## 4 Results
### Effect of Moisture Content on Mechanical Properties
#### 4.2.5 Overall Influence of Different Water Contents  
This experiment investigated the mechanical behavior of sandstone specimens with different moisture contents and found that the water content significantly affected the mechanical properties of the rock. As shown in Table 4 and Figure 20, with increasing moisture content from the dry to saturation states, the initiation, closure, and damage stresses of the sandstone decreased substantially. Specifically, for Path I, the initiation, closure, and damage stresses for the dry specimens were 9.58, 52.69, and 95.75 MPa, respectively. In contrast, with a saturated moisture content, the initiation, closure, and damage stresses dropped to 8.05, 39.06, and 88.79 MPa, respectively, indicating a noticeable overall reduction. As the moisture content increased, the mechanical properties of the rock gradually deteriorated. This was primarily due to the penetration of water into the rock fissures and pores, which weakened the cementation and friction between particles, thereby reducing the stiffness and strength of the rock. This effect varied under the different loading paths. In Path I, the influence of the moisture content on the mechanical parameters of the rock was most pronounced, with the largest decreases in the initiation, closure, and damage stresses, where the damage stress decreased by 26.81%. This suggests that under complex stress perturbation conditions, water plays a more significant role in promoting the expansion of microcracks and deterioration of the rock structure. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Path**} & **Moisture** & **Initiation** & **Closure Stress** & **Damage Stress** \\  & **Content (\%)** & **Stress (MPa)** & **(MPa)** & **(MPa)** \\ \hline \multirow{3}{*}{Path I} & 0 & 9.54 & 48.37 & 87.17 \\  & 30\% & 9.57 & 45.06 & 80.47 \\  & 100\% & 9.61 & 36.75 & 63.8 \\ \hline \multirow{3}{*}{Path II} & 0 & 9.58 & 52.69 & 95.75 \\  & 30\% & 9.57 & 50.61 & 91.59 \\  & 100\% & 8.05 & 39.06 & 88.79 \\ \hline \multirow{3}{*}{Path III} & 0 & 12.32 & 44.96 & 77.81 \\  & 30\% & 11.85 & 44.64 & 77.8 \\  & 100\% & 9.52 & 41.1 & 72.62 \\ \hline \multirow{3}{*}{Path IV} & 0 & 9.55 & 49.44 & 89.29 \\  & 30\% & 9.54 & 45.33 & 81.1 \\ \cline{1-1}  & 100\% & 9.69 & 39.69 & 69.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Variation in crack initiation, closure, and damage stresses in sandstone with different water contents. Figure 19: Failure modes of sandstone with different water contents: (**a**) dry; (**b**) 30% saturated; (**c**) saturated. To better explain the mechanical behavior and crack evolution mechanisms of water-saturated sandstone under different moisture conditions, this study combined a damage mechanics model using the damage stress point as a characteristic value to conduct a detailed analysis of the experimental results. The rock damage variable \(D\) is defined as the reduction in the elastic modulus during loading, given by:  
\[D=1-\frac{E_{r}}{E_{0}}, \tag{2}\]  
where \(E_{0}\) is the initial elastic modulus of the rock, and \(E_{r}\) is the instantaneous elastic modulus of the rock at damage stress. The initial elastic modulus refers to the modulus value during the elastic phase of the rock before any damage or crack initiation occurs and is calculated from the initial linear segment of the stress-strain curve. The equation used is as follows:  
\[E_{0}=\frac{\triangle\sigma}{\triangle\varepsilon}, \tag{3}\]  
where \(\triangle\sigma\) is the increment in stress, and \(\triangle\varepsilon\) is the increment in strain. Based on Equations (2) and (3), the damage variables of the sandstone samples with different water contents were calculated. The calculated damage variables are shown in Figure 21.  
Through the calculation of the damage variable, it was found that as the water content increased, the damage variable exhibited a significant increasing trend.