# Dynamic Characteristics of Post-Cyclic Saturated Loess
## 3 Results  
Dynamic Elastic and Shear Modulus Characteristics of the Saturated Loess before and after Pre-Seismic Reconsolidation (PSR)  
Based on the dynamic triaxial tests, the \(\sigma_{d}-\varepsilon_{d}\) curves of the saturated loess before and after the PSR process are drawn in Figure 7. As shown in Figure 7, the \(\varepsilon_{d}\) of the saturated loess before and after the PSR process shows a nonlinear growth with the increase in \(\sigma_{d}\). The pre-shock action has a significant effect on the \(\sigma_{d}-\varepsilon_{d}\) curves of saturated loess. Compared with the saturated loess without pre-shock, the \(\sigma_{d}\) of the saturated loess grows slowly with the increase in \(\varepsilon_{d}\) after pre-shock, indicating that the pre-shock caused a nonlinear enhancement of the loess. Furthermore, the \(\sigma_{d}-\varepsilon_{d}\) curves after pre-shock are significantly influenced by the effect of reconsolidation. The \(\sigma_{d}\) at the same level of \(\varepsilon_{d}\) grows monotonically with the increase in the OCR, indicating that the increase in the OCR attenuates the kinetic nonlinearity of the loess. When the OCR reaches three, the kinetic nonlinearity of the pre-shock saturated loess is weakened compared with that of the original loess before the pre-shock. The \(E_{d}\) is defined as the ratio of \(\sigma_{d}\) and \(\varepsilon_{d}\):  
\[E_{d}=\frac{\sigma_{d}}{\varepsilon_{d}} \tag{4}\]  
Figure 8 shows the \(E_{d}\) versus \(\varepsilon_{d}\) of the saturated loess under different PSR processes. The \(E_{d}\) of the saturated loess under different conditions reduces with an increase in the \(\varepsilon_{d}\), nonlinearly. After pre-shock, the \(E_{d}\) of the saturated loess decreases significantly at the same level as the \(\varepsilon_{d}\). However, with an increase in the OCR, the \(E_{d}\) of the saturated loess increases at the same level as the \(\varepsilon_{d}\) in an upward trend. When the OCR reaches three, the \(E_{d}\) of the loess after the PSR process is larger. Figure 6: Schematic diagram of the load path of the pre-shock reconsolidation cyclic shear process: stage 1: load for pre-shock, stage 2: consolidation for pre-shock, stage 3: pre-shock, stage 4: unload after pre-shock, stage 5: stabilization and saturation of the specimens, stage 6: load for cyclic shear, stage 7: consolidation for cyclic shear, stage 8: cyclic shear, and stage 9: unload after cyclic shear. The relationship between \(E_{d}\) and \(\varepsilon_{d}\) of the loess in different moisture contents are consistent with the Hardin-Dmevich (HD) model [1; 3; 35; 51]. The test results in Figure 7 are  
Figure 8: Dynamic elastic modulus: dynamic strain curves of the saturated loess under different reconsolidation conditions. Figure 7: Dynamic stress: dynamic strain curves of the saturated loess before and after pre-shock and reconsolidation. normalized and fitted nonlinearly using the HD model in the dynamic shear strain (\(\gamma_{d}\)) range of \(10^{-6}\) to \(10^{-2}\). The \(G_{d}\) and the \(\gamma_{d}\) are obtained using Equations (5) and (6), respectively. \[G_{d} =\frac{E_{d}}{2(1+\mu)} \tag{5}\] \[\gamma_{d} =(1+\mu)\varepsilon_{d} \tag{6}\]  
where \(\mu\) is the Poisson's ratio of the loess. On the basis of Figure 7, the \(G_{d}\), \(\gamma_{d}\), and the inverse of the \(G_{d}\) (\(1/G_{d}\)) are calculated. Note that the relationship between the \(1/G_{d}\) and the \(\gamma_{d}\) could be gained based on the test results, as follows in Equation (7), which is used to obtain the Hardin-Drnevich model parameters \(a\) and \(b\) for the saturated loess under different test conditions.