## 4 Results and Analysis
### Influence of Cracks Characteristics on the Wellbore Stability  
#### 4.2.1 Influence of Crack Orientation on the Wellbore Stability  
Figures 11 and 12 present the stress and displacement patterns around the wellbore, varying with the angle (\(\beta\)) between the crack strike and the maximum horizontal principal stress direction, as shown in Table 2. The observed trend is the following: with a decrease in \(\beta\), both the stress and displacement at all points around the wellbore gradually increase. The lowest stress and displacement values are recorded when \(\beta\) equals 90\({}^{\circ}\). For instance, at \(\beta\) = 0\({}^{\circ}\), the stress and displacement at point A are measured at 125.21 MPa and 1.53 mm, respectively. In contrast, at \(\beta\) = 90\({}^{\circ}\), these values drop to 105.61 MPa and 1.25 mm, representing decreases of 15.65% and 18.30%, respectively. This pattern suggests that when cracks align parallel to the maximum horizontal principal stress, the stress and deformation at the crack-wellbore intersection are at their peak. Conversely, these values progressively reduce as \(\beta\) increases. This can be attributed to the following reasons: At \(\beta\) = 0\({}^{\circ}\), the maximum horizontal stress causes the cracks near the wellbore to undergo tensile expansion, leading to concentrated stress and increased tensile displacement in the area. However, at \(\beta\) = 90\({}^{\circ}\), the maximum horizontal stress tends to close the cracks, resulting in lesser stress concentration and tensile displacement compared to the former situation.  
Figure 13 showcases the correlation between the equivalent drilling fluid densities of collapse pressure (\(\rho_{\rm c}\)) and the angle (\(\beta\)) between the crack strike and the maximum horizontal principal stress direction. A notable trend emerges from the graph: \(\rho_{\rm c}\) linearly diminishes with an increase in \(\beta\). Specifically, \(\rho_{\rm c}\) is 1.26 g/cm\({}^{3}\) at \(\beta\) = 0\({}^{\circ}\) but drops to 1.06 g/cm\({}^{3}\) at \(\beta\) = 90\({}^{\circ}\), marking a substantial reduction of 15.87%. When considered alongside the previously discussed stress and displacement data, this trend suggests a clear rule: in situations where cracks run parallel to the maximum horizontal stress, vertical cracks intersecting the wellbore are prone to tensile expansion. This expansion significantly  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Situation** & **Description** & **Result/g-cm\({}^{-3}\)** \\ \hline Without considering cracks and solution cavities & The formation is considered as the intact rock & 1.09 \\ \hline Only considering cracks & Two cracks with a dip angle of 19.81\({}^{\circ}\) are designed in the formation model. The width of one crack is 10 mm, while the width of the other is 3 mm & 1.14 \\ \hline Considering cracks and solution cavities & Two cracks with a dip angle of 19.81\({}^{\circ}\) and ten solution cavities are designed in the formation model. The width of one crack is 10 mm, while the width of the other is 3 mm. The diameters of the solution cavities range from 3 mm to 20 mm, with an average value of 10 mm. This situation is consistent with the actual situation on the site & 1.16 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Equivalent drilling fluid densities of collapse pressure for the three situations.