## 3 Experimental Analysis of Steam Curing and Orthogonal Matching Ratio
### Orthogonal Experiment Mix Proportion Design
#### 3.3.2 Extreme Value Analysis  
By calculating the total compressive strength of the specimens at each level of coal gangue content (denoted as M\({}_{1}\), M\({}_{2}\), and M\({}_{3}\)), a preliminary assessment of the influence of different content levels on concrete strength can be made. The corresponding average strength values (m\({}_{1}\), m\({}_{2}\), and m\({}_{3}\)) are then determined, and the range (R) is calculated to quantify the influence of each factor on strength. In this experiment, coal gangue content (Factor A), maximum aggregate particle size (Factor B), and additional water content (Factor C) were set as independent variables, while the average compressive strength at each factor level (K value) served as the dependent variable. Range analysis was conducted, and the relationship between each factor and its effect on compressive strength are summarized in Table 16. The range analysis results for specimen compressive strength are presented in Table 17.  
Based on the range analysis results, the optimal factor combinations for compressive strength at each curing age are as follows: 3 days (A\({}_{1}\)-B\({}_{3}\)-C\({}_{1}\)), 7 days (A\({}_{1}\)-B\({}_{1}\)-C\({}_{1}\)), 14 days (A\({}_{1}\)-B\({}_{3}\)-C\({}_{1}\)), and 28 days (A\({}_{1}\)-B\({}_{2}\)-C\({}_{1}\)). The ranking of factor importance influencing compressive strength at different ages is as follows: coal gangue content > additional water content  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Time/Indicator** & **k\({}_{1}\)** & **k\({}_{2}\)** & **k\({}_{3}\)** & **k\({}_{1}\)** & **k\({}_{2}\)** & **k\({}_{3}\)** & **k\({}_{1}\)** & **k\({}_{2}\)** & **k\({}_{3}\)** \\ \hline
3 d & 17.52 & 15.62 & 13.37 & 15.4 & 15.52 & 15.59 & 16.34 & 14.62 & 15.55 \\
7 d & 24.46 & 22.56 & 20.39 & 22.56 & 22.34 & 22.51 & 23.52 & 21.55 & 22.33 \\
14 d & 28.40 & 26.48 & 24.03 & 26.12 & 26.35 & 26.43 & 27.33 & 25.12 & 26.45 \\
28 d & 31.34 & 28.88 & 25.37 & 28.45 & 28.70 & 28.44 & 29.67 & 27.41 & 28.51 \\ \hline \hline \end{tabular}
\end{table}
Table 16: Compressive strength as a function of different indicators.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time/Indicator (R)** & **A** & **B** & **C** \\ \hline
3 d & 4.15 & 0.19 & 1.72 \\ optimal combination & & A\({}_{1}\), B\({}_{3}\), C\({}_{1}\) & \\
7 d & 4.07 & 0.22 & 1.97 \\ optimal combination & & A\({}_{1}\), B\({}_{1}\), C\({}_{1}\) & \\
14 d & 4.37 & 0.31 & 2.21 \\ optimal combination & & A\({}_{1}\), B\({}_{3}\), C\({}_{1}\) & \\
28 d & 5.97 & 0.26 & 2.26 \\ optimal combination & & A\({}_{1}\), B\({}_{2}\), C\({}_{1}\) & \\ order of priority & & A \(>\) C \(>\) B & \\ \hline \hline \end{tabular}
\end{table}
Table 17: Test specimen strength extreme value analysis table.  
Figure 6: Compressive strength variation with different orthogonal levels.  
\(>\) maximum aggregate particle size. Across all curing ages, the optimal coal gangue content level is A\({}_{1}\) (20%), and the optimal additional water content level is consistently C\({}_{1}\) (70% of saturated water absorption capacity). For maximum aggregate particle size, the optimal level is B\({}_{3}\) (20 mm) at 3 and 14 days, B\({}_{1}\) (10 mm) at 7 days, and B\({}_{2}\) (16 mm) at 28 days. Considering overall performance across all curing ages, B\({}_{3}\) (20 mm) is recommended as the optimal level for maximum aggregate particle size.  
In summary, based on the results of the range analysis, the optimal mix design parameters for coal gangue concrete under the specified experimental conditions are as follows: a coal gangue content of 20%, a maximum aggregate particle size of 20 mm, and an additional water content of 70%.