• Structural Engineering and Mechanics
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• v.11 no.6
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• pp.591-604
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• 2001

In this paper, a finite element with embedded displacement discontinuity which eliminates the need for remeshing of elements in the discrete crack approach is applied for the progressive fracture analysis of concrete structures. A finite element formulation is implemented with the extension of the principle of virtual work to a continuum which contains internal displacement discontinuity. By introducing a discontinuous displacement shape function into the finite element formulation, the displacement discontinuity is obtained within an element. By applying either a nonlinear or an idealized linear softening curve representing the fracture process zone (FPZ) of concrete as a constitutive equation to the displacement discontinuity, progressive fracture analysis of concrete structures is performed. In this analysis, localized progressive fracture simultaneous with crack closure in concrete structures under mixed mode loading is simulated by adopting the unloading path in the softening curve. Several examples demonstrate the capability of the analytical technique for the progressive fracture analysis of concrete structures.

• Journal of Korean Tunnelling and Underground Space Association
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• v.7 no.3
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• pp.227-237
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• 2005

In this study, the behavior of shallow 2-Arch tunnel due to excavation under horizontal discontinuity plane was verified experimentally. The model tests were carried out by varying the overburden height and the location of the discontinuity plane. The model tests followed exactly the real 2-Arch tunnel construction stages. As a result, it is discovered that stress-transfer mechanism and loosening area around the 2-Arch tunnel depends on the overburden heights and the location of the discontinuity plane. And central pillar load is also dependent on overburden height, location of discontinuity plane and construction stages.

• Proceedings of the Korean Geotechical Society Conference
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• 2008.03a
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• pp.1400-1405
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• 2008

Execute surface of the earth geological survey for stability analysis of stealing cutting sides and investigated wide area nature of soil structure. Inflected DIPS that measure discontinuity's direction that develop to slope and is slope stability a wide use program for Stereographic Projection Method analysis that utilize geometrical correlation of stealing four sides and discontinuity surface. It is principle that angle of internal friction that is basis element of stability estimation applies direct shear test result on joint side, Examination is impossible by case execution, suppose by 30 angles that apply more conservatively in base rock slope sides usually and achieved analysis. When analyze, consider discontinuity's various adult that develop in research slope, after conduct first each discontinuity different assay falling into fault, joint, executed stability estimation which synthesize whole discontinuity data. When ailment element is recognized as analysis result, wished to present stability countermeasure way of most suitable to take into account of execution, stability, economic performance.

• Tunnel and Underground Space
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• v.13 no.5
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• pp.373-388
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• 2003

The investigation on the rock discontinuity geometry has been usually undergone by direct measurement on the rock exposures. But this sort of field work has disadvantages, which we, for example, restriction of surveying areas and consuming excessive times and labors. To cover these kinds of disadvantages, image processing could be regarded as an altemative way, with additional advantages such as automatic and objective tools when used under adequate computerized algorithm. This study was focused on the recognition of the rock discontinuities captured in the image of rock exposure by digital camera and the production of the discontinuity map automatically. The whole process was written using macro commands builtin image analyzer, ImagePro Plus. ver 4.1(Media Cybernetic). The procedure of image processing developed in this research could be divided with three steps, which are enhancement, recognition and extraction of discontinuity traces from the digital image. Enhancement contains combining and applying several filters to remove and relieve various types of noises from the image of rock surface. For the next step, recognition of discontinuity traces was executed. It used local topographic features characterized by the differences of gray scales between discontinuity and rock. Such segments of discontinuity traces extracted from the image were reformulated using an algorithm of computer decision-making criteria and linked to form complete discontinuity traces. To verify the image processing algorithms and their sequences developed in this research, discontinuity traces digitally photographed on the rock slope were analyzed. The result showed about 75～80% of discontinuities could be detected. It is thought to be necessary that the algorithms and computer codes developed in this research need to be advanced further especially in combining digital filters to produce images to be more acceptable for extraction of discontinuity traces and setting seed pixels automatically when linking trace segments to make a complete discontinuity trace.

• The Journal of Engineering Geology
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• v.13 no.3
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• pp.321-334
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• 2003

This study is aimed at the effective measurement plan of discontinuity orientation on rock mass. The discontinuity orientation is expressed as three methods. strike/dip. dipdirection/dip (a three digit number / a two digit number) and right hand rule. Generally, strike/dip is measured with clinometer. and dipdirection/dip with silva compass(type15). A sign of strike/dip. discontinuity orientation is used to geological survey. and dipdirection/dip to engineering. Dipdirection/dip converted by strike/dip measured with clinometer is useful on the statistical analysis of a lot of data. To measure the azimuth of the dip with clinometer and to change strike/dip to dipdirection/dip may have potential errors in each person. The newly designed apparatus, clinometer equipped by a rotational azimuth plate and an arrow to measuring strike and dipdirection, has been developed to measure effectively the discontinuity orientation with two method (strike/dip and dipdirection/dip). The measuring method of discontinuity orientation with clinometer having newly designed apparatus is effective one for accurate measurement of strike as well as dipdirection which is degrees counted clockwise from true north. Used by clinometer with newly designed apparatus, concurrent measuring strike/dip and dipdirecton/dip of discontinuity is possible. In application to measuring discontinuity orientation on rock slope, it has been recognized that the newly designed method, unambiguously, led to drop measuring errors comparing with existing measuring apparatuses. Therefore, it is considered that measuring method of discontinuity orientation (strike/dip and dipdirecton/dip) by the newly designed apparatus is useful to one in geological engineering investigation of road design, and to unskilled investigator.

