## 3 Test Results and Analysis
### Freeze-Thaw Cycle Effects
#### 3.1.2 Dynamic Elastic Modulus  
The dynamic elastic modulus under the current dynamic load can be calculated by selecting the average value of dynamic stress and strain at both ends of the fourth to seventh hysteretic loop of each load stage from the following equation:  
\[E_{\text{d}}=\frac{\sigma_{\text{max}}-\sigma_{\text{min}}}{\varepsilon_{\text {max}}-\varepsilon_{\text{min}}} \tag{6}\]  
where, \(\sigma_{\text{max}}\) and \(\sigma_{\text{min}}\) are the maximum and minimum dynamic stresses on the hysteresis loop, \(\varepsilon_{\text{max}}\) and \(\varepsilon_{\text{min}}\) are the maximum and minimum dynamic strains on the hysteresis loop. The \(E_{d}\)-\(\varepsilon_{d}\) curve is shown in Figure 7.  
From Figure 7, it can be seen that the dynamic elastic modulus of a single specimen decreases rapidly with the increase of dynamic strain under the condition that the dynamic load is loaded step by step, and the slope of the curve gradually tends to be flat. The dynamic elastic modulus of the specimens is also affected by the times of freezing and thawing. The accumulation of the times of freezing and thawing makes the \(E_{d}\)-\(\varepsilon_{d}\) curve gradually shift downward. Under the same dynamic strain amplitude, the dynamic elastic modulus of the soil sample that has experienced multiple freezing and thawing is smaller. These are, reflected in the actual project, the decreases of the strength and the bearing capacity. The \(E_{d}\)-\(\varepsilon_{d}\) curve of the soils with 10% and 20% weathered sand is more closely distributed after freezing and thawing. In Figure 6b, the variation curves of maximum dynamic elastic modulus with the number of freeze-thaw cycles for specimens with different weathered sand content is shown. After one, three, six, and nine freeze-thaw cycles, the average change in modulus was \(-9.35\%\), \(-3.96\%\), \(0.01\%\), and \(-0.74\%\), respectively, for the four weathered sand contents. The trend of the maximum dynamic elastic modulus is highly similar to that of the ultimate dynamic stress amplitude: after one freeze-thaw, the modulus change is the largest, and then the modulus decrease slows down, and the initial dynamic elastic modulus fluctuates around the stable value after six freeze-thaws.  
In summary, the mechanical properties of expansive soils are highly correlated with freeze-thaw cycles. The freeze-thaw cycles cause changes in the pore structure inside the soil at the microscopic level, which leads to the changes in the soil structure at the macroscopic level, and ultimately leads to the decrease in the dynamic properties of the expansive soil. The specimens without freeze-thaws cycles are stronger because of less  
Figure 6: Fitting parameters vs. number of freeze–thaw cycles.  
pore space and reduced regular arrangement of soil particles. The soil is extruded and compacted under load, and the load is borne by the soil skeleton and pore water together. For freeze-thaw soil samples, during the low-temperature freezing process, the pore water in the saturated specimen is frozen into ice by the low-temperature influence, and the volume expansion generates the freeze expansion force to squeeze the surrounding soil particles, which causes dislocation and damage; during the high-temperature thawing process, the ice crystals in the pore space melt and the volume becomes smaller, and this phenomenon is called \"freeze expansion and thawing\" in macroscopic terms [20]. During a freeze-thaw cycle, the volume difference resulting from the phase change of pore water loosens the soil structure and reduces the strength of the soil. The first freezing-thawing caused the increase of macropores, so it had the most significant effect on strength. With the accumulation of freezing-thawing cycles, soil damage leads to an increase in the number of small particles. After the sixth freezing-thawing, due to the agglomeration, small particles formed aggregates, the contact between soils increased and the strength gradually stabilized [21].