# Effect of Cement Content on the Deformation Properties of Cemented Sand and Gravel Material
## 3 Results and Discussion
### Axial Strain at the Peak Points of the Test Curves  
In this study, the axial strain at the peak points of the stress-strain curves represent the failure strain, and the axial strain at the peak points of the volumetric strain-axial strain curves represents the axial strain at the initial dilatancy point. Figure 8 shows that these axial strains decrease with increasing cement content and decreasing confining pressure. However, the value of failure strain is larger than that of the axial strain at the initial dilatancy point under the same cement content and confining pressure. This suggests that the dilatancy is usually observed before failure of the CSG material. When the cement content is higher than 60 kg/m\({}^{3}\), the failure strain is almost the same and between 1.2% and1.5% under a certain confining pressure, which indicates that the brittleness of CSG material is more obvious with increasing cement content. The axial strain at the initial dilatancy point of CSG material with a certain cement content is also almost the same and between 0.9% and1.3%. According to the analysis in Figure 8, the relationship between failure strain \(\varepsilon_{\mathrm{m}}\) and confining pressure and the relationship between axial strain at the initial dilatancy point \(\varepsilon_{\mathrm{n}}\) and confining pressure can be expressed as follows:  
\[\varepsilon_{\mathrm{m}}=\lambda_{0}(\sigma_{3}/Pa)+d_{0}, \tag{6}\]  
\[\varepsilon_{\mathrm{n}}=\lambda_{1}(\sigma_{3}/Pa)+d_{1}, \tag{7}\]  
where \(\lambda_{0}\) and \(\lambda_{1}\) are dimensionless parameters related to the cement content and the slope of those lines; \(d_{0}\) and \(d_{1}\) are the vertical intercept and dimensionless parameters related to the cement content. Through a regression analysis of data from Figure 8, the values of \(E_{01}\) and \(n\) in Equation (6) are shown in Table 6. The values of \(E_{0}\) and \(n\) in Equation (7) can be obtained and are shown in Table 7. Values of \(\mathrm{R}^{2}\) in those tables that are greater than 0.95 indicate that the calculated results of Equations (6) and (7) can fit the experimental results well.  
The test values of \(\lambda_{1}\) and \(d_{1}\) under different cement contents are shown in Figures 11 and 12, respectively. By fitting the data of the triaxial shear test with the cement contents of 20, 40, 80, and 100 kg/m\({}^{3}\), we have  
\[\lambda_{1}=a_{1}\mathrm{e}^{-c_{1}(Cc/C_{0})}, \tag{10}\]  
\[d_{1}=l_{1}\mathrm{e}^{-m_{1}(Cc/C_{0})}+n_{1}, \tag{11}\]  
where \(a_{1}\) and \(c_{1}\) are the fitting coefficients of the relationship between \(\lambda_{1}\) and \(Cc\); \(l_{1}\), \(m_{1}\), and \(n_{1}\) are the fitting coefficients of the relationship between \(d_{1}\) and \(Cc\). The curves fitted by Equations (10) and (11) are shown in Figures 11 and 12, respectively. Values of R\({}^{2}\) that are greater than 0.98 indicate that the calculated results of Equations (10) and (11) fit the experimental results well.  
By substituting Equations (8) and (9) into Equation (6) and Equations (10) and (11) into Equation (7), we can derive the relationship between failure strain \(\varepsilon_{\mathrm{m}}\) and cement content \(Cc\) and confining pressure, and the relationship between the axial strain at the initial dilatancy point \(\varepsilon_{\mathrm{n}}\) and the cement content \(Cc\) and confining pressure as follows:  
Figure 11: The relationship between parameter \(\lambda_{1}\) and cement content \(Cc\).  
Figure 12: The relationship of parameter \(d_{1}\) and cement content \(Cc\).  
Figure 10: The relationship of the parameter \(d_{0}\) and cement content \(Cc\).  
\[\varepsilon_{\rm m}=a_{0}{\rm e}^{-c_{0}(Cc/C_{0})}(\sigma_{3}/Pa)+l_{0}{ \rm e}^{-m_{0}(Cc/C_{0})}+n_{0}, \tag{12}\] \[\varepsilon_{\rm n}=a_{1}{\rm e}^{-c_{1}(Cc/C_{0})}(\sigma_{3}/Pa)+l _{1}{\rm e}^{-m_{1}(Cc/C_{0})}+n_{1}. \tag{13}\]