# Effects of Cement Treatment on Mechanical Properties and Microstructure of a Granite Residual Soil
## 4 Discussion  
### Prediction of UCS and Secant Modulus  
Various methods have been proposed to predict the mechanical properties of cement-treated soils, among which the unconfined compressive strength, triaxial shear strength, and tensile strength were well-linked to an adjusted porosity/cement ratio, \(\eta/(C_{\text{vi}})^{5}\)[42; 43; 44]. Figure 16: Initial void ratio, intruded void ratio, and macro-void ratio of saturated untreated and cement-treated GRSs cured to 28 d.  
Figure 15: Delimitation of macro- and micro-pores in saturated untreated GRS based on results of an intrusion–extrusion cycle. The exponent \(\xi\) was found to be a positive value smaller than unity, meaning that, for a given soil type, various strengths of the treated soil cannot be predicted based on those of the untreated one (\(C_{\rm{vi}}=0\)). According to the literature review, the strength and stiffness of soils increases with the increasing cement content and the decreasing porosity (and the decreasing \(\eta/(C_{\rm{vi}})^{\xi}\) as a result). Hence, in this study, an alternative approach using a parameter \(\eta(C_{\rm{vi}})^{\xi}\) (\(\xi>0\)) was employed to merge the gap between the treated and untreated states, allowing for a prediction of the strength and stiffness of the treated soil based on its untreated state. The term \(\eta(C_{\rm{vi}})^{\xi}\) can describe the net effects of the porosity (\(\eta\)) and cement content (\(C_{\rm{vi}}\)), and the exponent \(\xi\) adjusts the weights of the two contradictory factors. Figure 17a presents the UCS-\(\eta(C_{\rm{vi}})^{\xi}\) relationship of the saturated untreated and treated specimens in the case of \(\xi=1\). For a given curing time, the UCS of the specimens exhibited a diminished increase with the increasing \(\eta\)Cvi and an exponential correlation can be established; these exponential tendencies do not change in the case of \(\xi>1\) but become irregular in the case of \(\xi<1\). Therefore, the \(\eta\)Cvi (i.e., \(\xi=1\)) was adopted for simplicity and an exponential function was formulated to fit the testing data at each curing time:  
\[\text{UCS}(\eta,C_{\rm{vi}})\ =\ \text{UCS}(\eta,C_{\rm{vi}}=0)+\alpha_{\text{ UCS}}[1-\exp(-\eta C_{\rm{vi}}/\beta_{\text{UCS}})] \tag{1}\]  
where UCS(\(\eta,C_{\rm{vi}}=0\)) is the UCS of the untreated specimen and depends on the porosity. The \(\alpha_{\text{UCS}}\) and \(\beta_{\text{UCS}}\) describe the diminished increase of the UCS with the \(\eta\)Cvi; they depend on the curing time and take into account the effects of curing on the porosity. The UCS(\(\eta=0.4\), \(C_{\rm{vi}}=0\)) was fixed at 78 kPa for the untreated specimen based on the test results and a direct fitting of the four data sets gave \(\beta_{\text{UCS}}=(8.7\pm 0.5)\times 10^{-3}\). Given its small variation, \(\beta_{\text{UCS}}\) was fixed at \(8.7\times 10^{-3}\), independent of the curing time. The adjusted fitting is presented in Figure 17a, and the dependence of \(\alpha_{\text{UCS}}\) on the curing time is shown in Figure 17b. The \(\alpha_{\text{UCS}}\) also presents a diminished increase with the curing time and an exponential function can be formulated:  
\[\alpha_{\text{UCS}}(t)\ =\alpha_{\text{UCS}}(t=0)+\lambda_{\text{UCS}}[1-\exp(-t/ \gamma_{\text{UCS}})] \tag{2}\]  
where, \(\alpha_{\text{UCS}}(t=0)\) is the \(\alpha_{\text{UCS}}\) for the non-cured specimen. The \(\lambda_{\text{UCS}}\) and \(\gamma_{\text{UCS}}\) describe the diminished increase of \(\alpha_{\text{UCS}}\) with the curing time. The \(\alpha_{\text{UCS}}(t=0)\), \(\lambda_{\text{UCS}}\), and \(\gamma_{\text{UCS}}\) were fitted to be 341 kPa, 1412 kPa, and 12.7 d, respectively (see Figure 17b).