## 2 Experimental Materials and Methods
### Experimental Procedure
#### 2.2.3 Nuclear Magnetic Resonance Principle and Test  
In recent years, low-field nuclear magnetic resonance (NMR) has emerged as a rapid, non-destructive, and intuitive detection technology in the geotechnical field, effectively revealing the microstructural pore characteristics of rocks. Under natural conditions, the spin states of 1H nuclei are randomly oriented and unmagnetized. When a sample is placed in the test chamber of an NMR instrument, the primary magnetic field causes the 1H nuclei to become magnetized. The interaction between the spin magnetization of the 1H nuclei and the applied magnetic field generates a measurable signal, which is a prerequisite for nuclear magnetic resonance. This phenomenon, known as nuclear magnetic resonance (NMR), involves the nuclei aligning with the applied magnetic field while releasing energy into their surroundings. The transition from a high-energy state to a low-energy state is called nuclear magnetic resonance relaxation. The transverse relaxation time decay (\(T_{2}\) decay) contains critical physical information about most porous samples, making \(T_{2}\) the primary parameter for rock NMR detection. Based on the principles of NMR detection, the grouting reinforcement body undergoes vacuum-forced saturation to ensure complete water saturation of its internal pores. The \(T_{2}\) spectra of the grouting reinforcement body are generated through NMR testing of the 1H nuclei in the water. By analyzing these spectra, the internal pore characteristics and their variation patterns can be determined. The \(T_{2}\) relaxation time is classified into surface \(T_{2}\) relaxation, free \(T_{2}\) relaxation, and diffusion \(T_{2}\) relaxation. In porous materials, such as the grouting reinforcement body, the relaxation time is primarily governed by surface \(T_{2}\) relaxation. Therefore, \(T_{2}\) can be expressed using the following Equation [24]:  
\[\frac{1}{T_{2}}=\rho_{2}\bigg{(}\frac{S}{V}\bigg{)} \tag{1}\]  
where \(T_{2}\) is transverse relaxation time (ms), \(\rho_{2}\) is the surface relaxation strength of \(T_{2}\) (\(\upmu\)m/ms), \(S\) is pore surface area (cm\({}^{2}\)), and V is pore volume (cm\({}^{3}\)). It can be observed that the transverse relaxation time \(T_{2}\) is proportional to the pore-specific surface area (\(S\)/\(V\)) and the surface relaxation strength. Thus, Equation (1) can be further simplified as follows:  
\[r=\rho_{2}F_{2}T_{2} \tag{2}\]  
where \(r\) is the pore radius (\(\upmu\)m). \(F_{2}\) is the shape aggregation factor, which is 3 for spherical pores and 2 for columnar pores, and \(\rho_{2}\) is the surface relaxation strength of \(T_{2}\) (\(\upmu\)m/ms). The corresponding values of these parameters are provided in Table 2[25]. The value of \(\rho_{2}F_{2}\) ranges from 0.01 to 0.15 \(\upmu\)m/ms [26; 27]; meanwhile, in this study, a value of 0.01 \(\upmu\)m/ms is adopted. Thereby, the relationship between the \(T_{2}\) and the pore radius (\(r\)) is established. A  
Figure 10: Time-temperature curve. larger \(T_{2}\) value corresponds to a larger pore radius, while a smaller \(T_{2}\) indicates a smaller pore size. The pore structure of the grouting reinforcement body includes both pore distribution and pore size, with the latter having a direct impact on the macroscopic strength of the samples. Pores are generally categorized into micropores, mesopores, and macropores, although no universally accepted classification standard currently exists. Table 3 summarizes the commonly used classification methods. Different classification schemes have been proposed for micropores, mesopores, and macropores. In this study, the pore size classification follows the method proposed by [PERSON]. According to this scheme, micropores are defined as pores with \(r<0.1\)\(\upmu\)m, corresponding to \(T_{2}<10\) ms; mesopores are those with \(0.1\)\(\upmu\)m \(<r<1\)\(\upmu\)m, corresponding to \(10\) ms \(<T_{2}<100\) ms; and macropores are defined as pores with \(r>1\)\(\upmu\)m, corresponding to \(T_{2}>100\) ms.