Site amplification is one of the most important factors in strong ground motion prediction at construction sites. In ground motion calculation methods such as the stochastic Green's function method, seismic motions are first synthesized on an outcrop of engineering bedrock with an S-wave velocity of more than 400 m/s. Ground motions on the ground surface are then evaluated using the substructure method by independently modeling only the shallow part of the subsurface structure, using ground motions on the outcropped engineering bedrock as input motions. This approach sometimes yields inaccurate results because the coupling effect between the shallow and deep parts of the subsurface structure is ignored.
In the present study, the calculation accuracy of the conventional substructure method is first investigated for various soil layers. A rigorous method that incorporates the coupling effect with the deep subsurface structure is then proposed based on the nonlinear substructure method in terms of velocity convolution integrals.
As an example, synthesized surface motions calculated by the conventional substructure method and a full rigorous analysis are compared using the S-wave structure of the Osaka Plain, where the S-wave velocity between the seismic bedrock and overlying sediments varies abruptly, for deep soil layers of various thicknesses. Although the onset S-wave parts coincide for both methods, differences in the later phase of the waveforms are observed. These differences occur because the reflected waves from seismic bedrock transmitted from the shallow layer to the deep layer are essentially ignored in the conventional substructure method.
Next, generalized soil models are used to assess errors in the conventional substructure method by varying three and fixing one of the following four parameters: the S-wave velocity just above the seismic bedrock, the S-wave velocity just above the engineering bedrock, and the thicknesses of the shallow and deep parts of the soil. The error index, FDE, is used to quantify the calculation accuracy of the conventional substructure method. The error becomes large when the thickness of the deep soil is small and the thickness of the shallow soil is large, due to the difference in the travel time of the waves reflected from the boundary of the seismic bedrock. The impedance ratio between the seismic rock and sediments also contributes to the error.
In order to rigorously incorporate the coupling effect of the deep and shallow soil layers into the conventional substructure method, a frequency-dependent dynamic impedance function is added to the bottom layer, instead of the viscous boundary for the engineering bedrock. First, the dynamic impedance function on an outcrop of engineering bedrock that includes the deep part of the soil is calculated in the frequency domain. The nonlinear behavior of the shallow soil layer requires a seismic response analysis in the time domain. The frequency-dependent dynamic impedance function for the deep soil layer is converted into a time-domain impulse response, which is used in the convolution integral of the velocity in the time-domain analysis.
The proposed method is applied to the ground motion evaluation using the subsurface structure of the Osaka Plain. The acceleration response time histories and the response spectra obtained by the proposed method coincide well with those obtained through a full rigorous analysis. In the case of the nonlinear analysis, the coupling effect decreases because of the hysteretic damping effects of the shallow soil. However, the results obtained using the proposed method have been verified to approximately coincide with those obtained through the full rigorous analysis, implying that the proposed method provides a rigorous solution that considers the coupling effect with the deep part of the subsurface structure.
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