## 4 Discussion
### Study on Damage Regularity of Weakly Consolidated Sandstone
This could be attributed to specimen crushing under the excessive confining pressure and the subsequent development of new transverse cracks. The findings of the abovementioned studies indicate that rocks may experience both tensile and shear failures under triaxial compression. In the UDEC model, the failure strength parameter for shear cracks is often higher than that for tension cracks. This leads to differing conditions and challenges for tensile and shear crack failures. Consequently, this paper enhances the expression of the damage variable, considering it as a combination of tensile and shear damage, as follows:  
\[D_{a}=\gamma\bigg{\{}\frac{N_{s}}{N_{S}}+\frac{N_{t}}{N_{T}}\bigg{\}} \tag{9}\]  
In the equation, \(N_{s}\) and \(N_{t}\) represent the numbers of tensile and shear cracks in the rock under different confining pressures, where \(N_{s}\) stands for the total potential tensile cracks and \(N_{t}\) represents the total potential shear cracks. \(\gamma\) is the modification coefficient for the damage variable. In the definition of the damage variable under different confining pressures, setting the damage variable at the maximum confining pressure (6 MPa) to 1 allows for a more effective comparison of the extent of damage under various confining pressures. However, it is crucial to emphasize that this normalization operation does not alter the actual degree of damage but merely scales the data for the sake of analysis and comprehension. Figure 16: Fracture development statistics under different confining pressures. Figure 15: Number of cracks under different confining pressures. As shown in Figure 17, variations in rock damage under different confining pressure conditions can be observed. Within the confining pressure range from 1 to 4 MPa, the damage variable of weakly cemented sandstone exhibits a decreasing trend, indicating better rock stability and compressive strength within this pressure range. However, as the confining pressure increases from 4 MPa to 5 MPa, the damage variable slightly increases, suggesting that the rock begins to exhibit more noticeable damage under this confining pressure. It is of particular note that, when the confining pressure increases to 6 MPa, the rock's damage variable sharply rises. This may imply that at this pressure level, the structural stability and compressive strength of weakly cemented sandstone significantly decrease, leading to a significantly increased likelihood of rock damage. This change reflects the rock's damage and failure patterns under varying confining pressure conditions. Figure 18 illustrates the variation in rock damage parameter \"D\" under different hydraulic pressure differentials. Through numerical simulations using the UDEC framework, several insights into the relationship between the damage parameter and permeability amplification in weakly cemented sandstone under the influence of hydraulic pressure differentials have been gained. The following patterns have emerged. At lower permeability levels, the simulation results may exhibit relatively modest values for the rock's damage parameter, aligning with theoretical models as expected. As the simulated hydraulic pressure gradually increases, the damage parameter may start to rise. With further increments in permeability during the simulation, there is a significant surge in the rock's damage parameter. This surge is driven by internal hydraulic pressures that initiate the extension and interconnection of fissures, thereby exacerbating the rock's state of deterioration. Upon reaching elevated levels of permeability, simulations may demonstrate the pinnacle of the rock's damage parameter, subsequently stabilizing. This occurrence signifies that the rock has undergone profound fragmentation and disintegration, potentially leading to fundamental reconfigurations in its internal structure and physical properties.