## 4 Pore Structure Characteristics and Nonlinear Permeability Mechanism of Clayey Sand
### Clayey Sand \(T_{2}\) Spectrum Distribution Law
To simplify the analysis, \(T_{2}\) = 2.5 ms was taken as the dividing line between the adsorption holes (0.1-2.5 ms) and permeability holes (2.5-100 ms), and a curve of the content of adsorbed water and capillary water in clayey sand changing with the \(\sigma_{r}\) could be obtained, as shown in Figure 16.  
As can be seen from Figure 16, the capillary water and adsorbed water content decreased with an increasing \(\sigma_{r}\) but the reduction forms of the two were different. The adsorbed water decreased in a linear relationship, while the capillary water decreased in a power function form. After the \(\sigma_{r}\) increased to 2 MPa, almost all of the capillary water was discharged, resulting in the capillary water content being less than 5% (the total water content of 1 MPa was 30% of the initial water content), leaving only some adsorbed water in the sample. At this time, the adsorbed water was mainly bound water, which has little influence on water infiltration. Based on this, a seepage model of clayey sand could be established, as shown in Figure 17. \begin{table}
\begin{tabular}{c c c c} \hline \(\mathbf{T_{2}}\) & **Aperture ‘D’** & **Pore Types** & **Pore Water Classifications** \\ \hline
0.1–2.5 ms & \textless{}0.1 \(\upmu\)m & Adsorption pore & Adsorbed water \\
2.5–100 ms & \textgreater{}0.1 \(\upmu\)m & Infiltration pore & Capillary water \\ \textgreater{}100 ms & - & Crack & Free water \\ \hline \end{tabular}
\end{table} 
Table 8: Corresponding relationship between the transverse relaxation time, \(T_{2}\), and pore throat diameter. Figure 16: Fitting curve of the capillary water and adsorbed water content with the \(\sigma_{r}\) in clayey sand. Pores in clayey sand and pore water play a decisive role in the seepage process. Because the bound water near the surface of soil clay particles has shear strength (\(\tau_{f}\)), its distribution decreases exponentially with the distance from the surface of clay particles. Under a certain water head or consolidation stress, some bound water with a smaller \(\tau_{f}\) is in a flowing state, while some bound water is in a solid-like state. Therefore, only some of the bound water is in a moving state in those pores filled with bound water, and that in the pores where bound water can flow is called a seepage hole, and its diameter is called the seepage diameter. Regarding the whole process of clayey sand infiltration, when \(p<2\) MPa, free water is dominant in soil pores, and the seepage fluid is mainly free and bound water. With an increasing consolidation pressure, the free water in pores is gradually discharged, causing pores to become smaller and the void ratio to change greatly, resulting in a great change in the \(k_{v}\). When \(p>4\) MPa, the bound water in the soil is dominant, and the bound water mainly seeps. When the head pressure difference exceeds the \(\tau_{f}\) of bound water, it has the nature of free water and participates in seepage. This part of bound water bears the pore water pressure, and this effect gradually decreases with an increasing \(\sigma_{r}\). Even if the head pressure difference increases, the proportion of bound water that can overcome the \(\tau_{f}\) does not change much. At this time, the pores change little and the \(k_{v}\) value tends to become stable. To sum up, according to the \(T_{2}\) spectrum distribution of clayey sand under different stress states, we can not only quantitatively analyze the pore structure in soil, but also judge the connectivity between pores. Moreover, the analysis results are consistent with the conclusions of the ETAS permeability test. The content of capillary water in pores plays a key role in the permeability of clayey sand, and its fitting relationship with the \(\sigma_{r}\) and between the \(k_{v}\) and \(\sigma_{r}\) all meet the power function relationship. Therefore, it is of great significance to explore the nonlinear permeability law of clayey sand through the capillary water distribution in pores to improve the existing permeability mechanism of porous media under high stress.