• Structural Engineering and Mechanics
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• v.23 no.2
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• pp.147-161
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• 2006

Recent developments in fractal theory suggest that fractal may provide a more realistic representation of characteristics of cementitious materials. In this paper, the roughness of fracture surfaces in cementitious material has been characterized by fractal theory. A systematic experimental investigation was carried out to examine the dependency of fracture parameters on the aggregate sizes as well as the loading rates. Three maximum aggregate sizes (4.76 mm, 12.7 mm, and 19.1 mm) and two loading rates (slow and fast loading rate) were used. A total of 25 compression tests and 25 tension tests were performed. All fracture parameters exhibited an increase, to varying degrees, when aggregates were added to the mortar matrix. The fracture surfaces of the specimens were digitized and analyzed. Results of the fractal analysis suggested that concrete fracture surfaces exhibit fractal characteristics, and the fractal geometry provide a useful tool for characterizing nonlinear fracture behavior of concrete. Fractal dimension D was monotonically increased as maximum aggregate sizes increase. A new fractal fracture model was developed which considers the size and shape of aggregate, and the crack paths in the constituent phases. Detailed analyses were given for four different types of fracture paths. The fractal fracture model can estimate fractal dimension for multiphase composites.

• Proceedings of the KSRS Conference
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• 2007.10a
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• pp.616-619
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• 2007

Nowadays, urbanized area expands its boundary, and distribution of urbanized area is gradually transformed into more complicated pattern. In Korea, SMA(Seoul Metropolitan Area) has outstanding urbanized area since 1950s. But it is ambiguous whether urban distribution is clustered or dispersed. This study aims to show the way in which expansion of urbanized area impacts on spatial distribution pattern of urbanized area. We use quadrat analysis, nearest-neighbor analysis and fractal analysis to know distribution pattern of urbanized area in time-series urban growth. The quadrat analysis indicates that distribution pattern of urbanized area is clustered but the cohesion is gradually weakened. And the nearest-neighbor analysis shows that point patterns are changed that urbanized area distribution pattern is progressively changed from clustered pattern into dispersed pattern. The fractal dimension analysis shows that 1972's distribution dimension is 1.428 and 2000's dimension is 1.777. Therefore, as time goes by, the complexity of urbanized area is more increased through the years. As a result, we can show that the cohesion of the urbanized area is weakened and complicated.

• Journal of the Korean Data and Information Science Society
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• v.24 no.1
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• pp.53-62
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• 2013

Currently we have 11 climatological stations registered in World Meteorological Organization. Geographically, these stations are unevenly distributed in Korea and are mainly located on seaside. Therefore station's density analysis should be performed to produce the high-quality climatological data. Using the correlation integral method, the density of climatological stations can be measured by the estimation of fractal dimension. In this study, new climatological stations having the higher fractal dimension were selected. Sequential or simultaneous selection method were carried out until 3 new stations were selected based on the fractal dimension.

• Computers and Concrete
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• v.2 no.3
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• pp.239-248
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• 2005

The article presents the results of examination of the fractal dimension D of concrete specimen fracture surfaces obtained in fracture toughness tests. The concretes were made from three different types of coarse aggregate: gravel, dolomite and basalt aggregate. Ordinary concretes (C40) and high-performance concretes (HPC) were subjected to testing after 7, 14, 28 and 90 days of curing, respectively. In fracture toughness and compressive tests, different behaviours of concretes were found, depending on the type of aggregate and class of concrete (C40, HPC). A significant increase in the strength parameters tested occurred also after a period of 28 days (up to the $90^{th}$ day of curing) and was particularly large for concretes C40. Fractal examinations performed on fracture replicas showed that the fractal dimension D was diverse, depending on the coarse aggregate type and concrete class being, however, statistically constant after 7 and 14 days for respective concretes during curing. The fractal dimension D was the greater, the worse strength properties were possessed by the concrete. A cross-grain crack propagation occurred in that case, due to weak cohesion forces at the coarse aggregate/mortar interface. A similar effect was observed for C40 and HPC made from the same aggregate. A greater dimension D was exhibited by concretes C40, in which case the fracture was easier to form compared with high-performance concretes, where, as a result of high aggregate/mortar cohesion forces, the crack propagation was of inter-granular type, and the resulted fracture was flatter.

