3.1 Orthogonal design of experiment
By designing the pretests, the particle sizes of coal aggregates were determined in ranges of ≤ 2 mm, ≤ 5 mm, and ≤ 10 mm, and the reasonable ranges of the high-water material content, cement content, and water content were ascertained. In the total mass (100%), the high-water material content, cement content, and water content remained in ranges of 3.0% ~ 6.0%, 15% ~ 25%, and 27% ~ 35%, respectively. Design of the mix proportions considered the strength and economy of the filling materials and ensured that the mechanical properties and economic benefits of the prepared samples were well balanced.
Combining with the field application of filling materials based on coal aggregates and according to actual conditions of Shuiliandong coal mine, different combinations of the proportions of high-water material, cement, and water were determined by designing the orthogonal test table when maintaining the total mass at 100%. This systematic scheme design provides more scientific and accurate guidance for preparation of the filling materials, makes the preparation of filling materials more in line with actual demand, and is convenient for further description and calculation.
The particle size of coal grains, proportion of high-water material, proportion of cement, and proportion of water were separately set as factors A, B, C, and D, and A, B, C, and D are used to indicate the four factors below (Table 6).
Table 6 Factors (designed in proportion to mass)
Levels
|
A. Particle size of coal grains
|
B. Proportion of high-water material
|
C. Proportion of cement
|
D. Proportion of water
|
1
|
0 ~ 2mm
|
3.00%
|
15.00%
|
27.00%
|
2
|
0 ~ 5mm
|
4.50%
|
20.00%
|
31.00%
|
3
|
0 ~ 10mm
|
6.00%
|
25.00%
|
35.00%
|
3.2 Ultrasonic experimental design
The temperature of the water used in the tests was controlled to about 26 ℃. After preparing the materials, they were mixed, stirred, and poured into the standard triplet mold, which was then placed on a vibrating machine to remove bubbles in the filling slurry. This improved the density of formed filling samples and the vibrated mold was put in a curing box to be set. After the samples were set to blocks and had certain strength, they were demolded and then cured in a standard curing box. The samples were taken out on the 28th day to conduct ultrasonic p-wave velocity measurements. Thereafter, the uniaxial compressive strength and uniaxial shear strength of each sample were tested and the test data are as listed in Table 2. The apparatus used in the tests included a standard triplet mold measuring 70.7 mm × 70.7 mm × 70.7 mm, a YH-60B curing box, a HICHANCE HC-U81 ultrasonic detector of concrete for testing the ultrasonic p-wave velocity, and an MTS electro-hydraulic servo-motor testing machine for measuring the strength. The test process is shown in Fig. 6. Parameters of ultrasonic detector are shown in Table 7.
Table 7 Ultrasonic tester parameter setting
Measurement point spacing (mm)
|
70.7
|
Sampling period (µs)
|
0.50
|
Ultrasonic frequency (Hz)
|
50k
|
Zero sound correction (µs)
|
12.50
|
Emission voltage (V)
|
500
|
Aggregate
|
coal
|
A substantial body of other relevant studies (Li et al. 2023; Zhang et al. 2022; Hou et al. 2021) has demonstrated that, in the testing of cohesive materials, pressure-waves exhibit faster propagation speeds and possess relatively greater penetration depth compared to SH waves and SV waves. Therefore, we selected pressure-waves as the focus of our current research.
By referring to the test method of ultrasonic wave velocity of concrete, the measurement method of the ultrasonic p-wave velocity of the filling body can be described as follows: firstly, a standard sample was placed between two probes, which were smeared with a special coupling agent. One of the probes was used as the acoustic emission source to emit a pulsed acoustic wave; the other was adopted as the acoustic receiver to capture acoustic pulses propagated back to the samples. When the acoustic waves propagated from the emission source to the sample, transmitted in the sample, and returned to the receiver, the receiver recorded the propagation time, that is, the arrival time (T). Based on the time and the long axis (L) along the height of the sample, the ultrasonic p-wave velocity in the sample is calculated thus: V = L/T.
To obtain accurate measurements, a same sample was tested for three times, during which the three arrival times were recorded. The arithmetic mean value of the three measurement results was calculated, which was regarded as the final test value of ultrasonic p-wave velocity.
Thereafter, the initial data in the ultrasonic detector were imported to a computer for post-processing. The method of measurement can be used to evaluate the propagation velocity of sound waves in filling bodies and therefore assess the performance and quality of filling bodies under different mix proportions.
3.3 Experimental data and analysis
Table 8 Summary of orthogonal test results
Test groups
|
Influencing factors
|
Test results
|
A
|
B
|
C
|
D
|
Wave velocity/ km·s-1
|
Compressive strength/ MPa
|
Shear strength/ MPa
|
1
|
2
|
3.00
|
15
|
27
|
1.826
|
2.387
|
0.537
|
2
|
2
|
4.50
|
20
|
31
|
1.873
|
2.455
|
0.748
|
3
|
2
|
6.00
|
25
|
35
|
1.891
|
0.333
|
0.135
|
4
|
5
|
3.00
|
20
|
35
|
1.596
|
1.393
|
0.484
|
5
|
5
|
4.50
|
25
|
27
|
2.357
|
5.521
|
1.388
|
6
|
5
|
6.00
|
15
|
31
|
1.790
|
1.879
|
0.565
|
7
|
10
|
3.00
|
25
|
31
|
1.922
|
2.888
|
0.591
|
8
|
10
|
4.50
|
15
|
35
|
1.886
|
1.806
|
0.281
|
9
|
10
|
6.00
|
20
|
27
|
2.190
|
3.601
|
0.690
|
Table 9 Ranged analysis of test data
Factor
|
Ultrasonic p-wave velocity/ km·s-1
|
A
|
B
|
C
|
D
|
k1
|
18.633
|
17.815
|
18.340
|
21.243
|
k2
|
19.143
|
20.384
|
18.863
|
18.616
|
k3
|
19.991
|
19.568
|
20.565
|
17.909
|
R
|
1.358
|
2.569
|
2.225
|
3.334
|
According to Table 8, the ultrasonic p-wave velocity, compressive strength, and shear strength of the coal-based paste filling materials are separately in the ranges of 1.596 to 2.357 km/s, 0.33 to 5.521 MPa, and 0.135 to 1.388 MPa. Various parameters are distributed within large ranges, indicating that various samples differ significantly in their p-wave velocity and strength.
As shown in Table 9, range analysis was performed for all test data. In range analysis, a large R value indicates the great influence of a factor on different samples. Therefore, comparison of R values in Table 9 shows that the four factors are listed in a descending order as D, B, C, and A according to their influences on the ultrasonic p-wave velocity. That is, factor D is the main factor influencing the ultrasonic p-wave velocity.