## 4 Discussion
### Fracture Evolution
The cracking stress reached 15.56 MPa with strain of 0.53%, while the peak stress was 28.04 MPa, and the strain was 0.95%. The complete rupture stress peaked at 25.59 MPa with maximal strain of 0.97%. Notably, the yielding stage exhibited the highest increase in strain, reaching 0.97%, with an increment of 0.42% and with the strain leading to an increase in red-striped regions, progressing until the termination of the maximum strain. After immersing the specimen in water for 5 days, the compressive stress was measured at 1.81 MPa, with strain of 0.13%. The cracking stress was 16.85 MPa, with strain of 0.59%, while the peak stress was 23.82 MPa, with strain of 0.81%. Finally, the complete rupture stress was recorded at 15 MPa. The specimen experienced stress of 27 MPa and maximal strain of 0.82%. During the linear elasticity stage, the strain had a notable increase of 0.46%, resulting in the development of a red band-like area in the strain cloud diagram. The red stripes in the strain cloud became more pronounced and continued to develop, culminating in the formation of flaky red strain concentration areas in the yielding stage. Eventually, these areas led to the formation of cracks in the lower-right part of the specimen. The specimen's compressive stress after being immersed in water for 7 days was 3.34 MPa with strain of 0.18%. The cracking stress was 15.60 MPa, with strain of 0.54%. The peak stress was recorded at 27.65 MPa, with strain of 0.92%. The complete rupture stress measured 23.37 MPa, with the maximum strain at 0.95%. During the yielding stage, the specimen had the highest strain increment of 0.38%. There were many red-striped areas observed in the strain map, and a crack was formed. Numerous red stripes are visible on the strain  
[PERSON] et al. [32] discussed the anisotropic properties of coal pillars under failure considering the effects of bedding planes. Their study revealed that the anisotropy of the coal pillar dam body is one of the most significant factors when the principal direction of the mechanical properties is \(\theta\) = 45\({}^{\circ}\) or \(\theta\) = 135\({}^{\circ}\). This conclusion is in line with the main direction of crack development in the damage area shown in Figure 13. Here, we continue to analyze the influence of water immersion on the mechanical properties and fracture evolution of coal pillars. The damage of coal pillar dams with immersion durations of 0 d, 20 d, 40 d, 60 d, 80 d, and 100 d was investigated. The mechanical properties of the coal \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \begin{tabular}{c} **Rock** \\ **Type** \\ \end{tabular} & \begin{tabular}{c} **Thickness** \\ **/m** \\ \end{tabular} & \begin{tabular}{c} **Density** \\ **/kg\(\cdot\)m\({}^{-3}\)** \\ \end{tabular} & \begin{tabular}{c} **Elastic** \\ **Modulus/GPa** \\ \end{tabular} & \begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ \end{tabular} & \begin{tabular}{c} **Cohesion** \\ **/MPa** \\ \end{tabular} & \begin{tabular}{c} **Friction/\({}^{\circ}\)** \\ **/MPa** \\ \end{tabular} & \
\begin{tabular}{c} **Tensile** \\ **Strength/MPa** \\ \end{tabular} &
\begin{tabular}{c} **Compressive** \\ **Strength/MPa** \\ \end{tabular} \\ \hline Aeolian sand & 20 & 1600 & 0.28 & 0.3 & 0.5 & 32 & 0.4 & 17.2 \\ Sandstone & 80 & 2330 & 15.1–29.50 & 0.2–0.34 & 6–13 & 23–35 & 1.4–4.75 & 36–48 \\ \(5^{-2}\) coal seam & 3 & 1320 & 4.89–9.30 & 0.2–0.34 & 0.5–8.8 & 12–38 & 0.25–1.36 & 13–18 \\ Sandstone & 10–60 & 2380 & 15.1–29.50 & 0.2–0.34 & 6–13 & 23–35 & 1.4–4.75 & 36–48 \\ Floor sandstone & 20 & 2430 & 38.0 & 0.20 & 3.2 & 38 & 2.5 & 36.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Physical and mechanical parameters of rock used in calculations [32]. Figure 12: (**a**) The model scale and conditions; (**b**) meshing of the model. pillar under different immersion durations are based on Equations (3) and (4). The strength criterion when judging the failure of anisotropic materials is achieved mainly through the combination of a series of stress-strength indices.