2.2. Experimental Equipment and Strength Calculation Method
The equipment used in this experiment mainly includes C64.106/1000 kN electro-hydraulic servo universal testing machine (Figure 2
) and C-CAST experimental system (Figure 3
). Figure 3
a,b show the physical diagram and 3D structure diagram of C-CAST system, respectively. The C-CAST system is mainly composed of the top adapter, the bottom adapter, the limiting groove and the connecting components. The top and bottom adapters have the same structure and are symmetrically arranged in the experiment, consisting of the base and the locating dial [40
]. The experimental system can realize the inclined loading of coal and rock samples, with an inclination range of 0°–30° and an interval of 5°.
The installation process of the experimental system can be divided into four steps. Firstly, the upper and lower locating dials are rotated to the specified angle according to the experimental requirements, and fixed on the corresponding adapter by bolts; secondly, the prefabricated standard coal samples are placed in the circular groove (the design depth is 10 mm) of the locating dial, and then the supporting accessories are installed into the limiting groove to prevent the slippage extrusion failure; thirdly, the top adapter installed with the sample is fixed on the loading end of the electro-hydraulic servo universal testing machine through a rigid fixed ring, so as to realize the servo control during the loading process of the sample; lastly, through the fine-tuning testing machine, the sample is slowly inserted into the circular slot of the locating dial of the bottom adapter. After the above installation, experiments can be carried out according to the loading scheme. The specific structural assembly of C-CAST system is shown in Figure 3
shows the deformation and stress condition of coal samples under traditional uniaxial compression and inclined uniaxial compression, respectively. As shown in Figure 4
, when the load applied by the testing machine to the end of coal samples is perpendicular to the axial direction of the sample, the axial stress and axial strain can be expressed as follows:
are the axial stress and axial strain of coal samples, respectively; F
is the vertical pressure applied by the testing machine to the end face of the sample; A
is the cross-sectional area of the coal sample; d
is the total vertical displacement of the testing machine after coal samples are loaded and damaged, namely the vertical compression displacement of the sample under the traditional uniaxial compression; and l
is the initial height of the sample.
When the vertical load applied by the testing machine to the end face of coal samples is distributed at an angle with the axial direction of coal samples, additional shear stress will be generated at the end face of coal samples. The vertical load applied by the testing machine on the end face of coal samples is decomposed into the compressive stress along the axial direction of coal samples and the shear stress parallel to the end face of coal samples. Subsequently, under the inclined uniaxial compression, the axial stress component, axial strain, shear stress component and shear displacement of the sample can be expressed as [40
is the inclination angle of coal samples; σθ
are the axial stress component and shear stress component of coal samples under inclined uniaxial compression; εθ
is the axial strain of coal samples under inclined uniaxial compression; and sθ
is the shear displacement of coal samples under the inclined uniaxial compression.
Equations (3)–(6) are simplified calculation forms of stress component of coal samples under inclined uniaxial compression to reveal the stress state of coal samples. This is of great significance to analyze the influence of shear stress component on the mechanical property and failure behavior of coal samples.
2.3. Experimental Scheme
In this experiment, the C-CAST experimental system was used to study the mechanical property and failure behavior of coal samples under different loading rates and inclination angles. However, C-CAST system also has a limitation. When the inclination angle of the sample is greater than 30°, it is difficult to exclude the large experimental error caused by the slip and dislocation of the adapter in the horizontal direction under the C-CAST system. Therefore, 6 groups of inclination angles were set in this experiment, namely 0°, 5°, 10°, 15°, 20° and 25°; 8 groups of loading rates were set, namely 0.05, 0.50, 1.00, 2.00, 3.50, 5.00, 7.50 and 10.00 mm/min. Each group of experiments was repeated 5 times; the maximum and minimum values were removed, respectively, and the middle three groups of experimental results were taken as the research data.
The specific experimental steps are as follows:
Firstly, according to the installation steps of C-CAST system, the installation of test sample and equipment under specific inclination angle is completed. The top adapter of C-CAST system installed with sample is fixed on the loading end of electro-hydraulic servo universal testing machine through a rigidly fixed ring, and the top adapter of the system is located in the middle of the loading end.
Secondly, petroleum jelly is applied on the end face of the sample to reduce the friction between the end of the sample in the circular groove and the surface of the circular groove in the scale disk to avoid the stress concentration. The universal testing machine is fine-tuned, the exposed end of the sample is slowly inserted into the circular groove of the lower scale disk of the C-CAST system, then the support block is installed and the test sample is fixed.
Thirdly, the acoustic emission probe is pasted on the coal sample surface, and the installation position is arranged symmetrically and 30 mm away from the end face of the sample. There are four acoustic emission probes in total, and then the lead breaking experiment is carried out to ensure the sound coupling between the acoustic emission probe and the sample, as shown in Figure 3
. The prestress of the testing machine is set to be 0.1 kN, that is, when the loading load of the sample reaches 0.1 kN, the experimental data will be recorded.
Fourthly, the program-controlled system of the universal testing machine is used, and the initial loading rate is set at 3 mm/min. when the prestress reaches 0.1 kN, the loading process is terminated automatically. At this time, it is necessary to check whether the sample is completely fixed in the C-CAST system. If the sample is not fixed, the location of the bottom adapter is adjusted, then the experimental program and the preloading is started again. If the sample is well fixed, the next step is performed
Lastly, after debugging all the equipment, the loading rate of the testing machine is set to the specified value according to the experimental scheme. At the same time, the testing machine and the acoustic emission acquisition system are started to ensure the synchronization of the collected data. When the sample is damaged, the above experimental system is terminated, and then the data are saved.
Slowly raise the testing machine, remove the sample, repeat steps 1–5., and carry out the next set of experiments.
2.4. Acoustic Emission Characterization of Cracking Mode
In essence, the failure process of coal samples under load is a gradual initiation and coalescence of tension and shear cracks. In this process, the distribution of cracks is highly associated with the failure behavior of coal samples and is significantly affected by external loads. Therefore, the research on the cracking mode of coal samples under different loading rates and inclination angles is carried out to reveal the instability mechanism of inclined pillar under mining from the microscopic point of view. Acoustic emission waveform analysis method has been proved to be an important technical means to study material crack mode, and widely used in civil engineering [42
], mining engineering [44
] and material science [46
In this experiment, four RS-54A acoustic emission (AE) sensors were symmetrically arranged. The sampling frequency was set at 3 MHz, the preamplifier was 40 dB, and the threshold value was 0.1 V. To ensure the acquisition accuracy, the peak definition time (PDT), impact definition time (HDT) and impact locking time (HLT) were set as 50, 100 and 500 μs, respectively.
The cracking mode of coal samples during loading can be characterized by the ratio of average frequency (AF
) and rising angle (RA
) of acoustic emission event characteristic parameters. Figure 5
shows the schematic diagram of the typical AE waveform and characteristic parameters. The characteristic parameters of single event acoustic emission waveform mainly include minimum amplitude and maximum amplitude (B
), duration from minimum amplitude to maximum amplitude (RT
), total duration of acoustic emission (DT
) and cumulative ringing count (CR
). The RA
can be determined by RT
, while the AF
can be determined by CR
. The specific expression is shown in Equations (7) and (8) [44
]. In this paper, the ratio of RA
is used to judge the crack mode. When RA
is less than 1, tensile crack is the visible crack type; when RA/AF
is greater than 1, shear crack is the visible crack type. This method has been used by many scholars and its accuracy has been widely verified [47