## 3 Results and Discussion
### Effect of Stress State on Resilient Modulus  
To investigate the effect of confining pressure and deviator stress on the variation trend of resilient modulus, the resilient moduli of two materials in an unfrozen state and after 1 to 7 F-T cycles were analyzed. The variation curves of resilient modulus versus deviator stress and bulk stress (\(\theta=\sigma_{1}+\sigma_{2}+\sigma_{3}\)) are shown in Figures 4 and 5, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Process**} & \multirow{2}{*}{
\begin{tabular}{c} **Deviator** \\ **Stress (kPa)** \\ \end{tabular} } & \multicolumn{8}{c}{**Resilient Modulus after Several F-T Cycles (MPa)**} \\ \cline{3-13}  & & \multicolumn{2}{c}{**0**} & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**3**} & \multicolumn{2}{c}{**5**} & \multicolumn{2}{c}{**7**} \\ \cline{3-13}  & & **Mean** & **SD** & **Mean** & **SD** & **Mean** & **SD** & **Mean** & **SD** & **Mean** & **SD** \\ \hline \multirow{3}{*}{40-1} & 25 & 126.28 & 1.56 & 81.12 & 0.98 & 80.68 & 0.76 & 78.98 & 0.86 & 80.01 & 1.24 \\  & 15 & 139.09 & 1.43 & 94.82 & 0.76 & 93.58 & 0.86 & 96.54 & 0.69 & 96.18 & 0.98 \\  & 5 & 159.55 & 1.67 & 118.17 & 1.03 & 119.56 & 0.74 & 121.58 & 0.89 & 117.69 & 0.65 \\ \hline \multirow{3}{*}{50-2} & 25 & 159.22 & 1.13 & 106.53 & 0.62 & 104.56 & 0.89 & 103.87 & 1.26 & 107.55 & 0.86 \\  & 15 & 182.24 & 0.85 & 131.97 & 0.89 & 132.98 & 1.32 & 130.75 & 0.65 & 134.39 & 0.74 \\  & 5 & 202.79 & 1.67 & 167.51 & 1.35 & 165.88 & 0.78 & 164.99 & 0.68 & 166.16 & 0.87 \\ \hline \multirow{3}{*}{40-3} & 25 & 126.82 & 1.48 & 83.54 & 0.69 & 84.12 & 1.13 & 82.95 & 0.74 & 84.56 & 0.69 \\  & 15 & 140.69 & 2.03 & 96.42 & 0.59 & 97.01 & 0.69 & 95.58 & 0.95 & 96.87 & 0.93 \\ \cline{1-1}  & 5 & 158.78 & 1.67 & 120.03 & 1.36 & 122.45 & 0.83 & 118.84 & 0.92 & 121.36 & 0.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Resilient modulus for SC modified by OSA and FA. OSA: oil shale ash; FA: fly ash. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Process**} & \multirow{2}{*}{ \begin{tabular}{c} **Deviator** \\ **Stress (kPa)** \\ \end{tabular}  } & \multicolumn{8}{c}{**Resilient Modulus after Several Freeze-Thaw (F-T) Cycles (MPa)**} \\ \cline{3-13}  & & \multicolumn{2}{c}{**0**} & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**3**} & \multicolumn{2}{c}{**5**} & \multicolumn{2}{c}{**7**} \\ \cline{3-13}  & & **Mean** & **SD** & **Mean** & **SD** & **Mean** & **SD** & **Mean** & **SD** & **Mean** & **SD** \\ \hline \multirow{3}{*}{40-1} & 25 & 123.69 & 2.09 & 99.56 & 1.98 & 78.92 & 1.60 & 68.55 & 0.68 & 62.96 & 1.05 \\  & 15 & 142.31 & 1.63 & 116.77 & 1.23 & 96.03 & 1.13 & 86.63 & 1.23 & 79.15 & 1.34 \\  & 5 & 161.56 & 1.06 & 137.65 & 1.45 & 1 Figure 4: Variation curve of resilient modulus versus deviator stress for test soils after (**a**) 0, (**b**) 1, and (**c**) 7 F-T cycles. Figure 5: _Cont._  
From Figure 4, the resilient moduli of both unmodified SC and the modified SC decrease with increasing deviator stress. The resilient modulus in high confining pressure (\(\sigma_{\rm c}\) = 50 kPa) is higher than that in low confining pressure (\(\sigma_{\rm c}\) = 40 kPa). From Figure 5, the resilient modulus increases with the increase of bulk stress. The variation trends of resilient modulus versus deviator stress and bulk stress are still significant after F-T cycles. In Figure 5, It should be noted that the shape of each data curve in Figure 5 is a break-line of horizontal \"\(\Lambda\)\". The starting point and end point of the \"\(\Lambda\)\" curve are the resilient moduli of loading sequences 40-1 and 40-3, respectively. When the horizontal \"\(\Lambda\)\" curve is close to an \"I\" shape, it means that the resilient modulus values of 40-1 and 40-3 are exactly equal. This phenomenon is in accordance with the coincident curves of 40-1 and 40-3 in Figure 4, which illustrates that the influence of loading path on resilient modulus is insignificant under the same stress state.