## 5 Conclusions  
This study adopts the CCSDOT model with the modified SQP method and 239 groups of concrete mix proportions with tested compressive strength, accordingly, to find the nature of the influence of slag, fly ash, and limestone flour on concrete compressive strength. In addition, two application cases are analyzed for the selection of the three supplementary cementitious materials and the design of concrete mix proportion for practical engineering. The main findings of our study are as follows:  
(1) The CCSDOT model has good performance in fitting the compressive strength of 239 groups of concrete from 18 practical engineering experiments and lab reports, and the _RMSRE_ of each group is acceptable in practical engineering.  
(2) Through the calculation of numerous data by the CCSDOT model, the main parameter laws of the CCSDOT model can be obtained as follows: most of the \(ss_{FA}\) are between \(-0.568\) and \(-0.327\), while the median of \(ss_{FA}\) is \(-0.415\). The \(ss_{SL}\) are generally between \(-0.078\) and \(0.449\), while the median of \(ss_{SL}\) is \(0.078\). Most of the \(ss_{LF}\) are between \(-0.437\) and \(-0.761\), the median of \(ss_{LF}\) is \(-0.676\). Most of the \(\lambda_{SL}\) are between \(0.668\) and \(0.918\), while the median of \(\lambda_{SL}\) is \(0.788\). Most of the \(\lambda_{LF}\) are between \(0.118\) and \(0.381\) and the median is \(0.194\).  
(3) The comparison among \(ss_{FA}\) from three kinds of concrete incorporated with fly ash is demonstrated in this study. Most of the \(ss_{FA}\) (\(FA+SL\)) are smaller than the \(ss_{FA}\) (\(FA\)), while most of the \(ss_{FA}\) (\(FA\)) are smaller than the \(ss_{FA}\) (\(FA+LF\)). Meanwhile, most of the \(\lambda_{FA}\) (\(FA+SL\)) are greater than the \(\lambda_{FA}\) (\(FA+LF\)), while most of the \(\lambda_{FA}\) (\(FA+LF\)) are greater than the \(\lambda_{FA}\) (\(FA\)).  
(4) The comparison among slag, fly ash, and limestone flour indicates that most of the \(ss_{LF}\) are smaller than the \(ss_{FA}\), while most of the \(ss_{FA}\) are smaller than the \(ss_{SL}\). In the meantime, most of the \(\lambda_{LF}\) are smaller than the \(\lambda_{FA}\), while most of the \(\lambda_{FA}\) are smaller than the \(\lambda_{SL}\).  
(5) Application in the Fengman hydropower station reconstruction project demonstrates that the maximum content of fly ash in Fengman hydropower station reconstruction project can be quickly found by using the CCSDOT model. Meanwhile, the usage of slag and fly ash in the Suofengying hydropower station can also be quickly found through the CCSDOT model to meet the design and financial requirements. It is helpful to guide the design and optimization of the engineering mix proportions.  
Conceptualization, J.Z.; Data curation, J.Z.; Formal analysis, J.Z.; Funding acquisition, G.L.; Investigation, J.Z.; Methodology, J.Z.; Project administration, J.Z.; Resources, J.Z.; Software, G.L.; Supervision, J.Z.; Validation, J.Z.; Visualization, J.Z.; Writing-original draft, J.Z.; Writing-review and editing, J.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China, grant number 51979244.  
Changjiang River Scientific Research Institute and China Institute of Water Resources and Hydropower Research are greatly acknowledged for 18 practical engineering and lab reports data used in this study. Thanks are also given to [PERSON] for the assist of processing data.  
The authors declare no conflict of interest.