Predicted ground motions do not show a relevant site dependent variability along the cross section for recording sites located away from the Kumamoto basin edges close to the target site, as we were expecting due to the simplified geometry adopted in the numerical model. Figure 5 shows the comparison between simulation at CPb and observation at KUMA site for Step2 in terms of Fourier amplitude spectra. There is a good match for the vertical component while for the horizontal components, especially for the NS, we have overpredicted the amplitude in the 1–3 Hz frequency band. A horizontal overestimation was expected after the calibration test of the model (Fig. 3), and indeed to fit the vertical components we had to accept an overestimation of horizontal motion. The PGA values obtained are about 70 cm/s2 and 10 cm/s2 on the horizontal and vertical components respectively. The NS component of simulated motion has a PGA bigger than the EW by a factor of about 1.5.
Figure 6 and Fig. 7 show the Step 3 results comparing observations, at CPb, to simulations, at KUMA, specifically for Mj 6.5 and Mj 7.3 events respectively, in terms of acceleration time series and Fourier amplitude spectra. The recording of the Mj 7.3 at SEVO was biased for T > 13.8 s due to technical issues with a backup battery (Tsuno et al. 2017), therefore our simulation is only partially comparable to the KUMA data observed where the full waveform was recorded.
The match is fairly good for both components for the Mj 6.5, and it was an expected and pleasant surprise when the observations were released by the organizing committee. The PGA values obtained are about 450 cm/s2 and 160 cm/s2 in the horizontal and vertical components respectively, the horizontal components are of the same order of magnitude.
The waveform comparison for the Mj 7.3 is again quite good in terms of acceleration and PGA levels for both the horizontal and vertical components (Fig. 7a). The simulated part of the strong motion data contains the maximum amplitude part of the signal. It is also clear an underestimation of Fourier spectra mainly in the low (< 2 Hz) reflecting a loss of energy in simulated signals due to their shorter duration. The PGA values obtained are about 600 cm/s2 and 400 cm/s2 on the horizontal and vertical components respectively, the horizontal components are of the same order of magnitude.
As required by the Blind test exercise, we have evaluated the maximum shear-strain versus depth for the Mj 5.9 and Mj 6.5 for both EW and NS components. Figure 8 shows results down to a depth of 150 meters. For both types of simulations, the maximum strain is reached at a depth of about 10 m with a value of about 0.022% (Mj 5.9) and 0.16% (Mj 6.5). At depths more than 150 meters the strain decreases rapidly, reaching, at the base of the model, values lower than 10− 4 for Mj 5.9, and 10− 3 and Mj 6.5 simulation.
To quantify the effect of a nonlinear soil behavior in our model, we also performed, for the Mj 6.5 event, a fully linear modeling, with the same Maxwell damping, in substitution of the Mohr-Coulomb constitutive model associated with Darendeli degradation curve and a Maxwell damping. Quite surprisingly for us, we obtained results very similar as shown in Fig. 9 in terms of Fourier spectra. Figure 10 shows the closeness of the stress-strain relationship produced by the elastic linear and the elasto-plastic nonlinear approaches indicating, possibly, that the plasticity threshold is not reached, and nonlinear effects are almost negligible. Following this line of thought, we have run a simple 1D linear equivalent as well as fully linear elastic Strata simulation (Kottke and Rathje, 2008), extrapolating the 1D velocity model at CPb and using the G/G0 Darendeli curves. The results, presented in Fig. 11, confirm that a linear elastic model can predict quite well the data observed while, using a linear equivalent approach, significant overdamping for frequency > 2 Hz, not seen in the data, is introduced. These results provide an important warning against the widespread use of 1D equivalent-linear code for ground response analysis, which, if used for predictions in the Kumamoto case, would have largely underestimated the recorded shaking at frequency of engineering interest.