• KCI Concrete Journal
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• v.14 no.1
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• pp.30-35
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• 2002

The fractal geometry is a non-Euclidean geometry which describes the naturally irregular or fragmented shapes, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cementitious composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is apparent.ent.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2004.09a
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• pp.159-163
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• 2004

This study was conducted to calculate the permeability coefficient in a single fracture while taking the true fracture geometry into consideration. The fracture geometry was measured using the confocal laser scanning microscope (CLSM). The CLSM geometry data were used to reconstruct a fracture model for numerical analysis using a homogenization analysis (HA) method. The HA is a new type of perturbation theory developed to characterize the behavior of a micro-inhomogeneous material that involves periodic microstructures. The HA permeability was calculated based on the local geometry and local material properties (water viscosity in this case). The results show that the permeability coefficients do not follow the theoretical relationship of the cubic law.

• International Journal of Concrete Structures and Materials
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• v.19 no.1E
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• pp.25-32
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• 2007

The fracture energy evaluated from the previous experimental results can be simulated by using the modified singular fracture process zone (S-FPZ) model. The fracture model has two fracture properties of strain energy release rate for crack extension and crack close stress versus crack width relationship $f_{ccs}(w)$ for fracture process zone (FPZ) development. The $f_{ccs}(w)$ relationship is not sensitive to specimen geometry and crack velocity. The fracture energy rate in the FPZ increases linearly with crack extension until the FPZ is fully developed. The fracture criterion of the strain energy release rate depends on specimen geometry and crack velocity as a function of crack extension. The behaviors of micro-cracking, micro-crack localization and full development of the FPZ in concrete can be explained theoretically with the variation of strain energy release rate with crack extension.

• Journal of the Korea Concrete Institute
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• v.13 no.2
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• pp.146-152
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• 2001

The fractal geometry is a non-Euclidean geometry which discribes the naturally irregular or fragmented shaps, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cemposite composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is appearent.ent.

• Structural Engineering and Mechanics
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• v.76 no.6
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• pp.725-736
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• 2020

In this work the mixed mode I/III fracture of sandstone has been studied experimentally and numerically. The experimental work used three-point bending specimens containing pre-existing cracks, machined at various inclination angles so as to achieve varying proportions of mode I to mode III loading. Dimensionless stress intensity factors were calculated using the extended finite element method (XFEM) for and compared with existing results from literature calculated using conventional finite element method. A total of 28 samples were used to conduct the fracture test with 4 specimens for each of 7 different inclination angles. The fracture load and the geometry of the fracture surface were obtained for different mode mixities. Prediction of the fracture loads and the geometry of the fracture surface were made using XFEM coupled with a cohesive zone model (CZM) and showed a good comparison with the experimental results.

• International Journal of Concrete Structures and Materials
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• v.18 no.3E
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• pp.213-219
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• 2006

Modified singular fracture process zone(S-FPZ) model is proposed in this paper to determine a fracture criterion for continuous crack propagation in concrete. The investigated fracture properties of the proposed fracture model are strain energy release rate at a micro-crack tip and the relationship between crack closure stress(CCS) and crack opening displacement(COD) in the FPZ. The proposed model can simulate the actual fracture energy of experimental results fairly well. The results of the experimental data analysis show that specimen geometry and loading condition did not affect the CCS-COD relation. However, the strain energy release rate is a function of not only specimen geometry but also crack extension. The strain energy release rate remained constantly at the minimum value up to the crack extension of 25 mm, and then it increased linearly to the maximum value. The maximum fracture criterion occurred at the peak load for specimens of large size. The fracture criterion remained at the maximum value after the peak load. The variation of the fracture criterion is caused by micro-cracking and micro-crack localization. The fracture criterion of strain energy release rate can simply be the size effect of concrete fracture, and it can be used to quantify the micro-cracking and micro-crack localizing behavior of concrete.

