Fracture analyses based on finite cover method (FCM) are conducted to investigate a fracture mechanism of granites. The analysis by the FCM, which is a cover-based generalized finite element method, has been extended for analyses of fracture process involving cracking within and/or between mineral grains in inhomogeneous rocks. A fracture process of numerical specimens which are prepared using X-ray CT image of African granites is studied. The analysis of material parameters, such as Young's modulus and tensile strength of minerals contained in the granites, is conducted to examine its influence on the fracture process and strength. Additionally, distribution of the mineral grains provides anisotropy for mechanical properties of granites. Comparison between numerical and experimental results presents that the important factors causing the anisotropy of macroscopic strength are the Young's modulus as well as the tensile strength of minerals distributed in the granites.
A fracture toughness is the most useful mechanical property in rock mechanics, describing resistance to fracture initiation . Igneous rocks generally contain microcracks, representing mechanical weakness. The orientation and distribution of the microcracks are dominant factors affecting mechanical strengths of rocks, such as the fracture toughness [2–4]. However, taking into account fracture process of rocks governed by the microscopic crack initiation, the fracture process is decided by microstructural parameters themselves: a type of matrix and minerals, dimensions, and distribution of mineral grains. Any preferred orientation of the microstructure provides anisotropy for mechanical properties of granites. Kataoka et al.  has conducted Semi-Circular Bend(SCB) tests using African granite including observation of thin section and X-ray CT method to examine influence of the microstructure on the anisotropy of mechanical properties. They presented that the dominant factor causing the anisotropy of mode I fracture toughness is the distribution of mineral grains rather than inherent microcracks in the rocks.
To discuss of the anisotropy of properties involves evaluating a fracture process including crack initiation and propagation in the microstructures. In this research, we will conduct numerical analyses of tensile crack initiation and propagation to examine the fracture process of rocks in detail. The analyses are based on finite cover method(FCM) which is a generalized cover-based FEM. It is enable us to simulate progressive fracture process involving crack initiation and propagation within and/or between mineral grains in inhomogeneous rocks .