# Analysis of Hydration-Mechanical-Durability Properties of Metakaolin Blended Concrete
## 2 Modeling of Hydration for Metakaolin Blended Concrete
### MK Reaction Model  
Metakaolin is a highly reactive pozzolanic material which reacts with calcium hydroxide (CH). The reaction products of metakaolin include calcium silicate hydrate (CSH), C\({}_{4}\)AH\({}_{13}\), C\({}_{3}\)AH\({}_{6}\), and C\({}_{2}\)ASH\({}_{8}\)[18]. [PERSON] et al. [18] designed trimethylsilylation studies of the hydration of metakaolin-calcium hydroxide paste. Based on the relationship between the amount of consumed CH and reacted metakaolin, they found that when 1 g of metakaolin reacted, 1.6 g of calcium hydroxide was consumed, and 0.4 g of chemically combined water was produced. Therefore, the content of CH in composite concrete containing MK can be determined as below:  
\[CH(t)=RCH_{CE}*C_{0}*\alpha-v_{MK}*\alpha_{MK}*P \tag{2}\]  
where \(CH(t)\) is the calcium hydroxide content; \(RCH_{CE}\) is the produced CH when 1 unit mass cement hydrates; \(v_{MK}\) is the consumed CH when 1 unit mass of MK reacts (\(v_{MK}=1.6\)[18]); \(\alpha_{MK}\) is the reaction degree of MK, and \(P\) is the mass of MK in mix proportions. \(RCH_{CE}*C_{0}*\alpha\) represents the amount of produced CH from cement hydration, and \(v_{MK}*\alpha_{MK}*P\) is the amount of consumed CH from the MK reaction. The amount of chemically combined water \(W_{cbm}\) in the MK blended concrete is determined as follows:  
\[W_{cbm}=v*C_{0}*\alpha+0.4*P*\alpha_{MK} \tag{3}\]  
where \(v\) denotes the content of chemically combined water when 1 unit mass cement hydrates (\(v=0.25\)[16; 17]). \(v*C_{0}*\alpha\) and \(0.4*P*\alpha_{MK}\) are the contents of the chemically combined water produced from the hydration reaction of cement and pozzolanic reaction of MK, respectively [18]. The amount of capillary water \(W_{cap}\) in the MK blended concrete is calculated as follows:  
\[W_{cap}=W_{0}-0.4*C_{0}*\alpha-0.55*\alpha_{MK}*P \tag{4}\]  
where \(0.4*C_{0}*\alpha\) and \(0.55*\alpha_{MK}*P\) are the mass of capillary water consumed from the hydration reaction of cement and the pozzolanic reaction of MK, respectively [19]. \(0.4*C_{0}*\alpha\) is the summation of chemically and physically combined water from cement hydration; and \(0.55*\alpha_{MK}*P\) is the summation of chemically and physically combined water from the MK reaction [19]. [PERSON] et al. [20] experimentally studied the isothermal heat release of MK blended concrete. They reported that like cement hydration, the reaction of cement-MK blends included an initial dormant process, a chemical reaction related process, and a diffusion related process. In addition, as metakaolin is a pozzolanic material, the reaction of MK was dependent on the CH content in cement-MKblends [21]. When considering these points, similar to the cement hydration equation [16; 17], the reaction of MK can be described as follows:  
\[\frac{d\alpha_{MK}}{dt}=\frac{m_{CH}(t)}{P}\frac{3\rho_{w}}{v_{MK}r_{MK0}\rho_{ MK}}\frac{1}{\left(\frac{1}{k_{MK}}-\frac{r_{MK0}}{D_{eMK}}\right)+\frac{r_{MK0}}{D_{eMK}} \left(1-\alpha_{MK}\right)^{\frac{-1}{3}}+\frac{1}{k_{rMK}}\left(1-\alpha_{MK} \right)^{\frac{-2}{3}}} \tag{5}\]  
\[k_{dMK}=\frac{B_{MK}}{\left(\alpha_{MK}\right)^{1.5}}+C_{MK}*\left(\alpha_{MK }\right)^{3} \tag{6}\]  
\[D_{eMK}=D_{eMK0}*\ln(\frac{1}{\alpha_{MK}}) \tag{7}\]  
where \(\rho_{w}\) is the density of water; \(r_{MK0}\) denotes the MK particle radius, \(\rho_{MK}\) denotes the MK density; \(k_{dMK}\) is the reaction rate parameter in the initial dormant stage (\(B_{MK}\) and \(C_{MK}\) are reaction parameters [16; 17]); \(D_{eMK0}\) denotes the incipient diffusion parameter; and \(k_{rMK}\) denotes the reaction rate parameter in the chemical reaction related stage. In Equation (5), the term \(\frac{m_{CH}(t)}{P}\) considers the pozzolanic reaction activity of MK. Aside from the chemical effect, the addition of MK has a dilution effect on cement hydration [12]. When MK is used to partially replace cement, the water to cement ratio increases. Regarding high strength concrete--which has a low water to powder ratio--the dilution effect due to the MK addition is crucial [16; 17].