# Effect of Cement Content on the Deformation Properties of Cemented Sand and Gravel Material
## 3 Results and Discussion
### Initial Modulus  
Figure 5 illustrates the initial modulus under varying confining pressures and cement contents. As shown in the figure, the initial modulus increases exponentially with an increase in confining pressure under a certain cement content. This is consistent with the observations made by previous studies on other types of CSG materials [10; 11; 12]. The relationship between the initial modulus and confining pressure of CSG material adopted by some of these studies is as follows [10]:  
\[E_{1}=E_{01}Pa(\sigma_{3}/Pa)^{n}, \tag{1}\]  
where \(E_{01}\) and \(n\) are dimensionless parameters related to the type of the soil, rockfill material, etc. ; the atmospheric pressure \(Pa\) is 100 kPa; \(E_{01}Pa\) represents the initial modulus when the confining pressure is 100 Pa; and \(n\) represents the growth index of the initial modulus. Through a regression analysis of data from Figure 5 and Equation (1), the values of \(E_{01}\) and \(n\) are obtained and are shown in Table 4. Values of Correlation coefficient \(\mathbb{R}^{2}\) in the table that are greater than 0.97 indicate that the calculated results of Equation (1) fit the experimental results well. However, when the confining pressure is 0, the initial modulus is 0 in Equation (1), and this is inconsistent with the actual value of the modulus. Thus, the relationship between the initial modulus and confining pressure for a CSG material, determined by [PERSON] et al. and [PERSON] et al., is expressed as follows [11; 13]:  
\[E_{1}=E_{0}Pa(1+\sigma_{3}/Pa)^{n}, \tag{2}\]  
where \(E_{0}\) and \(n\) are dimensionless parameters; \(E_{0}Pa\) represents the initial modulus of the CSG material when the confining pressure is 0; \(n\) represents the growth index of the initial modulus. Through a regression analysis of data from Figure 6 and Equation (2), the values of \(E_{0}\) and \(n\) are obtained and are shown in Table 5. Values of \(\mathbb{R}^{2}\) in the table that are greater than 0.98 indicate that the calculated results of Equation (2) fit the experimental results well, thereby demonstrating that Equation (2) can be used to describe the initial modulus of CSG material as a function of the confining pressure. \begin{table}
\begin{tabular}{c c c c c} \hline
**Cc (kg/m\({}^{3}\))** & **Formula** & **Correlation Coefficient \(\mathbb{R}^{2}\)** & \(E_{01}\) & \(n\) \\ \hline
20 & \(E_{1}=86,078(\sigma_{3}/100)^{0.51}\) & 0.98 & 860.78 & 0.51 \\
40 & \(E_{1}=109,766(\sigma_{3}/100)^{0.43}\) & 0.99 & 1097.66 & 0.43 \\
60 & \(E_{1}=213,587(\sigma_{3}/100)^{0.35}\) & 0.99 & 2135.87 & 0.35 \\
80 & \(E_{1}=366,396(\sigma_{3}/100)^{0.29}\) & 0.99 & 3663.96 & 0.29 \\
100 & \(E_{1}=833,524(\sigma_{3}/100)^{0.16}\) & 0.97 & 8335.24 & 0.16 \\ \hline \end{tabular}
\end{table} 
Table 4: Values of \(\mathbb{R}^{2}\), \(E_{01}\), and \(n\). The test values of \(E_{0}\) and \(n\) under different cement contents are also shown in Figures 6 and 7, respectively. As can be seen from Figure 6, when \(Cc\) is close to 0, \(E_{0}\) is close to the corresponding value of rockfill material. With an increase of \(Cc\), \(E_{0}\) increases. The parameter \(n\) is close to the corresponding value of rockfill material in Figure 7, when \(Cc\) is close to 0. Additionally, with an increase of \(Cc\), \(n\) decreases and is close to 0. Figure 5: The relationship between the initial modulus \(E_{i}\) and confining pressure \(\sigma_{3}\) under varying cement contents. Figure 6: The relationship between the parameter \(E_{0}\) and cement content \(Cc\).