EVALUATION OF SPECTRUM COMPATIBLE EARTHQUAKE RECORDS AND ITS EFFECT ON THE INELASTIC DEMAND OF CIVIL STRUCTURES

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1 NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 2-2, 24 Anchorage, Alaska EVALUATION OF SPECTRUM COMPATIBLE EARTHQUAKE RECORDS AND ITS EFFECT ON THE INELASTIC DEMAND OF CIVIL STRUCTURES R. L. Gascot and L. A. Montejo 2 ABSTRACT Three different methodologies available for the generation of spectrum compatible earthquake records are evaluated: () time domain adjustment by adding wavelets to an historic record (2) adjustment of the wavelet coefficients of a seed record via Continuous Wavelet Transform (CWT) and (3) frequency domain modification of an initial random process. The article examines the level of matching that can be attained by each of the 3 methodologies and the strong motion characteristics of the compatible records. To assess the effect on the nonlinear response of civil structures, incremental dynamic analyses are performed on a typical reinforced concrete bridge bent column using sets of spectrum compatible records generated with the three methodologies. It was found that an acceptable level of matching can be obtained by the three methodologies. The records generated with the frequency domain approach revealed the closest level of matching with the target spectrum. However, these records also unveiled unrealistic frequency content and stationary characteristics and a tendency to induce less inelastic demand on the structure evaluated. In the case of the methodologies that make use of a seed record, the characteristics of the record are well preserved as long as the seed already exhibits some level of compatibility with the target spectrum. The wavelet approach preserved better the accelerations time history features, but the CWT records depicted better behaved velocity and displacement time histories. The records generated via CWT using seed records with an initial level of match exhibited the smaller scatter in the nonlinear response of the structure. Graduate Research Assistant, Dept. of Civil Engineering, U. of Puerto Rico at Mayaguez, Mayaguez PR 68 2 Assistant Professor, Dept. of Eng. Science and Materials, U. of Puerto Rico at Mayaguez, Mayaguez PR 68 Gascot RL, Montejo LA. Evaluation of spectrum compatible earthquake records and its effect on the inelastic demand of civil structures. Proceedings of the th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 24.

2 Evaluation of Spectrum Compatible Earthquake Records and its Effect on the Inelastic Demand of Civil Structures R. L. Gascot and L.A. Montejo 2 ABSTRACT Three different methodologies available for the generation of spectrum compatible earthquake records are evaluated: () time domain adjustment by adding wavelets to an historic record (2) adjustment of the wavelet coefficients of a seed record via Continuous Wavelet Transform (CWT) and (3) frequency domain modification of an initial random process. The article examines the level of matching that can be attained by each of the 3 methodologies and the strong motion characteristics of the compatible records. To assess the effect on the nonlinear response of civil structures, incremental dynamic analyses are performed on a typical reinforced concrete bridge bent column using sets of spectrum compatible records generated with the three methodologies. It was found that an acceptable level of matching can be obtained by the three methodologies. The records generated with the frequency domain approach revealed the closest level of matching with the target spectrum. However, these records also unveiled unrealistic frequency content and stationary characteristics and a tendency to induce less inelastic demand on the structure evaluated. In the case of the methodologies that make use of a seed record, the characteristics of the record are well preserved as long as the seed already exhibits some level of compatibility with the target spectrum. The wavelet approach preserved better the accelerations time history features, but the CWT records depicted better behaved velocity and displacement time histories. The records generated via CWT using seed records with an initial level of match exhibited the smaller scatter in the nonlinear response of the structure. Introduction Despite the increasing number of available strong motion records, spectrum compatible records are still widely used for seismic design/assessment in zones where the number of available records is scarce and/or to reduce the number of analysis required while complying with design codes requirements. Three different methodologies used to generate spectrum compatible records are evaluated in this report: wavelet based modification of seed records, seed record adjustment based on the Continuous Wavelet Transform and synthetic record generation in the frequency domain. Different sets of compatible records are generating using each of these methodologies. The compatible records are evaluated based on the level of match with the target spectrum and its strong motion characteristics. The effect on the nonlinear seismic response is evaluated using these records as input motions for nonlinear time history analyses of a typical reinforced concrete (RC) bridge bent column model developed using a distributed plasticity fiber based finite element approach. The numerical model was validated using experimental data from a large scale shake table test program. Graduate Research Assistant, Dept. of Civil Engineering, U. of Puerto Rico at Mayaguez, Mayaguez PR 68 2 Assistant Professor, Dept. of Eng. Science and Materials, U. of Puerto Rico at Mayaguez, Mayaguez PR 68 Gascot RL, Montejo LA. Evaluation of spectrum compatible earthquake records and its effect on the inelastic demand of civil structures. Proceedings of the th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 24.

