# Simulation of seismic signals for transient dynamic studies

*by I. Zentner, EDF R&D / AMA*

*This work was done as part of EDF R&D OMARISI2016 project and was supported by the ANR project MODNAT.*

Numerical simulations in mechanics make it possible to assess the robustness of buildings and facilities submitted to seismic excitation and conduct probabilistic reliability studies. To conduct such studies, one should have a significant number of seismic signals, known as accelerograms. Seismicity being rather low in France, one does not have a very large number of records of natural earthquakes at disposal. An alternative is therefore to generate synthetic signals, described by stochastic models.

The seismic loading to take into account is generally defined by a Response Spectrum (RS). One must then seek a stochastic process in agreement with the spectrum content. This process is assumed to be Gaussian and is fully defined by a power spectral density (PSD).

New operator `GENE_ACCE_SEISME` enables the generation of seismic signals compatible with a given spectrum, through three options :

- (a) generation of one or more separate accelerograms, each compatible with the target spectrum ;
- (b) generation of accelerograms whose median spectrum is compatible with the target spectrum ;
- (c ) generation of accelerograms compatible with the (log-normal) distribution of the target spectrum, characterized by several parameters including correlation coefficients.

(a) SPEC_UNIQUE option |
(b) SPEC_MEDIANE option |

(c ) SPEC_FRACTILE option | |

Figure 1: three available options (a) compatibility with a EC8 spectrum, (b) and (c ) compatibility with spectra according to the attenuation law of Campbell and Bozorgnia |

The three available options are illustrated in Figure 1, in which the target spectrum appears in red. The blue curves show the accelerograms of the synthetic signals, where as the ones in magenta represent the median except for option (c ) where it is 84% fractile (1-sigma spectrum). More details can be found in the theory documentation R4.05.05.

The latest configuration generates seismic signals whose variability is closest to recorded signals available in international databases. The synthetic seismic signals are in agreement with a median spectrum and the variability given by the standard deviation of spectral acceleration and correlation coefficients.

Figure 2: accelerogram example and time histories of velocity and displacement signals |

Figure 2 shows an example of an accelerogram generated by the operator from the EC8 spectrum (see Figure 1 (a) ). The displacement and velocity signals obtained by the integration of the accelerogram, are also shown. Thanks to the high-pass filtering (corresponding to seismic parameter "*corner frequency*") implemented in the operator, the signals do not feature any drift in the displacement.

The operator `GENE_ACCE_SEISME` has been validated against the POWERSPEC software (Westinghouse) which generates non-stationary seismic signals complying with a target spectrum.

*Available in version 11 and 12.*