The dependence of conditional spectra on the choice of target periods

Document Type : Article


Department of Civil Engineering, Faculty of Engineering, Arak University, Arak, 38156-8-8349, Iran


The dependence of Conditional Mean Spectrum (CMS) and the corresponding standard deviation on different target period values has been investigated in this paper by means of two types of target spectra, i.e. based on Epsilon and Eta indicators. The structural collapse capacities, as well as the mean annual frequency (MAF) of exceeding a limit state, are taken into consideration. The results show that the dependence of Eta-based CMS (ECMS) on the choice of target period is insensitive to the target period in the case of MAF calculation. However, this dependence is meaningfully less in the case of ECMS when compared to CMS in Intensity based ground motion selection. The Sum of the Squared Error (SSE) is utilized to compare different CMS cases. SSE is less in the case of shorter return periods, e.g. 75 years, in comparison with longer return periods, e.g. 2475 years. This dependence is also a function of choosing attenuation relationships. Therefore, four Next Generation Attenuation (NGA) relationships have been employed in this study. In general, ECMS has shown less dependence in all cases when compared with the conventional CMS.


Main Subjects

1. Baker, J.W. Conditional mean spectrum: Tool for
ground motion selection", ASCE Journal of Structural
Engineering, 173(3), pp. 322-331 (2011).
2. Campbell, K.W. and Bozorgnia, Y. NGA ground
motion model for the geometric mean horizontal component
of PGA, PGV, PGD and 5% damped linear
elastic response spectra for periods ranging from 0.01
to 10 s", Earthquake Spectra, 24(1), pp. 139-171
3. Somerville, P.G. and Thio, H.K. Development of
ground motion time histories for seismic design", Proceedings
of the Ninth Paci c Conference on Earthquake
Engineering Building an Earthquake-Resilient Society,
Auckland, New Zealand, 14-16 April (2011).
4. Lin, T., Haselton, C.B. and Baker, J.W. Conditionalspectrum-
based ground motion selection, Part I: Hazard
consistency for risk-based assessments", Earthquake
Engineering and Structural Dynamics, 42(12),
pp. 1847-1865 (2013).
5. Lin, T., Haselton, C.B. and Baker, J.W. Conditional-
Spectrum-based ground motion selection. Part II:
Intensity-based assessments and evaluation of alternative
target spectra", Earthquake Engineering and
Structural Dynamics, 42(12), pp. 1867-1884 (2013).
6. Baker, J.W. and Jayaram, N. Correlation of spectral
acceleration values from NGA ground motion models",
Earthquake Spectra, 24(1), pp. 299-317 (2008).
7. Carlton, B. and Abrahamson, N. Issues and approaches
for implementing conditional mean spectra
in practice", Bulletin of the Seismological Society of
America, 104(1), pp. 503-512 (2014).
8. Hashash, Y., Abrahamson, N., Olson, S., Hague, S.
and Kim, B. Conditional mean spectra in site-speci c
seismic hazard evaluation for a Major River Crossing in
the Central united states", Earthquake Spectra, 31(1),
pp. 47-69 (2014).
9. Mousavi, M., Ghafory-Ashtiany, M. and Azarbakht,
A. A new indicator of elastic spectral shape for the
reliable selection of ground motion records", Earthquake
Engineering and Structural Dynamics, 40(12),
pp. 1403-1416 (2011).
10. Azarbakht, A., Shahri, M. and Mousavi, M. Reliable
estimation of the mean annual frequency of collapse
by considering ground motion spectral shape e ects",
Bulletin of Earthquake Engineering, 13(3), pp. 777-797
11. USGS. United State of Geological Survey, Available
12. Bazzurro, P. and Cornell, C.A. Seismic hazard analysis
of nonlinear structures I: Methodology", ASCE
Journal of Structural Engineering, 120(11), pp. 3320-
3344 (1994).
13. Cornell, C.A., Jalayer, F., Hamburteger, R.O. and
Foutch, D.A. Probabilistic basis for 2000 SAC federal
emergency management agency steel moment frame
guidelines", ASCE Journal of Structural Engineering,
128(4), pp. 526-533 (2002).
14. Chiou, B.S.J. and Youngs, R.R. An NGA model
for the average horizontal component of peak ground
motion and response spectra", Earthquake Spectra,
24(1), pp. 173-215 (2008).
15. Abrahamson, N.A. and Silva, W.J. Summary of the
Abrahamson & Silva NGA ground motion relations",
Earthquake Spectra, 24(1), pp. 67-97 (2008).
16. Boore, D.M. and Atkinson, G.M. Ground-Motion
prediction equations for the average horizontal component
of PGA, PGV, and 5%-damped PSA at spectral
periods between 0.01 s and 10.0 s", Earthquake Spectra,
24(1), pp. 99-138 (2008).
17. Baker, J.W. and Cornell, C.A., Vector-Valued Ground
Motion Intensity Measures for Probabilistic Seismic
Demand Analysis, PEER Report 2006/08, Paci c
Earthquake Engineering Research Center, University
of California, Berkeley, CA (2006).
18. Negro, P., Mola, E., Molina, F.J. and Magonette, G.E.
Full-scale testing of a torsionally unbalanced threestory
non-seismic RC frame", Proceedings of the 13th
World Conference on Earthquake Engineering, Paper
No. 968 (2004).
19. Fardis, M.N., Design of an Irregular Building for the
SPEAR Project-Description of the 3-Storey Structure,
University of Patras, Structures Laboratory, Greece
20. Fajfar, P., Dolsek, M., Marusic, D. and Stratan,
A. Pre- and post-test mathematical modeling of
a plan-asymmetric reinforced concrete frame building",
Earthquake Engineering and Structural Dynamics,
35(11), pp. 1359-1379 (2006).
21. Vamvatsikos, D. and Cornell, C.A. Incremental dynamic
analysis", Earthquake Engineering and Structural
Dynamics, 31(3), pp. 491-514 (2002).
22. Mousavi, M., Shahri, M. and Azarbakht, A. E CMS:
A new design spectrum for nuclear structure in high
levels of seismic hazard", Nuclear Engineering and
Design, 252, pp. 27-33 (2012).