3 Generation of the Compatible Records and Selection of Seed Records Two of the methodologies evaluated require of a seed record (i.e. an actual earthquake record) as start point to generate the spectrum compatible record: () The wavelet-based methodology is based on the adjustment in the time domain of the seed record by adding wavelets; variations of the algorithm have been proposed in [,2,3], in this work the program SeismoMatch [4] is used. (2) The Continuous Wavelet Transform (CWT) based methodology is based on the iterative scaling of the CWT detail functions (i.e. amplitude modulated functions with a very dominant frequency that compose the signal) of the seed record; variations of the algorithm have been proposed in [,6], in this work we use the algorithm as implemented in ArtifQuakeLet II [7]. The third methodology is similar to the popular program Simqke [8], it starts from a random process which frequency content is tailored until an acceptable level of match with the target spectrum is reached; in this work the adjustment of the frequency content is accomplished using Fourier Transforms as implemented in the program SeismoArtif [9]. The target spectrum was constructed following the provisions in ASCE 7- for soil type C and values of S ds =.83 and S d =.87. In order to investigate the effect of the initial level of matching of the seed record on the efficiency of the algorithms, two sets of records each were selected. One set contain records which response spectrum shape is close to the target spectrum, this set is denoted as the close match records (CM). The other set contains records whose response spectrum shape is distant from the target spectrum; this set is named distant match records (DM). Records with pulse like characteristics (near source records) were disregarded. All the records were selected from the Next Generation Attenuation of Ground Motions (NGA) database []. The initial level of matching of the seed records is estimated using the root mean square deviation (D rms ) between the spectral amplitudes (Eq. ). Since the selection is made based on the overall spectral shape resemblance, the seed records are multiplied by a scale factor a to reduce the spectral amplitude misfit []. The period range used to examine the level of matching in the response spectra was [.2 4] seconds. The period range used to generate the compatible records was [.2-4] seconds. = ( ) ( ) () where: N: number of periods at which the spectral shape is specified = ( ) ( ) S αr : spectral acceleration of the record at period T i S αt : target spectral acceleration at period T i A summary of the two set of records is presented in Tables and 2, including Joyner- Boore distance (Rjb) and the average shear- wave velocity between the and 3 meters depth (Vs3). The average D rms for the DM records is.79, more than twice the average deviation calculated for the CM records,.34. The response spectra for the scaled seed records are presented in Fig. along with the target spectrum. As expected, the CM records response spectra seem to be in closer agreement with the target spectrum than the DM records. For the frequency

