Geomechanical Model for Frictional Contacting and Intersecting Fracture Networks: An Improved 3D Displacement Discontinuity Method

The displacement discontinuity method (DDM) is widely used in large -scale engineering problems, such as hydraulic fracturing stimu-lation in unconventional reservoirs and enhanced geothermal systems, due to its convenient calculation and high precision. Although the 3D-DDM based on triangular elements can more accurately describe intrinsically geometric characteristics of artificial/natural fractures, due to the disadvantage of constant DDM, it will still produce large errors when calculating frictional contacting, close-spacing, and in-tersecting fractures, which greatly limits the universality of DDM in complex fracture networks. To the best of the authors' knowledge, few DDM- based models are capable of tackling partially contacting fracture networks with arbitrary intersecting angles. In this paper, we propose a more efficient 3D-DDM algorithm via integrating the analytical solution, the 20-point Gaussian quadrature formula for standard triangles (GQSTS) integration algorithm, and the adaptive Gaussian-Kronrod integration algorithm. Then, combining the "local mesh refinement " grid, the Mohr-Coulomb correction for negative fracture aperture, and two rough fracture deletion strategies, the optimized 3D-DDM algorithm with broader versatility is established. All optimization measures are validated by the relevant fracture model. In the optimized 3D-DDM algorithm, (1) the "local mesh refinement " technique effectively improves the calculation accuracy of intersect-ing fractures; (2) the adaptive Gaussian-Kronrod integration algorithm not only improves the integration accuracy of high oscillation functions but is also 50% faster than the traditional Gaussian integration algorithm; (3) the Mohr-Coulomb criterion serves as a rigorous constraint for frictional contacting fractures to avoid the occurrence of negative fracture aperture; and (4) using the rough "deep deletion " or "shallow deletion " strategy to replace the ultrahigh-quality mesh generation can more conveniently maintain the accuracy of the com-plex fractures model. This optimized 3D-DDM algorithm may serve as a basis for simulating nonplanar 3D fracture swarms' evolution, allowing for frictional contacting, closespacing, and intersecting fractures.