Abstract
This paper investigates the average response spectra and the evolutionary power spectra of random earthquake ground motion model with reference to the evaluation of reliability and safety of structural systems for future earthquake. In order to consider the influence of the irregular geological properties from the source-to-site and the unspecified faulting process in source region, the propagation path is assumed to be a random medium and the faulting process is expressed by the random dynamic response to the subevents which propagate on a fault line with variable rupture velocity, in this model. The average displacement, velocity and acceleration response spectra and the evolutionary power spectra of vertical, radial and cross-radial components of the earthquake model are calculated for Mach numbers M_n=0.6, 0.7, 0.8, and 0.9 and nondimensional rise time t_r=0.03 and the ratio of epicentral distance to focal depth R/H=1 and 5. The observation points of vertical and radial components are assumed to be in the direction of acceleration and deceleration of the fault rupture. The average response spectra of the earthquake model show good correspondence to the general trend derived from real earthquake ground motions. The responses of vertical and radial components become generally large when Mach number increases and the fault propagates toward the observation point. They show especially large value for the specific period related to the time interval between nucleation and stopping of faulting process. However, the responses of cross-radial component in the perpendicular direction of the fault line is insensitive to the fault movement and variation of Mach number. The difference is produced by the energy concentration and decentralization associated with fault movement and types of wave motion propagated. When the fault propagates toward the observation point, the acceleration response become generally large due to high frequency components generated by up-Doppler effect with fault movement. When the fault propagates in the opposite direction to the observation point, the displacement and velocity responses become large due to the low frequency components generated by down-Doppler effect with fault movement. Then, the relative position between rupture direction of fault and the observation point is important physical quantity for aseismic design of structural systems which would describe the maximum values, frequency characteristics and duration times of the earthquake ground motion. Since the responses of vertical component are almost half of those of radial component, considerable care should be paid for actual vertical response in aseismic design of structural systems if R/H is nearly and/or below one. Although the earthquake ground motions allow generally the influence of the rupture velocity, there are not so much differences among the characteristics of the response spectra as seismic wave motion propagates into the far-field. This depends on the fact that the energy transmission from the source to the site become gradually stationary with the increase of R/H. The evolutionary power spectra of random earthquake ground motion models show strong and weak nonstationarity in accordance with the up-and down-Doppler effect by fault movement and the increase and decrease of Mach number. However, the characteristics of them tends to be stationary as R/H becomes large. Therefore, the evolutionary power spectra are useful means to know time variation on the frequency characteristics and the energy envelope function during the formation of characteristics of earthquakes. Then, we are able to investigate the faulting process and the characteristics of wave traveling path if the estimation of evolutionary power spectra for multi-observation point system is possible for the activity of one earthquake.