4 domain approach compatible records were generated with durations between s and s. Table. Close match (CM) records Record ID Magnitude/Year Event D rms a Mechanism Rjb (km) Vs 3 (m/s) CM M Superstation Hills Strike-Slip CM2 M Imperial Valley Strike-Slip CM3 M Loma Prieta.29.8 Reverse-Oblique CM4 M Gazli.33.3 Unknown CM M Landers Strike-Slip CM6 M Chichi-Taiwan Strike-Slip CM7 M Chichi-Taiwan Reverse-Oblique - 68 CM8 M Loma Prieta Reverse-Oblique CM9 M Chichi-Taiwan Reverse CM M Northridge Reverse Table 2. Distant match (DM) records Record ID Magnitude/ Year Event D rms a Mechanism Rjb (km) Vs 3 (m/s) DM M Northridge Reverse DM2 M Northridge.4. Reverse DM3 M Coyote Lake.78. Strike-Slip DM4 M Loma Prieta Reverse-Oblique DM M Morgan Hill Strike-Slip DM6 M Chichi-Taiwan Reverse DM7 M Loma Prieta.8 8. Reverse-Oblique DM8 M Chichi-Taiwan 3.8. Reverse-Oblique DM9 M Chichi-Taiwan Reverse-Oblique DM M Chichi-Taiwan Reverse-Oblique PSA [g] PSA [g] Period [s] Period [s] Figure. Response spectra for the scaled seed records and the target spectrum (thick line). Left: close match records (CM), right: distant match records (DM)

5 Evaluation of the Compatible Records Goodness of match: The level of match attained by each of the methodologies is analyzed in Figs. 2. It is seen from Fig. 2a that all three methodologies evaluated were able to generate earthquakes records which response spectrum closely matches the target spectrum. Fig. 2b summarizes the mean square root deviations for all the compatible records generated ( groups of ). It is seen that the SeismoArtif (SA) records exhibit the smallest average spectral amplitude deviation from the target spectrum, followed by the ArtifQuakeLet (AQT II) and SeismoMatch (SM) records, respectively. Looking only at the goodness of the match obtained, the initial level of match of the seed record doesn t seem to play an important role on the generation of compatible records. PSA [g] Drms Period [s] CM SM DM SM CM AQTII DM AQTII SA Figure 2. Response spectra for the compatible records and the target spectrum (left) and root mean square deviations for the sets of records (right). Time histories behavior: In the sake of brevity only the compatible records obtained from seed records CM3 and DM6 using the Wavelet and CWT based methodologies are displayed in Fig. 3. For both methodologies the seed records characteristics are better retained when the CM record is used. Moreover, the acceleration features are better retained by Wavelet records and the velocity and displacement features are better retained by the CWT records. Arias Intensity (AI) and Significant Duration (SD): Arias Intensity is defined as the square of the acceleration time history integrated over the duration of the motion and is commonly used to evaluate the earthquake record intensity and damage potential. Arias Intensity is also used in the calculation of the so-called Significant Duration, frequently defined as the time interval across which % and 9% of the total Arias intensity is accumulated. AIs and SDs values are presented in Figs. 4. It is seen that AIs and SDs of the seed records are better preserved by SeismoMatch, this is particularly evident for the DM records where the ArtifQuakeLet II records exhibit AI and SD values much larger than the observed in the seed records. When the AI s for all the compatible records are compared Fig. 4d it is noticed that some of the SeismoArtif records reveal values that are unreasonable high. Frequency content: The frequency content of the records is analyzed using Fourier amplitude spectra and Wavelet maps via CWT, so that not only the frequency content is evaluated but also its evolution in time. The CWT was calculated using the complex Morlet wavelet with

6 bandwidth parameter (f b ) and central frequency parameter (f c ) of 2. An example of the results is presented in Figs. to 7. Figs.. show the results for CM3 and present the Fourier spectra and wavelet maps for the scaled seed record, the SeismoMatch artificial record and the ArtifQuakeLet II artificial record. It is seen that most of the non-stationary characteristics of the records are retained, i.e. the dominant frequencies remain approximately the same (Fourier spectra) and are occurring at about the same times (Wavelet map) for the original and compatible records. Similar results were obtained for the other CM records. Figs. 6 present the results obtained for the DM6 records. It is seen that the non-stationary characteristic are not retained. Moreover, both methodologies are adding high frequencies to the original seed record. In the case of SeismoMatch such frequencies are concentrated over the strong motion part of the record, in the ArtifQuakeLet II record the added high frequencies content seems to be distributed over the total duration of the record. Similar results were obtained for all the DM records. Finally, Figs. 7 show the same analysis for the SeismoArtif record of duration 3 seconds. It is seen that the non-stationary characteristics of this record are not realistic, with most of the dominant frequencies occurring over the total duration of the record. Similar results were obtained for the other 9 SeismoArtif records. a [g] a [%g] v [cm/s] d [cm] v [cm/s] a [g] d [cm] (a) (c) Figure 3. Acceleration, velocity and displacement time histories for the compatible (black lines) and scaled seed records (blue lines): (a) SesimoMatch CM3, (b) ArtifQakeLet CM3, (c) SeismoMatch DM6 and (d) ArtifQuakeLet DM6 v [cm/s] d [cm] a [g] v [cm/s] d [cm] 2-2 (b) (d)

