# Water Infusion on the Stability of Coal Specim under Different Static Stress Conditions
## 3 Results
### Stress Variation  
Figure 7 shows the stress variation versus saturation coefficient under different initial stress conditions. For the specimen with lower initial stress (\(k_{\text{s}}<0.65\)), its bearing stress decreases linearly until the specimen reached saturation in all cases, the specimen remains stable. When the instability occurs, the stress in the specimen suddenly drops. Generally, two stress falling modes, namely free-falling and step-falling, can be concluded for those damaged specimens. For specimens suffered free-falling, the stress decreases linearly at first then dropped rapidly to a very low level close to 0 when the saturation coefficient reached a certain value, indicating that the instability mode is violent and drastic. For specimens experienced step-fall instability, the stress drops several times in a relatively mild manner. It should be noted that there is a certain randomness for the instability mode. The failure evolution can be dominated by either free-fall instability or step-fall instability for different specimens under the same condition. For example, when \(k_{\text{s}}\) is 0.75, specimens in Cases 1, 3 and 4 were considered to be characterized by step-fall instability where stress dropped and then remained stable for some further saturation increase until the specimens reached total instability. However, the stress dropped dramatically to zero once the water saturation coefficient reached a certain point in the other cases where specimens were characterized by free-fall instability. We can also find that the \(k_{\text{s}}\) of 0.65 is the instability critical point in all cases. For specimens with \(k_{\text{s}}\) less than 0.65, they all released the stress stably until they reached saturation. However, when \(k_{\text{s}}\) was equal or greater than 0.65, the specimens collapsed with dramatic stress drop. Figure 7: Stress evolution versus \(k_{\text{s}}\) in different cases. To understand the coupled effects of pre-axial stress and water saturation coefficient, we introduced the critical instability water saturation coefficient (\(S_{cr}\)), i.e., the water saturation coefficient at the stress drop point. Figure 8 shows that \(S_{cr}\) decreases linearly with the increase of pre-stress when \(k_{s}\) is not less than 0.65. For example, under the \(k_{s}\) of 0.65, \(S_{cr}\) is 0.86. When \(k_{s}\) increases to 0.80, \(S_{cr}\) significantly drops to 0.41. This suggests that under higher the axial stress, little water saturation coefficient will result in the instability of rock pillar. To better describe the weakening effect of water on axial stress, here we define the stress decreasing rate \(v_{s}\) as the decrement of axial stress when the water saturation coefficient increased 1% during the linear stable stress-reduction period. For example, the linear stable stress-reduction period for the specimen with \(k_{s}=0.80\) in Case 1 was considered to be where the saturation coefficient increased from 0.00 to 0.35. As mentioned above, when \(k_{s}\) was greater than 0.65, the specimens finally reached instability with the increase of saturation coefficient. However, when \(k_{s}\) was less than or equal to 0.65, the weakening rate increased gently and stably until the specimen was fully saturated. It can be seen from Figure 9 that the stress decreasing rate \(v_{s}\) increased exponentially with \(k_{s}\) increasing. Therefore, the stress decreasing rate is believed to be a strong indicator for predicting pillar instability induced by water infusion. In practical engineering, the critical axial stress decreasing rate, which is about \(8.3\times 10^{-2}\) MPa per 1% of \(S_{c}\) in this study, can be determined according to laboratory experiments and numerical simulations. For a pillar with stress sensors mounted inside it, its stability can be assessed and predicted by comparing its current stress decreasing rate and the critical value, which is of great significance for engineering. Figure 8: Instability water saturation coefficient versus axial stress coefficient.