This paper presents a method for identifying the damping coefficient during earthquakes in quasi-real time using the information from sensors installed in real structures. The method uses a given number of points to perform a quadratic regression in such a way as to reduce the error in identification. A coefficient of determination is also used to discard values that have not been correctly identified. The validity of the method is assessed by dynamic analysis in single-degree-of-freedom systems, using the initial stiffness proportional damping model and the tangent stiffness proportional damping model. Good identification results are obtained using a data acquisition sampling frequency of 200 Hz. The same is true for using a sampling frequency of 100 Hz as long as the system period is greater than 0.40 s. Additionally, it is observed that a 20% identification error does not substantially affect the seismic response of the system. The method is also applied to results from shake table tests, and their identified values are analyzed. A comparison is made between the behavior of the damping coefficient observed in the experimental tests with the behavior assumed in the dynamic analysis. In general terms, it is observed that the damping coefficient does not present abrupt changes in its values when changing the instantaneous stiffness as occurs in the tangent stiffness proportional damping model. Additional conclusions are presented that allow us to continue expanding the knowledge on the damping coefficient behavior during earthquakes.

1. [1] M. J. N. Priestley and D. N. Grant, “Viscous damping in seismic design and analysis,” J. of Earthquake Engineering, Vol.9, No.sup2, pp. 229-255, 2005. https://doi.org/10.1142/S1363246905002365
2. [2] Applied Technology Council, “Modeling and acceptance criteria for seismic design and analysis of tall buildings,” ATC 72-1, 2010.
3. [3] R. H. Scanlan, “Linear damping models and causality in vibrations,” J. of Sound and Vibration, Vol.13, No.4, pp. 499-503, 1970. https://doi.org/10.1016/S0022-460X(70)80054-2
4. [4] C. Lee, “Can damping matrix depend on elemental or material response state?,” 18th World Conf. on Earthquake Engineering, 2024.
5. [5] D. J. Chrisp, “Damping models for inelastic structures,” Master’s thesis, University of Canterbury, 1980. https://doi.org/10.26021/15297
6. [6] J. F. Hall, “Problems encountered from the use (or misuse) of Rayleigh damping,” Earthquake Engineering & Structural Dynamics, Vol.35, No.5, pp. 525-545, 2006. https://doi.org/10.1002/eqe.541
7. [7] F. A. Charney, “Unintended consequences of modeling damping in structures,” J. of Structural Engineering. Vol.134, No.4, pp. 581-592, 2008. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:4(581)
8. [8] A. Chopra and F. McKenna, “Modeling viscous damping in nonlinear response history analysis of buildings,” 16th World Conf. on Earthquake Engineering, 2017.
9. [9] A. K. Chopra and F. McKenna, “Modeling viscous damping in nonlinear response history analysis of buildings for earthquake excitation,” Earthquake Engineering & Structural Dynamics, Vol.45, No.2, pp. 193-211, 2015. https://doi.org/10.1002/eqe.2622
10. [10] G. De Francesco and T. J. Sullivan, “Formulation of localized damping models for large displacement analysis of single-degree-of-freedom inelastic systems,” J. of Earthquake Engineering, Vol.26, No.8, pp. 4235-4258, 2022. https://doi.org/10.1080/13632469.2020.1826370
11. [11] A. M. Puthanpurayil, O. Lavan, A. J. Carr, and R. P. Dhakal, “Application of local elasticity continuum damping models in nonlinear dynamic analysis,” Bulletin of Earthquake Engineering, Vol.16, No.12, pp. 6365-6391, 2018. https://doi.org/10.1007/s10518-018-0424-7
12. [12] A. Lanzi and J. E. Luco, “Influence of viscous damping models on inelastic seismic response of fixed and base-isolated structures,” 16th World Conf. on Earthquake Engineering, Article No.2133, 2017.
13. [13] C.-L. Lee, “Proportional viscous damping model for matching damping ratios,” Engineering Structures, Vol.207, Article No.110178, 2020. https://doi.org/10.1016/j.engstruct.2020.110178
14. [14] C.-L. Lee, “New elemental damping model for nonlinear dynamic response,” Advances in Nonlinear Dynamics, Vol.1: Proc. of the 3rd Int. Nonlinear Dynamics Conf., pp. 387-397, 2024. https://doi.org/10.1007/978-3-031-50631-4_33
15. [15] J. Dowgala and A. Irfanoglu, “A method for extracting building empirical capacity curves from earthquake response data,” Earthquake Spectra, Vol.32, No.4, pp. 2229-2244, 2016. https://doi.org/10.1193/122714EQS219M
16. [16] J. D. Dowgala, “Detecting and quantifying damage in buildings using earthquake response data and capacity curves,” Ph.D. thesis, Purdue University, 2013.
17. [17] R. W. Clough and J. Penzien, “Dynamics of structures,” 2nd Ed., McGraw-Hill Book Company, 1993.
18. [18] A. K. Chopra, “Dynamics of structures: Theory and applications to earthquake engineering,” 4th Ed., Pearson, 2014.
19. [19] L. Petrini, C. Maggi, M. J. N. Priestley, and G. M. Calvi, “Experimental verification of viscous damping modeling for inelastic time history analyzes,” J. of Earthquake Engineering, Vol 12, No.sup1, pp. 125-145, 2008. https://doi.org/10.1080/13632460801925822
20. [20] S. Otani, “Hysteresis models of reinforced concrete for earthquake response analysis,” J. of the Faculty of Engineering, University of Tokyo, Series B, Vol.36, No.2, pp. 407-441, 1981.
21. [21] E. M. Hernandez and G. May, “Dissipated energy ratio as a feature for earthquake-induced damage detection of instrumented structures,” J. of Engineering Mechanics, Vol.139, No.11, pp. 1521-1529, 2013. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000534
22. [22] H. Pan and K. Kusunoki, “A wavelet transform-based capacity curve estimation approach using seismic response data,” Structural Control and Health Monitoring, Vol.25, No.12, Article No.e2267, 2018. https://doi.org/10.1002/stc.2267
23. [23] R. G. Zafra, K. Kawashima, T. Sasaki, K. Kajiwara, and M. Nakayama, “Effect of polypropylene fiber reinforced cement composites for enhancing the seismic performance of a full-scale bridge column based on E-Defense excitation,” 15th World Conf. on Earthquake Engineering, 2012.
24. [24] National Research Institute for Earth Science and Disaster Resilience, “ASEBI: Archives of E-Defense shaking table experimentation database and information,” Project ID E200909, 2020. https://doi.org/10.17598/nied.0020
25. [25] C. Cruz and E. Miranda, “Damping ratios of the first mode for the seismic analysis of buildings,” J. of Structural Engineering, Vol.147, No.1, Article No.04020300, 2021. https://doi.org/10.1061/(asce)st.1943-541x.0002873
26. [26] C. Cruz and E. Miranda, “Towards an evidence-based damping model for the seismic analysis of buildings,” 18th World Conf. on Earthquake Engineering, 2024.
27. [27] P. Gulkan and M. A. Sozen, “Response and energy-dissipation of reinforced concrete frames subjected to strong base motions,” Civil Engineering Studies: Structural Research Series No.377, University of Illinois, 1971.