## 3 Analysis of the Penetration Test Results
### Analysis of the Influence of Confining Pressure on the Permeability Coefficient, \(k_{v}\)
#### 3.3.2 Loading and Unloading of the \(\sigma_{r}\) Step by Step  
When the osmotic pressure difference of the clayey sand sample was constant at 200 kPa, the same sample was subjected to progressive loading and unloading permeability tests, and the fitting curves of the permeability coefficients of the unloading path and the  
Figure 11: Fitted curves of the \(k_{v}\) and \(\sigma_{r}\).  
unloading path changing with the \(\sigma_{r}\) during the loading-unloading permeability test were obtained, as shown in Figure 12, while the corresponding test parameters and results are shown in Table 3.  
As can be seen from Figure 12 and Table 3, when the \(\sigma_{r}\) increased from 1 to 8 MPa, the permeability coefficient first continuously decreased and then continuously increased when the \(\sigma_{r}\) was gradually unloaded from 8 to 1 MPa, but its permeability coefficient could not be restored to the initial value. That is, under the same \(\sigma_{r}\), the permeability coefficient during loading was greater than that during unloading. The reason is that the clayy sand sample underwent shrinkage deformation with an increasing \(\sigma_{r}\),  
Figure 12: Relationship curves between the permeability coefficient and \(\sigma_{r}\) in the loading–unloading process.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
\begin{tabular}{c} **Confining** \\ **Pressure** \\ **(\(\sigma_{r}\))/MPa** \\ \end{tabular} & \multicolumn{3}{c}{**Low-Confined Water Infiltration**} & \multicolumn{3}{c}{**High-Confined Water Infiltration**} \\ \cline{2-10}  & \(\mathbf{f_{load}}\) & \(\mathbf{k_{load}}\) & \(\mathbf{i_{unload}}\) & \(\mathbf{k_{unload}}\) & \(\mathbf{i_{load}}\) & \(\mathbf{k_{load}}\) & \(\mathbf{i_{unload}}\) & \(\mathbf{k_{unload}}\) \\ \hline
1 & 208.7 & 208.7 & 214.6 & 25.21 & 208.7 & 208.7 & 214.6 & 25.21 \\
2 & 210.2 & 11.45 & 215.2 & 2.322 & 210.2 & 10.45 & 214.9 & 4.425 \\
4 & 213.2 & 0.641 & 215.8 & 0.315 & 212.8 & 1.054 & 215.6 & 0.525 \\
6 & 215.4 & 0.324 & 216.2 & 0.183 & 214.9 & 0.324 & 215.9 & 0.211 \\
8 & 216.7 & 0.114 & 216.7 & 0.114 & 216.2 & 0.130 & 216.2 & 0.130 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Relationships between the permeability coefficient (\(10^{-8}\) cm/s) and hydraulic gradient in loading–unloading process.  
be recovered and the other part could not. The recoverable shrinkage deformation was mainly caused by the change in pore volume between sand particles. The pores were compressed with an increase in the \(\sigma_{r}\) and restored with a decrease in the \(\sigma_{r}\). Meanwhile, the irrecoverable shrinkage deformation was caused by breakage of the structural strength formed by sand particles and clay particle rearrangement.  
Through the power function fitting curve in Figure 12, it can be found that the loading-unloading permeability coefficient of clayy sand was basically consistent with the fitting curve of the \(\sigma_{r}\) in low- and high-confined water permeability, but under the same \(\sigma_{r}\), the recovery degree of the two confined conditions was different. In view of this phenomenon, [PERSON] [30] defined the recovery ratio of the loading-unloading permeability coefficient under different \(\sigma_{r}\) values: Recovery ratio = \(k_{\text{unload}}/k_{\text{load}}\), and the calculation results are shown in Table 4.  
It can be seen from Table 4 that the recovery ratio of the permeability coefficient of high-confined water was greater than that of low-confined water, and the recovery ratio of the permeability coefficient increased with an increasing \(\sigma_{r}\).