## 3 Results and Discussion
### Effect of Mixing Rubber Fibers on Elastic Modulus of Expansive Clay  
Elastic modulus is an important mechanical parameter for soil materials. The stress-strain curves shown in Figure 3 are not straight lines, indicating that the secant elastic modulus is different at different strain levels. Some scholars have defined the elastic modulus of soil as the secant elastic modulus at 1% axial strain [34; 49]. In this study, the elastic modulus was calculated from the secant elastic modulus at 2% axial strain based on the stress-strain curves of the specimens, as expressed in Equation (1), and the results are shown in Figure 6.  
\[E_{2\%}=\frac{\Delta\sigma}{\Delta\epsilon}=\frac{(\sigma_{1}-\sigma_{3})_{2 \%}}{\varepsilon_{1,2\%}} \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**References**} & \multirow{2}{*}{**Soil Types**} & **Test** & **Number of** & **Confining** \\  & & **Method** & **Freeze–Thaw Cycles** & **Pressures/kPa** \\ \hline [PERSON] et al. [49] & Expensive clay & CU & 0, 1, 3, 5, 9 & 100, 200, 300 \\ [PERSON] et al. [50] & Expensive clay & CU & 0, 1, 4, 6, 10 & 50, 100, 200, 300 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Test conditions.  
Figure 5: Variation in normalized shear strength with freeze–thaw cycles [49; 50].  
where \(E_{2\%}\) is the elastic modulus, \((\sigma_{1}-\sigma_{3})_{2\%}\) is the deviatoric stress at 2% axial strain, and \(\varepsilon_{1,\,2\%}\) is 2% axial strain.  
The results shown in Figure 6 indicate that the elastic modulus of rubber fiber-reinforced expansive clay decreases slowly from an overall point of view at the confining pressures of 100 kPa and 200 kPa. However, at the confining pressure of 300 kPa, the decrease in the elastic modulus of the rubber fiber-reinforced expansive soil is more significant. The results of the elastic modulus of unreinforced expansive clay under freeze-thaw conditions from previous studies were referred to compare the effect of mixing rubber fibers on the elastic modulus of expansive soil [49; 50]. The results of the normalized elastic modulus are shown in Figure 7 and the test conditions are presented in Table 2.  
Figure 7 shows the variation in the normalized elastic modulus with the number of freeze-thaw cycles, and the different curves in the same color represent different confining pressures. The normalized elastic modulus of rubber fiber-reinforced expansive clay showed a decreasing trend within 15 freeze-thaw cycles. The elastic modulus of rubber fiber-reinforced expansive clay decreased by approximately 10% (average) after 15 freeze-thaw cycles. However, the elastic modulus of unreinforced expansive clay decreased  
Figure 6: Elastic modulus with different number of freeze–thaw cycles.  
Figure 7: Variation in normalized elastic modulus with freeze–thaw cycles [49; 50].  
by approximately 36% (average) after 9 freeze-thaw cycles in [PERSON] et al. [49], and by approximately 37% (average) after 10 freeze-thaw cycles in [PERSON] et al. [50]. The rubber fibers produce tensile forces that weaken the development of cracks (caused by freeze-thaw cycles) in the expansive clay, thus reducing the effect of freeze-thaw cycles on the elastic modulus of the expansive clay [53; 55; 56]. Based on the above discussion, the mixing of rubber fibers lowers the effect of freeze-thaw cycles on the elastic modulus and thus improves the engineering performance of expansive clay in seasonal frozen regions.