# Particle Packing Optimization for CCR-GGBS-FA Binder Stone Waste pavement Base Material
## 3 Design and Optimization of a Stone Waste Gradation Method Based on Response Surface Methodology  
### Response Surface Methodology  
Compared with the orthogonal test method commonly used at present, the response surface method can obtain the function expression between the influencing factors and the response value in order to obtain the optimal combination between the influencing factors and the optimal solution of the response value. Moreover, when the test factor level values are higher, if an orthogonal test is used, a large number of tests need to be carried out, which is cumbersome. Response surface methodology has been widely used in many fields because of the small number of tests required and the high precision of prediction; this method was first used for the fitting of physical tests. In recent years, the response \begin{table}
\begin{tabular}{c c c} \hline \hline \(\lambda\) & **Mass of Sample/g** & \(\gamma\)_d_(max)/(g/cm\({}^{3}\))** \\ \hline
0.14 & 377.64 & 1.515 \\
0.17 & 381.53 & 1.531 \\
0.20 & 391.34 & 1.570 \\
0.23 & 398.32 & 1.598 \\
0.26 & 397.26 & 1.594 \\
0.29 & 387.93 & 1.556 \\
0.32 & 384.35 & 1.542 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test results of stone waste density. Figure 7: Stone waste particle gradation design. surface method has become an optimization theory method that is widely used in China and abroad in the fields of medicine, chemistry, environment, materials, and others. Since CGF stone waste is a brand-new gelling system, the influences of CGF gelling materials, water, etc., were not considered in this study, and the value of \(\lambda\) was not continuous. Therefore, the results obtained based on the theory of closest stacking contain errors that must be further calculated and analyzed. The results indicate that \(\lambda\) = 0.23, \(P(2)\) = 80%, \(P(0.075)\) = 33%, and \(P(0.005)\) = 13%, which means that the 2 mm, 0.075 mm, and 0.005 mm sieve pass rates of the stone waste material are 80%, 33%, and 13%, respectively. Moreover, the stone debris accounted for 67% of the waste material (of which 20% consisted of 2-4.75 mm and 0.075-2 mm particles, and 13% consisted of the stone waste material), stone chips of 0.075-2 mm accounted for 47%, fine stone powder accounted for 20%, and ultrafine stone powder accounted for 13%. CGF was added to the optimized stone waste materials to investigate the mechanical property changes in the optimized CGF stone waste-cured specimens. Based on the considerations of engineering economy and applicability, the dosage of CGF was set to be 10%. During an indoor test conducted in a previous study, it was determined that the specimens were better formed when the water/cement ratio was 1.0; therefore, the test was set to have a water/cement ratio of 1.0. Response surface design was used to optimize the stone waste gradation method by including a wider range of values and fitting the second-order equation. In this test, the Box-Behnken design response surface method was selected for optimization of the stone waste gradation design, and subsequently, a three-factor, three-level experimental design was adopted, with the three influencing factors set to be 2 mm, 0.075 mm, and 0.005 mm sieve pass rates, represented by \(X_{1}\), \(X_{2}\), and \(X_{3}\), respectively, and with the specimens' unconfined 7 and 28 d compressive strengths as the two response values, denoted by \(Y_{7}\) and \(Y_{28}\), respectively. Since the relationship between the three influencing factors and the response values in this test is not linear, a higher-order polynomial, i.e., a second-order equation, is required. \(P(2)\) = 80%, \(P(0.075)\) = 33%, and \(P(0.005)\) = 13% were used as the centroids of \(X_{1}\), \(X_{2}\), and \(X_{3}\), respectively, and the ranges of variation, \(X_{1}\), \(X_{2}\), and \(X_{3}\), were set at 70-90%, 23-43%, and 8-18%, respectively. The three levels of the influencing factors were coded as \(-1\) (low), 0 (medium), and +1 (high).