Influence of Aftershocks on Non-Linear Seismic Responseof Non-Deteriorating SDOF Systems

Amadin Osagiede and Ricardo A. MedinaDepartment of Civil Engineering, University of New Hampshire, Durham, NH

This research is supported by the McNair GraduateOpportunity Program with many thanks to my advisor, Dr.Ricardo A. Medina.

• The goal of this study is to understand the response ofSingle-Degree-Of-Freedom (SDOF) systems designed towithstand main shock (MS) hazards when they areexposed to additional hazards posed by aftershocks.

Acknowledgements

ReferencesCoburn, A., & Spence, R., (2002). Earthquake Protection (2nd Edition). West Sussex: John Wiley & Sons, Ltd.Dunbar, P.K., Lockridge, P.A., & Whiteside, L.S. (1992). Catalog of significant earthquakes 2150 B.C. to 1991 A.D., including quantitative

casualties and damage (Report SE49). Boulder, CO: National Geophysical Data Center.FEMA 356, 2000, Prestandard and Commentary for the Seismic Rehabilitation of Buildings, prepared by the American Society of Civil Engineers

for the Federal Emergency Management Agency, Washington, D.C.Jaiswal, K. & Wald, D.J. (2008). Creating a global building inventory for earthquake loss assessment and risk management (Open-File Report

2008-1160). Reston, VA: U.S. Geological Survey.Jones, L.M. et al. (2008). The ShakeOut Scenario (Open-File Report 2008-1150). Reston, VA: U.S. Geological Survey.Lee K., Foutch, D.A. Performance evaluation of damaged steel frame buildings subjected to seismic loads. ASCE Journal of Structural

Engineering 2004; 130(4): 588-599.

Li, Q., & Ellingwood, B. R. (2007). Performance evaluation and damage assessment of steel buildings under main shock-aftershock earthquake sequences. Earthquake Engineering and Structural Dynamic, 36, 405-427.

Luco, N., Bazzurro, P., & Cornell, C. A. (2004). Dynamic versus static computation of the residual capacity of mainshock-damaged building to withstand an aftershock. Proceedings from the 13th World Conference on Earthquake Engineering. Vancouver, Canada.

Maffei, J., Telleen, K., & Nakayama, (2008). Probability-based seismic assessment of buildings, considering post earthquake safety. Earthquake Spectra, 24, 667-699.

Ruiz-Garcia, J., & Maldonado, A. Evaluation of the response of existing buildings subjected to main shock-aftershock sequences. Proceedings of the 16th Mexican Congress on Earthquake Engineering 2007, Ixtapa-Zihuatenejo, Guerrero, Mexico.

Yeo, G. L., & Cornell, C.A. (2009). A probabilistic framework for quantification of aftershock ground-motion hazard in California: Methodology and parametric study. Earthquake Engineering and Structural Dynamics, 38 (1), 45-60.

Methods

Introduction

ConclusionsThis study –a base case scenario– demonstratesthat, with respect to ductility, peak displacement,and residual displacement, the effect of theaftershock is significant in the response of thesystem. Significant observations include:

• Aftershocks tend to increase the displacement demandsfor non-deteriorating SDOF systems, particularly forsystems with relatively long periods of vibration, i.e.,0.85 seconds or more.

Comparative Analysis: MS vs. MS+AS

Figure 3: Ductility of Clough model at 5% damping forSDOF system in response to main shock.

Problem Statement

Amadin Osagiede <anx22@unh.edu>Civil Engineering, The University of New Hampshire

Contact Information

Results

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• To understand if aftershocks should be exclusivelyaccounted for in the design and evaluation ofbuildings, analyses of SDOF and MDOF systemswith deterioration must be investigated.

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Figure 4: Ductility of Clough model at 5% damping for

SDOF system in response to main shock-aftershocksequence.

Figure 5: Peak Displacement of Clough model at 5%

damping for SDOF system in response to main shock.

Figure 6: Peak Displacement of Clough model at 5%

damping for SDOF system in response to main shock-aftershock sequence.

