*3.1.1 Relationship between the cohesion increment and strength-stress ratio of surrounding rock*

The strength-stress ratio and cohesion increment of the 29 underground plants in **Table 2** are plotted as 29 data points in **Figure 5**. These data are fitted by a least-squares curve to obtain Eq. (4).

$$\mathbb{E}\left[\Delta \mathbf{C}\_{\rm b}\right] = \mathbf{0}.45\left(2K\_{\sigma}{}^{-2} + K\_{\sigma}{}^{-4}\right) + \mathbf{0}.163\tag{4}$$

As shown in **Figure 5**, most of the 29 data points are distributed near the fitted curve, forming a data band around a certain distance above and below the curve, and the cohesion increment of the surrounding rock increases with a decrease in the strength-stress ratio. The trend of the curve in **Figure 5** shows that when the strengthstress ratio *K<sup>σ</sup>* > 6.0, the support strength reflected by the cohesion increment of the surrounding rock gradually tends to be constant. However, when the strength-stress ratio ranges from 3.0 ≤ *K<sup>σ</sup>* < 6.0, the curve gradually rises, indicating that the required support strength of the surrounding rock increases significantly as the strength-stress ratio decreases. When the strength-stress ratio *K<sup>σ</sup>* < 3, the underground plant surrounding rock is in a high-very high-stress state, requiring an even higher support strength, and the cohesion increment Δ*Cb* and strength-stress ratio show �2 times nonlinearity. Eq. (4) shows that the smaller the strength of the surrounding rock and the higher the in situ stress of the underground plant are, the greater the support strength required, but the growth rate shows a nonlinear relationship with the strength-stress ratio.
