| Summary: | 博士 === 國立成功大學 === 資源工程學系碩博士班 === 96 === Numerical techniques in rock fracture mechanics have become indispensable tools for solving all kinds of science and engineering problems. Extensive research has been carried out for the development of new numerical methods to determine the stress intensity factors (SIFs). The evaluation of the SIFs may have direct practical applications in obtaining the safety factor of the elastic structures in engineering design. Due to the varied engineering conditions in this research area, it is imperative to develop new numerical methods or to explore alternative techniques for the purpose of solving the complicated problems and to improve the efficiency and accuracy of the existing or new numerical methods.
This thesis presents the dual boundary element method (dual-BEM) or single-domain BEM to analyze the mixed-mode SIFs in a linear anisotropic elastic rock. The mixed-mode (I-II) SIFs (KI and KII) for two-dimensional (2-D) cracked ring disk, and the mixed-mode (I-II-III) SIFs (KI, KII and KIII) for a three-dimensional (3-D) cuboid with either an embedded crack or edge surface crack are selected to explore the fracture mechanics problems. The transversely isotropic plane of the material and the crack surface can both orient arbitrarily with respect to a fixed global coordinate system.
Five types of three-node quadratic elements and nine types of nine-node quadrilateral elements are utilized to approximate the crack tip (front) as well as the outer boundary, and the mixed-mode SIFs are evaluated using the asymptotical relation between the SIFs and the relative crack opening displacements (COD) via the Barnett-Lothe tensor. In the 3-D case, it is for the first time that the special nine-node quadrilateral shape function is applied to the boundary containing the crack mouth. The numerical method developed can be applied to the SIF calculation in a finite transversely isotropic cuboid within an inclined surface crack. The computational approach and the results of SIFs are of great value for the modeling and design of anisotropic elastic structures.
A new methodology by combining the dual-BEM and the cracked ring test are presented to determine the mixed-mode (I-II) fracture toughness (KIC and KIIC) in 2-D anisotropic rocks. It has been proved that the proposed dual-BEM program can be used to calculate the SIFs of cracked anisotropic plate with good accuracy. An anisotropic Hualien marble of Taiwan with clear foliation was selected to carry out the cracked ring tests. Based on the measurement of failure load during the test, the mixed-mode fracture toughness of Hualien marble can be determined. Experimental results show that fracture toughness of rocks varies with the radius ratio, material inclined angle and crack angle.
For the embedded crack case in 3-D, our numerical results show that the mode-I SIF arrives at the largest possible value when the material inclined angle and dig angle are equal to 45 degree, and the crack inclined angle and dip angle are equal to 0 degree. It is further observed that when the crack is oriented vertically or nearly vertically, the mode-I SIF becomes negative, indicating that the crack closes due to an overall compressive loading normal to the crack surface. Variation of the SIFs for modes II and III along the crack fronts also shows some interesting features for different combinations of the material and crack orientations. For the edge crack case, the numerical results show clearly the influence of the material and crack orientations on the mixed-mode SIFs. For comparison, we have also calculated the mode-I SIF when a horizontal rectangular crack is embedded entirely within the cuboid. It is observed that the SIF values along the crack front are larger when the crack is closer to the surface of the cuboid than those when the crack is further away from the surface.
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