# Analysis of Multilayered Ground Amplification Characteristics by Scaled-Down Model Tests
## 3 Multilayered Flat Model Ground Test Results and Analysis  
### Shear Wave Velocity  
The shear wave velocity is usually used to characterize the dynamic property of soil in geotechnical engineering, and the importance of shear wave velocity in geotechnical seismic engineering has been widely recognized and applied in seismic design and seismic performance evaluation [14]. The average shear wave velocity of the model was obtained by substituting the difference between the distance between the two accelerometers buried in the ground and the arrival time of the shock wave into the velocity formula by giving an impact to the lower part of the soil box in Equation (1). Figure 6 shows the shear wave velocity measurement method used in this study. \[\mathrm{V}=\frac{\mathrm{S_{interval}}}{\mathrm{I_{interval}}} \tag{1}\]  
where, \(\mathrm{V}\) is the shear wave velocity, \(\mathrm{S_{interval}}\) is the distance between measuring points and \(\mathrm{I_{interval}}\) is the time taken for the shock wave to arrive. Figure 5: Time-histories of the input ground motions used in this study: (**a**) artificial earthquake wave; (**b**) sine sweep wave; (**c**) sine 10 Hz wave. For a single-layer ground model, in order to measure the shear wave velocity, the hammer test should be carried out on the outer side of the soft soil bottom end to measure the average shear wave velocity of the ground. However, for the multilayered flat model ground, the thickness of each layer is less than 0.3 m. Since the impact of the hammer will pass through the ground at a faster rate than the data collection interval, the accuracy of the average breaking wave velocity calculated by the hammer test has decreased. In order to make up for this defect, each layer of the multilayered ground was formed into a single soil layer with a thickness of 0.6 m, and the hammer tests were carried out separately to obtain the average shear wave velocity. [PERSON] and [PERSON] (2015) proposed a shear wave velocity map, which represents the upper and lower layers of the surface in Equation (2). \[V_{s}(z)=\overline{V_{s}}\bigg{[}\frac{\sigma_{v}^{\prime}(z)}{\overline{ \sigma_{v}}^{\prime}}\bigg{]}^{n} \tag{2}\]  
where \(V_{s}(z)\) is the shear wave velocity at depth \(z\), \(\overline{V_{s}}\) is the average shear wave velocity in the layer, \(\sigma_{v}^{\prime}(z)\) is the effective normal stress at the depth \(z\), \(\overline{\sigma_{v}}^{\prime}\) is the effective normal stress calculated in the middle of the layer and \(n\) is the stress index. The n value of clay, silky, and sandy soils are 1/3, the n value of gravel and rock are 1/4. A total of three hammer tests were conducted, with ten hammer strikes per test. The values of obvious errors were excluded and the average value was taken. Figure 7 shows the acceleration-time history of the multilayered upper ground (loose ground) as a single layer ground with a thickness of 0.6 m, and the hammer test was performed by embedding an accelerometer in the bottom and surface layers of the soil. The average shear wave velocity of the layer was determined using the time difference between the first peaks and the distance between the buried accelerometer, and the average shear wave velocity obtained by repeating the hammer test was 76.57 m/s, 70.75 m/s and 68.75 m/s, and their average value, 72.02 m/s, was determined as the average shear wave velocity of loose ground. Figure 8 shows the acceleration-time history of the multilayered lower ground (dense ground) as a single layer ground with a thickness of 0.6 m, and the hammer test was performed by embedding an accelerometer in the bottom and surface layers of the soil. The average shear wave velocity of the layer was determined using the time difference between the first peaks and the distance between the buried accelerometer; the average shear wave velocities obtained by repeating the hammer test were 139.80 m/s, 138.74 m/s and 133.96 m/s, and the average value of 137.5 m/s was determined as the average shear wave velocity of the dense ground.