Crack Propagation Analysis Based On Numerical Manifold Method And Its Application On Geotechnical Engineering

In underground engineering, such as tunneling, the large deformation of surrounding rock often causes very serious disasters, which brings a lot of damage to the development of the state. According to research findings, the large deformation of the surrounding rock is a complex process from continuum to non-continuum, the main issue of which is crack propagation. The traditional theoretical solution and laboratory tests are unable to quantify this process. The numerical manifold method (NMM) is a unified continuous and discontinuous numerical method, which adopts two cover systems, namely the mathematical cover and physical cover, and is one of the most suitable numerical algorithm for crack propagation simulation. Based on the basic concept of numerical manifold method, the main work of this dissertation is to develop a numerical algorithm for crack propagation simulation on Matlab platform. The main contents of this dissertation are briefly introduced as below.(1) A Matlab programme of NMM is developed first based on the basic concept of it. And the effectiveness of the NMM on treatment of statics and dynamics problems are verified by a few numerical examples. In addition to that, the convergence property of the NMM is also studied.(2) In order to improve the accuracy of the NMM on dealing with crack problems, the crack-tip asymptotic field interpolation is used to enrich the displacement of the physical covers near the crack tip. And two enrichment methods, namely the topological enrichment and the geometrical enrichment, are proposed to find the physical covers that need to be enriched. After that, the interation intergral is incorporated into the NMM to calculate stress intensity factors (SIFs). Then the maximum circumferential stress criterion is used to simulate linear elastic fracture propagation and the NMM is applied to linear elastic fracture mechanics.(3) In order to calculate SIFs directly from the solution of the governing equation, the NMM is improved by incorporating the hybrid crack element (HCE) method. The improved NMM divides the problem domain into two parts, namely the HCE domain and the NMM domain. The truncated Williams' stresses and displacements solutions are used inside the HCE domain, while the boundary displacements of the HCE domain are made compatible with the polynomial displacements of the NMM domain. In order to further increase the accuracy of the SIFs obtained by the improved NMM, the mixed high and low order cover system is adopted; that is, only the order of the local displacements of physical covers near the HCE boundary are increased by directly implementing p-adaptive. Further, in order to minish the displacement jump between the truncated Williams'displacement and the displacement on HCE boundary, the least-square method is used to calculated the complete Williams'displacement. Numerical examples show that the improved NMM only needs boundary integral in HCE domain and very accurate SIFs can be obtained directly from the solution of governing equations.(4) The characteristics of the points, lines and loops in the NMM are introduced, and it is found by analysis that the Shi's loop search algorithm is not suitable for loop search when simulating crack propagation. Thus, based on a few basic graphic algorithm, the crack tip automatic searching algorithm, the crack-tip physical cover automatical searching algorithm, the tree cutting algorithm for the newly generated crack segments and the manifold element updating algorithm are proposed. In addition, a new kind of loop searching algorithm based on manifold elements is developed, which make up for the deficiency of Shi's algorithm and can treat loop search work when simulating complex crack propagation. Then, based on the newly developed loop searching algorithm, the physical cover updating algorithm is developed. The renumbering methods for the manifold element and the physical cover are also studied, aiming to keep the governing matrix sparsely when cracking. At last, multi-crack propagations are simulated based on three-parameter Mohr-Coulomb criterion, and the robustness of the proposed algorithm is verified.(5) The process of large deformation and failure of the surrounding rock of a deep roadway after excavation in a typical engineering project is considered. Two different models are constructed and crack propagation is simulated based on the proposed algorithm.