Development of an explicit numerical manifold method for dynamic stability analysis of rock slope

In this thesis, an explicit version of the numerical manifold method (NMM) has been developed for dynamic stability analysis of rock slope. Firstly, Newmark integration scheme used in the NMM is brief introduced and derived in detail to further deepen understanding of the NMM and its implementations. The numerical results present the explicit scheme is more efficient in solving the nonlinear dynamic systems and such problems compared to implicit scheme. Then, an explicit time integration scheme for the NMM is proposed to improve the computational efficiency. The developed explicit NMM (ENMM) is validated by several examples. The calibration study of the ENMM on P-wave propagation across a rock bar has been conducted. Various considerations in the numerical simulations are discussed and parametric studies have been carried out to obtain an insight into the influencing factors in wave propagation simulation. The numerical results from the ENMM and NMM modelling are accordant well with the theoretical solutions, but the ENMM is more efficient than the original NMM. The temporal and spatial coupled explicit-implicit (E-I) algorithms for the numerical manifold method (NMM) are proposed. The time integration schemes, transfer algorithm, contact algorithm and damping algorithm are studied in the temporal coupled E-I algorithm to merge both merits of the explicit and implicit algorithms in terms of efficiency and accuracy. In particular, onefold cover system is drawn into the coupled spatial E-I algorithm, in which the contact algorithm based on the onefold cover system is discussed and derived in detail. The simulated results are well agreement with the implicit and explicit algorithms simulations, but the efficiency is improved evidently. The dynamic stability analysis of rock slope failure using the NMM is studied. Conservational pseudo-static methods (PSMs), Newmark method and numerical methods applying into the seismic stability analyses are investigated, the advantages and limitations of which are studied by contrast of the NMM. An alternative ENMM and coupled E-I algorithms are applied to study the seismic stability of rock slope. Furthermore, parallel computing with OpenMP is evaluated to improve efficiency of the NMM. To reveal the validity and applicability of the developed ENMM, some numerical examples of rock slope stability analysis are investigated, in which one example of rock slope is taken into account to present the coupled ENMM with discontinuous deformation analysis (DDA) in terms of efficiency. Simulated results of the NMM will compare with the field measurements to illustrate the applicability of the NMM. The present study showed the developed ENMM is more efficient while without losing the accuracy, comparing to the original implicit version of the NMM. Therefore, it can be predicted that the proposed ENMM is promising and can be extend applied to larger scale project of rock slope with dynamic stability analysis.