## 3 Strength Characterization
### Effect of Slurry Concentration on the Strength of the Cemented Backfill  
The slurry concentration represents the percentage of the total mass of solids in the filling slurry. The effect of slurry concentration on the strength of the cemented backfill was plotted based on the test data. Figure 6a-c illustrate the variation in the strength with the mass concentration of the slurry for the same cement-sand ratio. Through measurement of the strength of the cemented backfill at 3, 7, and 28 days, we found that the strength of the filler was more influenced by the concentration of the slurry when the cement-sand ratio was kept constant at these three stages. The coefficient of fit \begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{**Curing Age**} & \multirow{2}{*}{**Type of Fit**} & \multicolumn{6}{c}{**Slurry Consistency**} \\ \cline{3-8}  & & **68\%** & **69\%** & **70\%** & **71\%** & **72\%** & **Average** \\ \hline
3 & exponential & 0.99 & 0.98 & 0.99 & 0.97 & 0.99 & 0.984 \\
7 & exponential & 0.97 & 0.95 & 0.95 & 0.98 & 0.98 & 0.966 \\
28 & exponential & 0.97 & 0.97 & 0.99 & 0.99 & 0.96 & 0.976 \\ \hline \end{tabular}
\end{table} 
Table 7: Correlation coefficient values (R\({}^{2}\) values) between the cement-sand ratio and cemented backfill strength. Figure 6: Effect of slurry concentration on the strength of cemented backfill. (**a**) Cement-sand ratio of 1:3. (**b**) Cement-sand ratio of 1:4. (**c**) Cement-sand ratio of 1:5. (R\({}^{2}\)) for this strength variation law was obtained using function fitting. Table 8 suggests that R\({}^{2}\) is larger than 0.95, which demonstrates that the exponential function can more accurately reflect the relationship between the slurry concentration and the UCS of the filling body. Figure 6a-c depict the relationship between the strength of the filler and the mass concentration of the slurry for a given condition. The corresponding fitted curves are obtained by the fitting method, and the fitting coefficients are derived accordingly. It can be observed from the graphs that the strength increases as a significant exponential function with the increase in slurry concentration. This indicates that under the same conditions, the strength of the cemented backfill varies considerably with the slurry concentration. At a given addition of the cemented backfill, the compressive strength increases with increasing concentration of the filler slurry because of the following reasons:  
* As the concentration of the slurry increases, differences in the settling rates of the various particle sizes will lead to the occurrence of segregation in the slurry. However, as the concentration of the slurry increases, this difference will disappear, and eventually, a complete mix will be formed and the particle distribution of the cemented backfill will become more balanced. As a result of the reduced cement loss, the quality of the filler will be greatly improved and the compressive strength of the filler will increase [24]. * As the concentration of the slurry increases, it will possess a higher viscosity, which will effectively inhibit the precipitation of coarse particles, and as the water in the slurry decreases, the rate of precipitation will slow down accordingly, which will substantially improve the delamination phenomenon caused by uneven particle distribution and will further enhance the structural stability of the filler [25]. * When the filler is dewatered, the fine mud and cement will be mixed to fill the pores in the tailing, which will result in the formation of a more compact particle structure and also will lead to the expansion of the contact surface of the particles [26]. This will greatly improve the structure of the tailing particles and cause the strength of the filler to considerably improve. Figure 7 shows the failure morphology of specimens with a cement-sand ratio of 1:3 after 7 days of curing. As shown in the figure, the failure modes of specimens vary significantly with different slurry concentrations.