• Proceedings of the KIEE Conference
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• 1997.07e
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• pp.1758-1760
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• 1997

Automatic detection system to detect acoustic emission pulse and fractal dimension were developed, to observe tree deterioration phenomena in LDPE. The purpose of our work are to use acoustic emission system and fractal dimension and to investigate the treeing phenomena in polymeric insulation under applied AC voltage 11[kV] with an artificial needle-shaped void(1.5[mm]) using the above system. We analyzed and phase angle-acoustic emission pulse amplitude-deterioration time ($\Phi$-AEA-t) pattern and phase angle-acoustic emission pulse number-deterioration time($\Phi$-AEN-t) pattern using statistical operators such as skewness, fractal dimension. In this paper show that the correlation of $\Phi$-AEA-t, $\Phi$-AEN-t, fractal dimension using regression analysis by the method of least squares can be used to predict the breakdown just before the breakdown occurs.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.24 no.1
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• pp.124-129
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• 2010

When a phenolic resin is carbonized by the leakage current flowing along its surface, the carbonization pattern is one of the most important factors to determine its carbonization characteristics. However, the typical carbonization pattern of a phenolic resin is too complicated to be analyzed by conventional Euclidean geometry. In most cases, such a complicated shape shows a fractal structure. It is possible, therefore, to examine the characteristics of the carbonization pattern regarding a given phenolic resin. In order to quantitatively investigate the carbonization pattern of the phenolic resin carbonized by a leakage current, in this paper, the fractal dimension of the carbonization pattern has been calculated as a function of the magnitude of a leakage current and the distance between two electrodes. For reliability of calculation, the correlation function as well as the box counting method has been used to calculate the fractal dimension. According to the result of calculation, the fractal dimension increases as the current increases at the constant electrode gap distance. However, there is no significant relation between the fractal dimension and the electrode gap distance at a constant current.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• v.38 no.2
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• pp.96-100
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• 2012

Objectives: This study sought to evaluate trabecular changes in the mandible using fractal analysis and to explain the transient osteopenia related to rapid orthodontic tooth movement after orthognathic surgery. Materials and Methods: Panoramic radiographs were taken of 26 patients who underwent bilateral sagittal split ramus osteotomy. Radiographs taken before the surgery and 1 month after surgery were overlapped, and $40{\times}40$ pixel square regions of interest were selected near the mandibular canines and 1st molars. After the image processing procedure, the fractal dimension was calculated using the box-counting method. Results: Fractal dimension after orthognathic surgery decreased in a statistically significant manner (P<0.05). The change in fractal dimension on the canine side had greater statistical significance as compared to that seen on the 1st molar side. Conclusion: This study found that bone density decreases after orthognathic surgery due to transient osteopenia related to the regional acceleratory phenomenon. This result can provide a guide to evaluating orthodontic tooth movement after orthognathic surgery.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.7 no.5
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• pp.7-14
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• 1998

In this paper, Fractal analysis applied to evaluate machined surface profile. The spectrum method was used to calculate fractal dimension of generated surface profiles by Weierstrass-Mandelbrot fractal function. To avoid estimation errors by low frequency characteristics of FFT, the Maximum Entropy Method (MEM) was examined. We suggest a new criterion to define the MEM order m. MEM power spectrum with our criterion is proved to be advantageous by the comparison with the experimental results.

• Journal of the Korean Geotechnical Society
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• v.18 no.6
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• pp.25-32
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• 2002

The fractal dimension that was evaluated with soil components from the traditional particle-size distribution(PSD) curve was analyzed using the results of Wu et al.(1993) and Bittelli et al.(1999). In order to find the change of the variation of fractal dimension with the upper and lower limit, three limit values(200$\mu{m}$, 63$\mu{m}$, and 125$\mu{m}$) were chosen, and these results of fractal dimension analysis were compared to the result that was evaluated in the whole range of the soils. The results showed that it is possible to evaluate fractal dimension from the traditional PSD curve with the soil contents, and it showed that Bittelli et at.(1999)'s upper and lower limit value was more reasonable than Wu et al.(1993). Equations that were presented by Bittelli et at.(1999) also showed a good agreement with the analytical results in the silt domain.

• Journal of Ocean Engineering and Technology
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• v.14 no.1
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• pp.29-36
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• 2000

Surface micro-crack grows along intergranular or transgranular region of crystal grains. But if it meets the barrier such as sessile dislocation and precipitates it loses straightness and deflects. Investigators had many difficulties in estimating fatigue life of smooth specimen because of the random distribution growth and coalescence of surface micro-cracks. The path of surface micro-crack has irregularity due to nonhomogeneous microstructure. Euclidian geometry can't quantify the shape of surface micro-crack but fractal geometry can. Therefore in this paper fractal dimension is measured at various stage of cycle ratio and estimated cycle ratio in 2024-T3 aluminium, alloy.