# A New Shear Strength Model with Structural Damage for Red Clay in the Qinghai-Tibetan Plateau
## 4 Discussion
### Analysis of Microstructure  
The shear strength of red clay is continuously deteriorating due to the action of FTCs (see Figures 7 and 8). Through NMR test results, as the number of FTCs increases, an increase in macropores leads to a loose structure and weakens the strength of red clay. During the freezing phase, the low ambient temperature causes the pore water to turn into ice. The ice crystals squeeze the soil skeleton, causing irreversible damage and reducing the bond between soil structures. This will result in a sharp reduction in cohesion and deterioration in the shear strength of red clay. The formation of through pores or cracks weakens the friction and occlusion between soil particles, causing a slight reduction in the friction angle.  
Recalling that the pore size distribution of saturated soils can be reflected through \(T_{2}\) distribution curves, the calculation method of the area below the \(T_{2}\) distribution curves is to sum the signal amplitude \(I\) corresponding to the \(T_{2}\) value, and the result is shown in Figure 9.  
Figure 8: The shear strength parameters of red clay change with the number of freeze–thaw cycles.  
According to Figure 9, as the number of FTCs increases, the area of micropores declines to a stable level, while the area of macropores increases to a stable level. After five FTCs, the \(T_{2}\) spectral area largely stays in place and the pore size distribution remains unaltered. It indicates that the red clay has reached a new stable structure at the microscale. The corresponding macroscale performance is that the shear strength of the specimens essentially reaches a stable value. This demonstrates that the structural damage of red clay caused by FTCs is mainly caused by macropores. Therefore, a damage factor based on the area of \(T_{2}\) spectral is defined as \(\eta\), which can represent the changing rate of \(T_{2}\) spectral area after FTCs. The redistribution of pores inside the red clay will lead to soil structure looseness and strength deterioration. The damage factor can characterize the damage degree of soil microstructure caused by FTCs. The greater the value of \(\eta\), the greater the deterioration of the soil structure. The calculation formula of \(\eta\) is as below  
\[\eta=\frac{\sum I_{\text{N}}/\sum I_{\text{Micropore,N}}-\sum I_{0}/\sum I_{ \text{Micropore,0}}}{\sum I_{0}/\sum I_{\text{Micropore,0}}} \tag{4}\]  
where \(I_{0}\) is the signal amplitude corresponding to the \(T_{2}\) value of the specimen without FTC, and \(I_{\text{N}}\) is the signal amplitude corresponding to the \(T_{2}\) value of the specimen after \(N\) FTCs. \(I_{\text{Micropore,0}}\) is the signal amplitude corresponding to the \(T_{2}\) value of peak 1 without FTC, and \(I_{\text{Micropore, N}}\) is the signal amplitude corresponding to the \(T_{2}\) value of peak 1 after \(N\) FTCs.  
The change in \(\eta\) with the increase in the number of FTCs can be fitted as Equation (5), and the result is illustrated in Figure 10.  
\[\eta=3\Big{(}1-e^{-0.4N}\Big{)} \tag{5}\]  
Figure 10 reveals that as the number of FTCs increases, the damage factor gradually rises to a stable state. This suggests that the redistribution of pores significantly influences the shear strength of red clay. Therefore, the study of such pores should be given special attention in engineering practices.  
Figure 9: Variation of \(T_{2}\) spectral area with the number of freeze–thaw cycles.