames by Endurance Time Method, Journal of Constructional Steel Research, v64, n2, p145-155, doi:10.1016/j.jcsr.2007.05.010
21. Riahi, H. T. ; Estekanchi, H. E. and Vafai, A. (2009), Estimates of Average Inelastic Deformation Demands for Regular Steel Frames by the Endurance Time Method, Scientia Iranica, v16, n5, p388-402, Link
22. Hasani, H., Golafshani, A., Estekanchi, H. Seismic performance evaluation of jacket-type offshore platforms using endurance time method considering soil-pile-superstructure interaction. Scientia Iranica, 2017; 24(4): 1843-1854. doi: 10.24200/sci.2017.4275 http://scientiairanica.sharif.edu/article_4275_f79d8b4fdd0cc8d159b91b1a3b968585.pdf
23. Estekanchi, H. E. and Basim, M. Ch. (2011), "Optimal damper placement in steel frames by the Endurance Time method", The Structural Design of Tall and Special Buildings, v20, n5, p612-630, doi:10.1002/tal.689
24. Shirkhani A., Farahmand Azar, B., Charkhtab Basim, M., & Mashayekhi M. (2021). Performance-based optimal distribution of viscous dampers in structure using hysteretic energy compatible endurance time excitations. International Journal of Numerical Methods in Civil Engineering, 5 (3), 46-55. http://dx.doi.org/10.52547/nmce.5.3.46
25. Shirkhani, A., Mualla, I. H., Shabakhty, N., & Mousavi, S. R. (2015). Behavior of steel frames with rotational friction dampers by endurance time method. Journal of Constructional Steel Research, 107, 211-222. https://doi.org/10.1016/j.jcsr.2015.01.016
26. Shirkhani, A., Farahmand Azar, B., & Basim, M. C. (2020). Optimum slip load of T-shaped friction dampers in steel frames by endurance time method. Proceedings of the Institution of Civil Engineers-Structures and Buildings, 173(10), 746-760. https://doi.org/10.1680/jstbu.18.00169
27. Shirkhani, A., Farahmand Azar, B., & Charkhtab Basim, M. (2021). Seismic loss assessment of steel structures equipped with rotational friction dampers subjected to intensifying dynamic excitations. Engineering Structures, 238. https://doi.org/10.1016/j.engstruct.2021.112233
28. Application of Endurance Time (ET) method in optimal design of energy dissipation systems [Online]. https://sites.google.com/view/ascivil/endurance-time/
29. Mirzai, A, Estekanchi, H. E. and Vafai, A. (2010), "Application of Endurance Time Method in Performance Based Design of Steel Moment Frames", Scientia Iranica, v17, n6, p482-492, Link
30. Mirzai A., Estekanchi, H. E. and Vafai, A. (2012), "Improved methodology for endurance time analysis: From time to seismic hazard return period", Scientia Iranica, doi: 10.1016/j.scient.2012.06.023
31. Mirzaee, A., & Estekanchi, H. E. (2015). Performance-based seismic retrofitting of steel frames by the endurance time method. Earthquake Spectra, 31(1), 383-402. https://doi.org/10.1193/081312EQS262M
32. Basim, M. C., & Estekanchi, H. E. (2015). Application of endurance time method in performance-based optimum design of structures. Structural safety, 56, 52-67. https://doi.org/10.1016/j.strusafe.2015.05.005
33. Jaberi, V., Jaberi, M., & Asghari, A. (2024). A new performance-based seismic design method using endurance time analysis for linked column frame system and a comparison of structural systems and seismic analysis methods. The Structural Design of Tall and Special Buildings, e2100. https://doi.org/10.1002/tal.2100
34. Jaberi, V. (2023). Collapse-based design method for simple seismic design of complex structural systems such as linked column frame system. Structures, 2023 Sep 1 (Vol. 55, pp. 482-497). https://doi.org/10.1016/j.istruc.2023.06.059
35. Charkhtab Basim, M., E Estekanchi, H., & Vafai, A. (2016). A methodology for value based seismic design of structures by the endurance time method. Scientia Iranica, 23(6), 2514-2527. https://dx.doi.org/10.24200/sci.2016.2310
36. Mirfarhadi, S. A., & Estekanchi, H. E. (2020). Value based seismic design of structures using performance assessment by the endurance time method. Structure and Infrastructure Engineering, 1-19. https://doi.org/10.1080/15732479.2020.1712436
