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Summary The displacement discontinuity method (DDM) is widely used in large-scale engineering problems, such as hydraulic fracturing stimulation 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 intersecting 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 intersecting 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 complex 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. Introduction In recent years, fracturing technology has played an important role in the exploitation of low-permeability oil/gas reservoirs and enhanced geothermal systems (Ghassemi and Zhou 2011; Kumar and Ghassemi 2016).
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