An algorithm for spectrally matching bi-directional ground motions to a target RotD100 spectrum while maintaining the radial spectral acceleration pattern
Restricted accessResearch articleFirst published online August, 2023
An algorithm for spectrally matching bi-directional ground motions to a target RotD100 spectrum while maintaining the radial spectral acceleration pattern
An integrated algorithm to spectrally match two seed-recorded horizontal bi-directional ground motion components to a maximum-direction response spectrum (RotD100) while maintaining the radial spectral acceleration pattern (RadSAP) at target natural periods is presented. The algorithm is based on the complex-discrete-Fourier-transform (CDFT) and iterative manipulation of the seed-recorded bi-directional ground motions. Initially, a population of candidate bi-directional ground motion pairs is generated, and the candidate resulting in the minimum error in RadSAP is picked. Subsequently, the CDFT coefficients of the picked bi-directional ground motion near the target natural periods are rotated to modify the orientation angle, which contributes to the modification of RadSAP. Then, a double iterative method is introduced to modify the bi-directional ground motion after CDFT coefficients rotation to be spectral and envelope shape compatible in the frequency and time domain. In order to show the effectiveness of the proposed algorithm, two target response spectra are determined following the current ASCE/SEI 7-16 and CJJ 166-2011 specifications, and 10 bi-directional ground motions are selected based on the resemblance in response spectrum for each target spectrum. It is shown that with the proposed algorithm, the RotD100 response spectra estimated from the modified bi-directional ground motions closely match the smooth target RotD100 response spectrum, and the RadSAPs at these target natural periods show an improved match with the seed-recorded bi-directional ground motions than the previous version method. Furthermore, the waveforms of the results obtained using the proposed method are similar to that of the scaled seed records in terms of acceleration, velocity, and displacement. Thus, the generated bi-directional ground motions can be used for future seismic risk assessment of buildings considering the directionality effects.
American Society of Civil Engineers (ASCE) (2016) Minimum Design Loads and Associated Criteria for Buildings and Other Structures (ASCE/SEI 7-16). Reston, VA: ASCE.
2.
BendatJSPiersolAG (2011) Random Data: Analysis and Measurement Procedures. Hoboken, NJ: John Wiley & Sons.
3.
BooreDM (2010) Orientation-independent, nongeometric-mean measures of seismic intensity from two horizontal components of motion. Bulletin of the Seismological Society of America100(4): 1830–1835.
4.
BooreDMWatson-LampreyJAbrahamsonNA (2006) Orientation-independent measures of ground motion. Bulletin of the Seismological Society of America96(4A): 1502–1511.
5.
BozorgniaYAbrahamsonNAAl AtikLAnchetaTDAtkinsonGMBakerJWBaltayABooreDMCampbellKWChiouBSJDarraghRDaySDonahueJGravesRWGregorNHanksTIdrissIMKamaiRKishidaTKottkeAMahinSARezaeianSRowshandelBSeyhanEShahiSShantzTSilvaWSpudichPStewartJPWatson-LampreyJWooddellKYoungsR (2014) NGA-West2 research project. Earthquake Spectra30(3): 973–987.
6.
CacciolaPColajanniPMuscolinoG (2004) Combination of modal responses consistent with seismic input representation. Journal of Structural Engineering: ASCE130(1): 47.
7.
CampbellKWBozorgniaY (2014) NGA-West2 ground motion model for the average horizontal components of PGA, PGV, and 5% damped linear acceleration response spectra. Earthquake Spectra30(3): 1087–1115.
8.
ChibaT (1985) Characteristics of nonstationary rotary spectrum of earthquake motions. Doboku Gakkai Ronbunshu356: 499–506 (in Japanese).
9.
ChibaTKimuraJ (1970) Appropriateness of rotary spectral analysis for the study of array observation records. WIT Transactions on the Built Environment15: 235–246.
10.
ChiouBSJYoungsRR (2014) Update of the Chiou and Youngs NGA model for the average horizontal component of peak ground motion and response spectra. Earthquake Spectra30(3): 1117–1153.
11.
CloughRWPenzienJ (2010) Dynamics of Structures. New York: Computers & Structures, Inc.
12.
DwivediAReddyKSKSomalaSN (2022) Study of seismic orientation of structure with bi-directional response analysis in the vicinity of branched fault earthquake rupture. Structures37: 613–623.
13.
FayazJZareianF (2021) An efficient algorithm to simulate site-based ground motions that match a target spectrum. Earthquake Engineering & Structural Dynamics50(13): 3532–3549.
14.
FayazJAzarSDabaghiMZareianF (2021) An efficient algorithm to simulate hazard-targeted site-based synthetic ground motions. Earthquake Spectra37(2): 876–902.
15.
Federal Emergency Management Agency (FEMA) P-2082-1 (2020) FEMA P-2082-1 NEHRP Recommended Seismic Provisions for New Buildings and Other Structures (National Earthquake Hazards Reduction Program (NEHRP). Washington, DC: FEMA.
16.
FengRWangXYuanWYuJ (2018) Impact of seismic excitation direction on the fragility analysis of horizontally curved concrete bridges. Bulletin of Earthquake Engineering16(10): 4705–4733.
17.
GaspariniDAVanmarckeEH (1976) Simulated earthquake motions compatible with prescribed response spectra. Research report R76-4764. Cambridge, MA: Department of Civil Engineering, Massachusetts Institute of Technology.
18.
GonellaJ (1972) A rotary-component method for analysing meteorological and oceanographic vector time series. Deep Sea Research and Oceanographic Abstracts19(12): 833–846.
19.