7 Arias intensity [cm/s] (a) Scaled seed record SeismoMatch ArtifQuakeLet II Arias intensity [cm/s] 2 (b) CM CM2 CM3 CM4 CM CM6 CM7 CM8 CM9 CM DM DM2 DM3 DM4 DM DM6 DM7 DM8 DM9 DM Significant duration [s] (c) Significant duration [s] (d) CM CM2 CM3 CM4 CM CM6 CM7 CM8 CM9 CM DM DM2 DM3 DM4 DM DM6 DM7 DM8 DM9 DM (e) 4 Arias intensity [cm/s] 3 2 CMSM CMAQT II DMSM DMAQT II SA Figure 4. Arias Intensity and Significant Duration for the original scaled and compatible records (a to d) and summary of Arias Intensity values for all the compatible records generated (e)

8 freq. [Hz] freq. [Hz] Figure F Fourier spectra (left) and wavelet maps (right) for the scaled, SeimoMatch and ArtifQuakelet (top to bottom) versions of the CM3 record Figure F Fourier spectra (left) and wavelet maps (right) for the scaled, SeimoMatch and ArtifQuakelet (top to bottom) versions of the DM6 record.

9 2 2 Figure F A Fourier spectra (left) and wavelet maps (right) for the 3 seconds SeismoArtif record. Effect on the Nonlinear Response of a RC Bridge Bent Column The structure to analyze is a full scale RC bridge column subjected to a shake table test performed at the Network for Earthquake Engineering Simulation (NEES) Large High Performance Outdoor Shake Table (LHPOST) at the University of California- San Diego. The complete experiment data is available from the NEEShub repository [2] and was used to calibrate a distributed plasticity fiber based numerical model capable of replicating the column nonlinear seismic behavior. The test specimen consists of a 7.3m (24ft) length /.22m (4ft.) diameter cantilevered reinforced concrete column. The test protocol consisted of records applied sequentially to the column covering a large range of inelastic demands. Figs. 8 shows an example of the results obtained, further results and details on the numerical model used are available elsewhere [3,4]. a [g] μ Figure 8. Experimental (gray) and simulated (blue) acceleration (top) and displacement ductility (bottom) time histories for earthquake motion #7 of the test protocol. The calibrated model was used to perform Incremental Dynamic Analyses (IDA) [] using the compatible records as input motions. The intensity measure used was the spectral accelerations a the vibration period exhibited by the structure at ductility Sa(T*). Two damage measures were investigated: peak displacement ductility and the Park and Ang damage index (DI) [6]. The resulting average IDA curves are presented in Figs. 9 along with the corresponding coefficients of variation. It is seen that the record-to-record dispersion for the damage measures evaluated is relatively low, e.g. mostly below.2. In the case of the peak displacement ductility the lowest values are dominated by the records generated using the