• Tunnel and Underground Space
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• v.15 no.1 s.54
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• pp.47-54
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• 2005

One of the standard procedures of discontinuity survey is the joint set identification from the population of field orientation data. Discontinuity set identification is fundamental to rock engineering tasks such as rock mass classification, discrete element analysis, key block analysis. and discrete fracture network modeling. Conventionally, manual method using contour plot had been widely used for this task, but this method has some short-comings such as yielding subjective identification results, manual operations, and so on. In this study, the method of discontinuity set identification using genetic algorithm was introduced, but slightly modified to handle the orientation data. Finally, based on the genetic algorithm, we developed a FORTRAN program, Genetic Algorithm based Clustering(GAC) and applied it to two different discontinuity data sets. Genetic Algorithm based Clustering(GAC) was proved to be a fast and efficient method for the discontinuity set identification task. In addition, fitness function based on variance showed more efficient performance in finding the optimal number of clusters when compared with Davis - Bouldin index.

• Journal of Korean Tunnelling and Underground Space Association
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• v.13 no.3
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• pp.215-231
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• 2011

In this study, the behavior of a shallow 2-arch tunnel during the excavation in the sandy ground containing vertical discontinuity plane was experimentally studied. Load transfer mechanism in the pillar caused by a 2-arch tunnel excavation was observed. The position of the vertical discontinuity plane was varied. Model tests were carried out in the normal construction sequence of 2-arch tunnel. Test results-showed that the load transfer caused by the 2-arch tunnel excavation was concentrated in the discontinuity plane, and was cut by the discontinuity plane, so no load transfer took place above the discontinuity plane. It was also shown that the effect of adjacent tunnel excavation on the pillar load and the ground deformation was greater when excavating the upper half-face of the main tunnel, more than when excavating the lower half-face.

• Tunnel and Underground Space
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• v.17 no.3 s.68
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• pp.175-185
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• 2007

When filling material such as clay is included along the discontinuity, it may cause instability on a slope even if the direction of discontinuity works in a positive way. In the study area, slope sliding occurred at the boundary between a clay filling material and weathered soil because the physical properties differ across the boundary; and this is very similar to the situation where foliation in a rock works as a weak zone during a structural behavior, causing an inter-layer slip. In most analysis, if there exists a clay filling material, a single discontinuity is assumed to perform analysis. In those cases, the discontinuity is modeled as a slip surface within clay. Therefore, the characteristics of the boundary are not considered in the analysis, so that ultimately the physical property of clay usually prevails. The result of evaluating the slope stability affected by clay filling material shows the significant difference in the safety level due to the strength parameter depending on the failure type of the discontinuity by a filling material.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.375-389
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• 2017

The purpose of this study is to analyze the difference and inter-connectivity between the definition of continuity in school mathematics and the definition of academic mathematics in four perspectives. These difference and inter-connectivity have not analyzed in previous papers. According to this study, the definition of 'continuity and discontinuity at one point' in school mathematics depends on the limit processing but in academic mathematics it depends on the topology of the domain. The target function of the continuous function in school mathematics is a function whose domain is limited to an interval or a union of intervals, but the target function of the continuous function in academic mathematics is all functions. Based on these results, the following two opinions are given in relation to the concept of continuity in school mathematics. First, since the notion of local continuity in school mathematics is based on limit processing, the contents of 2009-revised textbooks that deal with discontinuity at special point not belonging to the domain is appropriate. Here the discontinuity appears as types of infinite discontinuity, removable discontinuity, and step discontinuity. Second, the definition of a general continuous function is proposed to "if there is no discontinuity point in the domain of a function y = f(x), we call the function f a continuous function." This definition allows the discontinuity at special point in non-domain, but is consistent with the definition in academic mathematics.

• Structural Engineering and Mechanics
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• v.17 no.3_4
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• pp.409-428
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• 2004

In this paper, a Holder exponent, a measure of the degree to which a signal is differentiable, is presented to detect the presence of a discontinuity and when the discontinuity occurs in a dynamic signal. This discontinuity detection has potential applications to structural health monitoring because discontinuities are often introduced into dynamic response data as a result of certain types of damage. Wavelet transforms are incorporated with the Holder exponent to capture the time varying nature of discontinuities, and a classification procedure is developed to quantify when changes in the Holder exponent are significant. The proposed Holder exponent analysis is applied to various experimental signals to reveal underlying damage causing events from the signals. Signals being analyzed include acceleration response of a mechanical system with a rattling internal part, acceleration signals of a three-story building model with a loosing bolt, and strain records of an in-situ bridge during construction. The experimental results presented in this paper demonstrate that the Holder exponent can be an effective tool for identifying certain types of events that introduce discontinuities into the measured dynamic response data.