Partition-of-unity method based on dual-cover approximation technique for fractured rock mass modeling

• A dual-cover approximation technique (DCAT) is developed for fractured rock mass modeling. • The PU approximation construction for multiple discontinuities is significantly simplified. • Blending element issues inherent in the PU methods are fundamentally eliminated. • Cut-induced ill-conditioning problems in the PU methods are effectively resolved. A partition-of-unity (PU) method based on dual-cover approximation technique (DCAT) is developed for fractured rock mass modeling. In the DCAT, the problem domain is discretized using a structured square mesh independent of discontinuities and boundaries. Sub-blocks generated from the square elements fully cut by discontinuities, as well as the square elements containing crack tips, are termed isolated blocks, while remaining elements are normal blocks. Asymptotic approximations are defined for near-tip isolated blocks based on block cover concept, while the PU approximations are constructed on the remaining blocks based on nodal cover concept. A discontinuous Galerkin (DG) approach is introduced to ensure continuity between isolated blocks and their surrounding blocks. Since the approximations on each block are complete interpolation functions, the DCAT fundamentally eliminates the blending element issues inherent in the conventional PU methods such as the extended/generalized finite element method (XFEM/GFEM) and the numerical manifold method (NMM). By replacing the degrees of freedom of small-area block with those of its adjacent large-area block, the DCAT also provides a straightforward solution to the small-area block trouble. These innovations enable robust simulations of complex fractures with stable computations. Several numerical examples highlight the accuracy, efficiency, and robustness of the present DCAT.