A statistical investigation to determine dominant frequency of layered soil profiles

Abstract

Energy based seismic design getting attraction since it accounts for all structural (hysteretic behavior of structural members), earthquake (amplitude, duration and frequency content) and soil (bearing capacity, frequency content) characteristics. To develop an efficient energy based seismic design procedure, accurate determination of the fundamental periods of the soil deposits is crucial. Hence, several analytical, numerical and approximate methods were suggested in the literature to find out fundamental periods of layered soil profiles. However, practitioners tend to use the simplest and the roughest methods, generally. In this particular research, a statistical study was performed to find out the best fit coefficient for the total travel time having minimum standard deviation. In the analyses, the calculated fundamental periods of 459 different soil profiles are compared with the results of almost exact analytical equations. Resultantly, the equation generally preferred by the practitioners is improved. It is proved that the improved equation has higher accuracy with lowest standard deviation and higher correlation. Therefore, using the improved equation to determine fundamental period of the layered soil profiles is highly suggested.

Keywords

• Energy based seismic design
• Layered soil profile
• Fundamental period
• Resonance

References

1. Dobry R, Oweis I & Urzua A (1976). Simplified procedures for estimating the fundamental period of a soil profile. Bulletin of Seismological Society of America 66:1293–1321.
2. Gazetas G (1982). Vibrational characteristics of soil deposits with variable wave velocity. Int. J. Numer. Anal. Methods Geomech. 6, 1–20, doi:10.1002/nag.1610060103.
3. Ghofrani H, Atkinson G M, & Goda K (2013). Implications of the 2011 M9.0 Tohoku Japan earthquake for the treatment of site effects in large earthquakes. Bull. Seismol. Soc. Am. 11, 171–203, doi:10.1007/s10518-012-9413-4.
4. Goda K, Kiyota T, Pokhrel RM, Chiaro G, Katagiri T, Sharma K & Wilkinson S (2015). The 2015 Gorkha Nepal earthquake: insights from earthquake damage survey, Frontiers in Built Environment, 1, 1-8. https://doi.org/10.3389/fbuil.2015.00008.
5. Güllü A, Yüksel E, Yalçın C, Dindar A A, Özkaynak H, Büyüköztürk O (2019). An improved input energy spectrum verified by shake table tests. Earthq. Eng. Struct. Dynam. 48(1), 27-45. doi: 10.1002/eqe.3121
6. Hadjian A H (2002). Fundamental period and mode shape of layered soil profiles. Soil. Dynam. Earthq. Eng. 22, 885–891. doi: 10.1016/S0267-7261(02)00111-2.
7. National Research Institute for Earth Science and Disaster (2019). NIED K-NET, KiK-net, National Research Institute for Earth Science and Disaster Resilience. doi:10.17598/NIED.0004.
8. Madera G A (1970). Fundamental Period and Amplification of Peak Acceleration in Layered Systems. Research Report R70-37, Dept. of Civil Engineering, MJ.T., Cambridge, Mass.

9. Mathworks Inc, MATLAB available at www.mathworks.com.
10. Sextos A, De Risi R, Pagliaroli A et al (2018), Local site effects and internal damage of buildings during the 2016 central Italy earthquake sequence, Earthquake Spectra, 34(4), 1639-1669. https://doi.org/10.1193/100317EQS194M.
11. Urzua A, Dobry R & Christian J (2017). Is harmonic averaging of shear wave velocity or the simplified Rayleigh method appropriate to estimate the period of a soil profile. Earthq. Spectra 33, 895–915. doi:10.1193/101716EQS174M.
12. Vijayendra K V, Nayak S & Prasad S K (2014). An Alternative Method to Estimate Fundamental Period of Layered Soil Deposit, Indian Geotech J. doi: 10.1007/s40098-014-0121-7
13. Wang S, Shi Y, Jiang W, Yao E & Miao Y (2018). Estimating Site Fundamental Period from Shear-Wave Velocity Profile. Bulletin of the Seismological Society of America,Vol. 108, No. 6, pp. 3431–3445. doi: 10.1785/0120180103.
14. Zhao J X (1996). Estimating modal parameters for a simple soft-soil site having a linear distribution of shear wave velocity with depth. Earthq. Eng. Struct. Dynam. 25, 163–178. doi: 10.1002/(SICI)1096-9845(199602) 25:2<163::AID-EQE544>3.0.CO;2-8.
15. Zhao J X (1997). Modal analysis of soft-soil sites including radiation damping. Earthq. Eng. Struct. Dynam. 26, 93–113. doi: 10.1002/(SICI)1096-9845(199701)26:1<93::AID-EQE625>3.0.CO;2-A
16. Zhao J X, Zhang J, Asano A, Ohno Y, Oouchi T, Takahashi T, Ogawa H, Irikura K, Thio H K & Somerville P G (2006). Attenuation relations of strong ground motion in Japan using site classification based on predominant period. Bull. Seismol. Soc. Am. 96,898–913, doi: 10.1785/0120050122.
17. Zhao J X & Xu H (2013). A comparison of VS30 and site period as site effect parameters in response spectral ground-motion prediction equations, Bull. Seismol. Soc. Am. 103, 1–18, doi: 10.1785/0120110251.
18. Zhao J X, Hu J S, Jiang F, Zhou J, Zhang Y B, An X M, Lu M & Rhoades D A (2015). Nonlinear site models derived from 1D analyses for ground-motion prediction equations using site class as the site parameter. Bull. Seismol. Soc. Am. 105, 2010–2022, doi: 10.1785/0120150019.