The intersection of fractures, particularly the intersection of discontinuities, occurs frequently in practical engineering, mainly manifesting as a mixed-mode failure. In the present study, the three-point bend test was conducted on the semicircular bend (SCB) of pre-cracked shale samples with a bedding layer. A numerical model for simulating mixed-mode fracture propagation was constructed using the extended finite element method. The minimum strain energy density criterion was applied for crack initiation and propagation. According to the experimental results, the minimum strain energy density criterion better indicates the fracture path. When the approach angle was set at 30°, the mode I fracture toughness was 0.85 MPa m^1/2 and the mode II fracture toughness was 0.38 MPa m^1/2. Furthermore, the mixed-mode fracture path and the crack initiation angle of the SCB with a bedding layer were discussed. As the approach angle became smaller and more prone to crack propagation, a tendency for the fracture propagation path to transfer to the fracture diversion was observed. If the Young's modulus of the layer is greater than the Young's modulus of the shale, the propagation path of the fracture would be far away from the layer. With the decrease in the tensile strength of the bedding layer, the fracture was more likely to propagate along the bedding layer orientation. The present study aimed to better understand the crack initiation and expansion in the mixed-mode fracture process with a bedding layer.

裂缝的交叉点，特别是不连续点的交叉点，在实际工程中经常发生，主要表现为混合模式破坏。在本研究中，三点弯曲试验是在具有层理层的预裂页岩样品的半圆形弯曲（SCB）上进行的。使用扩展有限元方法建立了模拟混合模式裂缝扩展的数值模型。最小应变能密度标准适用于裂纹的萌生和扩展。根据实验结果，最小应变能密度准则更好地指示了断裂路径。当接近角设为30°时，模式I的断裂韧性为0.85MPa·m ^1/2，模式II的断裂韧性为0.38MPa·m ^1/2。此外，还讨论了带有垫层的SCB的混合模式断裂路径和裂纹萌生角度。随着靠近角变小并且更易于裂纹扩展，观察到裂缝传播路径转移到裂缝转移的趋势。如果该层的杨氏模量大于页岩的杨氏模量，则裂缝的传播路径将远离该层。随着垫层的抗拉强度的降低，断裂更可能沿着垫层取向传播。本研究的目的是更好地理解带有垫层的混合模式断裂过程中的裂纹萌生和扩展。