Applications Of Manifold Method In Numerical Analyses Of Fracture Behavior And Crack Development Of Rock Masses

As a type of geomaterials naturally formed, rock mass is usually composed of many natural joints and cracks or other types of intact discontinuities due to long-term deformation and damage. When loaded, cracks will be initiated and expand in the rock mass and the then mechanical properties of rock mass will change. The study on the crack expansion is very important for the evaluation of damage and stability of rock masses.The main techniques for investigating rock mass include experimental method and numerical analysis method. Through numerical analyses, a large number of usable data can be obtained. But it is not convenience to apply this method, and it needs much manpower and financial resources. Numerical analyses can analyze problems of rock mass quickly. In this paper, crack expansion of rock mass is analyzed and computed with numerical manifold method.In recent years, the numerical analysis methods of geomechanics have achieved considerable development. As a new technique, the manifold method, proposed by Genhua, Shi in 1990s is based on the concept of topology manifold and differential manifold in mathematics. This method takes the advantage of both the traditional FEM technique and the discontinuous deformation analysis method (DDA). In this method, the finite-cover technique is used. The finite-covers can unify the mathematical description for both continuous problems and discontinuous problems in geomechanics and hence it can solve the discontinuous problems more rationally. Therefore, the manifold method is combined with fracture mechanics in this thesis to deal with the problems of crack expansion.The fundamental principle of the manifold method is demonstrated comprehensively in this thesis. The formulations of the high-order manifold methods with complete first order polynomial cover functions and the complete second order polynomial cover functions are presented. Then, the possibilities of applying the manifold method to numerical analyses of fracture behavior and crack expansion of rock masses are discussed. The treatments for the related special issues are given. The static fracture mechanics is used for analysis, in which the growth rule of crack is mainly taken into account by static equilibrium condition. However the velocity of crack growth is overlooked. In order to overcome such a shortcoming, the kinetic fracture mechanics is employed, in which the growth of crack is governed by kinetics and effect of crack growth velocity is considered. In the thesis, manifold method is incorporated with both static and kinematical theories of fracture mechanics to numerical simulation of the fracture behavior and initiation and development of cracks.The general description of the problem is stated and stress intensity factor (SIF) is calculated and the criterion of crack growth is presented. The method is numerically implemented and numerical analyses for a number of benchmark problems are made.Then, the arresting mechanism of crack upon loading is discussed based on the proposed method. The crack growth velocity is introduced based on kinematical theory of fracture mechanics. The stress intensity factors of crack will be varied with crack development. Considering the effect of crack growth velocity on the stress intensity factors, the stress intensity factors computed by the proposed method are compared with the fracture roughness and the development process of crack can be predicted. The arresting will occur under the condition when the computed stress intensity factor is less than fracture roughness. Therefore the initiation, development and arresting which may be displayed in the process loading of rock masses can be presented by the proposed method.A special scheme for meshing and pre-treatment is required in applications of the manifold method. Based on the auto-meshing techniques used for finite element method (FEM) and the object oriented programming (OOP) method, a new meshing technique specially adapted for manifold method is developed in this thesis. The scheme is numerically impleme...