10 frequency domain approach (SeismoArtif) and the largest values by the records generated using the wavelet approach (SeismoMatch) with distant match seed records (DMSM). The damage index exhibited the lowest dispersion and was not dominated by either set of records. The lowest dispersion in the structural response is obtained for the records generate using the CWT approach (ArtifQakeLet II) along with close match records (CMAQT II). Displacement ductility CMSM CMAQT II DMSM DMAQT II SA COV Damage Index CMSM CMAQT II DMSM DMAQT II SA COV Sa(T*) [g].. 2 Sa(T*) [g].. 2 Sa(T*) [g].. 2 Sa(T*) [g] Figure 9. Average IDA curves and COVs for the peak displacement ductility (left) and damage index (right) Conclusions The three methodologies evaluated were successful generating acceleration series with a response spectrum that matches a prescribed design spectrum. The compatible records with the best matching were the generated using a frequency domain approach, followed by the CWT based approach and the Wavelets approach, respectively. These results were somehow expected as the frequency domain approach starts from a white noise signal (i.e. frequency content in the whole frequency range) while the other two methodologies start from an actual earthquake record (i.e. limited frequency content to work with). Nevertheless, the frequency domain record unveiled unrealistic characteristics and a tendency to induce less inelastic demand. For the methodologies working with seed records it was found that the initial level of match of the record does not significantly affect the level of matching that can be attained for the final compatible record. However, the characteristics of the seed records are better preserved in the compatible records and the scatter in the inelastic response is reduced when the initial spectral match is close. It should be noticed that these conclusions applied only to structures like the one examined, i.e. well detailed ductile structures with a very dominant mode of vibration. Acknowledgments This work was performed under award NRC-HQ-2-G-38-8 from the US Nuclear Regulatory Commission. The statements, findings, conclusions, and recommendations are those of the authors and do not necessarily reflect the view of the US Nuclear Regulatory Commission. The experimental data used in this work was obtained from the NEEShub Project Warehouse, a centralized data repository for sharing and publishing earthquake engineering research data from

11 experimental and numerical studies authors would like to thank Dr. Matthew Schoettler and Professor Jose Restrepo for making the raw data for this set of tests publicly available in a timely manner. References. Abrahamson NA. Non-stationary spectral matching. Seismological Research Letters 992; 63(): Hancock J, Watson-Lamprey J, Abrahamson NA, Bommer J.J, Markatis A, McCoy E, Mendis R. An improved method of matching response spectra of recorded earthquake ground motion using wavelets. Journal of Earthquake Engineering 26; : Al Atik L, Abrahamson N. An improved method for non-stationary spectral matching. Earthquake Spectra 2; 26(3): Seismosoft. SeismoMatch version ; Mukherjee S, Gupta, VK. Wavelet-based generation of spectrum-compatible time-histories. Soil Dynamics and Earthquake Engineering 22; 22(9): Suarez LE, Montejo LA. Applications of the wavelet transform in the analysis and generation of artificial accelerograms. Journal of Structural Engineering and Mechanics 27; 27(2): Montejo LA, Suárez LE. An improved CWT based algorithm for the generation of spectrum compatible records. International Journal of Advanced Structural Engineering 23; (26). 8. Gasparini D, Vanmarcke EH. SIMQKE: A Program for Artificial Motion Generation. Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA, Seismosoft. SeismoArtif version... 22; Pacific Earthquake Engineering Research Center PEER., Next Generation Attenuation of Ground Motions NGA Database 23, Beyer K, Bommer JJ. Selection and scaling of real accelerograms for bi-directional loading: a review of current practice and code provisions. Journal of Earthquake Engineering 27, : Schoettler MJ, Restrepo JI, Guerrini G, Duck DE, Carrea F. A Full-Scale Single-Column Bridge Bent Tested by Shake-Table Excitation. Center for Civil Engineering Earthquake Research, Department of Civil Engineering, University of Nevada, Aguirre DA, Gaviria CA, Montejo LA. Wavelet based damage detection in reinforced concrete structures subjected to seismic excitations. Journal of Earthquake Engineering 23, 7(8): Aguirre DA, Montejo LA. Damping and frequency changes induced by increasing levels of seismic inelastic demand on reinforced concrete structures. Smart Structures and Systems, submitted for publication.. Vamvatsikos D, Cornell CA. Incremental dynamic analysis. Earthquake Engineering and Structural Dynamics 22, 3(3): Park YJ, Ang AHS. Mechanistic seismic damage model for reinforced concrete. Journal of Structural Engineering 98, (4):