## 3 Results and Discussion
### Resilient Modulus
\begin{array}{l}a=a_{1}a_{w}^{2}+b_{1}a_{w}+c_{1}\\ b=a_{2}a_{w}^{2}+b_{2}a_{w}+c_{2}\end{array} \right. \tag{5}\]  
where \(a_{1,2}\), \(b_{1,2}\), and \(c_{1,2}\) are all the fitting coefficients related to the confining pressure. Then, a general formula can be deduced as:  
\[y=\alpha\sigma_{3}^{2}+\beta\sigma_{3}+\gamma \tag{6}\]  
where \(\sigma_{3}\) is the confining pressure, \(\alpha\), \(\beta\), and \(\gamma\) are also the fitting coefficients, which can be deduced in Table 2.  
As illustrated in Figure 9, the resilient modulus of sandy lightweight soil is higher than that of silty clay lightweight soil under confining pressures of 50 kPa and 150 kPa. The same condition also applies to the strength and recoverable elastic strain of the lightweight soil samples (as shown in Table 3). For the basic physical characteristics, the granular sand has smaller specific surface area and less activity than the silty clay. When cement is added, the granular sand and the cement have a rapid cementation speed with the help of water. The more cemented material is produced, the higher cementation strength would be generated to constrain the deformation of the EPS particles, resulting in smaller elastic deformation and higher resilient modulus. Although the silty clay is flattened with strong activity, the cement's hydrolysis and the hydration reactions mainly happen around a certain active medium. Therefore, the reaction is slow but needs a long time, and less cementing material is produced within a certain curing time. Moreover, the cemented silty clay has a lower strength to restrict the EPS particles, resulting in a lower strength than the sandy lightweight soil, as well as the resilient modulus. Due to the existence of a layer of bound water film around the fine-grained soil particle, silty clay has better deformation adaptability than sand, indicating that the silty clay lightweight soil has lower strength and resilient modulus than that of the sandy lightweight soil. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Fitting Parameters**} & \multicolumn{3}{c}{**LSS**} & \multicolumn{3}{c}{**LCES**} \\ \cline{2-7}  & \(\mathbf{\alpha}\) & \(\mathbf{\beta}\) & \(\mathbf{\gamma}\) & \(\mathbf{\alpha}\) & \(\mathbf{\beta}\) & \(\mathbf{\gamma}\) \\ \hline \(a_{1}\) & \(4.082\) & \(-871.570\) & \(47,389.000\) & \(-0.887\) & \(130.350\) & \(4556.900\) \\ \(b_{1}\) & \(-1.372\) & \(295.900\) & \(-15,571.000\) & \(0.194\) & \(-23.908\) & \(-1809.500\) \\ \(c_{1}\) & \(0.118\) & \(-25.067\) & \(1346.900\) & \(-0.005\) & \(0.104\) & \(238.290\) \\ \(a_{1}\) & \(-0.032\) & \(7.820\) & \(-446.140\) & \(0.003\) & \(-0.125\) & \(-45.564\) \\ \(b_{2}\) & \(0.011\) & \(-2.769\) & \(159.200\) & \(-0.000\) & \(-0.140\) & \(23.901\) \\ \(c_{2}\) & \(-0.001\) & \(0.243\) & \(-14.364\) & \(-0.000\) & \(0.030\) & \(-3.080\) \\ \hline \hline \end{tabular} Note: LSES is the sand mixed lightweight soil, LCES is the silty clay mixed lightweight soil.  
\end{table} 
Table 2: Deduced values of \(\alpha\), \(\beta\), and \(\gamma\). Figure 9: Resilient modulus versus axial total strain under different confining pressures: (**a**) aw = \(14\%\); (**b**) aw = \(20\%\). As shown in Figure 9a, with a lower confining pressure of 50 kPa and a smaller cement content of 14%, when the axial total strain of the specimen exceeds 8%, the resilient modulus of the sandy lightweight soil is smaller than that of the silty clay lightweight soil. This is rather unusual in the overall condition of these tested samples. When the shear deformation of the specimen becomes larger (i.e., the axial total strain exceeds 8%), the degree of particle breakage increases, and the sandy lightweight specimen starts to loosen, resulting in a decrease in the cohesion, as well as the resilient modulus. Although the same thing happened to the silty clay lightweight soil, the above reduction in cohesion and resilient modulus under the same shear deformation are relatively smaller than the sandy soils.