*4.1. Relationship between K and Coal Quality Index*

Coal quality indexes mainly include gas emission initial velocity Δ*p*, firmness coefficient *f*, volatile matter *Vdaf*, ash *Aad*, etc. They macroscopically reflect some essential characteristics related to coal and gas desorption. Among them, Δ*p* and *f* are commonly used in regional outburst risk prediction. Because Δ*p*, *f*, *Vdaf*, *Aad*, etc. are all coal quality indicators unrelated to gas pressure, the relationship between them and the values under certain gas pressure conditions can only be considered. In Table 2, the *K*<sup>1</sup> value is calculated when the gas pressure *p* = 1 MPa. Through nonlinear fitting of the data in Tables 1 and 2, the relationship between (*K*1)*<sup>p</sup>*=1 and Δ*p*, *f*, *Vdaf*, *Aad* is obtained, as shown in Figure 1.

**Figure 1.** Relationship between (*K*1)*<sup>p</sup>*=1 and coal quality index. (**a**) Relationship between (*K*1)*<sup>p</sup>*=1 and Δ*p*. (**b**) Relationship between (*K*1)*<sup>p</sup>*=1 and *f* . (**c**) Relationship between (*K*1)*<sup>p</sup>*=1 and *Aad.* (**d**) Relationship between (*K*1)*<sup>p</sup>*=1 and *Vdaf*.

It can be seen from Figure 1a that the relationship between (*K*1)*<sup>p</sup>*=1 and Δ*p* conforms to the power function increasing relationship. With the increase in Δ*p*, the value of (*K*1)*<sup>p</sup>*=1 also increases correspondingly. The correlation coefficient *R2* is 0.812, indicating that there is a significant correlation between *K*<sup>1</sup> and Δ*p*, and Δ*p* significantly affects the positive (*K*1)*p*=1. It can be seen from Figure 1b that (*K*1)*<sup>p</sup>*=1 is in accordance with the logarithmic function attenuation relationship. As *f* increases, the value of (*K*1)*<sup>p</sup>*=1 decreases accordingly. The correlation coefficient *R2* is 0.657, indicating that there is also a certain correlation between (*K*1)*<sup>p</sup>*=1 and *f*, and *f* affects negative (*K*1)*p*=1, but the significance is lower than Δ*p*. It can be seen from Figure 1c that the distribution of 24 coal samples represented by 24 points in the figure is relatively disordered. The relationship between (*K*1)*<sup>p</sup>*=1 and *Aad* is an approximately logarithmic function, and the correlation coefficient *R2* is only 0.129, indicating that the correlation between (*K*1)*<sup>p</sup>*=1 and *Aad* is not close. It can be seen from Figure 1d that 24 points are concentrated in the range of 13.10~18.61 of *Vdaf*, and (*K*1)*<sup>p</sup>*=1 has no correlation with *Vdaf*.

From the above analysis, it can be seen that under the same gas pressure condition, the value of *K*<sup>1</sup> mainly depends on Δ*p*. In theory, *K*<sup>1</sup> is the same as Δ*p*, which is an index to reflect the risk of outburst by the amount of initial gas desorption. Their fundamental difference is only the difference of adsorption gas pressure; that is, *K*<sup>1</sup> index reflects the change of adsorption gas pressure more than Δ*p*. The firmness coefficient *f* mainly reflects the ability of coal to resist damage. In many cases, the lower the strength of a coal seam, the greater the initial gas desorption. The regression analysis shows that under the condition of certain gas pressure, *K*<sup>1</sup> decreases with the increase in *f* in a negative exponential law. The volatile matter *Vdaf* of coal reflects the metamorphic degree of coal, and the ash *Aad* reflects the yield of effective carbon. Both of them are not closely related to the initial gas desorption amount. In short, *K1* is most affected by Δ*p* and less affected by *Vdaf* and *Aad*. Therefore, Δ*p* is the main influencing factor of *K*1, and *f*, *Vdaf* and *Aad* are secondary influencing factors.
