# Experimental Research into the Ultrasonic P-Wave Velocity of Coal Slime Based Backfill Material
## 7 Conclusions  
(i) Orthogonal tests of the ultrasonic p-wave velocity were conducted on four factors including the mass concentration of coal slime, content of high-water-content material, cement content, and content of fly ash that were set at three levels using the orthogonal test method. Afterwards, analysis shows that the ultrasonic p-wave velocity of the coal slime based backfill materials is in the range of 3.916-8.319 km/s.  
(ii) The wave velocity was found to have a positive correlation with compressive strength, with a correlation coefficient of 0.87. It also exhibited a positive correlation with  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**The Specimen Number** & **A. Mass** & **B. Content of** & \\
**Number** & **Concentration of Coal Slime** & **High-Water-Content Material** & **C. Cement Content** & **D. Content of Fly Ash** \\ \hline C1 & 0.35 & 0.037 & 0.06 & 0.10 \\ C2 & 0.31 & 0.039 & 0.07 & 0.11 \\ C3 & 0.32 & 0.041 & 0.10 & 0.05 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Design of verification schemes.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**The Specimen Number** & **Materials** & **Wave Velocity/km\(\cdot\)s\({}^{-1}\)** \\ \hline \multirow{3}{*}{C1} & Predicted value & 4.133 \\  & Experimental value & 4.324 \\  & Error/\% & 4.413\% \\ \hline \multirow{3}{*}{C2} & Predicted value & 3.965 \\  & Experimental value & 4.231 \\  & Error/\% & 6.270\% \\ \hline \multirow{3}{*}{C3} & Predicted value & 3.891 \\  & Experimental value & 4.051 \\ \cline{1-1}  & Error/\% & 3.950\% \\ \hline \hline \end{tabular} Analysis unveils that the parameters calculated using the synthetic forecasting model conform well to the test values. The relative errors of various indices are in a range of 4% to 6%, with an average value of 4.878%.  
\end{table}
Table 14: Analysis of verification results.  
shear strength, with a correlation coefficient of 0.65. Various factors are listed in descending order as A, D, B, and C according to their influences on the ultrasonic p-wave velocity, suggesting that the mass concentration of coal slime and content of fly ash are main factors influencing the ultrasonic p-wave velocity.  
(iii) The mathematical relationships of factors A, B, C, and D with the ultrasonic p-wave velocity were fitted. The wave velocity has a quadratic polynomial relationship with factor A while being governed by exponential relationships with factors B, C, and D. The synthetic forecasting model was obtained through the multiple regression equation, and the ultrasonic p-wave velocity calculated thereby has an average error of 4.878% with the test data.  
Supervision, B.A. and J.R.; Conceptualization, B.A.; Resources, B.A.; Writing--original draft, C.C.; Writing--review and editing, B.A. and J.W.; Formal analysis, C.C. and D.W.; Investigation, C.C., D.W. and Q.Y.; Funding acquisition, B.A. and J.R.; Data curation, D.W. and C.C.; Validation, J.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (NO. 52274117 and NO. 52174128).  
Not applicable.  
The authors declare no conflict of interest.