## 3 Results and Analyses
### Uniaxial Compressive Properties
Figure 6 displays the fitted curves for the compressive strength, peak strain, elastic modulus, and natural water absorption rate of coal rock with varied immersion durations. According to the figure, the natural water absorption rates of different coal rocks decrease logarithmically; it exhibits a negative logarithmic function relationship as the immersion duration increases. This relationship is represented in Equation (2):  
\[r=0.2891\ln(h)+1.0043, \tag{2}\]  
where \(h\)--water immersion duration (d); \(r\)--natural water absorption rate of coal rock (%). Under the conditions of short-term water immersion (0-7 d), the compressive strength of the coal rock decreases sporadically with an increase in the water immersion duration. After one day of water immersion, the softening effect of water damages the internal structure of the coal rock, resulting in a reduction in strength. With an increase in water immersion for three days, the natural water absorption rate in the coal rock increases; this increase in the internal natural water absorption rate leads to an enhancement in the plasticity of the coal rock, and, as a result, the strength of the coal rock rises. There are  
Figure 5: Secant modulus of coal during compression. Figure 6: The relationship of the compressive strength, peak strain, elastic modulus, and natural water absorption rate. variations in porosity among different coal rocks. The peak compressive strength of the coal rock is low after 5 days of water immersion. In addition, the peak compressive strength remains low. Later, after 7 days of water immersion, the natural water absorption rate increases and the compressive strength increases again. However, it remains lower than that observed after 3 days of water immersion. The natural water absorption rate of the coal rock increases after being immersed for 7 days, causing an increase in compressive strength. However, the strength is still lower than that obtained after 3 days of immersion. According to the analysis above, the optimal natural water absorption rate for coal rock is 1.61% and the immersion duration should be around 3 days for maximum strength. Under long-term water immersion (10-30 d), the compressive strength of coal rock gradually decreases and the water softening effect significantly increases. Considering the natural water absorption rate, the coal rock becomes saturated after being immersed in water for around 25-30 days. At this point, the compressive strength of the coal rock drops to as low as 9.59 MPa, rendering it unable to bear any pressure. This is a clear indication of coal rock saturation. Overall, the compressive strength of the coal rock fits a negative exponential function relationship with the water immersion duration. Equation (3) displays the relationship:  
\[\sigma_{c}=29.463e^{-0.024h}, \tag{3}\]  
where \(\sigma_{c}\)--peak strength of coal rock (MPa); \(h\)--water immersion duration (d). The varying porosity of coal rock results in a more distinct peak strain. However, with an increase in the water immersion duration, the peak strain of the coal rock decreased overall. During short-term flooding, the peak strain was greatest when the coal rock had an optimal natural water absorption rate. This indicates the significant plasticity of the coal rock at this juncture. However, long-term water immersion drastically weakened the compressive strength of the coal rock, which made it susceptible to crushing without undergoing sufficient plastic deformation. The elastic modulus of the coal rock increased initially when submerged but decreased as the submergence period elapsed, with the highest elastic modulus being observed when optimal natural water absorption rate was reached. The peak strain of coal rock exhibits a negative exponential relationship with the water immersion duration, as shown in the Figure 6. Additionally, as per Equation (4), a linear function relationship is observed between the water immersion duration and the elastic modulus:  
\[\left\{