# Analysis of Hydration-Mechanical-Durability Properties of Metakaolin Blended Concrete
## 3 Property Evaluations of MK Blended Concrete
### Results and Discussion
#### 3.2.3 Strength Development of Cement-MK Blends  
The reaction products of binders fill the pore spaces of concrete. Mechanical properties such as compressive strength, develop with the progress of binder reactions. According to [PERSON] strength theory, concrete compressive strength can be calculated as follows:  
\[f_{c}(t)=Ax_{c}{{}^{n}} \tag{8}\]  
where \(f_{c}(t)\) is concrete compressive strength; \(A\) is the intrinsic strength of concrete; \(x_{c}\) is the gel-space ratio of concrete; and \(n\) is the strength exponent. The gel-space ratio denotes the volumetric ratio of the binder reaction products to the summation of the hydrated binders and capillary pore. For cement-MK blends, 1 mL of hydrated cement takes up 2.06 mL of space [22], and 1 mL of reacted MK occupies 2.52 mL of space [22]. When considering the cement hydration and MK reaction, the gel-space ratio of MK blended concrete can be calculated as:  
\[x_{c}=\frac{2.06(1/\rho_{C})\alpha C_{0}+2.52(1/\rho_{MK})\alpha_{MK}P}{(1/\rho _{C})\alpha C_{0}+(1/\rho_{MK})\alpha_{MK}P+W_{0}} \tag{9}\]  
where \(\rho_{C}\) is the density of cement. For cement-MK blends, [PERSON] et al. [3] found that as the replacement level of MK increased, so did the compressive strength. However, once the replacement level of MK exceeded 10%, the concrete compressive strength decreased. Similarly, [PERSON] and [PERSON] [8] found that when the  
Figure 4: Parameter studies of the reaction degree of binders. (**a**) reaction degree of cement; (**b**) reaction degree of MK; and (**c**) effect of specific surface on reaction degree of MK. water to binder ratios were 0.4 and 0.35, the concrete containing 12.5% MK had a higher strength than the concrete with 10% and 15%. [PERSON] and [PERSON] (2016) also reported that when the water to binder ratios were 0.27, 0.3, and 0.33, the concrete containing 10% MK showed a higher strength than the concrete with 5% and 15% MK. [PERSON] and [PERSON] (2016) found that when the water to binder ratio was 0.55, the mortar containing 10% MK showed a higher strength than the mortar with 5% and 15% MK. These findings described in References ([PERSON] et al., 2016; [PERSON] et al., 2016; [PERSON] and [PERSON], 2016) may relate to the compositions of the reaction products and the intrinsic strength of concrete. Hence, we assumed that the intrinsic strength of concrete was a parabolic function of MK replacement levels as follows:  
\[A=a1+a2*\frac{P}{C_{0}+P}+a3*\left(\frac{P}{C_{0}+P}\right)^{2} \tag{10}\]  
where \(a1\), \(a2\), and \(a3\) are strength coefficients (MPa). Based on the compressive strength of MK blended paste at different curing stages (3, 7, 28, and 90 days), the strength coefficients \(a1\), \(a2\), and \(a3\) of the strength model were determined as 164, 292, and \(-782\), respectively. The strength exponent was determined as 2.2. As shown in Figure 5, due to the high reactivity of metakaolin, the strength of MK blended paste had a higher strength than the control paste ever since the early stages. For the plain paste, the increment of strength after 28 days was marginal, which was due to the cement hydration essentially stopping after 28 days. For the MK blended paste, after 28 days, the strength continuously increased due to the contribution of the MK reaction. At both the early and late stages, the paste containing MK showed higher strength than plain paste. For the cement-MK blended pastes, the paste containing 10% MK had a higher strength than the other MK contents (5% and 20% MK). Figure 5e shows that the analysis results generally conformed to the experimental data. The correlation coefficient between the analysis results and experimental data was 0.97. Therefore, the proposed hydration-strength integrated model is useful to calculate the compressive strength development of various cement-MK blends at both early and late stages.