• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.757-777
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• 2019

In this paper, we study the convergence analysis of the sequences generated by the proximal point method for an infinite family of pseudo-monotone equilibrium problems in Banach spaces. We first prove the weak convergence of the generated sequence to a common solution of the infinite family of equilibrium problems with summable errors. Then, we show the strong convergence of the generated sequence to a common equilibrium point by some various additional assumptions. We also consider two variants for which we establish the strong convergence without any additional assumption. For both of them, each iteration consists of a proximal step followed by a computationally inexpensive step which ensures the strong convergence of the generated sequence. Also, for this two variants we are able to characterize the strong limit of the sequence: for the first variant it is the solution lying closest to an arbitrarily selected point, and for the second one it is the solution of the problem which lies closest to the initial iterate. Finally, we give a concrete example where the main results can be applied.

• The Journal of Engineering Geology
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• v.17 no.3
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• pp.381-391
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• 2007

A series of talus slope stability analyses were carried out using 2D FEM and 3D limit equilibrium methods for this study. The FEM analyses on Phase 2 were performed to delineate failure depths based on stress distributions for each slope. The results revealed that the failure surface exist in the colluvium layer of about 3-10 m thickness. Three dimensional models, derived from the FEM analyses and geological field survey, were made for the use in a 3D limit equilibrium analysis. The result shows that all the talus slopes are stable under dry condition, but unstable under saturated condition due to heavy rain.

• Journal of the Korean Geotechnical Society
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• v.30 no.11
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• pp.5-15
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• 2014

It is very important to design and construct slopes safely because damage cases are increasing due to slope failure. Recently, Limit Equilibrium Method (LEM) based programs are commonly used for slope designs. Though LEM can give factors of safety through simple calculation, it has a disadvantage that the sliding surface should be assumed in advance. On the other hand, the use of Finite Difference Method (FDM) is increasing since the factor of safety can be easily estimated by using shear strength reduction technique. Therefore the purpose of this study is to present a reasonable slope design methodology by comparing the two commonly used analysis approaches; LEM and FDM. To this end, the reinforcement effects of the two methods were compared in terms of the support pattern of soil nailing reinforced in the section where plane failure is anticipated. As a result, the reinforcement effects by nail angle and nail spacing turned out to be equal. Also it was found that the factor of safety increased in LEM, but not changed in FDM when the nail length increased.

• Economic and Environmental Geology
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• v.33 no.1
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• pp.77-88
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• 2000

The goal of this study is to assess the spatial distribution of natural slopes and cutting slopes under would-be development. For this goal, a quantitative slope stability analysis method using GIS integrated with a computer program was developed. Through field investigations, the discontinuity parameters were collected such as orientation of discontinuity, persistence, spacing, JRC, JCS, and water depth. The distributions were interpolated from the ordinary kriging method in ARC/INFO GIS after variogram analysis. The layers showing all parameters needed for limit equilibrium analysis were constructed. The final layer using GIS works composed of 162,352 polygons, that is, unit slopes. The rock slope stability analysis program was coded by C++ language. This program can calculate geometrical vectors related to rock block failures using input orientation data and direction and dimension of strength to occur failure. Also, this can calculate shear strength of joints through empirical equations and quantitative factors of safety. This methodology was applied to the study area which is located in Jaecheon city and Danyang-gun of the northeastern Keumsu is about 135$km^2$. As a result, the study area was entirely stable but unstable, that is, factor of safety less than 1.0dominantly at the slopes near Keumsil, Daejangri, Keumsungmyun and Sojugol, Mt. Dongsan, Juksongmyun by the natural slope stability analysis. Assuming the cutting slope showing the same direction immediate, and quantitative analysis of factors of safety for a regional area could be conducted through GIS integrated with a computer program of limit equilibrium.

• Journal of the Korean Geotechnical Society
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• v.19 no.5
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• pp.163-173
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• 2003

In this paper, a numerical comparison of predictions by limit equilibrium analysis and 3D analysis is presented for slope/pile system. Special attention is given to the coupled analysis based on the explicit finite difference code, FLAC 3D. To this end, an internal routine (FISH) was developed to calculate a factor of safety for a file reinforced slope according to shear strength reduction technique. The case of coupled analyses was performed for stabilizing piles in slope in which the pile response and slope stability are considered simultaneously. In this study, by using these methods, the failure surfaces and factors of safety were compared and analyzed in several cases, such as toe, middle and top of the slope, respectively. Furthermore, the coupled method based on shear strength reduction technique was verified by the comparison with other analysis results.

