# Effect Mechanism of Material Ratio on Ultrasonic P-wave Velocity in Coal Based Paste Fill Materials
## 3 Orthogonal Test Schemes and Test Results
### Ultrasonic Experimental Design  
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 the 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 [40].  
The water temperature for the tests was regulated to approximately 26 \({}^{\circ}\)C. The materials, once prepared, were blended, agitated, and decanted into the standard triplet mold. This was followed by placing the mold on a vibrator to extricate air from the slurry, enhancing the density of the resultant fill samples. After setting in the mold and reaching an initial solidity, the samples were demolded and placed in a standard curing box. On the 28 th day, the samples were extracted for the measurement of ultrasonic p-wave velocity, as referenced in [41; 42]. Following this, the uniaxial compressive and shear strengths were tested, with the data recorded in Table 2. The equipment utilized in these tests included a standard triplet mold with dimensions of 70.7 mm \(\times\) 70.7 mm \(\times\) 70.7 mm, a curing box (model YH-60B), a HICHANCE HC-U81 ultrasonic concrete detector (Tianjin Kean Instrument Technology Co., Ltd., Tianjin, China), and an MTS electro-hydraulic servo testing machine (Shandong Wanchen testing machine Co., Ltd., Jinan, China) for strength assessment. Figure 6 illustrates the testing process, while Table 9 details the parameters of the ultrasonic detector.  
Relevant literature [27; 28; 29] has confirmed that pressure waves, when tested on cohesive materials, travel more rapidly and penetrate more deeply than SH and SV waves, leading to the selection of pressure waves for the focus of this research.  
The procedure for measuring the ultrasonic p-wave velocity of the fill bodies was adapted from the test method used for concrete. It consisted of placing a standard specimen between two transducers coated with a coupling agent. One transducer acts as the transmitter of the acoustic pulse, while the other serves as the receiver. The receiver documents the time taken for the waves to travel from the transmitter, through the specimen, and back to the receiver, denoted as the arrival time (\(T\)). The ultrasonic p-wave velocity (\(V\)) within the specimen is then calculated using the formula \(V=L/T\), where \(L\) is the long axis of the sample.  
Figure 6: Ultrasonic p-wave velocity measurement of specimens.  
\begin{table}
\begin{tabular}{c c c} \hline Measurement point spacing (mm) & 70.7 & Sampling period (\(\upmu\)s) & 0.50 \\ Ultrasonic frequency (Hz) & 50 k & Zero sound correction (\(\upmu\)s) & 12.50 \\ Emission voltage (V) & 500 & Aggregate & coal \\ \hline \end{tabular}
\end{table}
Table 9: Ultrasonic tester parameter setting.  
For precise results, each sample underwent three tests, recording the arrival time for each. The arithmetic mean of these three results was computed and taken as the final ultrasonic p-wave velocity.  
The initial readings from the ultrasonic detector were then processed on a computer. This measurement method is instrumental in evaluating the sound wave propagation speed through the fill bodies to assess the quality and performance of the materials under different mixing ratios.