## 3 Results and Discussion
### Gel/Space Ratio and Compressive Strength  
Although the literature [19] presents a series of models for cement strength prediction, such as empirical relations between compressive strength and porosity, relations between strength and microstructure or pore size distribution, the much simplified and suitable model adopted in this work follows closely that of [PERSON] [18]. The compressive strength of cement paste is related to the gel/space ratio, defined as the degree to which the saturated gel (hydration products) fills the available space. In the pure cement paste, the available space is the total volume of the system (water + cement) minus the room occupied by the unhydrated cement particles. The saturated gel volume can be calculated by the degree of hydration and the specific volume of saturated gel. The pure cement paste gel/space ratio \(X\) is calculated as follows:  
\[X=\frac{\
u_{sg}\alpha_{c}}{w/c+\
u_{c}\alpha_{c}} \tag{5}\]  
where \(\
u_{sg}\) and \(\
u_{c}\) are the specific volumes of saturated gel and cement, respectively; \(\
u_{sg}\) = 0.67 and \(\
u_{c}\) = 0.32, according to the literature [20,21]; \(w/c\) is the water-to-cement ratio; \(\alpha_{c}\) is the reaction degree of the cement. Therefore, the relationship between gel/space ratio \(X\) of cement paste and the hydration degree of cement can be expressed as:  
\[X=\frac{0.67\alpha_{c}}{w/c+0.32\alpha_{c}} \tag{6}\]  
It can be seen from Figure 3 that the initial setting time of the cement paste occurs when the gel/space ratio is 0.09 \(\pm\) 0.02, and the final setting time appears when the gel/space ratio is 0.15 \(\pm\) 0.02. Referring to the results of the previous first-order derivative of the NMR signal intensity in Figure 1, it is known that the initial and final setting takes place during the acceleration stage. At this stage, the hydration rate is accelerated, a large amount of hydration products is formed, and the gel/space ratio is also rapidly increased. The results indicate that the initial and final setting is precisely attributed to the gel/space ratio reaching a certain threshold. Figure 2: Hydration degree during the hydration process. [PERSON] [18] proposed the concept of the gel/space ratio, and a typical relationship was then identified between the gel/space ratio and the compressive strength, making it possible to connect the microscopic evolution and the macroscopic properties of cement pastes. It is worth mentioning that [PERSON] law was obtained by fitting the compressive strength vs. gel/space ratio for cement-sand mortars. Since the strength of sand is constant, the gel/space ratio is the dominant variable, the increase in strength is mainly due to the cement paste of the increased gel/space ratio. Therefore, [PERSON] model is more sensible for describing the relationship between compressive strength and the gel/space ratio for cement paste, which can be expressed by the following formula:  
\[\sigma_{\mathrm{C}}=AX^{n} \tag{7}\]  
where \(\sigma_{c}\) is the compressive strength; \(A\) is a constant, indicating the intrinsic strength of the gel, approximately the theoretical strength of the gel when the gel/space ratio \(X=1\); \(n\) is a fitting parameter. It can be seen from Figure 4 that the measured compressive strength of the cement paste of the three water-to-cement ratios has a good correlation with the calculated gel/space ratio based on the nuclear magnetic signal intensity. It is in a power function relationship and conforms to the [PERSON] model. In this experiment, the value of \(A\) is 425 MPa, the value of \(n\) ranges between 2.97 and 3.12. Lower water-to-cement ratio results in a larger value of \(n\). Figure 4: Relationship between the measured compressive strength and gel/space ratio. Figure 3: Gel/space ratio during the hydration process. Standard Vicat needle method is time-consuming, discontinuous, while the conventional strength test is destructive, and difficult to test at a very early age due to low rigidity.