## 5 Conclusions  
The goal of this investigation is to measure the influence of the amount of quartz powder substitution on various properties of concrete (i.e., hydration heat, strength, hydration products, and electrical resistivity). We conducted a series of micro- and macro-experimental studies and created a numerical hydration model of binary mixtures of quartz powder and cement. The substitution rates of the quartz powder were 0% (Qu0), 7.5% (Qu7.5), and 15% (Qu15). The main conclusions are as follows:  
Figure 12: Prediction of strength development using the proposed model: (**a**) heat normalized by cement mass; (**b**) heat normalized by cement-plus-quartz mass; (**c**) relationship between strength and hydration heat.  
In the early stage of the hydration reaction (the first three days), as the amount of quartz powder substitution increased, the cumulative hydration heat also increased. This is mainly because the nucleation effect of quartz powder accelerated the hydration reaction of cement. In the later stage of the hydration reaction (about seven days), as the amount of quartz powder substitution increased, the cumulative hydration heat decreased. This is mainly due to the diluting effect of quartz powder.
2. For Qu0, Qu7.5, and Qu15, the 1-day compressive strength values were 13.6, 11.84, and 10.81 MPa, respectively, and the reduction in compressive strength was not obvious. The compressive strengths at 28 days were 54.82, 46.11, and 41.55 MPa, respectively. Compared with that at Day 1, the compressive strength at 28 days decreased more obviously.
3. Overall, there was an exponential relationship between the measurement results for UPV and compressive strength at 1, 3, 7, and 28 days. There was also an exponential relationship between the measurement results for resistivity and compressive strength at 1, 3, 7, and 28 days.
4. The XRD test results showed that the main products of the reaction were AFt, CH, Hc, and Mc. From Day 1 to Day 28, the AFt content became insignificant because of the transition from AFt to AFm. In addition, from 1 day to 28 days, the Mc content became obvious because, compared with Hc, Mc has a better chemical stability.
5. The TG test results showed that the mass loss decreased as the amount of quartz powder substitution increased. From 1 day to 28 days, the amount of mass loss increased. This is because the increase in hydration products resulted in the generation of more chemically bound water. As the amount of quartz powder substitution increased, the hydration product content decreased.
6. For different specimens (Qu0, Qu7.5, and Qu15) at different test times (3 and 28 days), there was an exponential function relationship between chemically bound water and strength. The correlation coefficient between the test and regression results was 0.98.
7. A numerical hydration model was proposed for cement-quartz binary blends. The parameters of the hydration model were determined based on hydration heat normalized by cement mass. Moreover, the hydration heat at 28 days was calculated using the proposed model. The strength development of all specimens and all test periods can be expressed as an exponential function of the hydration heat. The coefficient of determination of the regression was 0.9163.  
G.-Y.Z.: investigation, data curation, writing--original draft. S.O.: data curation, investigation. C.L.: data curation, investigation. Y.H.: investigation, data curation. R.-S.L.: data curation, investigation. X.-Y.W.: supervision, methodology, funding acquisition. All authors have read and agreed to the published version of the manuscript.  
This work was supported by a National Research Foundation of Korea grant funded by the Korean government (MSIT) (No. RS-2023-00208720).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.