# Comparative Study of the Seismic Response Characteristics of Three Special Soils
## 5 Calculation Results and Analysis
### Analysis of the Calculation Results of the Actual Soil Profiles  
This paper selects the actual soil profiles of the three special soils as the calculation models and takes the four ground motion time histories obtained by modulating the El Centro wave amplitude as the input seismic wave inputs. The SOILQUAKE program is utilized for the calculation, and the dynamic shear modulus ratios of the three special soils in typical areas are selected. The maximum, minimum, average and measured values of the damping ratio are calculated for each profile, and the results are compared and analyzed to ascertain the influences of different dynamic parameter values on the design response spectrum of each special soil site. Tables 10-13 list the dynamic shear modulus ratios and damping ratios of the special soils. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **Parameter** & \multicolumn{8}{c}{**Shear Strain (\(\times 10^{-4}\))**} \\ \cline{3-10}  & **0.05** & **0.1** & **0.5** & **1** & **5** & **10** & **50** & **100** \\ \hline \multirow{3}{*}{Measured Value} & G/Gmax & 0.9963 & 0.9926 & 0.9639 & 0.9303 & 0.7275 & 0.5717 & 0.2107 & 0.1178 \\  & \(\lambda\) & 0.0226 & 0.0313 & 0.0544 & 0.0685 & 0.1104 & 0.1293 & 0.1602 & 0.1665 \\  & G/Gmax & 0.9972 & 0.9945 & 0.9729 & 0.9472 & 0.7821 & 0.6422 & 0.2642 & 0.1522 \\ \multirow{3}{*}{Maximum Value} & \(\lambda\) & 0.0446 & 0.0543 & 0.0855 & 0.1040 & 0.1552 & 0.1788 & 0.2198 & 0.2288 \\  & G/Gmax & 0.9953 & 0.9906 & 0.9548 & 0.9139 & 0.6853 & 0.5253 & 0.1856 & 0.1028 \\ \multirow{3}{*}{Average Value} & \(\lambda\) & 0.0342 & 0.0426 & 0.0707 & 0.0873 & 0.1336 & 0.1531 & 0.1836 & 0.1900 \\  & G/Gmax & 0.9919 & 0.9839 & 0.9243 & 0.8592 & 0.5497 & 0.3790 & 0.1088 & 0.0508 \\ \multirow{3}{*}{Minimum Value} & \(\lambda\) & 0.0205 & 0.0267 & 0.0489 & 0.0630 & 0.1068 & 0.1240 & 0.1512 & 0.1568 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: List of values for dynamic shear modulus ratio and damping ratio of silty clay. Figure 5: Characteristic periods and platform values of three special soils under different input ground motion intensities. In this paper, SOILQUAKE_1.3 soil layer response analysis software is used for the group calculation. The time step is 0.02 s, the acceleration unit is gal and the modulated peak amplitude of the input ground motion acceleration is half of the proportional modulated amplitude. The seismic response spectrum obtained is calibrated with the differential evolution algorithm. Figure 6 presents a schematic diagram of the deviations in the characteristic period, platform value and peak acceleration obtained under different dynamic parameter values from the actual measured characteristic period, platform value and peak acceleration. Analyzing Figure 6 readily reveals the following: (1) Under different dynamic parameter values, the deviation between the characteristic periods of the design response spectra of special soils is mostly between \(-5\%\) and \(5\%\), and the largest deviation appears in the laterite model. At 0.2 g, when the kinetic parameter takes the minimum value, the calculated characteristic period of the design response spectrum is quite different from the measured characteristic period of the design response spectrum, with a deviation of 21%. Furthermore, when the input earthquake intensity is 0.4 g, the deviations between the values of the dynamic parameters of the site models and the measured values are between 10% and 20%. (2) The difference between the design response spectrum platform