A procedure for simulating synthetic accelerograms compatible with correlated and conditional probabilistic response spectra

Abstract The modeling of seismic load is a major topic that has to be addressed thoroughly in the framework of performance based seismic analysis and design. In this paper, a simple procedure for simulating artificial earthquake accelerograms matching the statistical distribution of response spectra, as given by median ground motion prediction equations, the standard deviation and correlation coefficients, is proposed. The approach follows the general ideas of the (natural) ground motion selection algorithms proposed by Baker [4] and Wang [43] but using simulated (artificial) “spectrum-compatible” accelerograms. This allows to simulate spectrum-compatible accelerograms featuring variability similar to the one of recorded accelerograms when the match of median and ±1 standard-deviation response spectra is imposed by the regulator. The procedure is illustrated by an application to the NGA ground motion data and models.

[1]  Armen Der Kiureghian,et al.  Simulation of synthetic ground motions for specified earthquake and site characteristics , 2010 .

[2]  A. Kiureghian.  A response spectrum method for random vibration analysis of mdf systems , 1981 .

[3]  E. Vanmarcke.  Properties of Spectral Moments with Applications to Random Vibration , 1972 .

[4]  J. Stewart,et al.  Prediction Equations for Significant Duration of Earthquake Ground Motions considering Site and Near-Source Effects , 2006 .

[5]  Sanaz Rezaeian,et al.  Stochastic Modeling and Simulation of Ground Motions for Performance-Based Earthquake Engineering , 2010 .

[6]  J. Baker,et al.  Correlation of Spectral Acceleration Values from NGA Ground Motion Models , 2008 .

[7]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[8]  Gang Wang,et al.  A ground motion selection and modification method capturing response spectrum characteristics and variability of scenario earthquakes , 2011 .

[9]  André Preumont,et al.  The generation of non-separable artificial earthquake accelerograms for the design of nuclear power plants , 1985 .

[10]  Christian Soize.  Méthodes mathématiques en analyse du signal , 1993 .

[11]  Anastasios Sextos,et al.  Selection of earthquake ground motion records: A state-of-the-art review from a structural engineering perspective , 2010 .

[12]  Goodarz Ahmadi,et al.  Generation of artificial earthquake records with a nonstationary Kanai–Tajimi model , 2001 .

[13]  M. Shinozuka,et al.  Simulation of Stochastic Processes by Spectral Representation , 1991 .

[14]  E. Vanmarcke.  On the Distribution of the First-Passage Time for Normal Stationary Random Processes , 1975 .

[15]  Jack W. Baker,et al.  Conditional Mean Spectrum: Tool for Ground-Motion Selection , 2011 .

[16]  K. Campbell,et al.  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 , 2008 .

[17]  Jack W. Baker,et al.  A Computationally Efficient Ground-Motion Selection Algorithm for Matching a Target Response Spectrum Mean and Variance , 2011 .

[18]  André Preumont.  A method for the generation of artificial earthquake accelerograms , 1980 .

[19]  Gang Wang,et al.  Empirical correlations between cumulative absolute velocity and spectral accelerations from NGA ground motion database , 2012 .

[20]  M. K. Kaul,et al.  Stochastic characterization of earthquakes through their response spectrum , 1978 .

[21]  Ludovic Margerin,et al.  Nonstationary Stochastic Simulation of Strong Ground Motion Time Histories Including Natural Variability: Application to the K-Net Japanese Database , 2006 .

[22]  Yu-Kweng Michael Lin.  Probabilistic Theory of Structural Dynamics , 1976 .

[23]  Gary C. Hart,et al.  Simulation of artificial earthquakes , 1973 .

[24]  Kenneth W. Campbell,et al.  A Ground Motion Prediction Equation for the Horizontal Component of Cumulative Absolute Velocity (CAV) Based on the PEER-NGA Strong Motion Database , 2010 .

[25]  J. Baker,et al.  Spectral shape, epsilon and record selection , 2006 .

[26]  Brendon A. Bradley,et al.  Empirical Correlations between Peak Ground Velocity and Spectrum-Based Intensity Measures , 2012 .

[27]  Pierfrancesco Cacciola,et al.  A stochastic approach for generating spectrum compatible fully nonstationary earthquakes , 2010 .

[28]  Mihailo D. Trifunac.  Earthquake response spectra for performance based design—A critical review , 2012 .

[29]  K. L. Chandiramani,et al.  Some First-Passage Problems in Random Vibration , 1966 .

[30]  Ellen M. Rathje,et al.  A Semi-Automated Procedure for Selecting and Scaling Recorded Earthquake Motions for Dynamic Analysis , 2008 .

[31]  Irmela Zentner,et al.  Enrichment of seismic ground motion databases using Karhunen–Loève expansion , 2012 .

[32]  N. Abrahamson,et al.  Selection of ground motion time series and limits on scaling , 2006 .

[33]  N. Abrahamson,et al.  Empirical Response Spectral Attenuation Relations for Shallow Crustal Earthquakes , 1997 .

[34]  Farzad Naeim,et al.  Selection and Scaling of Ground Motion Time Histories for Structural Design Using Genetic Algorithms , 2004 .

[35]  Jeffrey C. Lagarias,et al.  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions , 1998, SIAM J. Optim..

[36]  Jack W. Baker,et al.  Conditional spectrum‐based ground motion selection. Part I: Hazard consistency for risk‐based assessments , 2013 .

[37]  Goodarz Ahmadi,et al.  Nonstationary Kanai-Tajimi models for El Centro 1940 and Mexico City 1985 earthquakes , 1990 .

[38]  C. Cornell,et al.  Correlation of Response Spectral Values for Multicomponent Ground Motions , 2006 .

[39]  P. D. Spanos,et al.  A statistical approach to generation of design spectrum compatible earthquake time histories , 1985 .

[40]  Pierfrancesco Cacciola,et al.  Generation of response-spectrum-compatible artificial earthquake accelerograms with random joint time-frequency distributions , 2012 .