This series includes technical reports prepared by faculty, students and staff who are associated with the John A. Blume Earthquake Engineering Center at Stanford University. While the primary focus of Blume Center is earthquake engineering, many of the reports in this series encompass broader topics in structural engineering and materials, computational mechanics, geomechanics, structural health monitoring, and engineering life-cycle risk assessment. Each report includes acknowledgments of the specific sponsors for the report and underlying research. In addition to providing research support, the Blume Center provides administrative support for maintaining and disseminating the technical reports. For more information about the Blume Center and its activities, see https://blume.stanford.edu.
A model of release of the seismic energy in an earthquake is developed by assuming that a seismic event is created by the progressive rupture of small coherent patches over the entire rupture surface. The motion at the site created by the rupture of a patch is analytically found by using a dislocation model where the fault plane is assumed to be a geometrical discontinuity across which there exists a sudden discontinuity in the displacement vector. The characteristics of the dislocation are represented by a ramp function. The solution is limited in the present case to body S-waves generated by the small patch sources.
Since the motion parameter is obtained as the Fourier Transform of the acceleration, in the complex domain, the effect of the rupture of the entire fault is obtained by superimposing the effect of all the individual patches with the proper phasing.
The model developed here is a three-dimensional model. It accounts not only for the directivity effects due to the relative position of the site with regard to the fault trace, but also for the dipping of the fault plane and the non horizontal direction of the average propagation of the rupture. In order to generate a realistic earthquake motion, the source parameters are taken as random variables with a given probability distribution. The propagation of the rupture in the fault plane is modeled by a random-walk type process. For use in seismic risk analysis, the uncertainty in the geometry of the system is also recognized (uncertainty in the location and orientation of the fault plane). A Monte Carlo simulation technique provides the statistics.
Savy, JB. (1978). Determination of Seismic Design Parameters: A Stochastic Approach. John A. Blume Earthquake Engineering Center Technical Report 34. Stanford Digital Repository. Available at: http://purl.stanford.edu/xb192dk3981
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