37. Nozari, A and Estekanchi, H. E. (2011) "Optimization of Endurance Time acceleration functions for seismic assessment of structures, International Journal of Optimization in Civil Engineering, v1, n2, 257–277, Link
38. Sarcheshmehpour, M., Estekanchi, H. E., & Ghannad, M. A. (2020). Optimum placement of supplementary viscous dampers for seismic rehabilitation of steel frames considering soil–structure interaction. The Structural Design of Tall and Special Buildings, 29(1), e1682. https://doi.org/10.1002/tal.1682
39. Bai, J., Jin, S., Zhao, J., & Sun, B. (2019). Seismic performance evaluation of soil-foundation-reinforced concrete frame systems by endurance time method. Soil Dynamics and Earthquake Engineering, 118, 47-51. https://doi.org/10.1016/j.soildyn.2018.12.011
40. Estekanchi, H. E. and Alembagheri, , M. (2012), "Seismic analysis of steel liquid storage tanks by Endurance Time method", Thin-Walled Structures, v50, n1, p14-23, doi: 10.1016/j.tws.2011.08.015
41. Valamanesh, V; Estekanchi, H. E., Vafai, A and Ghaemian M. (2011), "Application of Endurance time method in seismic analysis of concrete gravity dams", Scientia Iranica A, v18, n3, p326-337, doi:10.1016/j.scient.2011.05.039
42. Ghaffari, E., E Estekanchi, H., & Vafai, A. (2020). Application of endurance time method in seismic analysis of bridges. Scientia Iranica, 27(4), 1751-1761. https://dx.doi.org/10.24200/sci.2018.5041.1382
43. Guo, A., Shen, Y., Bai, J., & Li, H. (2017). Application of the endurance time method to the seismic analysis and evaluation of highway bridges considering pounding effects. Engineering Structures, 131, 220-230. https://doi.org/10.1016/j.engstruct.2016.11.009
44. He, H., Wei, K., Zhang, J., & Qin, S. (2020). Application of endurance time method to seismic fragility evaluation of highway bridges considering scour effect. Soil Dynamics and Earthquake Engineering, 136, 106243. https://doi.org/10.1016/j.soildyn.2020.106243
45. Bazmooneh, Amirali (2009), Application of Endurance Time method in seismic evaluation of existing steel buildings, Thesis presented to the Department of Civil Engineering as a partial requirement for degree of Master of Science, Sharif University of Technology http://library.sharif.ir/parvan/resource/290141/
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47. Estekanchi, H. E., Riahi, H. T. and Vafai, A. (2011), Application of Endurance Time Method in Seismic Assessment of Steel Frames", Engineering Structures, v33, n9, p2535-2546 doi:10.1016/j.engstruct.2011.04.025
48. Mohsenian, V., Hajirasouliha, I., & Nikkhoo, A. (2020). Multi-level Response Modification Factor Estimation for Steel Moment-Resisting Frames Using Endurance-Time Method. Journal of Earthquake Engineering, 1-21. https://doi.org/10.1080/13632469.2020.1845875
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50. Pang, Y., Cai, L., He, W., & Wu, L. (2020). Seismic assessment of deep water bridges in reservoir considering hydrodynamic effects using endurance time analysis. Ocean Engineering, 198, 106846. https://doi.org/10.1016/j.oceaneng.2019.106846
51. Hariri Ardebili M., Mirzabozorg H., Kianoush R., "A Study on Nonlinear Behavior and Seismic Damage Assessment of Concrete Arch Dam-Reservoir-Foundation System Using Endurance Time Analysis". Iran University of Science & Technology. 2012; 2 (4) :573–606 Link
52. Tavazo, M., Estekanchi H.E. and Kaldi P. (2012), "Endurance time method in the linear seismic analysis of shell structures", International Journal of Civil Engineering, v10, n3, p169-178,Link
53. Alembagheri, M and Estekanchi, H. E. (2011), "Seismic Assessment of Unanchored Steel Storage Tanks by Endurance Time Method", Earthquake Engineering and Engineering Vibration, v10, n4, p591-604, doi:10.1007/s11803-011-0092-y
54. Madarshahian, R., Estekanchi, H. E. and Mahvashmohammadi, A. (2011), "Estimating seismic demand parameters with Endurance Time method", Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), v12, n8, p616-626, doi:10.1631/jzus.A1000389