Extended numerical manifold method for engineering failure analysis

In this thesis, the numerical manifold method (NMM) has been extended for engineering failure analysis. The NMM has been coupled with the fracture mechanics to simulate the complex cracks and their growth. A new concept ‘singular physical cover’ is introduced. Asymptotic crack tip functions extracted from the analytical solution are chosen as the local approximation spaces of the singular physical covers. The domain form of the interaction integral and the maximum circumferential stress criterion are employed to evaluate the stress intensity factors at the crack tips and to predict the crack growth direction, respectively. Several typical crack problems are simulated. The numerical results show that the extended NMM can resolve the stress singularities around the crack tips well, and it is efficient and robust for complex crack problems. In addition, the extended NMM is obviously superior to the conventional finite element method (CFEM) and its various modifications, such as the extended finite element method (XFEM), the generalized finite element method (GFEM), etc. The NMM has also been extended to account for the practical rock failure process. The Mohr-Coulomb criterion with a tensile cutoff is employed to predict the crack initiation and propagation. A cover-division strategy is adopted to fulfill the crack initiation and propagation. The cover-division strategy can avoid the mesh dependency to some extent because of the non-local nature of the stress. Algorithms are implemented to treat the manifold elements, the physical covers and the loops during the fracturing process. The developed program has been applied to simulate the progressive failure of rock slopes with non-persistent joints. Numerical results indicate that it is able to capture the fracturing in intact rock bridge and finally allow the kinematic release. The developed program has also been applied to investigate the potential failure mechanisms of footwall slopes in surface coal mining.Doctor of Philosophy (CEE