Displcament Discontinuity Method And Its Apllication In Rock Engineering

In nature, a rock mass may contain large numbers of discontinuities or weaknesses at all scales, including cracks, joints and faults. The existance of the discontinuities gives rise to complex mechanical properties of fractured rock masses, which are much different from homogenous materials. It is difficult to understand the key role of these discontinuities and their propagation by using traditional finite element methods or other exiting numerical techniques.The displacement discontinuity method (DDM), a sort of indirect boundary element method, is proved to be an appropriate tool for use with fractured rock masses. Some improvement is made here to solve more problems in rock mechanics and rock engineering. In particular, the following questions have been investigated.1. The improved DDM is developed for rock mechanics problems in layered half-plane with discontinuities. Combined with the Fourier transform and the Airy stress function in elastic theory under conditions of plain strain, the uniform displacement discontinuity fundamental solutions are obtained by using the propagation matrix and stiff matrix methods for the first time. Next, a frame work using DDM for multi-layered elastic media in a half-plane is established. The displacement distribution of the tunnel roof in layered rock masses is presented, which shows that the layering feature of rock can not be ignored. At last, some other related fundamental solutions are discussed, for example, the compound plane.2. On the basis of the dual porosity media model and DDM, a frame work for handling saturated poroelastic media, where seepage and deformation are coupled, is put forward. Based on the Laplace-Fourier transform and the McNamee's displacement functions, the general solution of the Biot's consolidation functions for plane strain is easily obtained. Based on the continuity conditions of displacements and stresses, the unknowns are determined. Finally, the displacement discontinuity fundamental solutions for saturated poroelastic media are deduced through inverse Laplace-Fourier transform. After the discrete displacement discontinuity model is built, the problem of the single crack in an infinite plane is studied in detail. It is shown that the displacement discontinuity method, combined with the fractured porous media model, can reasonably simulate the coupling effects of ground water and rock masses.3. Three-dimensional problems of fractured rock masses are investigated using DDM. Friction between the surfaces of closed cracks under compression is considered by establishing a simple and efficient iterative algorithm based on contact resistance mitigation. The Mohr-coulomb rule is satisfied by iteration when the closed crack is in a sliding condition. The effect of fault structure on ground stress field is studied by using the displacement discontinuity method. The results indicate that the geometric configuration of the fault, mechanical property of the fault, and the loading condition are the main factors of ground stress distribution at the ends and vicinity of a fault. Considering the creep characteristics of the fault, it can be found that energy keeps on accumulating when the fault creeps, which will eventually bring on a structural earthquake. The displacement and stress fields of the Longmen fault zone are investigated.4. In order to understand the fracture process in rock masses, linear elastic fracture mechanics is applied. The stress intensity factories are obtained by an approximative regression method. A type of special crack tip element is introduced. Further, three-dimensional quasi-static crack propagation in fractured rock masses under complex loadings is investigated by using the DDM code MCP3D for the first time. Under the assumption that propagation occurs only in the perpendicular plane at each point in front of the crack, the maximum circumferential stress criterion for two-dimensional crack growth is used. Numerical examples of penny-shaped cracks subject to tension or compression in an infinite elastic media are analyzed. Comparison with both experimental and theoretical rerults shows that the code is accurate and effective.5. The rules of fatigue crack growth in brittle rocks under freeze-thaw cycles are investigated using DDM. A simplified physical model is proposed firist. If the water filling between both faces of the crack is totally frozen, the crack is modeled as a continuous filled joint and subjected to periodic frost heaving pressure on both faces of the crack. The frost heaving force can be determined by satisfying the compatible deformation condition. The maximum circumferential stress theory is used to predict the crack stability and the direction of propagation at each step.By introducing the effective stress intensity factor amplitude, the classic Paris'equation is extended to this case. Finally, the multi-axial fatigue propogation path of a single inclined microcrack is simultated, and the fatigue life is calculated.