• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.655-681
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• 1998

Discontinuous solutions or interfaces are common in nature, for examples, shock waves or material interfaces. However, their numerical computation is difficult by the feature of discontinuities. In this paper, we summarize the numerical approaches for discontinuities and interfaces appearing mostly in the system of hyperbolic conservation laws, and explain various numerical methods for them. We explain two numerical approaches to handle discontinuities in the solution: shock capturing and shock tracking, and illustrate their underlying algorithms and mathematical problems. The front tracking method is explained in details and the level set method is outlined briefly. The several applications of front tracking are illustrated, and the research issues in this field are discussed.

• Structural Engineering and Mechanics
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• v.80 no.5
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• pp.625-643
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• 2021

In this paper, we present a new method to calculate interface warping functions for the analysis of beams with geometric and material discontinuities in the longitudinal direction. The classical Saint Venant torsion theory is extended to a three-dimensional domain by considering the longitudinal direction. The interface warping is calculated by considering both adjacent cross-sections of a given interface. We also propose a finite element procedure to simultaneously calculate the interface warping function and the corresponding twisting center. The calculated interface warping functions are employed in the continuum-mechanics based beam formulation to analyze arbitrary shape cross-section beams with longitudinal discontinuities. Compared to the previous work by Yoon and Lee (2014a), both geometric and material discontinuities are considered with fewer degrees of freedom and higher accuracy in beam finite element analysis. Through various numerical examples, the effectiveness of the proposed interface warping function is demonstrated.

• Journal of the Korean earth science society
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• v.32 no.1
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• pp.12-20
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• 2011

The gravity measurement was conducted at 256 stations around Chungju Lake to study subsurface geological distributions and subterranean mass discontinuities by the results of gravity anomaly in Metamorphic Complex, Okcheon Group, Great Limestone Group of Choson Supergroup, and Cretaceous biotite granites. Okcheon Group showed a high Bouguer gravity anomaly while Great Limestone Group of Choson Supergroup relatively a low anomaly. The mean depth of subterranean mass discontinuities is about 2.0 km and downward along the Suchangri Formation from the Hwanggangri and Moonjuri formations. In general, Okcheon Group appeared shallower than the depth of Great Limestone Group of Choson Supergroup when imaging the subterranean mass discontinuities from the Bouguer gravity anomaly.

• Tunnel and Underground Space
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• v.25 no.1
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• pp.68-75
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• 2015

Rock mass includes such discontinuities as fault, joint, bedding, crack, schistosity, cleavage. The rock mass behavior, therefore, is influenced by the discontinuity behavior. In this study, a stability and deformation analysis method considering discontinuities in rock mass is proposed, and then applied to the rock collapse disaster site. As the method, the stability analysis by the stereographic projection method was carried out in an actual site, the deformation analysis program by the finite element method including the joint element was developed, and performed. To demonstrate the applicability of this developed stability and deformation analysis method considering discontinuities in rock mass, the analysis results are examined and compared with the failure behavior at the rock mass.

• Journal of Industrial Technology
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• v.23 no.A
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• pp.69-81
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• 2003

Numerical analysis is important for the design, construction and maintenance of large caverns. The rock mass contains generally discontinuities such as faults, joints and fissures. The mechanical behavior and geometric characteristics of these discontinuities would have a significant impact on the stability of the caverns. In this research the Distinct Element Method(DEM) was used to analyze the structural stability of the large cavern. The Barton-Bandis Joint Model (B-B J.M) was used as a constitutive model for the joint. In addition, two different cases 1) analysis with a support system and 2) analysis with no support system, were analyzed to optimize a support system and to investigate reinforcing effects of a support system. The most significant parameters of in-situ stress, JRC of in-situ natural joints, and spatial distribution characteristics of discontinuities were acquired through field investigation. Displacement (horizontal, joint shear), maximum joint opening, maximum and minimum principal stresses, range of relaxed zone, rockbolt axial forces and shotcrete stresses were calculated at each excavation stage. As a result of analysis the calculated values proved to be under the allowable value Rockbolts also proved to be an efficient support measure to control joint shear displacement which had significant effects on extending the relaxed zone. As a consequence, the structural stability of the cavern was assured with an appropriate support system.

