# Study on Hydration Heat Release Model and Its Influence Coefficient of Addition Concrete
## 4 Modeling of Heat of Hydration of Mineral Admixture Concrete
### Data Fitting to Solve the Hydration Exothermic Model for Impact Coefficients  
The temperature curves of the concrete test block mixed with two additions and the conventional concrete test block were obtained, as shown in Figure 7. It can be seen from the figure that the maximum temperature of the core part of the concrete decreases significantly after the two additions, which indicates that different combinations of double additions have a certain effect on reducing the temperature of the concrete during aging. Different combinations of double-doped additions have different effects on the temperature of concrete. According to the experimental analysis, F20S0L20K0 is the concrete specimen with the lowest heat release. Therefore, taking F20S0L20K0 as an example, the above finite element analysis method of the hydration exotherm was used to continuously adjust the influence coefficients \(a\) and \(b\) of the composite exponential hydration exotherm model in the subroutine. The iterative adjustment of the coefficients was performed such that the temperature curve of the model is constantly in good alignment with the measured temperature curve of F20S0L20K0, and thus, the hydration exotherm model of F20S0L20K0 evolved. Table 4 shows the adjustment coefficients of the heat of hydration and the total amount of heat of hydration of concrete with different additions according to Equation (5). Total heat of hydration (\(Q_{0}\)) of F20S0L20K0 is 270.5 kJ/kg. Figure 8 shows the process of fitting the influence coefficient of the composite exponential hydration exothermic model of F20S0L20K0. Initially, the model impact coefficients \(a\) and \(b\) are set to the same impact coefficients as in the F0S0L0K0 model, and \(Q_{0}\) is set to 270.5 kJ/kg. Post simulation curves are presented in Figure 8a, and it can be observed that the simulated values have deviated away from the measured value, and there is a need to \"squash\" the simulated curves. According to the sensitivity analysis law, the values of the impact coefficients \(a\) and \(b\) are adjusted to 0.59 and 0.66, respectively, and the numerical simulations are repeated. From Figure 8b it can be observed that the simulation curve is in close alignment with the measured curve. The influence coefficients \(a\) and \(b\) are repeatedly \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Heat of** & **Total** & & **Heat of** & **Total** \\
**Specimen** & **Hydration** & **Exothermic** & **Specimen** & **Hydration** & **Exothermic** \\
**Number** & **Adjustment** & **Hydration Q\({}_{0}\)** & **Number** & **Adjustment** & **Hydration Q\({}_{0}\)** \\  & **Factor \(k\)** & **(kJ/kg)** & & **Factor \(k\)** & **(kJ/kg)** \\ \hline F0S0L0K0 & 1 & 330.0 & F15S12.5L12.5K0 & 0.87 & 287.0 \\ F20S20L0K0 & 0.88 & 290.4 & F15S0L12.5K12.5 & 0.92 & 303.6 \\ F20S0L20K0 & 0.82 & 270.5 & F15S12.5L0K12.5 & 0.95 & 313.5 \\ F20S0L0K20 & 0.92 & 303.6 & F10S10L10K10 & 0.91 & 300.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Heat of hydration of concrete with different additions. Figure 7: Temperature curve of a concrete test block mixed with two additions. adjusted so that the simulation curve and the measured curve gradually approach the final curve, as shown in Figure 8f, at which point both curves nearly overlap. This approximates the composite exponential hydration exothermic model for F20S0L20K0 with influence coefficients \(a\) and \(b\) equal to 0.52 and 0.62, respectively. Therefore, the hydration exothermic model for F20S0L20K0 can be expressed as follows: \(Q(t)=270.5-\left(1-e^{-0.52\mu\delta\epsilon^{2}}\right)\). Figure 8: Fitting the exothermic model of hydration for solving F20S0L20K0 influence coefficients. (**a**) Commissioning impact factor 1. (**b**) Commissioning impact factor 2. (**c**) Commissioning impact factor 3. (**d**) Commissioning impact factor 4. (**e**) Commissioning impact factor 5. (**f**) Commissioning impact factor 6.