## 4 Pore Structure Characteristics and Nonlinear Permeability Mechanism of Clayey Sand
### Clayey Sand \(T_{2}\) Spectrum Distribution Law  
According to the relaxation principle of low-field NMR, water in small pores experiences greater surface relaxation, so it relaxes faster than water in large pores. Therefore, the \(T_{2}\) distribution is similar to the pore size distribution, in which each relaxation time corresponds to the pore size: Larger pores correspond to longer relaxation times and smaller pores correspond to shorter relaxation times [40]. [PERSON] [41] proved that the pore structure corresponds to the \(T_{2}\) spectrum distribution one by one through a mercury injection test; that is, the larger the pore throat diameter, the greater the corresponding \(T_{2}\) value. \(T_{2}\) spectrum distribution features include the number, size, and location of \(T_{2}\) spectrum peaks, among which different spectrum peaks reflect various types of seepage paths of clayey sand. In order to quantitatively analyze the pore structure of clayey sand under different stress states, after the permeability test, \(T_{2}\) spectrum distribution characteristic curves of saturated clayey sand under different stress states were obtained using low-field NMR technology and reflecting the pore structure with the \(T_{2}\) value of pore liquid water, as shown in Figure 15.  
As can be seen from Figure 15, the \(T_{2}\) spectrum distribution law of clayey sand was almost the same under different stress states, basically of the bispectrum peak type. The first spectrum peak was located in the range of transverse relaxation time, \(T_{2}\) = 0.01-5 ms, and the second spectrum peak was located in the range of transverse relaxation time, \(T_{2}\) = 10-100 ms. The signal amount of the first spectrum peak was large, so it can be assumed that there are a large number of tiny pores in clayey sand. Because clayey sand contains more fine clay particles and large specific surface areas, there are more tiny pores in clayey sand. The first peak is the main spectrum peak, the second peak is the subspectrum peak, with almost no nuclear magnetic signal between the two peaks, which indicates that the connectivity between the two pores was poor. With an increase in \(\sigma_{r}\), the signal intensity and interval width of the first and second spectrum peaks decreased, which shows the closure of seepage pore and the decrease in channels. Specifically, in the interval of transverse relaxation time \(T_{2}\) = 0.01-5 ms, the pore structure under different stress states  
Figure 15: Distribution of the ‘\(T_{2}\)’ spectrum of clayey sand under different stress conditions. was almost the same, but with an increase in \(\sigma_{r}\), the peak point of the spectrum peak in the interval decreased continuously, indicating that the number of adsorption pores in clayey sand decreased. At the same time, the end point value at the left end of the interval remained almost unchanged, while the end point value at the right end decreased, indicating that the pore size of the clayey sand adsorption hole decreased. In the range of \(T_{2}\) = 5-10 ms, the number of pores was zero and the connectivity between the pores was poor. In the range of \(T_{2}\) = 10-100 ms, the signal intensity of the \(T_{2}\) spectrum under different stress states was small, which indicates that the number of permeable macropores in clayey sand is small and the permeability is poor. With an increase in the \(\sigma_{r}\), the peak value and width of the spectrum in this range obviously decreased. When the \(\sigma_{r}\) increased to 4 MPa, the peak value of the spectrum almost dropped to zero, while a large number of seepage pores in the sample closed, and the permeability plummeted. The variation law of pores with an \(\sigma_{r}\) was the same as that of \(k_{v}\), which shows that analyzing the permeability law of porous media by the \(T_{2}\) spectrum distribution curve of NMR technology is highly reliable.