## 3 Results and Discussion  
Adsorption-Instantaneous Pressure Relief Test Study for Gases with Different Adsorption Characteristics  
It can be seen from the test results that the overall trend of the coal body in the adsorption process was consistent. Therefore, the strain variation law of the various directions in the adsorption process of the coal body can be characterized by the law of the volumetric strain variation. The volumetric strain is calculated by the following formula, wherein compression is positive while expansion is negative according to the conventional representation of rock mechanics. \[\varepsilon_{V}=\varepsilon_{1}+2\varepsilon_{2} \tag{1}\]  
wherein, \(\varepsilon_{V}\), \(\varepsilon_{1}\), and \(\varepsilon_{2}\) represent volumetric strain, axial strain, and radial strain, respectively. Comparing the curves of different gas strains versus time, it can be seen that there were differences in the deformation and adsorption equilibrium time caused by the adsorption of different gases on coal samples. Table 2 lists the axial strains, radial strains, and volumetric strains of coal samples after adsorption equilibrium under different adsorption pressures of different gases. Table 3 illustrates the axial strain, radial strain, and volumetric strain of the damaged coal sample after the pressure relief expansion deformation. It can be seen from the test data that the coal briquettes exhibited similar isotropic mechanical properties. However, the axial strain and radial strain had different values in the adsorption equilibrium process, in which the axial strain was slightly larger than the radial strain. It can be seen from Figures 3-5 that the adsorption equilibrium pressure significantly affected the adsorption and expansion deformation of the coal body. With increasing pressure, the adsorption expansion deformation of the coal sample increased. In addition, the increment varied with the pressure. Under N\({}_{2}\) atmosphere, as can be seen from Figure 3, when the gas pressure increased from 0.4 MPa to 0.8 MPa, the axial strain, radial strain, and volumetric strain of coal increased by 26 \(\upmu\varepsilon\), 29 \(\upmu\varepsilon\), and 94 \(\upmu\varepsilon\), respectively. When the gas pressure increased from 0.8 MPa to 1.2 MPa, axial strain, radial strain, and volumetric strain increased by 132 \(\upmu\varepsilon\), 240 \(\upmu\varepsilon\), and 712 \(\upmu\varepsilon\), respectively. Under the CH\({}_{4}\) atmosphere, as can be seen from Figure 4, as the gas pressure increased, the amount of adsorption expansion increased. When the gas pressure increased from 0.4 MPa to 0.8 MPa and 1.2 MPa, the axial strains increased by 53 \(\upmu\varepsilon\) and 241 \(\upmu\varepsilon\), respectively. The radial strains increased by 45 \(\upmu\varepsilon\) and 220 \(\upmu\varepsilon\), and the volumetric strain increased by 143 \(\upmu\varepsilon\) and 681 \(\upmu\varepsilon\), respectively. Under CO\({}_{2}\) gas atmosphere, as shown in Figure 5, the corresponding axial strain, radial strain, and volumetric strain were \(-\)458 \(\upmu\varepsilon\), \(-\)415 \(\upmu\varepsilon\), and \(-\)1288 \(\upmu\varepsilon\), respectively, when the gas pressure was 0.4 MPa. When the gas pressure increased to 0.8 MPa, the corresponding axial strain, radial strain, and volumetric strain were \(-\)551 \(\upmu\varepsilon\), \(-\)510 \(\upmu\varepsilon\), and \(-\)1571 \(\upmu\varepsilon\), which were increased by 93 \(\upmu\varepsilon\), 95 \(\upmu\varepsilon\), and 283 \(\upmu\varepsilon\), respectively. When the gas pressure was 1.2 MPa, the axial strain, radial strain, and volumetric strain were \(-\)747 \(\upmu\varepsilon\), \(-\)701 \(\upmu\varepsilon\), and \(-\)2149 \(\upmu\varepsilon\), which were increased by 196 \(\upmu\varepsilon\), 191 \(\upmu\varepsilon\), and 578 \(\upmu\varepsilon\), respectively. When the gas containing coal was instantaneously relieved, the gas with different adsorption characteristics exhibited different deformation characteristics under different pressures.