Abstract: By introducing two covers, namely, the mathematical cover and physical cover, the numerical manifold method can solve continuous and discontinuous problems in geotechnical engineering in unified way. At present, the application of NMM is mainly limited to two-dimensional analysis which is not realistic for many underground engineering. In this paper, three-dimensional numerical manifold method based on hexahedron element is proposed; and two kinds of high-order displacement functions are used as the cover function. The stiffness matrix, loading matrix, displacement resistance matrix are given according to the cover function; and the methods of handling rank deficiency induced by high degree polynomials as local approximation is discussed. Corresponding program is made by Matlab. One simple example is calculated by the program and the numerical results, being compared with the result of other methods, proves its correctness and effectiveness. It shows that the solution accuracy of numerical manifold method will be improved, when high-order displacement function is used. An example of underground chamber is also presented. Finally, the prospects of the method in tunnel and underground engineering are given.

Key words: numerical manifold method, high-order, tunnel and underground engineering