Since rocks generally are brittle materials, the generating, propagating, and combining of cracks in rocks play an important roles in the failure progress of rocks. Many researchers have concluded that the crack pattern have fractal properties, and the fractal method can be used to analyze the failure of rock. In this article, the box fractal dimension of two kinds of rock has been measured based on an experiment of SEM. The results illustrated that fractal dimension values varied with rocks. By numerical methods, the mechanism of the variation and relation to the stress and mineral composition in rocks have been studied. Further more, the failure properties characterized by the variation of fractal dimension are also studied by energy method.
Since rocks generally arc brittle materials, the generating, propagating, and combining of cracks in rocks play an important role in the failure progress of rocks. For rocks stability evaluating, it's important to analysis the development of microcracks in fracturing rocks. A series of experiments have been carried out by many researchers to observe the fracture process of stressed rocks, both by SEM (scanning electron microscope) and by optical microscope. Based on the observation, some of the researchers concluded that the developing cracks in stressed rocks have fractal characteristics, and the fractal method can be used to study the fracture area in rocks and the failure properties of rocks. In this paper, based on the SEM observation of rock specimen(slotted or drilled), including Hong Kong granite and Wuhan marble, the fractal dimension which is varied with the developing of cracks in rock specimens is measured and calculated. Furthermore, by comparing the differences of the fractal characteristics of cracks in different kinds of rock material, it is illustrated that there is a relationship between the variation of fractal characteristics and the mineral composition and formation of rocks. and the attempt to explain the internal mechanism of the variation of fractal dimension values and its effect on the failure properties of rocks has also been conducted In this article.
Box-dimension Method, which counts the number of boxes required to cover or include all cracks as a function of box size, is applied to determine the fractal characteristic of crack pattern in rock specimen. A and d can be gained by simulating method from the testing result. The measurement of fractal dimension is based on the SEM experiment of rock specimen under uniaxial pressure. Samples tested include granite extracted from H.K. and marble from Wuhan, the total number of the specimen measured is 6. Fractal dimensions of different area of specimen at different stress stage have been attained. The box sizes used in this test are varied according to the scale of the selected area and the photograph. Only one specimen (M I I) was manufactured a 45° inclined slot in center previously, as shown in fig.1.a, all the other samples were prefabricated a round hole in center, as shown in fig.l.b.
