# Effect Mechanism of Material Ratio on Ultrasonic P-wave Velocity in Coal Based Paste Fill Materials
## 7 Conclusions  
The process of working with coal based cemented backfill materials involved steps of weighing, mixing, and transferring the homogenized mixture into molds. Prior to this transfer, a lubricating liquid was applied to the mold's inner layer to aid in the specimen's release.  
Correlation analysis demonstrated a robust positive relationship between wave velocity and compressive strength, with a correlation coefficient of 0.87. A similar positive correlation was found with shear strength, measured by a correlation coefficient of 0.65. The descending order of factors affecting ultrasonic p-wave velocity, as shown by ANOVA results, was P\({}_{\rm D}\), P\({}_{\rm B}\), P\({}_{\rm C}\), and P\({}_{\rm A}\), highlighting water content and coal particle size as key influencing factors.  
The ultrasonic p-wave velocity's mathematical relationships with factors P\({}_{\rm A}\), P\({}_{\rm B}\), P\({}_{\rm C}\), and P\({}_{\rm D}\) were quantified and fitted. Factor P\({}_{\rm B}\) was associated with a quadratic polynomial relationship, whereas factors P\({}_{\rm A}\), P\({}_{\rm C}\), and P\({}_{\rm D}\) were linked to exponential relationships. The established comprehensive predictive model, based on the multiple regression equation, yielded ultrasonic p-wave velocity data with an average error of 4.915% when compared to empirical test data.  
Ultrasonic waves are commonly used in various applications such as non-destructive testing and flaw detection of concrete components in engineering. The propagation characteristics of p-waves in ultrasonic waves are applied to analyze cracks in concrete components based on received wave data. By using this principle, similar experiments were conducted on coal based filling materials to investigate the variation of wave velocity in coal based filling materials using ultrasonic waves. This study serves as a theoretical foundation for future underground applications.  
Conceptualization, B.A. Resources, B.A. Writing--original draft, C.C. Writing--review and editing, B.A., J.S. and C.C. Investigation, C.C., J.R. and J.L. Formal analysis, C.C., J.R. and J.W. Funding acquisition, B.A. and J.L. Data curation, J.S., C.C. and J.W. Supervision, B.A. and J.L. Validation, J.S., W.B. and 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 [52274117 and 52274080], the Excellent Youth Fund of the Education Department of Hunan Province [Grant No. 21B0487], the Xinjiang Key Research and Development Special Project (No. 2022B03028-3, 2023B03009-1) and the Natural Science Foundation of Jiangsu Province (No. BK20210499).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
Authors [PERSON] and [PERSON] were employed by the company Binxian Shuiliandong Coal Mine Co., Ltd. Author [PERSON] was employed by the company Shandong Energy Group Northwest Mining Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.