## 4 Test Results
### Quantitative Analysis of Particle Structure of Silt under Freeze-Thaw Cycles by LST  
#### 4.2.1 Particle Characteristic Evaluation Parameters Establishment  
The particle characteristics of soil could be further measured by LST. Under the condition of vertical confining pressure 150 kPa, effective confining pressure 75 kPa, freezing temperature \(-20\)\({}^{\circ}\)C, and relative bulk density 0.827, the particle bulk density curves of silt with different freeze-thaw cycles are shown in Figure 8. It can be seen that as the silt experienced more freeze-thaw cycles, the content of clay particles smaller than 5 \(\upmu\)m is reduced; the content of 5-10 \(\upmu\)m particles changes in a stable fluctuating state; the content of 5-50 \(\upmu\)m particles increases significantly; the content of 50-60 \(\upmu\)m particles remains basically unchanged; the content of 60-200 \(\upmu\)m particles decreases; the content of particles larger than 200 \(\upmu\)m does not change significantly. Combined with the SEM images of silt under long-term freeze-thaw cycles (Figure 7), it can see that the freeze-thaw action probably induces the clay particles (less than 5 \(\upmu\)m) to aggregate and form flocculent structure; probably inducing the part silt and sand particles (60-200 \(\upmu\)m) in breakage. The diameters of formed flocculent structures (aggregated) and broken particles are distributed from 5-60 \(\upmu\)m.  
Figure 8: The particle bulk density curves of silt. Figure 7: The SEM images of silt under different freeze–thaw cycles. (**a**) Unfrozen; (**b**) freeze–thaw 10 times; (**c**) freeze–thaw 20 times; (**d**) freeze–thaw 30 times; (**e**) freeze–thaw 50 times; (**f**) freeze–thaw 100 times. As early as 1985, [PERSON] [14] defined a parameter crushing index \(B_{r}\) to evaluate the particle size variation in soil shearing. It took the area enclosed by \(d\) = 0.074 mm, \(P\) = 100% (\(P\) is the percentage content of particles less than a certain size (%), \(d\) is the soil particle size (mm)), and the gradation curve before particle breakage in \(P\)-lg\(d\) coordinate system as the crushing potential \(S_{\text{p}}\), and the reduced area of gradation curve after testing was taken as the particle crushing amount \(S\), and the two were divided to obtain the crushing index \(B_{r}\). \[B_{r}=S/S_{\text{p}} \tag{1}\]  
The model is mainly aimed at particle breakage size greater than 0.074 mm of sand particles [15; 16] (he regarded that the shear failure of soil could not affect particles below 0.074 mm [10; 17]). However, in our research, the fine particles of soil account for 88.3%. As shown in the SEM images (Figure 7) and preliminary analysis of Figure 8, for silt under long-term freeze-thaw cycles, the soil particles were main influenced at a range of 1-2000 \(\upmu\)m and soil particles both could break and aggregate in 5-60 \(\upmu\)m, so a particle size index \(B_{\text{f}}\) of silt is defined in this paper to describe the total particle size variation characteristics of silt under long-term freeze-thaw cycles:  
\[B_{\text{f}}=(\mid\text{S1}\mid+\mid\text{S2}\mid)/S_{\text{p}} \tag{2}\]  
where \(S\) is the amount of particle size variation (%\(\bullet\)mm), which is characterized by the area between the particle accumulation curve of silt before and after freeze-thaw cycles in \(P\)-lg\(d\) coordinate system (note: this area is the sum of the variation amount including particles aggregation \(\mid\)S1\(\mid\) and particles breakage \(\mid\)S2\(\mid\). Shown in Figure 9); \(S_{\text{p}}\) is the variation potential (%\(\bullet\)mm), which is characterized by the area along with \(d\) = 0.001 mm, \(P\) = 100%, and particle accumulation curve in \(P\)-lg\(d\) coordinate system. From SEM image observing (Figure 7) and preliminary analysis of LST (Figure 8), freeze-thaw cycles not only change particle size, but also affect particle shape. Analogously, the concept of sphericity potential is proposed in this paper.