• Journal of the Korean GEO-environmental Society
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• v.7 no.6
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• pp.13-22
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• 2006

The geotextile have been used in filtration and drainage for over 30 years in many applications of civil and environmental projects. Geotextile tube is compound technology of filtration and drainage property of geotextile. Geotextile have been used for various types of containers, such as small hand-filled sandbags, 3-dimensional fabric forms for concrete paste, large soil and aggregate filled geotextile gabion, prefabricated hydraulically filled containers, and other innovative systems involving containment of soils using geotextile. They are hydraulically filled with dredged materials. It have been applied in coastal protection and scour protection, dewatering method of slurry, and isolation of contaminated material. Recently, geotextile tube technology is no longer alternative construction technique but suitable desired solution. This paper presents the behavior of geotextile tube composite structure by 2-D limit equilibrium and plane strain analysis. 2-D limit equilibrium analysis was performed to evaluate the stability of geotextile tube composite structure for the lateral load and also the plane strain analysis was conducted to determine the design and construction factors. Based on the results of this paper, the three types of geotextile tube composite structure is stable. And the optimum tensile strength of geotextile is 151kN/m and maximum pumping pressure is 22.7kN/m.

• Proceedings of the Korean Geotechical Society Conference
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• 1997.03a
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• pp.97-102
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• 1997

• Journal of the Korean GEO-environmental Society
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• v.12 no.2
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• pp.45-53
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• 2011

Soil nailing method was often designed by the slope stability analysis based on limit equilibrium. However, in the case of shorten length of nails, although the calculated factor of safety is within the design factor of safety, the horizontal displacement of soil nailed walls occurred above the allowable limit. In this study, relationship between the load and factor of safety, and relationship between the load and displacement ratio based on the test results were analysed. From the analysed results, the relationship between factor of safety and displacement ratio was estimated. For the mobilized horizontal displacement of the walls within the serviceability limit corresponding to the displacement of less than 0.3% displacement ratio, the calculated factor of safety by limit equilibrium analysis had to satisfy above 1.35. Also, although the minimum factor of safety is estimated above 1.35, the maximum horizontal displacement is often mobilized above 0.3% of excavation height. Therefore, it is necessary to perform the numerical analysis of soil nailed walls in the case of low shear strength or high excavation.

• Proceedings of the Korean Geotechical Society Conference
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• 1993.10a
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• pp.63-68
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• 1993

Soil nailing is a method of reinforcing natural deposits of soil with passive inclusions, called nails, of steel or other materials. Its purpose is mainly to increase the tensile and shear strength of the soil mass. This method has been widely used during the last two decades to stabilize steep slopes in several countries (France, Germany, USA, Japan, etc.). The design methods that have been mostly used are Davis method, German method, and French method which are based on limit equilibrium approaches, and Juran method which utilizes the kinematical limit equilibrium design concept. This paper is focussed on the evaluation of the available design methods(especially, the France, Davis and German design methods) through comparison with each different assumption for the failure surface, the concept of failure mechanism and the definition of safety factor. The parametric study to identify the effects of design parameters on the overall factor of safety has also been conducted. By considering the results along with the associated assumptions which have been postulated in the several methods, the applicability of the method for a given soil and nail conditions has been evaluated.

• Bulletin of the Society of Naval Architects of Korea
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• v.17 no.2
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• pp.1-10
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• 1980

The optimal plastic design of framed structures has been treated as the minimum weight design while satisfying the limit equilibrium condition that the structure may not fail in any of the all possible collapse modes before the specified design ultimate load is reached. Conventional optimum frame designs assume that a continuous spectrum of member size is available. In fact, the vailable sections merely consist of a finite range of discrete member sizes. Optimum frame design using discrete sections has been performed by adopting the plastic collapse theory and using the Complex Method of Box. This study has presented an iterative approach to the optimal plastic design of plane structures that involves the performance of a series of minimum weight design where the limit equilibrium equation pertaining to the critical collapse mode is added to the constraint set for the next design. The critical collapse mode is found by the collapse load analysis that is formulated as a linear programming problem. This area of research is currently being studied. This study would be applied and extended to design the larger and more complex framed structures.