## 3 Results and Discussion
### Effect of Rubber Fibers on Pore Size Distribution  
Relaxation refers to the process by which the spin of a proton is stabilized from an excited state to an equilibrium state. Transverse relaxation refers to the time required for the maximum excited state to approach zero. The transverse relaxation time is determined using the proton relaxation time \(T_{\text{2B}}\) and surface relaxation time \(T_{\text{2S}}\). \[\frac{1}{T_{2}}=\frac{1}{T_{\text{2B}}}+\frac{1}{T_{\text{2S}}}\approx\rho_{2 }\bigg{(}\frac{S}{V}\bigg{)} \tag{5}\]  
where \(\rho_{2}\) is the surface relaxation rate, which is related to the physicochemical properties of the soil. \(S\) and \(V\) are the surface area and pore volume, respectively, of the porous medium. The porosity and pore distribution characteristic parameters of the soil were calculated using the NMR transverse relaxation time \(T_{2}\) spectrum. The relationship between the relaxation time and pore size is shown in Equation (6). From this equation, \(T_{2}\) is linearly related to the pore size. Therefore, if the value of the surface relaxation rate \(\rho_{2}\) is known, the pore-size distribution in the ESR can be obtained by measuring \(T_{2}\). According to [PERSON] [48], the \(\rho_{2}\) of expansive soil is considered as 3 \(\upmu\)m s\({}^{-1}\). \[\frac{1}{T_{2}}\approx\rho_{2}\bigg{(}\frac{S}{V}\bigg{)}\approx\rho_{2} \bigg{(}\frac{2}{R}\bigg{)} \tag{6}\]  
Figure 11 shows the relaxation curves of the ESR for different rubber fiber contents. The variation characteristics of the \(T_{2}\) spectrum for different rubber fiber content were almost identical. This indicates that the distribution of internal pores was approximately identical. The \(T_{2}\) spectra of the ESR with different fiber contents consist of two spectral peaks: a primary peak and secondary peak. The secondary peak is significantly smaller than the main peak. This indicates that the internal pore size had good continuity. Using ESR-8 as an example, the relaxation time corresponding to the vertex was 1.589 ms. Of this, the main peak accounted for 97.6%. To compare the data more visually, the spectral distributions of the other rubber fiber contents are presented in Table 4. As shown in Figure 11, the \(T_{2}\) spectrum curve shifts to the left to a certain extent as the rubber fiber content increases. Comparing ESR-8 and ESR-11, the relaxation time corresponding to the main peak is equal (1.589 ms). However, the peak area of ESR-11 is larger than that of ESR-8. Figure 10: The variation in \(\psi_{\text{max}}\) with the rubber content [25; 36; 39; 45; 47]. This indicates that when the rubber fiber content attained 15%, the pores in the sample were destroyed because of the excessive rubber fiber content. The fibers were intertwined into a clump, and the porosity increased. This affected the mechanical properties of the expansive soil. When the rubber content is 5-10%, the relaxation time of the main peak of the spectrum is 1.383 ms. This is less than that of ESR-8 and ESR-11. This result reveals that when the rubber fiber content is in the range of 5-10%, the interface between the expansive soil particles and rubber fibers displays effective bonding. This can effectively inhibit the development of soil cracks and reduce the pore space around the cracks. To quantitatively analyze the pore number distribution of ESR with different diameters, it is necessary to subdivide the pore size of the ESR. The pore diameter of the ESR at different rubber fiber contents can be obtained using Equation (6). According to [PERSON] et al. [49], the pore diameters of soil can be divided into five types: macrotypes (>3 \(\upmu\)m), medium pores (1-3 \(\upmu\)m), small pores (0.2-1 \(\upmu\)m), micropores (0.01-0.2 \(\upmu\)m), and ultra-micropores (<0.01 \(\upmu\)m). Figure 12a, b show the pore size distribution curves and pore content curves, respectively, of the ESR with different rubber fiber content.