Earthquake Ground Motion Selection And Scaling Methods For Structural Time-history Analysis

Structural time-history analysis is a widely accepted method for seismic design and assessment of structures.In general,results of structural dynamic response have an unacceptable level of variability when several random records are used as input for the analysis.Therefore,to reduce bias and to control dispersion in structural time-history analysis,an appropriate ground motion selection and scaling method should be adopted.To date,several ground motion selection and scaling methods have been developed,but they have shortcomings.The spectral matching method,which is the most commonly proposed method for selecting earthquake records,is used in this research.When selecting target spectra,Newmark spectra are used as target spectra and two "Conditional Newmark spectra" are also developed.In the spectral matching procedure,weighted scaling methods are proposed that take into account the different contributions of higher modes to structural dynamic responses.Additionally,spectral matching using arithmetic values of response spectra is compared to the procedure using logarithmic values.These ground motion selection and scaling methods that use the target spectra and the scaling methods developed in this research are compared to traditional methods by analyzing their predictions of the structural mean response.This study aimed to develop earthquake ground motion selection and scaling methods for structural time-history analysis.The major contents and conclusions of this work are listed below.(1)A Newmark spectrum perfectly correlates with short-,medium-,and long-period structural responses;thus,it is proposed that Newmark spectra are used as target spectra in the method(i.e.,NM).Three target spectra that are calculated based on the average Newmark spectra for the three ground motion sets developed in the SAC Steel Project are presented here.These three target spectra represent 50%,10%,and 2%probabilities exceeded in 50 years,in terms of seismic risk levels.The 3-,9-,and 20-story steel moment resisting frame structures,which represent low-,medium-,and high-rise buildings designed in Los Angeles for the SAC steel project,are used as examples for nonlinear time-history analysis.NM is compared to the method using traditional spectral accelerations as target spectra(i.e.,SM)by analyzing their predictions of structural mean response.The feasibility of the NM was verified for the low-,medium-,and high-rise buildings.Absolute values of the relative errors corresponding to structural peak inter-story drift ratio demands can be less than 20%,while the required number of records is 7 or 10.The accuracy of structural mean response estimates made by NM is similar to estimates made by SM.The main advantage of the NM is that it performs well in reducing the variability of structural response results.The advantage is more significant for the longer-period structures or the structures with a severer nonlinear response.(2)A weighted scaling method(WSM)is developed for selecting and modifying structure-specific earthquake records in the time-history analysis.To match with the target spectrum,matching errors and scaling factors are calculated by the weighted least-squares method over a wider matching period range.The weight factors are determined by the modal mass participation factors that take into account the different contributions of higher modes to structural dynamic responses.Ground motion ranking scheme A(unweighted scaling priority)and scheme B(weighted scaling priority)are considered and the average spectral accelerations are used as target spectra.The accuracy of structural mean response estimates made by the WSM are similar to the methods that use equal weighted scale factors(i.e.,SM).The absolute values of the relative errors of the peak inter-story drift ratio demands are all less than 20%by the WSM when the number of records in the groups reaches 7 or 10.The main advantage of the WSM is that it has an excellent capacity for reducing variability in the structural response results.The advantage is independent of structural periods,response nonlinearity,ground motions ranking,and the number of records in the groups.(3)Differences in the results of the nonlinear structural time-history analysis using arithmetic and logarithmic values of response spectra in spectral matching procedures(i.e.,ASM and LSM methods)are compared.The physical meaning of the ASM is translated by the theory of the high dimension vectors,meanwhile,the mathematical explanation of the scaling factors calculated by the LSM is introduced.The scaling factors calculated by the LSM are larger than the ASM results,because the ASM scaling factors are mainly controlled by the short and medium-short period ranges in response spectra;however,the LSM scaling factors are mainly controlled by the long-period range.The relative errors of the peak inter-story drift ratio demands both can be controlled within an acceptable range(±20%)by the ASM and LSM.However,the LSM performed better at reducing variability in the results of the structural responses as compared to the ASM.This advantage is more significant for longer-period structures that have more severe nonlinear responses.In addition,the physical meaning of the ASM and the mathematical explanation of the LSM can verify clearly the necessity and innovation of the NM and WSM.(4)The "conditional distribution" theory of the CMS was embedded into the Newmark spectrum.Next,the "Conditional Newmark spectrum based on ground-motion prediction equations(i.e.CNM-GMPE)" and the "Conditional Newmark spectrum based on amplification factors(i.e.CNM-AF)" are proposed.Conditional Newmark spectra have close attenuation relationships with Probabilistic Seismic Hazard Analysis.The methods that use the CNM-GMPE and CNM-AF as target spectra are compared to the method that matches with the CMS.The accuracy of the CNM-AF and CMS methods for estimating structural mean responses is similar.However,the structural mean responses predicted by the CNM-GMPE method are less than the responses predicted by the above two methods,since the CNM-GMPE method has the lowest number of matching errors.A method for adjusting the damping ratios of the CMS is also developed.This method has a wider range of damping ratios(0.5%～30%)and periods(0.01 s～10 s)and is not influenced by ground motion prediction equations.