• Economic and Environmental Geology
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• v.30 no.5
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• pp.433-442
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• 1997

A dual-permeability fractal model of fluid flow is proposed. The model simulates groundwater flow in fissured dual aquifer system composed of Aquifer 1 and Aquifer 2. For this model. groundwater flow originates only from Aquifer 1 on the pumping well. The model considers wellbore storage and skin effects at the pumping well and then shows exact drawdown at the early time of pumping. Type curves for different flow dimensions and for two cases are presented and analyzed. The case 1 represents the aquifer system which consists of Aquifer 1 with low permeability and high specific storage and Aquifer 2 with high permeability and low specific storage. The case 2 is inverse to the case 1. Dimensionless drawdown curves in Aquifer 1 and Aquifer 2 shows characteristic trend each other. Consequently, the model will be useful to analyze pumping test data of different draw down patterns on the pumping well and observation wells.

• Geomechanics and Engineering
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• v.13 no.2
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• pp.333-352
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• 2017

A comparison study is made between the dynamic properties of an argillaceous siltstone and its grouting-reinforced body. The purpose is to investigate how grout injection can help repair broken soft rocks. A slightly weathered argillaceous siltstone is selected, and part of the siltstone is mechanically crushed and cemented with Portland cement to simulate the grouting-reinforced body. Core specimens with the size of $50mm{\times}38mm$ are prepared from the original rock and the grouting-reinforced body. Impact tests on these samples are then carried out using a Split Hopkinson Pressure Bar (SHPB) apparatus. Failure patterns are analyzed and geotechnical parameters of the specimens are estimated. Based on the experimental results, for the grouting-reinforced body, its shock resistance is poorer than that of the original rock, and most cracks happen in the cementation boundaries between the cement mortar and the original rock particles. It was observed that the grouting-reinforced body ends up with more fragmented residues, most of them have larger fractal dimensions, and its dynamic strength is generally lower. The mass ratio of broken rocks to cement has a significant effect on its dynamic properties and there is an optimal ratio that the maximum dynamic peak strength can be achieved. The dynamic strain-softening behavior of the grouting-reinforced body is more significant compared with that of the original rock. Both the time dependent damage model and the modified overstress damage model are equally applicable to the original rock, but the former performs much better compared with the latter for the grouting-reinforced body. In addition, it was also shown that water content and impact velocity both have significant effect on dynamic properties of the original rock and its grouting-reinforced body. Higher water content leads to more small broken rock pieces, larger fractal dimensions, lower dynamic peak strength and smaller elastic modulus. However, the water content plays a minor role in fractal dimensions when the impact velocity is beyond a certain value. Higher impact loading rate leads to higher degree of fragmentation and larger fractal dimensions both in argillaceous siltstone and its grouting-reinforced body. These results provide a sound basis for the quantitative evaluation on how cement grouting can contribute to the repair of broken soft rocks.

• Imaging Science in Dentistry
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• v.33 no.2
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• pp.113-119
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• 2003

Purpose : To evaluate the relationship between morphometric analysis of bone microstructure from digital radiographic image and trabecular bone strength. Materials and Methods : One hundred eleven bone specimens with 5 mm thickness were obtained from the mandibles of 5 pigs. Digital images of specimens were taken using a direct digital intraoral radiographic system. After selection of ROI (100 × 100 pixel) within the trabecular bone, mean gray level and standard deviation were obtained. Fractal dimension and the variants of morphometric analysis (trabecular area, periphery, length of skeletonized trabeculae, number of terminal point, number of branch point) were obtained from ROI. Punch sheer strength analysis was performed using Instron (model 4465, Instron Corp., USA). The loading force (loading speed 1 mm/min) was applied to ROI of bone specimen by a 2 mm diameter punch. Stress-deformation curve was obtained from the punch sheer strength analysis and maximum stress, yield stress, Young's modulus were measured. Results: Maximum stress had a negative linear correlation with mean gray level and fractal dimension significantly (p<0.05). Yield stress had a negative linear correlation with mean gray level, periphery, fractal dimension and the length of skeletonized trabeculae significantly (p < 0.05). Young's modulus had a negative linear correlation with mean gray level and fractal dimension significantly (p < 0.05). Conclusions : The strength of cancellous bone exhibited a significantly linear relationship between mean gray level, fractal dimension and morphometric analysis. The methods described above can be easily used to evaluate bone quality clinically.

• The Journal of Engineering Geology
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• v.12 no.4
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• pp.421-437
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• 2002

In order to quantify the anisotropic properties of rock included joints and shear behavior in joint surface, the mold is Produced for rock joint surface using gypsum Plaster and Peformed for replicated joint models made of cement mortar. Rock sample is measured using mechanical profilometer before testing and their result is expressed quantitatively. The statistical parameters and the fractal dimension by fractal theory for roughness is investigated its coordinate value for numerical process. The shear strength to the shear displacement in low level normal stress ismaintained or increased in most joint models. Their results present that this relationship is depended several roughness properties in joint model for natural rock joint. The relationship between the shear strength and the Properties for profiles estimated by some statistical parameter in roughness has the low correlation and is not constant. The result between the data for direct shear test and using Barton's equation, Barton's equation has not the effectiveness for the effect of anisotropy and has not suitable to recognizing the properties for joint surface. It means that JRC has not the properties of anisotropic rock surface. The fractal dimension is well correlated with the data of direct shear test than those of JRC. New experimental formulae using fractal dimension is comported with the anisotropic properties for direct shear test.

