Design codes provide response spectra to be used in structural seismic analyses. Different response spectra are prescribed for various locations, corresponding to the local soil conditions. An example is provided in Fig. 2a, where the first three types of response spectra correspond to the Uniform Building Code (International (1994)), with type 1 for rock and stiff soils, type 2 for deep cohesionless or stiff clay soils, and type 3 for soft to medium clays and sands. The foutrh response spectrum, with a range of maximum spectral values corresponding to frequencies that are lower than for types 1,2 and 3, is characteristic for locations close to the epicenter.
Figure: 2 Response spectrum compatible acceleration time histories: a. prescribed response spectra; b. prescribed and resulted values for the type 4 response spectrum; c. simulated sample functions.
A methodology proposed by Deodatis (1996) is used to generate seismic ground motion time histories at several locations on the ground surface that are compatible with prescribed response spectra, are correlated according to a given coherence function, include the wave propagation effect, and have a specified duration of strong ground motion. The duration of the strong motion is controlled by modulating functions selected according to the model suggested by Jennings et al (1968). The effectiveness of the algorithm is illustrated in Fig. 2b, where the prescribed type 4 response spectrum (continuous line) is compared to the response spectrum (dotted line) computed from the corresponding simulated acceleration time history. Two generated sample functions, compatible with type 2 and type 4 response spectra, respectively, are plotted in Fig. 2c.