# Study on Slump and Compressive Strength of Gangue Based on Aggregate Size Gradation
## 4 Experimental Results and Analysis
### Analysis of Compressive Strength Results of Aggregate Size Gradation  
Figure 7 shows the experimental results of compressive strength of filling paste test blocks at ages of 1 d, 3 d, 7 d, and 28 d.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Paste Type** & \(\mathbf{a_{1}}\) & \(\mathbf{b_{1}}\) & \(\mathbf{R^{2}}\) & \(\mathbf{p}\) \\ \hline Coarse–fine aggregate ratio 7:3 & \(-11.95\) & \(1184.7\) & \(0.98\) & \(1.353\times 10^{-4}\) \\ Coarse–fine aggregate ratio 6:4 & \(-9.55\) & \(1012.7\) & \(0.99\) & \(1.345\times 10^{-2}\) \\ Coarse–fine aggregate ratio 5:5 & \(-8.45\) & \(884.7\) & \(0.99\) & \(4.989\times 10^{-5}\) \\ Coarse–fine aggregate ratio 4:6 & \(-7.4\) & \(793.9\) & \(0.99\) & \(2.712\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Linear fitting parameters of slump–mass fraction curve.  
Figure 6: Relationship between slump and mass fraction.  
The compressive strength of the filling paste is a key factor in determining its stability. As shown in Figure 7, with a decrease in coarse aggregate and an increase in fine aggregate, the compressive strength of the filling paste test blocks at different ages increased. First, the voids within the paste were reduced when the amount of fine aggregate was increased. This leads to an increase in the cohesion and viscosity of the paste, ultimately resulting in an increase in its yield stress. Second, when the ratio of coarse aggregate to fine aggregate ranges from 7:3 to 5:5, the skeleton structure of the paste transitions from a framework-pore structure to a framework-dense structure, as shown in Figure 8a,b. This structure is formed because the gangue auxiliary material is adsorbed around the fine aggregate, which is then surrounded by the coarse aggregate. Coarse aggregates interlock with each other, creating a relatively stable spatial skeleton. When the ratio of coarse aggregate changed from 5:5 to 6:4, the yield stress of the paste test block decreased. This is because the proportion of coarse aggregates is reduced, and the proportion of fine aggregates increases. As a result, the internal structure of the paste changed from a framework-dense structure to a suspension-dense structure, as shown in Figure 8c.  
Figure 8: Structure diagram of gangue paste backfill [27]. (**a**) Framework–pore structure, Ratio 7:3 and 6:4; (**b**) framework–dense structure, Ratio 5:5; (**c**) suspend–dense structure, Ratio 4:6.  
Figure 7: Compressive strength of filling paste test blocks at different ages.  
The model is suitable for filling paste slurries with different aggregate size gradations that are mixed with water and cement. In this study, only four pastes with different aggregate size ratios are compared. Therefore, it is necessary to conduct slump and compressive strength tests on filling pastes of various particle size gradations. This will help verify the suitability of the model and determine the range of constant terms for predicting the yield stress in pastes with different particle size gradations. These empirical parameters are valuable for practical application. In addition, it is necessary to study the influence of the binder on the parameters of the model to further optimize the parameter model.