• Tunnel and Underground Space
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• v.15 no.5 s.58
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• pp.369-377
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• 2005

The stability of underground openings is a major concern for the safety and productivity of mining operations. Rock mass classification methods provide the basis of many empirical design methods as well as a basis for numerical analysis. Of the many factors which influence the stability of openings, the span of the opening for a given rock mass condition provides an important parameter of design. In this paper, the critical span curves proposed by Lang, the Mathews stability graph method and the modified critical span curve suggested by the authors have been assessed. The modified critical span curve was proposed by using Mathews stability graph method. The modified critical span curve by the author have been used to assess the stability of underground openings in several limestone mines.

• Journal of Advanced Marine Engineering and Technology
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• v.39 no.2
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• pp.159-165
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• 2015

Motion control schemes are generally classified into three categories (point stabilization, trajectory tracking, and path following). This paper deals with the problem which is associated with the initial deployment of a group of Unmanned Surface Vehicle (USVs) and corresponding point stabilization. To keep the formation of a group of USVs, it is necessary to set the relationship between each vehicle. A forcing functions such as potential fields are designed to keep the formation and a graph Laplacian is used to represent the connectivity between vehicle. In case of fixed topology of the graph representing the communication between the vehicles, the graph Laplacian is assumed constant. However the graph topologies are allowed to change as the vehicles move, and the system dynamics become discontinuous in nature because the graph Laplacian changes as time passes. To check the stability in the stage of deployment, the system is modeled with Kronecker algebra notation. Filippov's calculus of differential equations with discontinuous right hand sides is then used to formally characterize the behavior of USVs. The stability of the system is analyzed with Lyapunov's stability theory and LaSalle's invariance principle, and the validity is shown by checking the variation of state norm.

• Steel and Composite Structures
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• v.23 no.6
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• pp.683-690
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• 2017

In the stability and sensitivity design and diagnosis approaches, there are various methodologies available. Bond graph modeling by lumping technique is one of the universal methodologies in methodical analysis used by many researchers in all over the world. The accuracy of the method is validated in different arenas. Bond graphs are a concise, pictorial representation of the energy storage, dissipation and exchange mechanisms of interacting dynamic systems, subsystems and components. This paper proposes a bond graph modeling for distributed parameter systems using lumping techniques. Therefore, a steel frame structure was modeled to analyze employing bond graph modeling of distributed system using lumping technique. In the analytical part, the effectiveness of bond graphs to model this system is demonstrated. The dynamic responses of the system were computed and compared with those computed from the finite element analysis. The calculated maximum deflection time histories were found to be comparable. The sensitivity and the stability of the steel frame structure was also studied in different aspects. Thus, the proposed methodology, with its simplicity, can be used for stability and sensitivity analyses as alternative to finite element method for steel structures. The major value brought in the practical design is the simplicity of the proposed method for steel structures.

• Tunnel and Underground Space
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• v.18 no.4
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• pp.243-251
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• 2008

Recently, the mining methods are changing from surface mining to underground mining because of the increment of the environmental issues and legal regulations. Therefore, the stability of underground openings is a major concern for the safety and productivity of mining operations. In this paper, a survey of structural geology and discontinuities were carried out at a limestone mine. The relevant mechanical properties of rocks were determined by the laboratory tests and rock mass classifications (RMR and Q-system) for the mine design and input data for the stability analysis. The dimensions of unsupported span for underground openings and pillar were decided based on the RMR values of rock mass classifications. The stability analysis for the suggested mine design was examined through the empirical methods (stability graph method and critical span curve) and 3-D numerical analysis (Visual-FEA).

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.255-271
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• 2023

In this paper, we deal with random attractors for dynamical systems forced by a deterministic noise. These kind of systems are modeled as skew products where the dynamics of the forcing process are described by the base transformation. Here, we consider skew products over the Bernoulli shift with the unit interval fiber. We study the geometric structure of maximal attractors, the orbit stability and stability of mixing of these skew products under random perturbations of the fiber maps. We show that there exists an open set U in the space of such skew products so that any skew product belonging to this set admits an attractor which is either a continuous invariant graph or a bony graph attractor. These skew products have negative fiber Lyapunov exponents and their fiber maps are non-uniformly contracting, hence the non-uniform contraction rates are measured by Lyapnnov exponents. Furthermore, each skew product of U admits an invariant ergodic measure whose support is contained in that attractor. Additionally, we show that the invariant measure for the perturbed system is continuous in the Hutchinson metric.

