抄録
Nonlinear site amplification during strong shaking has been recognized in observed strong motion records, and nonlinear soil response analyses have been conducted. This application, however, has not been fully verified because of the limitation in the number of available strong motion records with large amplitude. This study examines the nonlinear site amplification model based on strong motion records including large amplitude records from the 2011 Tohoku earthquake (M9.0). To extract the site factor from the records, spectral ratios are calculated from rock-soil site pairs. As shown in Fig. 1, eight rock sites in the Tohoku region where the record higher than 0.1g has been observed are selected. The near-by soil sites are selected in the zone within 25 km from the rock sites, and twenty-five site pairs are constructed from the selected rock and soil sites as shown in Table 1. The locations of the sites and the epicenters of the earthquakes are shown by triangles and circles in Fig. 1, respectively.
Figure 2 shows the method for evaluation of the site amplification. Firstly, the near-by soil-rock site pair is selected. Secondly, the response spectra at the sites are calculated. Thirdly, spectral ratios are calculated for soil sites with respect to the reference rock site, and the spectral ratios are averaged across a short-period band (0.1-0.5 sec) and mid-period band (0.4-2.0 sec) to get the short-period amplification, Fa, and mid-period amplification, Fv, respectively. Lastly, both amplifications are plotted with respect to the peak ground acceleration at the reference rock site, PGAr, for each site pair. An example is shown in Fig. 3.
For all twenty-five site pairs, the regression equations between site amplification F and PGAr shown by Eq. (1) are obtained. The amplifications at different PGAr values are calculated from the regression equations for each site pair, and are plotted with Vs30 of the soil site, as shown in Fig. 4. When PGAr is 0.1g or smaller, both of Fa and Fv decrease with increase of Vs30. When PGAr is 0.3g or 0.5g, Fv shows the same tendency, whereas Fa tends to be constant with Vs30.
To model the relationship of the amplifications with Vs30 at different ground motion levels, the model shown by Eq. (2) is adopted. Figure 5 shows the resultant relationships at different PGAr. For Fa, the dependence of Vs30 decreases with increase of PGAr. For Fv, however, the relationships at different PGA show no significant change. The coefficients a and b in Eq. (2) show the dependence of PGAr as shown in Fig. 6. To generalize the amplification model, the regression analysis for the coefficients is conducted, and the results of the regression analysis are shown by Eqs. (3) and (4). By substituting Eqs. (3) or Eqs. (4) for Eq. (2), nonlinear amplification models for Fa or Fv are constructed as the function of Vs30 and PGAr. The standard deviation of the residual errors of the equation from the original data is 0.31 for Fa and 0.21 for Fv in common logarithm.
Figure 7 shows a comparison of the nonlinear site amplification model by this study with that by Seyhan and Stewart (2014) derived from combination of the soil response analysis and data analysis of observed strong motion records. For the short-period amplification,, the both results agree each other at stiff or intermediate soil. At soft soil, however, the value by Seyhan and Stewart (2014) is smaller than that by this study at high PGAr. The same tendency is observed in the mid-period amplification. This indicates that the nonlinearity of our model is weaker than that of Seyhan and Stewart model at soft soil.
