## 4 Discussion  
### Joint and Pore Size Development Characteristics  
To provide a more comprehensive analysis of the permeability variations in weakly cemented sandstone, this study further conducted numerical simulations to analyze the influence of internal jointing and apertures within the rock. In this section, we will analyze the internal jointing and apertures of weakly cemented sandstone under varying confining pressures. Figure 8: Influence of confining pressure on permeability. Figure 9: Permeability changes under different confining pressures. By analyzing the impact of internal jointing and apertures on permeability, we can gain further insights into the permeability changes in weakly cemented sandstone. Combined with the earlier findings related to confining pressure changes and the results under 5 MPa confining pressure, we can assess the relative significance of different factors in permeability variations. This will provide more accurate guidance for rock engineering design and practice. Through this comprehensive analysis, a better understanding of the permeability characteristics of weakly cemented sandstone can be achieved, offering a more reliable basis for permeability assessment and prediction in rock engineering. In UDEC numerical simulations, the influence of the pressure difference on jointing and apertures is manifested in several aspects. (1) Joint Opening and Closure: the pressure difference causes joints or fractures to open or close. When fluid flows from a high-pressure area to a low-pressure area, if the fluid pressure exceeds the stress on both sides of the joint, the joint may further open. Conversely, if the fluid pressure is lower than the stress on both sides of the joint, the joint may close. This phenomenon is especially evident in joint systems. (2) Aperture Changes: apertures change due to the pressure difference. If the fluid pressure in the pore exceeds the stress of the surrounding rock, it can lead to aperture enlargement. Conversely, if the pressure is lower than the surrounding rock stress, it may result in aperture contraction. (3) Permeability Changes: joint opening and aperture changes further impact the material's permeability. If joints open or apertures expand, permeability may increase; conversely, if joints close or apertures shrink, permeability may decrease. The rock's interior contains various pores and fractures of varying sizes. These pores and fractures can change under different stresses and varying pore pressure conditions, leading to rock softening, deformation, and failure, thereby compromising the stability of the rock [25]. The development of fractures under pore pressure difference differs from the development of joints in conventional specimens under compressive conditions. In the conventional state, fractures within the specimen tend to develop more uniformly, predominantly from the upper and lower ends toward the middle, resulting in connected through-going fractures. In contrast, under pore pressure conditions, as shown in Figure 10, the pressure difference gradually spreads from the top to the bottom. This leads to higher stress conditions at the top, with less influence at the bottom. Consequently, the pattern of fracture development primarily focuses on the upper half of the model and then extends downward. Moreover, most of the joints are in a shear failure state, indicating that when fluid pressure exceeds the stress on both sides of the joint, the joint may further open. In UDEC, fluid flows through joint surfaces, and the orientation and characteristics of these surfaces can have a significant impact on permeability [29]. In particular, the extent of joint opening can change due to the application of mechanical conditions, and fluid pressure within the joints can affect the mechanical calculations. When the internal joint apertures reach their minimum size, changes in mechanical conditions will no longer affect the variation in permeability. Figure 11 illustrates the pattern of changes in apertures as the pore pressure difference increases.