Modeling Hydraulic Fracture Propagation and Analyzing Fracture Aperture Morphology Using the Displacement Discontinuity Method

The propagation morphology of hydraulic fractures plays a critical role in the stimulation effectiveness of unconventional oil and gas reservoirs. Based on the displacement discontinuity method (DDM) within a boundary element framework, this study establishes the transformation relationship between the global and local coordinate systems for fracture elements. The induced stress field generated by an arbitrary fracture element and the corresponding theoretical stress–displacement relationships are subsequently derived, enabling the numerical solution of stress intensity factors at the fracture tip. By introducing a circular-arc fracture model, analytical solutions for the stress intensity factor and energy release rate are further obtained. The error between the numerical and analytical solutions is < 5%, validating the reliability of the DDM. Furthermore, the numerical solutions for fracture width obtained via the DDM are verified against the analytical solutions derived from the Khristianovic–Geertsma–de Klerk (KGD) model, with the error in peak width remaining within 5%. This study systematically analyzes the width distribution in both single fractures and T-shaped fractures during hydraulic fracturing. The results indicate that within the T-shaped configuration, the single fracture and the branch fractures exhibit an arch-shaped width distribution, whereas the main fracture demonstrates a tower-shaped profile with a peak width significantly larger than that of the branch fractures. These findings provide theoretical and numerical insights for understanding fracture propagation mechanisms and optimizing fracturing design.