• Journal of the Korean Geosynthetics Society
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• v.14 no.4
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• pp.1-9
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• 2015

According to national regulations and its commentary, such as Rivers Design Criteria & Commentary (KWRA, 2009), Foundation Structure Guideline and its Commentary(MLTM, 2014 and KGS, 2009), the integrity evaluation of river levee includes slope stability evaluation of both riverside/protected low-land and piping stability evaluation with respect to foundation and levee body along with water level conditions. In this case the design hydro-graph can be the most important input factor for the integrity evaluation, however it is fact that the national regulations do not provide any proper determination methods regarding hydro-graph. The authors thus executed an integrity evaluation of sluice gate in levee by changing each hydro-graph factor, including rising ordinary water level, lasting flood water level, falling water level, and flood frequency, in order to suggest a determination method of reasonable hydro-graph. As a result, the authors suggested that at least over 57 hours of rising ordinary water level and over 53 hours of lasting flood water level should be considered for the design hydro-graph of sluice gate in levee at Mun-san-jae.

• Tunnel and Underground Space
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• v.22 no.5
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• pp.297-309
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• 2012

The stability assessment of abandoned gangway for the purpose of services was performed. Among the many factors that affect the stability of openings, the span of the opening in a given rock mass condition provides an important element of design. In this paper, the stability of gangway was assessed by the critical span curves proposed by Lang, the modified Mathews'stability graph method and using support measures of the Q system. In the evaluation of stability as a whole the gangway is considered as stable. But the rockfalls of wedge-shaped blocks were expected in the area in which the horizontal joints of low angle appear. The support measures such as local rock bolts are required to use for commercial purposes of the abandoned gangway. And entrance section may require the particular attention as unstable section. Since there are so many spalling due to bad blasting in the roof and sidewall of gangway, the scaling operations should be followed primarily.

• Journal of Korean Society for Quality Management
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• v.50 no.3
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• pp.473-490
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• 2022

Purpose: The purpose of this study is to propose a new useful suggestion to monitor the stability of process by developing a stability ratio or index related to investigating how well the process is controlled or operated to the specified target. Methods: The proposed method to monitor the stability of process is building up a new measure index which is making up for the weakness of the existing index in terms of short or long term period of production. This new index is a combined one considering both stability and capability of process to the specification limits. We suppose that both process mean and process variation(or deviation) are changing on time period. Results: The results of this study are as follows: regarding the stability of process as well as capability of process, it was shown that two indices, called SI(stability index) and PI(performance index), can be expressed in two-dimensional X-Y graph simultaneously. This graph is categorized as 4 separated partitions, which are characterized by its numerical value intervals of SI and PI which are evaluated by test statistics. Conclusion: The new revised index is more robust than the existing one in investigating the stability of process in terms of short and long period of production, even in case both process mean and variation are changing.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.799-805
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• 1996

In many cases, the magnetic farce model is linearized at the origin in designing the controller of a magnetic bearing system. However. this linear assumption is violated by the unmodeled nonlinear effect such as sensor dislocation and backup bearing dislocation. Therefore, a direct probe into the nonlinear magnetic force model in an active magnetic bearing system is necessary. To analyze the nonlinear magnetic force model of a magnetic bearing system, phase plot analysis which is to plot the numerical solution of the nonlinear equation in several initial points in the interested region is applied. Phase plot analysis is used to observe a nonlinear dynamic system qualitatively (not quantitatively). With this method, we can get much useful information of the nonlinear system. Among this information, a bifurcation graph that represents stability and locations of fixed points is essential. From the bifurcation graph, a stability criterion of magnetic bearing system is derived.

• Geomechanics and Engineering
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• v.28 no.5
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• pp.463-475
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• 2022

In the mine exploitation stage; one of the critical issues is the stability assessment of post-pillars. The instability of post-pillars leads to serious safety hazards in mining operations. The focus of this study is to assess the stability of post-pillars in the 130# stope in the central ore body at Trepça hard rock mine by employing both conventional (i.e., critical span curve) and numerical methods (i.e., FLAC3D). Moreover, a new numerical based index (i.e., Pillar Yield Ratio-PYR) was proposed. The aim of PYR index is to determine a border line between stable, potentially unstable, and failure state of post-pillars at a specific mine site. The critical value of pillar width to height ratio is 2.5 for deep production stopes (e.g., > 800 m). Results showed that pillar size, mining height and mining depth significantly have affected the post-pillar stability. The reliability of numerical based index (i.e., PYR) is verified based on empirical underground pillar stability graph developed by Lunder, 1994. The proposed pillar yield ratio index and pillar stability graph can be used as a design tool in new mining areas at Trepça hard rock mine and for other situations with similar geotechnical conditions.