# Dynamic Characteristics of Post-Cyclic Saturated Loess
## 3 Results
\[\frac{1}{G_{d}}=a+b\gamma_{d} \tag{7}\]  
In accordance with the Equation (7), the reference shear strain \(\gamma_{dr}=a/b\), so the dynamic shear modulus ratio \(G_{d}/G_{dmax}\) follows as [3; 52]:  
\[\frac{G_{d}}{G_{dmax}}=\frac{1}{1+\gamma_{d}/\gamma_{dr}} \tag{8}\]  
The normalized curves of the \(G_{d}/G_{dmax}\) versus the \(\gamma_{d}\) of the saturated loess before and after the PSR process are calculated using Equation (8) and shown in Figure 9. According to Figure 9, the \(G_{d}/G_{dmax}\) of the saturated loess reduces nonlinearly with the growth of \(\gamma_{d}\). Under the same consolidation conditions, the \(G_{d}/G_{dmax}-\gamma_{d}\) curves of the saturated loess before and after pre-shock show obvious differences. Before the pre-shock, the \(G_{d}/G_{dmax}\) of the saturated loess decreased from 1 to 0.94 in the small shear strain stage (\(10^{-6}<\gamma_{d}<10^{-4}\)). However, in the large shear strain stage (\(10^{-4}<\gamma_{d}<10^{-2}\)), the \(G_{d}/G_{dmax}\) are 0.76, 0.61, 0.24, and 0.13 at the characteristic shear strains of 0.0005, 0.001, 0.005, and 0.01, respectively. After the pre-shock, the \(G_{d}/G_{dmax}\) of the saturated loess reduced to 0.9 with increasing the \(\gamma_{d}\) in the small shear strain stage. With the large shear strain stage, the \(G_{d}/G_{dmax}\) are 0.76, 0.61, 0.24, and 0.13 at the characteristic shear strains of 0.0005, 0.001, 0.005, and 0.01, respectively. The \(G_{d}/G_{dmax}\) of the saturated loess decays to 0.90 at the small shear strain stage and changes to 0.66, 0.49, 0.14, and 0.09 at the large shear strain stage with characteristic strains of 0.0005, 0.001, 0.005 and 0.01, respectively. The \(G_{d}/G_{dmax}\) of the saturated loess decreased obviously with the increase in the \(\gamma_{d}\) after the pre-seismic action, indicating that the impact of pre-shock on the kinetic stiffness of the saturated loess is more significant. Note that the difference between the \(G_{d}/G_{dmax}\) of the saturated loess before and after pre-seismic action is more obvious when the \(\gamma_{d}\) range is 0.0001-0.005; however, the difference presents a decreasing tendency when the \(\gamma_{d}\) range is 0.005-0.01. The relationship of the \(G_{d}/G_{dmax}\) versus the \(\gamma_{d}\) of the after or pre-shock saturated loess under different reconsolidation conditions is shown in \[E_{d}=\frac{\sigma_{d}}{\varepsilon_{d}} \tag{4}\]0 As seen in Figure 9, after the OCR reaches two, the \(G_{d}/G_{dmax}\) of the saturated loess reduces to 0.94 at the small shear strain stage, and the \(G_{d}/G_{dmax}\) is 0.74, 0.59, 0.23, and 0.13 at the large shear strain stage with the characteristic strains of 0.0005, 0.001, 0.005, and 0.01, respectively. This result is similar to the \(G_{d}/G_{dmax}\) of the original saturated loess at the same \(\gamma_{d}\). Furthermore, the decay of the \(G_{d}/G_{dmax}\) is obviously slower than that of the saturated loess with an OCR of one. When the OCR is three or four, the decay trend of \(G_{d}/G_{dmax}\) of the saturated loess is the same as that of the OCR of two. When the OCR is four, the decay trend of the curves in the small-strain stage is similar to that of the original saturated loess. However, in the large shear strain stage, the \(G_{d}/G_{dmax}\) corresponds to the four characteristic shear strains of 0.78, 0.64, 0.26, and 0.15, respectively, which are slightly stiffer than other groups.