Three dimensional numerical manifold method and rock engineering applications - He, Lei (2011)
Among various numerical methods, the numerical manifold method (NMM) is one of most suitable method to simulate deformations and stabilities of rock masses. The NMM itself can be thought as a bridge connecting two branches of numerical method: continuum methods (e.g. FEM) and discontinuum methods (e.g. DDA). Since it was first proposed in 1991, most of research works on the NMM were carried out within the two-dimensional (2-D) framework. However, it will be more realistic and beneficial to the practicing industry to address the problem with a three-dimensional model and an advanced numerical method is highly demanded in rock engineering. This thesis extends the numerical manifold method to the 3-D domain based on the 2-D fundamentals. First, the conceptual framework of the 3-D NMM is established, including the definitions of the mathematical cover, physical cover, manifold pattern and manifold element in the 3-D domain. A new general 3-D contact algorithm is subsequently developed for the 3-D NMM. The proposed contact treatment procedure consists of distinct features, including: three operation phases for the checking process, NMM hierarchical contact system, contact warning based on mathematical patterns (MPs), transformation of two essential entrance modes, transferring contact information, penalty treatment for contact constraints, open-closed iteration process, and lagged verification on contact state. These features equip 3-D NMM with an efficient and accurate strategy of contact treatment. A total of ten numerical examples are analyzed in the present thesis, including verification of the 3-D NMM formula, analysis of a discrete blocky system, verification of the contact algorithm, and two scenarios in rock engineering, i.e., stability analysis of rock slopes and tunnels. The proposed 3-D NMM is proved to be a robust, efficient and stable tool with both static and dynamic analysis ability. It has great potential to be further developed and applied in practical rock engineering.