Papers by Keyword: Box-Counting

Abstract: In the paper, fractal geometry is used to study the crack evolving process of reinforce concrete beams. The fractal dimensions on surface of the reinforced concrete beam and the mechanical properties of the beam have the linear relationships perfectly. In order to compare the accuracy of the fractal dimensions, box counting method and the digital image box method in practical engineering are used to calculate the fractal dimension separately. The advantages and the disadvantages of these methods are analyzed. And the calculating conditions of these two methods are obtained. The research result gives a better way for determining the fractal dimension of the cracks on the reinforced concrete beam.

Abstract: A fractal is a property of self-similarity, each small part of the fractal object is similar to the whole body. The traditional box-counting method (TBCM) to estimate fractal dimension can not reflect the self-similar property of the fractal and leads to two major problems, the border effect and noninteger values of box size. The modified box-counting method (MBCM), proposed in this study, not only eliminate the shortcomings of the TBCM, but also reflects the physical meaning about the self-similar of the fractal. The applications of MBCM shows a good estimation compared with the theoretical ones, which the biggest difference is smaller than 5%.

Abstract: A comprehensive study of fractal property applied in earthquakes is analyzed based on the aftershock of 2008 Wenchuan earthquake. Different fractal parameters are analyzed to study the magnitude, epicenter and hypocenter structural distributions in time or space. The b-value is found to be 0.86 closed to which is usually 1.0 observed worldwide. This indicates there is a relative abundance of small magnitude events than large ones in the studied range. The spatial correlation is calculated using correlation integral technique, indicating that epicenters are approaching a two-dimensional region and the aftershocks are uniformly distributed along the trend of the aftershock zone. The rate of the fall of aftershock activity with time reflects the decrease of stress is modestly slow. Temporal correlation is 0.59 for aftershocks of M >4.0, indicating a non continuous aftershock activity. Geometrical probability dimension reflecting epicenter clustering degrees of the region was also analyzed. Also the volume fractal dimension of the aftershock region has been calculated using the box-counting technique to study the hypocenter distributions. From the assessment of slip on different faults it is inferred that 67.9% displacement is accommodated on the primary fault and the remainder on secondary faults.