# Particle Packing Optimization for CCR-GGBS-FA Binder Stone Waste pavement Base Material
## 4 Discussion and Conclusions  
In this study, the applicability of the most-compact stacking theory for stone wastes was determined, and a grading design method, i.e., the MAA-SW model, applicable to stone wastes was constructed. Initially, seven groups of granular graded stone wastes were designed, and the test group with the highest density was selected to control the CGF dosing of 10% and the water/cement ratio of 1.0. Subsequently, based on the response surface design methodology, 2 mm sieve pass rate (\(X_{1}\)), 0.075 mm sieve pass rate (\(X_{2}\)), and 0.005 mm sieve pass rate (\(X_{3}\)) were identified as the three influencing factors, and the unconfined compressive strengths of the specimens at 7 and 28 d (\(Y_{7}\), \(Y_{28}\)) were selected as the two response values. A second-order equation was fitted, and the test results were analyzed using ANOVA. The following conclusions are obtained:  
(1) According to the ANOVA results, \(X_{1}\), \(X_{2}\), and \(X_{3}\) all play an important role in the 7 and 28 d unconfined compressive strengths of the solidified rock waste specimens; \(X_{1}\) and \(X_{2}\) significantly affect the unconfined compressive strength of the solidified rock waste specimens at 7 d, whereas it is \(X_{1}\) and \(X_{3}\) that have a significant effect at 28 d.  
(2) Second-order equations were fitted to the response surface test data to derive the strength prediction equations between 2 mm sieve pass (\(X_{1}\)), 0.075 mm sieve pass (\(X_{2}\)), and 0.005 mm sieve pass (\(X_{3}\)) rates and the unconfined compressive strengths of the specimens at 7 and 28 d (\(Y_{7}\), \(Y_{28}\)); the strength prediction formulas were derived when \(X_{1}\), \(X_{2}\), and \(X_{3}\) were 85.4, 36.6, and 16.5, respectively. The solidified rock waste specimen has the greatest strength, and the predicted 7 and 28 d unconfined compressive strengths are 6383 and 8907 kPa, respectively, while the error between the predicted and actual values is small. Compared with the CGF solidified rock waste material, the 28 d unconfined compressive strength of the optimized graded specimen was improved by about 2.1 MPa, which was about 29.8% higher, and it was about 2.6 MPa higher than the strength of the cemented solidified rock waste material, with the strength being improved by about 39.3%.  
Z.W.: conceptualization, data curation, formal analysis, writing--original draft and editing, visualization, and investigation. J.Y.: funding acquisition, writing--review and editing, data curation, and investigation. Y.W.: writing--review and editing, data curation, and investigation. Y.W.: writing--review and investigation. All authors have read and agreed to the published version of the manuscript.  
This study is supported by the National Natural Science Foundation of China (Grant Nos. 52378380, 52078474, and 51779235).  
Not applicable.  
The data presented in this study are available from the corresponding author upon request. The data are not publicly available due to the confidentiality of the research subject.  
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.