The EQUAKE module generates earthquake acceleration time histories that are compatible with given seismic design ground response spectra. The EQUAKE module combines both frequency domain and time domain algorithms to generate the spectrum compatible accelerograms. The frequency domain matching algorithm is based on the Levy-Wilkinson (LW) algorithm, while the time domain matching algorithm is based on an Abrahamson (AB) algorithm also implemented in the RspMatch. The LW algorithm is used first to get a RS approximation, and then, the AB algorithm is used to improve accuracy of the computed RS to the target RS.

The EQUAKE module can be used to simulate acceleration histories with random phases, or based on the so-called “seed records” as described in the new ASCE 04-2016 standard. In the latter case, the simulated accelerograms preserve the Fourier phasing of the “seed record” components for X, Y and Z directions.

The EQUAKE module uses a refined baseline correction algorithm that includes the complex frequency algorithm used in the FLUSH code, plus additional polynomial corrections in timedomain.

The generated spectrum-compatible input accelerations are in compliance with the US NRC requirements included in SRP 3.7.1 for single time-history input, Option 1, Approach 2. The applied SRP criteria include the following aspects:

  • Total motion duration is at least 20 seconds; if input duration is less than 20 seconds, a warning message will show up on screen and in the output file;
  • The Nyquist frequency is not higher than 100 Hz. The maximum frequency is given by the time step size. If the time step size is larger than 0.005 seconds, a warning will show up on screen and in the output file;
  • Minimum 100 points per frequency decade are used between the lowest and the highest frequencies as defined in the input text file that contains the response spectrum amplitudes. The input file format is two columns, frequency and amplitude for a given damping ratio.
  • The computed 5% damping response spectrum will have no point with more than 10% below the target spectra and no more than 30% larger than the target response spectrum at any frequency;
  • No more than 9 adjacent frequency points falling below the target response spectrum are permitted.

The EQUAKE module also computes a few feature parameters of the computed acceleration time histories; such as strong motion duration (between Arias intensities 5% and 75%), V/Av and AD/V2 (A: peak ground acceleration; V: peak ground velocity; D: peak ground displacement).

If more than one-component acceleration time history is generated, then, the stationary and nonstationary cross-correlation coefficients are computed. If the user gives the target power spectral density (PSD), EQUAKE checks if the generated acceleration time history meets power spectral density requirements.

The EQUAKE input file has extension .equ and it is created by the AFWRITE command. The generated accelerograms are then used for site response analysis and SSI analysis through the SOIL, MOTION and STRESS modules. The EQUAKE module computes the response spectra, power spectral density (PSD) and the positive frequencies portion of the complex Fourier Transform (FFT) of the simulated acceleration histories, or external acceleration histories input by the user. Outputs from all these computations are also saved separately for user control.

The PSD is computed using a plus/minus 20% frequency averaging intervals in compliance with the ASCE 4 standard and the USNRC requirements. The strong motion duration is defined by the time interval between 5% and 75% Arias intensities. To compute the FFT and PSD only the strong motion duration part is considered.

The EQUAKE output file includes the input data information, the generated acceleration time history input parameters, the statistical pair correlations between components for the entire motion duration (stationary correlation) and for a 2-second moving window (nonstationary correlation). The nonstationary correlation values for recorded motion components (NS, EW and Vertical) could be used to generate simulated acceleration histories with the same nonstationary correlation patterns. This is an alternative to the use of recorded motion phasing for simulating acceleration histories. Also, the nonstationary correlation information provides useful insights on the incoming wave patterns for the recorded motions. Nonstationary correlation could be used for computing the principal axes of motion.