GrantDN (2011) Response spectral matching of two horizontal ground-motion components. Journal of Structural Engineering: ASCE137(3): 289–297.
20.
HuangYNWhittakerASLucoN (2008) Maximum spectral demands in the near-fault region. Earthquake Spectra24(1): 319–341.
21.
International Building Code (IBC) (2018) International Building Code. Country Club Hills, IL: International Code Council (ICC).
JayaramNLinTBakerJW (2011) A computationally efficient ground-motion selection algorithm for matching a target response spectrum mean and variance. Earthquake Spectra27(3): 797–815.
24.
KaulMK (1978) Stochastic characterization of earthquakes through their response spectrum. Earthquake Engineering & Structural Dynamics6(5): 497–509.
25.
KwonOSElnashaiA (2006) The effect of material and ground motion uncertainty on the seismic vulnerability curves of RC structure. Engineering Structures28(2): 289–303.
26.
LiZKotronisPWuH (2017) Simplified approaches for Arias Intensity correction of synthetic accelerograms. Bulletin of Earthquake Engineering15(10): 4067–4087.
27.
MagliuloGMaddaloniGPetroneC (2014) Influence of earthquake direction on the seismic response of irregular plan RC frame buildings. Earthquake Engineering and Engineering Vibration13(2): 243–256.
28.
MasiAVonaMMucciarelliM (2011) Selection of natural and synthetic accelerograms for seismic vulnerability studies on reinforced concrete frames. Journal of Structural Engineering: ASCE137(3): 367–378.
29.
Ministry of Housing and Urban-Rural Development (MOHURD) (2011) Code for Seismic Design of Urban Bridge (CJJ 166-2011). Beijing China: Architecture and Building Press (in Chinese).
30.
MontejoLA (2021) Response spectral matching of horizontal ground motion components to an orientation-independent spectrum (RotDnn). Earthquake Spectra37(2): 1127–1144.
31.
NaeimFMarshallL (1995) On the use of design spectrum compatible time histories. Earthquake Spectra11(1): 111–127.
32.
NanosNElenasA (2006) Seismic duration effects on the vulnerability of buildings. In: Proceedings of the 1st European conference on earthquake engineering and seismology, Geneva, 3–8 September.
33.
OhsakiY (1979) On the significance of phase content in earthquake ground motions. Earthquake Engineering & Structural Dynamics7(5): 427–439.
34.
PetersenMDShumwayAMPowersPMMuellerCSMoschettiMPFrankelADRezaeianSMcNamaraDELucoNBoydOSRukstalesKSJaiswalKThompsonEMHooverSMClaytonBFieldEHZengY (2020) The 2018 update of the US National Seismic Hazard Model: Overview of model and implications. Earthquake Spectra36(1): 5–41.
35.
PieterseVBlackPE (2005) Dictionary of Algorithms and Data Structures. Gaithersburg, MD: National Institute of Standards and Technology (NIST).
36.
PoulosAMirandaE (2022a) Probabilistic characterization of the directionality of horizontal earthquake response spectra. Earthquake Engineering & Structural Dynamics51: 2077–2090.
37.
PoulosAMirandaE (2022b) Proposal of orientation-independent measure of intensity for earthquake-resistant design. Earthquake Spectra38(1): 235–253.
38.
PoulosAMirandaEBakerJW (2022) Evaluation of earthquake response spectra directionality using stochastic simulations. Bulletin of the Seismological Society of America112(1): 307–315.
39.
PowerMChiouBAbrahamsonNBozorgniaYShantzTRobleeC (2008) An overview of the NGA project. Earthquake Spectra24(1): 3–21.
40.
Rivera-FigueroaAMontejoLA (2021) Spectral matching RotD100 target spectra: Effect on records characteristics and seismic response. Earthquake Spectra38(2): 1570–1586.
41.
ShenYFreddiFLiYLiJ (2023) Enhanced strategies for seismic resilient posttensioned reinforced concrete bridge piers: Experimental tests and numerical simulations. Journal of Structural Engineering: ASCE149(3): 04022259.
42.
ShenYLiJFreddiFIgarashiAZhouJ (2022) Numerical investigation of transverse steel damper (TSD) seismic system for suspension bridges considering pounding between girder and towers. Soil Dynamics and Earthquake Engineering155: 107203.
43.
TanYDangJIgarashiAHimenoTHamadaY (2023) Hysteretic restoring force model of high damping rubber bearings including thermo-mechanical coupled effect. Engineering Structures277: 115449.
44.
ThangappaR (2019) Implications of spectral matching of multicomponent ground motions for response verification. Master’s Thesis, North Carolina State University, Raleigh, NC.
45.
WaldenAT (2013) Rotary components, random ellipses and polarization: A statistical perspective. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences371: 20110554.
46.
YamaneTNagahashiS (2008) A generation method of simulated earthquake ground motion considering phase difference characteristics. In: Proceedings of the 14th world conference on earthquake engineering (WCEE), Beijing, China, 12–17 October.
47.
ZentnerIPoirionF (2012) Enrichment of seismic ground motion databases using Karhunen–Loève expansion. Earthquake Engineering & Structural Dynamics41(14): 1945–1957.
48.
ZhouJIgarashiA (2022) Response spectral matching of bi-directional horizontal ground motion to orientation-independent spectrum. In: Proceedings of the Japan Society of Civil Engineers 2022 annual meeting, Kyoto, Japan, 15–16 September.
49.
ZhouJLiJShenY (2022) Quasi-static testing of railway rounded rectangular hollow tall piers having semi-hinged column-base details. Engineering Structures250: 113403.
