## 4 Conclusions  
This paper conducted splitting tests on fine sandstone with pre-existing cracks of different dip angles, and investigated the effect of pre-existing cracks on the tensile strength and failure mode of fine sandstone. Based on the digital image correlation method, the displacement and strain evolution laws of different rock failure modes were analyzed. Additionally, the absorbed energy during the deformation and failure process was calculated and investigated. The relationship between maximum absorbed energy and crack dip angle, tensile strength, and acoustic emission energy was also studied, and the following conclusions were drawn. This provides a reference for the design and construction of tunnels or mines in rock formations with pre-existing cracks. The tensile strength of sandstone specimens with pre-existing cracks is observed to be approximately 60% to 80% of that of intact specimens. The tensile strength first decreases and then increases with the increase in pre-existing crack dip angle, showing a \"V\" shape change. Specifically, at a crack dip angle of \(\alpha=45^{\circ}\), the tensile strength reaches its minimum, corresponding to approximately 60.3% of that of intact specimens. Conversely, at a crack dip angle of \(\alpha=90^{\circ}\), the strength is at its maximum, reaching approximately 77.2% of that of intact specimens. The difference in tensile strength is relatively minor when the crack dip angles are \(\alpha=30^{\circ}\), \(45^{\circ}\), and \(60^{\circ}\). Similarly, the failure displacement exhibits a similar pattern of initially decreasing and then increasing with the increase in crack dip angle. When the crack dip angle is \(\alpha=45^{\circ}\), the failure displacement is the minimum, approximately 72.85% of that of intact specimens, indicating the highest level of damage caused by the crack in the specimen. On the other hand, at a crack dip angle of \(\alpha=90^{\circ}\), the damage caused by the crack is minimal, and the failure displacement is approximately 85% of that of intact specimens. The failure modes of sandstone specimens with pre-existing cracks can be categorized into three types based on the crack morphology and formation mechanism. These types are as follows: tensile failure along the central point of the disc (Type I), tensile failure along the tip of the pre-existing crack (Type II), and tensile-shear combined failure along the tip of the pre-existing crack (Type III). The failure crack morphology can be classified into three typical cracks: central crack, wing-shaped crack at the crack tip, and central crack at the crack tip. When the dip angle of the pre-existing crack is \(\alpha=0^{\circ}\), the failure mode of the fine sandstone specimen is tensile failure along the central point of the disc (Type I) and tensile failure along the tip of the pre-existing crack (Type II), and the tensile crack during failure passes through the center of the disc. When \(30^{\circ}\leq\alpha\leq 60^{\circ}\), the failure crack extends along the tip of the pre-existing crack toward the loading end and expands in a wing shape; the failure mode is tensile-shear combined failure along the tip of the pre-existing crack (Type III). When the dip angle of the pre-existing crack is \(\alpha=90^{\circ}\), the failure crack of the specimen is parallel to the loading direction, passing through the crack tip; the failure mode is tensile failure parallel to the loading direction (Type I and Type II). The absorbed energy and vertical displacement ratio of fine sandstone during loading deformation show a nonlinear relationship, and the dip angle of the pre-existing crack strongly affects the evolution curve of absorbed energy.