Figure 7: Residual Displacement of Clough model at 5%damping for SDOF system in response to main shock.

Figure 8: Residual Displacement of Clough model at 5%damping for SDOF system in response to main shock.

Ratios of Engineering Demand Parameters

Ductility:

Figures 3 and 4, showing displacement ductility response for difference strengthreduction factors (R Factors), demonstrates that aftershocks influenced theoverall ductile response of the system.

Peak Displacement:

Figures 5 and 6 are developed for SDOF systems with a constant lateral strength. It can be seen that at shorter periods the peak displacement responses to MS and MS-AS sequences are comparable. At longer periods the presence of aftershocks tends to increase the peak displacement demands significantly.

Residual Displacement:

Figures 7 and 8 shows the greatest difference between the SDOF responses to MS and MS-AS ground motions. They demonstrate that the aftershock has a significant impact on the residual displacement exhibited by the system. Once again, this difference is more evident at longer periods.

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Figure 9: Ductility ratio of main shock to main shock-aftershock sequence hazards at 5% damping.

Figure 10: Peak Displacement ratio of main shock to mainshock-aftershock sequence hazards at 5% damping.

Figure 12: Residual Displacement ratio of main shock tomain shock-aftershock sequence hazards at 5% damping.

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Figure 11: Ductility ratio of main shock to main shock-aftershock sequence hazards at 2% damping.

Damping Ratios:

Figures 9 and 11 were derived using the same MS and AS records but at different damping ratios. Both plots, however, are almost identical. This suggests that the relative difference between MS and MS-AS sequence responses is weakly dependent on the damping in the analysis of the ductile response of SDOF systems.

Ductility & Peak Displacement Ratios:

Figures 9 and 10 indicate that the effect of aftershocks on the ductility and peak displacement responses for periods between 0.05 to 0.85 seconds is not very significant when compared to the responses obtained using MS ground motions only. This observation applies to systems with R Factors less than 6. At periods less than 0.35 seconds and greater than 0.85 seconds aftershocks have shown to produce a significant increase in both ductility and peak displacement demands.

Residual Displacement Ratios:

Figure 12 demonstrates that the overall residual displacement experienced by the system due to main shock-aftershock sequences is greater than with the main shock alone. At certain periods, the response drops below a value of 1 indicating that the aftershock countered the impact of the main shock and stabilized the system to some degree.

Figure 2: Magnitude (Mw) and distance to the source relationship for main shocks

for NEHRP site class D (a) and a visualization of an SDOF system (b).

Figure 1: A building that was slightly damaged due to the 1999 Turkey Kocaeli main

shock (M7.4) (a) and the collapsed structure after it was exposed to a M5.9aftershock a month later (b) .

a b

• Earthquakes have claimed approximately eight millionlives over the last two thousand years (Dunbar,Lockridge, & Whiteside, 1992).

• Seventy-five percent of earthquake-related humancasualties are caused by the collapse of structures(Coburn & Spence, 2002).

• Building codes in the United States do not explicitlyaccount for the influence of aftershocks in the estimationof seismic demands used for design. It is assumed that ifa structure can withstand a main shock, it can endure anaftershock without collapse.

• In order to reduce the risk of injuries, loss of lives, andfinancial losses linked to the collapse of structures, adeeper level of understanding of the dynamic responseof structures exposed to aftershock hazards is needed.

• This study consists of the statistical quantification ofengineering demand parameters via response historyanalyses with a set of recorded main-shock aftershock(MS-AS) sequences.

• Ground motions were classified according to sitecharacteristics. This final set consists of 12 MS-AS sequences for hard rock and rock, 84 for very densesoil and soft rock, and 65 for regular stiff (Figure 2a),with each sequence having two horizontal components.

a b

• Aftershocks may counter the impact of the main shock and help stabilize the system to some degree, at shorter periods of vibration.

• The observations presented in this study are weaklydependent on the damping ratio assumed for the SDOFsystem.