• Tunnel and Underground Space
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• v.29 no.4
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• pp.230-242
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• 2019

While various automatic rock fracture survey methods have been researched, the evaluation of the accuracy of these methods raises issues due to the absence of a metric which fully expresses the similarity between automatic and manual fracture maps. Therefore, this paper proposes a geometry similarity metric which is especially designed to determine the overall similarity of fracture maps and to evaluate the accuracy of rock fracture survey methods by a single number. The proposed metric, Scanline Intersection Similarity (SIS), is derived by conducting a large number of scanline surveys upon two fracture maps using Python code. By comparing the frequency of intersections over a large number of scanlines, SIS is able to express the overall similarity between two fracture maps. The proposed metric was compared with Intersection Over Union (IoU) which is a widely used evaluation metric in computer vision. Results showed that IoU is inappropriate for evaluating the geometry similarity of fracture maps because it is overly sensitive to minor geometry differences of thin elongated objects. The proposed metric, on the other hand, reflected macro-geometry differences rather than micro-geometry differences, showing good agreement with human perception. The metric was further applied to evaluate the accuracy of a deep learning-based automatic fracture surveying method which resulted as 0.674 (SIS). However, the proposed metric is currently limited to 2D fracture maps and requires comparison with rock joint parameters such as RQD.

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.333-338
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• 2001

Fractal geometry is a non-Euclidean geometry which has been developed to quantitative analysis irregular or fractional shapes. Fractal dimension of irregular surface has fractal values ranging from 2 to 3 and of irregular line profile has fractal values ranging from 1 to 2. In this paper, quantitative analysis of crack growth patterns during the fracture processing of fiber-reinforced cement composites based on fractal geometry. The fracture behaviors of fiber reinforced mortar beams subjected to three-point loading in flexure. The beams all had a single notch depth, but varing volume fractions of polypropylene, cellulose fibers. The crack growth behaviors, as observed through the image processing system, and the box counting method was used to determine the fractal dimension, Df. The results showed that the linear correlation exists between fractal dimension and fracture energy of the fiber reinforced cement mortar.

• Journal of the Korean Institute of Gas
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• v.25 no.1
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• pp.20-29
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• 2021

During multi-stage fracturing in a low permeable shale formation, stress interference occurs between the stages which is called the "stress shadow effect(SSE)". The effect may alter the fracture propagation direction and induce ununiform geometry. In this study, the stress shadow effect on the hydraulic fracture geometry and the well productivity were investigated by the commercial full-3D fracture model, GOHFER. In a homogeneous reservoir model, a multi-stage fracturing process was performed with or without the SSE. In addition, the fracturing was performed on two shale reservoirs with different geomechanical properties(Young's modulus and Poisson's ratio) to analyze the stress shadow effect. In the simulation results, the stress change caused by the fracture created in the previous stage switched the maximum/minimum horizontal stress and the lower productivity L-direction fracture was more dominating over the T-direction fracture. Since the Marcellus shale is more brittle than more dominating over the T-direction fracture. Since the Marcellus shale is more brittle than the relatively ductile Eagle Ford shale, the fracture width in the former was developed thicker, resulting in the larger fracture volume. And the Marcellus shale's Young's modulus is low, the stress effect is less significant than the Eagle Ford shale in the stage 2. The stress shadow effect strongly depends on not only the spacing between fractures but also the geomechanical properties. Therefore, the stress shadow effect needs to be taken into account for more accurate analysis of the fracture geometry and for more reliable prediction of the well productivity.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.06a
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• pp.1324-1327
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• 2003

The compressed fracture of spine caused by osteoporosis is one of the most frequent diseases in bone fracture. Recently the vertebroplasty has drawn much attention as a medical treatment for the compressed fracture of spine, which strengthens the vertebral body and corrects deformity, and relieves pain in patients by injecting bone cement. The finite element analysis is used to investigate the vertebroplasty quantitatively. Previous works with finite element analysis have drawbacks in their simplified models geometry of vertebral body and with material properties of bone. In this paper the exact geometry of vertebral body has been constructed from medical image data and the biomechanical property changes of vertebral body in vertebroplasty have been investigate by using three dimensional finite element analysis.