Fractal analysis for space filling and shape of fractures in rock sections

Abstract

Space filling and shape of fractures were investigated on rock sections of the Tamagawa Welded Tuffs distributed around Hachimantai, Northeast Japan. Various scales of natural fracture patterns which were obtained from 10m×10m, 5m×5m, 50cm×50cm and 1.6mm×1.6mm observation areas were used for fractal analysis. Space filling of natural fracture patterns in sections of the Tamagawa Welded Tuffs shows a statistical self-similarity, and its fractal dimension determined by a box-counting algorithm lied in the range from 1.08 to 1.48. Mean values of fractal dimension in various scales of fracture pattern of the Tamagawa Welded Tuffs were approximately equal. These facts suggest that the fractal dimension of space filling of the zoom sequences had an unique fractal property and the value of the fractal dimension was about 1.28. Fracture shape in the section which is sliced in random orientation also showed fractal property, and its fractal dimension was in the range between 1.01 and 1.05. The fractal observed in space filling and shape on natural rock suggests that the characteristic fractal dimensions could be estimated by fracture pattern of other scales. In order to compare the fractal dimensions of fracture space filling among various observation areas of different scales, it is necessary that the ratio of the sensitivity of measurement (l_min: the minimum length of between ends of fracture) to the maximum cell dimension (R) has the same value with the ratio of the minimum cell dimension for box-counting r_{d, min} to R in each observation area. When the values of l_min/R and r_{d, min}/R was about from 0.02, we could reasonably compare the fractal dimensions of fracture space filling in the rage from microscope scale to decimeter scale of different observation areas.