• Journal of the Korean Geotechnical Society
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• v.40 no.4
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• pp.49-60
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• 2024

Ground-penetrating radar (GPR) enables rapid data acquisition over extensive areas, but interpreting the obtained data requires specialized knowledge. Numerous studies have utilized numerical analysis methods to examine GPR signal characteristics under various conditions. To develop more realistic numerical models, the heterogeneous nature of the ground, which causes clutter, must be considered. Clutter refers to signals reflected by objects other than the target. The Peplinski material model and fractal techniques can simulate these heterogeneous characteristics, yet there is a shortage of research on the necessary input parameters. Moreover, methods for quantitatively evaluating the similarity between field and analytical data are not well established. In this study, we calculated the autocorrelation coefficient of field data and determined the correlation length using the autocorrelation function. The correlation length represented the temporal or spatial distance over which data exhibited similarity. By comparing the correlation length of field data with that of the numerical model incorporating fractal weights, we quantitatively evaluated a numerical model for heterogeneous ground. Consequently, the results of this study demonstrated a numerical modeling technique that reflected the clutter characteristics of the field through correlation length.

• Water for future
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• v.28 no.4
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• pp.185-194
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• 1995

The objective of this study is to explore scale problem and to analyze the relations between scale and geomorphologic parameters of the rainfall-runoff model. Generally, measurement and calculation of geomorphologic parameters rely on and are sensitive to the resolution of source information available. Therefore, rainfall-runoff models using geomorphologic parameters should take account of the effects of the map scale used in their development. The derived rainfall-runoff model considering scale problem in this research is the GIUH type model, that is a basin IUH consisting of the channel network response and hillslope response. The cannel network response is computed by means of the diffusion analogy transformed from linearized St. Venant equation and hillslope response is calculated by 2-parameter gamma distribution function. Representing geomorphologic structure of the channel network and initial distribution of its response is width function. This width function is derived by fractal theory and Melton's law to consider scale problems and is weighted by the source location function (SLF) proposed in this research to increase the applicability.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.416-421
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• 2000

We have developed a simple model for describing the non-spherical particle growth phenomena using modified 1-dimensional sectional method. In this model, we solve simultaneously particle volume and surface area conservation sectional equations which consider particles' irregularities. From the correlation between two conserved properties of sections, we can predict the evolution of the aggregates' morphology. We compared this model with a simple monodisperse-assumed model and more rigorous two dimensional sectional model. For the comparison, we simulated silica and titania particle formation and growth in a constant temperature reactor environment. This new model shows a good agreement with the detailed two dimensional sectional model in total number concentration, primary particle size. The present model can also successfully predict particle size distribution and morphology without costing very heavy computation load and memory needed for the analysis of two dimensional aerosol dynamics.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.7
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• pp.1020-1027
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• 2000

A simple model for describing the non-spherical particle growth phenomena has been developed. In this model, we solve simultaneously particle volume and surface area conservation sectional equations that consider particles' non-sphericity. From the correlation between two conserved properties of sections, we can predict the evolution of the aggregates' morphology. This model was compared with a simple monodisperse-assumed model and more rigorous two-dimensional sectional model. For comparison, formation and growth of silica particles have been simulated in a constant temperature reactor environment. This new model showed good agreement with the detailed two-dimensional sectional model in total number concentration and primary particle size. The present model successfully predicted particle size distribution and morphology without costing very heavy computation load and memory needed for the analysis of two dimensional aerosol dynamics.

• Geomechanics and Engineering
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• v.22 no.2
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• pp.133-142
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• 2020

The evolution of the mining-induced fracture network formed during longwall top coal caving (LTCC) has a great influence on the gas drainage, roof control, top coal recovery ratio and engineering safety of aquifers. To reveal the evolution of the mining-induced stress and fracture network formed during LTCC, the fracture network in front of the working face was observed by borehole video experiments. A discrete element model was established by the universal discrete element code (UDEC) to explore the local stress distribution. The regression relationship between the fractal dimension of the fracture network and mining stress was established. The results revealed the following: (1) The mining disturbance had the most severe impact on the borehole depth range between approximately 10 m and 25 m. (2) The distribution of fractures was related to the lithology and its integrity. The coal seam was mainly microfractures, which formed a complex fracture network. The hard rock stratum was mainly included longitudinal cracks and separated fissures. (3) Through a numerical simulation, the stress distribution in front of the mining face and the development of the fracturing of the overlying rock were obtained. There was a quadratic relationship between the fractal dimension of the fractures and the mining stress. The results obtained herein will provide a reference for engineering projects under similar geological conditions.

• Geomechanics and Engineering
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• v.18 no.1
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• pp.11-20
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• 2019

The purpose of this study was to propose a new approach for quantifying in situ rock mass damage, which would include a degree-of-damage and the degraded strength of a rock mass, along with its prediction based on real-time Acoustic Emission (AE) observations. The basic approach for quantifying in-situ rock mass damage is to derive the normalized value of measured AE energy with the maximum AE energy, called the degree-of-damage in this study. With regard to estimation of the AE energy, an AE crack source location algorithm of the Wigner-Ville Distribution combined with Biot's wave dispersion model, was applied for more reliable AE crack source localization in a rock mass. In situ AE wave attenuation was also taken into account for AE energy correction in accordance with the propagation distance of an AE wave. To infer the maximum AE energy, fractal theory was used for scale-independent AE energy estimation. In addition, the Weibull model was also applied to determine statistically the AE crack size under a jointed rock mass. Subsequently, the proposed methodology was calibrated using an in situ test carried out in the Underground Research Tunnel at the Korea Atomic Energy Research Institute. This was done under a condition of controlled incremental cyclic loading, which had been performed as part of a preceding study. It was found that the inferred degree-of-damage agreed quite well with the results from the in situ test. The methodology proposed in this study can be regarded as a reasonable approach for quantifying rock mass damage.