## 4 Pore Structure Characteristics and Nonlinear Permeability Mechanism of Clayey Sand
### Clayey Sand \(T_{2}\) Spectrum Distribution Law
According to the \(T_{2}\) spectrum curve cluster of clayey sand in different stress states in Figure 15, the \(T_{2}\) spectrum area was analyzed [42], as shown in Table 7.  
It can be seen from Table 7 that with an increase in the \(\sigma_{r}\), the total water content of clayey sand and the pore water content corresponding to the first and second peaks all decreased rapidly, while the proportion of water content in the first peak increased. This indicates that the pore type corresponding to the second peak controlled the permeability of the sample during the increase in the \(\sigma_{r}\). Distribution Characteristics of the Pore Structure of Clayey Sand and Its Micro-Mechanism of Permeability  
Pores in porous media are usually composed of two different (double-pore) systems, including primary and secondary pores. The primary pore system consists of micropores and mesopores (\(<\)0.1 \(\upmu\)m), while the secondary pore system includes macropores (\(>\)0.1 \(\upmu\)m), micro-fractures and cleat and natural fractures, forming a pipeline for large-flow fluid transfer. Micropores and mesopores are also called adsorption pores, while macropores are called permeability pores, and their permeability threshold is 0.1 \(\upmu\)m. In view of this phenomenon, [PERSON] [43; 44; 45; 46] provided the corresponding relationship between the transverse relaxation time, \(T_{2}\), and pore size, as shown in Table 8. Because the adsorption pores were saturated with bound water, they could not be used as the seepage path of pore water in the permeability test, which has little influence on the permeability of clayey sand, while the permeability pores were saturated with free water, which could be used as the seepage path in the permeability test. Thus, the size and number of permeability pores determine the permeability of porous media. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Confining Pressure (\(\sigma_{r}\))/MPa** & **Total Peak Area** & **First Peak Area** & **First Peak Percentage / \%** & **Second Peak Area** & **Second Percentage / \%** \\ \hline
1 & 5703.32 & 5304.09 & 93.00 & 399.23 & 7.00 \\
2 & 4749.73 & 4546.92 & 95.73 & 202.81 & 4.27 \\
4 & 4049.60 & 3911.91 & 96.60 & 137.69 & 3.40 \\
6 & 3248.41 & 3170.77 & 97.61 & 77.64 & 2.39 \\
8 & 2624.56 & 2585.98 & 98.53 & 38.58 & 1.47 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The “\(T_{2}\)” spectrum area of clayey sand under different stress conditions. Table 8 shows that different \(T_{2}\) intervals correspond to different pore types. The interval of \(T_{2}\) = 0.1-2.5 ms corresponds to adsorption pores, a pore size of less than 0.1 \(\upmu\)m, and most pores being film-adsorbed water, which hardly permeates due to the strong adsorption force on the particle surface. The \(T_{2}\) = 2.5-100 ms interval corresponds to the seepage hole, a pore size greater than 1 \(\upmu\)m, and capillary water being in the hole. This part of water is only bound by capillaries and can permeate under the action of \(i\), which is the main part of permeability. In the \(T_{2}\) > 100 ms interval, there are cracks, and the pores are free water, which has very little constraint and can very easily infiltrate. Therefore, the smaller the pore size, the more difficult it is for pore water to eliminate the constraints and infiltrate. During the infiltration process, cracks and pores infiltrate in turn, according to the pore size, while the adsorbed water in the adsorption pores only decreases the thickness of the adsorption film with increasing pore water pressure and does not infiltrate [47]. In addition, for clayey sand, the comprehensive proportion of adsorption and permeability holes was larger than that of 97%, and the proportion of fissure pores was too small to be ignored.