# Dynamic Characteristics of Post-Cyclic Saturated Loess
## 4 Discussion
To further illustrate the influence of the PSR process on the nonlinear kinetic properties of the saturated loess, the variation laws of the maximum dynamic shear modulus \(G_{dmax}\), the maximum dynamic shear stress amplitude \(\tau_{dult}\) and the maximum damping ratio  
Figure 13: Influence of the OCR on the dynamic shear modulus ratio and damping ratio: (**a**) the relationship between \(G_{\rm u}\) and OCR and (**b**) the relationship between \(D_{\rm u}\) and OCR. with pre-seismic and reconsolidation ratio is analyzed. According to Equation (7), the \(G_{dmax}\) is as follows:  
\[G_{dmax}=\frac{1}{a} \tag{12}\]  
Based on the definition of \(G_{d}\), there are:  
\[\tau_{d}=\frac{\gamma_{d}}{a+b\gamma_{d}} \tag{13}\]  
According to Equations (7) and (13), there are:  
\[\tau_{dult}=\lim_{\gamma_{d}\rightarrow\infty}\frac{\tau_{d}}{\gamma_{d}}= \frac{1}{b} \tag{14}\]  
According to Equation (10):  
\[B=\frac{1}{D}-\frac{A}{\gamma_{d}} \tag{15}\]  
When \(\gamma_{d}\rightarrow\infty\),  
\[D=D=\frac{1}{B}_{max} \tag{16}\]  
The \(G_{dmax}\), \(\tau_{dult}\), and \(D_{\max}\) are calculated according to Equations (12), (14) and (16), respectively, and their relationship curves with the OCR were drawn, as shown in Figure 14. In Figure 14, the changes of \(G_{dmax}\), \(\tau_{dult}\), and \(D_{\max}\) before and after pre-seismic are given when OCR = 1. After pre-seismic, \(G_{dmax}\) decreases significantly and \(D_{\max}\) increases significantly, which is consistent with the results in Figures 8 and 11. Furthermore, \(\tau_{dult}\) decreases significantly after pre-seismic, and it is only half of that before pre-seismic. Considering that \(\tau_{dult}\) represents the possible extreme value of dynamic shear stress in the \(\tau_{d}-\gamma_{d}\) curve, it can reflect the dynamic strength of the soil. Therefore, the pre-seismic effect also leads to a significant attenuation of the strength of saturated loess, which is the same as those studies on the seismic subsidence of unsaturated loess in the literature [35]. Figure 14 also shows the effect of reconsolidation on \(G_{dmax}\), \(\tau_{dult}\), and \(D_{\max}\) of post-earthquake saturated loess. From the graph, it can be seen that \(G_{dmax}\) has a trend of moderate growth-sharp growth-moderate growth with an increase in the OCR; when \(2\leq\) OCR \(\leq\) 3, the growth is faster. In addition, there is a positive linear correlation between \(\tau_{dult}\) and OCR. \(D_{\max}\) decreases nonlinearly and its increasing trend decreases with an  
Figure 14: Influence of OCR on \(G_{dmax}\), \(\tau_{dult}\), and \(D_{\max}\). increase in the OCR. Combined with Figure 13a, it should be noted that the \(G_{dmax}\) increases rapidly at \(2\leq\text{OCR}\leq 3\), while \(G_{\text{u}}\) hardly increases at this stage, and even decreases slightly at the large shear strain stage. Considering the definition of \(G_{d}/G_{dmax}\), the variation tendency of \(G_{\text{u}}\) is mainly affected by the rapid growth of \(G_{dmax}\). In other words, when \(2\leq\text{OCR}\leq 3\), reconsolidation still has a significant influence on the dynamic stiffness of saturated loess after an earthquake. Influence Mechanism of Strong Earthquake and Post-Earthquake Reconsolidation on Nonlinear Dynamic Characteristics of Saturated Loess  
The variation of microstructure of soil under different conditions is the fundamental cause of the change in its mechanical behaviors [6; 18; 53]. To illustrate the influencing mechanism of a strong earthquake and post-earthquake reconsolidation on the nonlinear kinetic characteristics of saturated loess, the microstructure photos of each group of samples before cyclic shear were obtained based on the SEM test, as shown in Figure 15. Among them, Figure 15a shows the original saturated loess under the OCR of 1, Figure 15b shows the aftershock loess with OCR = 1, Figure 15c shows the aftershock loess with OCR = 3, and Figure 15e shows the aftershock loess with OCR = 4.