Formulation of a rhree-dimensional numerical manifold method with tetrahedron and hexahedron elements

Numerical Manifold Method (NMM) is an extension of Discontinuous Deformation Analysis which contains and combines FEM and joint/block oriented DDA in a unified form. At present, application of NMM is mainly limited to two-dimensional analysis which is not realistic for many underground excavation works. In the present paper, three-dimensional NMM based on tetrahedron and hexahedron elements is proposed. The corresponding three-dimensional cover contact detection algorithms which have some fundamental properties different from the corresponding two-dimensional analysis are also developed. Based on the present formulations, engineering problems with arbitrarily oriented discontinuities can be modeled and realistic modeling of construction works becomes possible.