## 3 Analysis of the Penetration Test Results
### Analysis of the Evolution Pattern of the Permeability Coefficient (\(k_{v}\) ) with Time  
The \(k_{v}\) can be calculated according to the following steps [32]: After the consolidation test was completed, several groups of permeability tests with different osmotic pressure differences (\(\Delta p_{i}\)) (\(i=1,2,\ldots\)) were set under the condition of keeping a certain \(\sigma_{r}\) unchanged. Then, the test data under a certain \(\Delta p_{i}\) were divided into \(N\) sections according to 10 min, and the seepage discharge increment, \(\Delta Q\), and corresponding seepage velocity, \(v\), in this time period were calculated. According to the \(\Delta p_{i}\) of this stage and the height of the soil sample, \(H\), the hydraulic gradient was calculated as \(\Delta p_{i}/(\gamma_{w}H)\), where \(\gamma_{w}\) is the bulk density of water. Then, [PERSON]'s law was used to calculate the permeability coefficient, \(k_{v,i,j}=\gamma_{w}H\Delta Q/At\Delta p_{i}\), in the \(j-\)th period of \(N\) periods under a certain \(\Delta p_{i}\). Following this, the obtained \(k_{v,i,j}\) was analyzed. The principle is as follows: Write the calculated values of \(k_{v,i,j}\) in \(N\) time periods in the form of \(k_{v,i,j}=B\times 10^{-n}\), select more than four results whose difference between the maximum and minimum \(B\)-values of the same power \(n\) is not more than 2.0, take the average value as the \(k_{v,i,j}\) under the \(\Delta p_{i}\) of this level, and then take the average value of \(k_{v,i,j}\) under the \(\Delta p_{i}\) of all levels as the \(k_{v,i,j}\) corresponding to the stable porosity ratio when the \(\sigma_{r}\) of a certain level is constant. The clayey sand was subjected to permeability tests at a certain \(\sigma_{r}\) for 1\(\sim\)3 h. The osmotic pressure differences (\(\Delta p\)) were uniformly 200 kPa, and the relevant test parameters and results after the seepage stability are shown in Table 2.  
The variation of the permeability coefficient with time for clayey sand during the permeability of low- and high-confined water is shown in Figures 9 and 10, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Pressure Bearing** & **Confining** & **Back Pressure** & **Back Pressure** & **Hydroalic** & **Permeability** \\
**Type** & **Pressure (\(\sigma_{r}\))** & **(\(p_{1}\))/kPa** & **(\(p_{2}\))/kPa** & **Gradient** & **Coefficient** \\  & **/MPa** & & & & **/(10\({}^{-8}\) cm/s)** \\ \hline  & 1 & 500 & 300 & 208.7 & 208.68 \\ Low-confined water & 2 & 500 & 300 & 214.3 & 1.26 \\  & 4 & 500 & 300 & 212.3 & 0.53 \\  & 6 & 500 & 300 & 210.7 & 0.35 \\  & 8 & 500 & 300 & 216.2 & Impermeable \\ \hline  & 1 & 500 & 300 & 208.7 & 208.69 \\ High-confined water & 2 & 1000 & 800 & 206.2 & 8.05 \\  & 4 & 2000 & 1800 & 212.7 & 3.47 \\  & 6 & 3000 & 2800 & 210.5 & 0.21 \\  & 8 & 4000 & 3800 & 216.2 & 0.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test parameters and results after permeation stabilization. Figure 10: \(Cont.\)  
Figure 9: Curves of the low-confined water permeability coefficient with time under different \(\sigma_{r}\) values. Comparing the curves of the permeability coefficient of low- or high-confined water of clayey sand with time under different \(\sigma_{r}\) values, it can be found that the permeability coefficient \((k_{v2})\) calculated from the \(\Delta Q_{2}\) decreased gradually with increasing time under different \(\sigma_{r}\) values. However, the permeability coefficient \((k_{v1})\) calculated by the \(\Delta Q_{1}\) gradually increased and tended to become stable with increasing time under different \(\sigma_{r}\) values. It is inferred that the hydrophobic effect of the sample in the early stage of the permeability test was greater than that of osmotic pressure differences, and the hydrophobic effect was almost over in the middle and late stages of the test, only affected by the osmotic pressure differences.