## 3 Test Result
### Response of the Model Soil
#### 3.4.2 Spectrum Characteristics of the Acceleration Response of the Model Soil  
According to the theory of structural dynamics, the acceleration response spectrum can reflect the response of the structure under input motions and the characteristics of the structure [23]. Taking the measuring point AX6 of the model soil as an example, the acceleration response spectra of the measuring point AX6 with different duration compression ratios are shown in Figures 12 and 13. Figure 11: The peak acceleration amplification ratio of the model soil under scaled Wolong records. Figure 10: The peak acceleration amplification ratio of the model soil under scaled El Centro records. This implies that the spectra were affected by the model soil and the amplitudes increased greatly in the specified period range (about 0.1 s), especially for the scaled El Centro record. There were obvious differences in seismic response of model soil with the duration compression ratios of 1/4, 1/2, and 1/1. Under the input of the El Centro record, for the frequency band with the periods less than 0.2 s, the differences between duration compression ratios of 1/4 and 1/2 were relatively small, and for the frequency band with the periods greater than 0.2 s, the differences between duration compression ratios of 1/2 and 1/1 were relatively small. Under the input of the Wolong record, the differences between duration compression ratios of 1/4, 1/2, and 1/1 were large, which differed from the response law of El Centro record. The characteristics of the test results for the three input motion PGAs were basically consistent, while the degree of difference in response varied under the inputs of El Centro and Wolong record, which was more significant in Wolong record. These results mean that the actual input motions to the model structure were different for the shaking table tests with different duration compression ratios. The selection of duration compression ratio directly affected the acceleration response of model soil and the evaluation of the prototype soil. From the above analysis, it is clear that the variation of the acceleration response spectrum was not consistent under the same PGA and different types of ground motion. This was due to the difference in the spectral characteristics between the El Centro record and the Wolong record. In order to eliminate the influence of this difference and study the effect of duration compression ratios on spectrum characteristics intuitively, the transfer function was introduced. Transfer function \(f\) (T) is the ratio of acceleration response spectrum of each measuring point to that of table output motion, as shown below. \[f_{\mathrm{i,q}}(\mathrm{T})=\frac{S_{\mathrm{i,q}}(\mathrm{T})}{S_{\mathrm{ Tab}}(\mathrm{T})} \tag{3}\]  
where \(S_{\mathrm{i,q}}(\mathrm{T})\) is the acceleration response spectrum of measuring point i when the duration compression ratio is q, here, q = 1/4, 1/2, and 1/1; \(S_{\mathrm{Tab}}(\mathrm{T})\) is the acceleration response spectrum of table output motion. Taking the measuring point AX6 in upper model soil as an example, the transfer functions \(f_{\mathrm{AX6,q}}(\mathrm{T})\) of the measuring point AX6 under input motions with different duration compression ratios are shown in Figures 14 and 15. When the PGA of input motion is large, the softening and nonlinearity of model soil will affect the study of duration compression ratio. When the PGA of input motion is small, the nonlinearity of model will have less influence, and the law of transfer function is more representative. Therefore, the comparisons of transfer functions should be focused when the PGAs are 0.05 g and 0.15 g. As shown in Table 3, the period corresponding to the first-order frequency of the model soil was about 0.1 s. It can be seen from the comparison of transfer functions that when the PGAs were 0.05 g and 0.15 g, the amplitude of transfer function with the duration compression ratio of 1/2 was the largest near the period of 0.1 s, but that with the duration compression ratio of 1/1 was the smallest.