• Computers and Concrete
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• v.23 no.4
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• pp.235-243
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• 2019

The discontinuous Galerkin method (DGM) has become widely used as it possesses several qualities, such as a natural ability to dealing with discontinuities. DGM has its major success related to fluid mechanics. Its major importance is the ability to deal with discontinuities and still provide high order of approximation. That is an important advantage when simulating cracking propagation. No remeshing is necessary during the propagation, since the crack path follows the interface of elements. However, DGM comes with the drawback of an increased number of degrees of freedom when compared to the classical continuous finite element method. Thus, it seems a natural approach to combine them in the same simulation obtaining the advantages of both methods. This paper proposes the application of the combined continuous-discontinuous Galerkin method (CDGM) to crack propagation. An important engineering problem is the simulation of crack propagation in concrete structures. The problem is characterized by discontinuities that evolve throughout the domain. Crack propagation is simulated using CDGM. Discontinuous elements are placed in regions with discontinuities and continuous elements elsewhere. The cohesive zone model describes the fracture process zone where softening effects are expressed by cohesive zones in the interface of elements. Two numerical examples demonstrate the capacities of CDGM. In the first example, a plain concrete beam is submitted to a three-point bending test. Numerical results are compared to experimental data from the literature. The second example deals with a full-scale ground slab, comparing the CDGM results to numerical and experimental data from the literature.

• The Journal of Engineering Geology
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• v.16 no.1 s.47
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• pp.23-30
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• 2006

This study was carried out to understand the relationship between orientation of tecto-lineaments obtained from aero-photograph and orientation of discontinuities measured at field for the rock types of igneous, sedimentary and metamorphic rocks in Andong area. Total 847 tecto-lineaments were extracted from the aero-photographs and total 1,940 discontinuities including joints, foliations and faults were measured during geologic survey. By using the software DIPS, preferred trends of tecto-lineaments were deduced as N30E-N40E for igneous rocks and N50E-N60E for both sedimentary and metamorphic rocks, while the trends of discontinuities were found as N40E-N50E for igneous rocks, N50E-N80E for sedimentary rocks and N50E-N60E for meta morphic rocks. Even though both orientations for a given rock type showed relatively good agreement in its trend, some discrepancy is also appeared. Since construction safety of geo-structures such as tunnel and slope, etc., is significantly affected by the orientation of discontinuities in rock masses, it is highly recommended to perform a detailed geologic survey as well as an aero-photograph interpretation at a design stage.

• The Journal of Engineering Geology
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• v.26 no.4
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• pp.505-513
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• 2016

The qualitative distribution of a fractured aquifer was characterized by electrical resistivity surveying as a part of basic groundwater investigation in Jangseong. The results were then used to choose sites for observation wells. The locations and distributions of permeable discontinuities were studied by analyses of temperature logs, a borehole image-processing system (BIPS), and hydraulic pressure testing using a double packer. The pressure test showed that the size of the discontinuities correlated with the Lugeon value and the results of the temperature log. The results show that temperature measurement is an effective method to identify permeable discontinuities, with the temperature difference correlating with the size of the aperture of the discontinuity.

• Journal of Korea Multimedia Society
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• v.8 no.8
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• pp.1069-1079
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• 2005

Though there have been many methods to detect features in spatial domain, in the case of a compressed image it has to be decoded, processed and encoded again. Alternatively, we can manipulate a compressed image directly in the Discrete Cosine Transform (DCT) domain that has been used for compressing videos or images in the standards like MPEG and JPEG. In our previous work we proposed a model-based discontinuity evaluation technique in the DCT domain that had problems in the rotated or non-ideal discontinuities. In this paper, we propose a fuzzy filtering technique that consists of height fuzzification, direction fuzzification, and forty filtering of discontinuities. The enhancement achieved by the fuzzy tittering includes the linking, thinning, and smoothing of discontinuities in the DCT domain. Although the detected discontinuities are rough in a low-resolution image for the size (8${\times}$8 pixels) of the DCT block, experimental results show that this technique is fast and stable to enhance the qualify of discontinuities.

• Tunnel and Underground Space
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• v.32 no.6
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• pp.549-557
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• 2022

Tunnel face mapping involves the determination of rock discontinuities or weak rock conditions where extra support might be required. In this study, we investigated the application of Lidar scanning and photogrammetry to quantitatively characterize discontinuities of the rock mass on the tunnel face during excavation. The 3D models of tunnel faces generated by using these methods enable accurate and automatic discontinuity measurement to overcome the limitations of manual mapping. The results of this study show that both photogrammetry and Lidar can be used to reconstruct the 3D model of the tunnel face, although the photogrammetric 3D model is less detailed than its counterpart produced by Lidar. Given acceptable accuracy and cost-effectiveness, photogrammetry can be a fast, reliable, and low-cost alternative to Lidar for acquiring 3D models and determining rock discontinuities on tunnel faces.