The Numerical Manifold Method (NMM) is one of important numerical methods tomodel rock mechanics problems at present. The NMM comes from the discontinuousdeformation analysis, and is mainly used to combine continuous and discontinuous mechanicsinto a system. Two meshes are employed in the method: the mathematical meshenables the nodes to build a finite cover system of the solution domain and theweighted functions, while the physical mesh provides the sub-domains of integration.The mathematical mesh is used to form mathematical covers. The physical covers aredefined by the intersection of the mathematical covers and the physical mesh. And anelement in the manifold method is defined by the intersection of physical covers. Theadvantages of the NMM are that the mathematical mesh and the physical mesh aregenerally independent, and that the manifold element is different from the finite element,and the mathematical mesh can be easily re-meshed to obtain a better accuracy ofthe solution. The NMM can simulate the open and close process of crack in thefractured rockmass due to the fact that the kinematics theory of theblock system is considered in it. Therefore themethod has been widely used in rock mechanics, and has been studied by manyscholars in recent years. In the paper, the advances of the numerical methods of thefractured rockmass from continuous to discontinuous domains are discussed. Thecomponents of the numerical manifold method and its applications in rock mechanicsand the advances in corresponding fields are discussed in detail. Finally, someproblems, such as the NMM for three-dimension problems, physical nonlinearproblems, crack propagation, related coupled methods etc., are discussed.
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