• Tunnel and Underground Space
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• v.28 no.5
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• pp.426-441
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• 2018

Recently, the generalized Hoek-Brown (GHB) failure criterion has been actively employed in various rock engineering calculations, but the analytical form of the corresponding Mohr failure envelope is not available, making it difficult to extend the application of the GHB criterion. In order to overcome this disadvantage, this study proposes a new method to express the tangential friction angle as an explicit function of normal stress by invoking the polynomial best-fitting to the relationship between normal stress and tangent friction angle implied in the GHB failure function. If this normal stress - tangential friction angle relationship is best-fitted with linear or quadratic polynomial function, it is possible to find the analytical root for tangential friction angle. Subsequently, incorporating the root into the relationship between shear stress and tangential friction angle accomplishes the derivation of the approximate Mohr envelope for the GHB criterion. It is demonstrated that the derived approximate Mohr failure envelopes are very accurate in the entire range of GSI value.

• Tunnel and Underground Space
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• v.24 no.5
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• pp.366-372
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• 2014

The generalized Hoek-Brown (H-B) function provides a unique failure condition for a jointed rock mass, in which the strength parameters of rock mass are deduced from the intact values by use of the GSI value. Since it is actually the only failure criterion which accounts for the rock mass conditions in a systematic manner, the generalized H-B criterion finds many applications to the various rock engineering projects. Its nonlinear character, however, limits more active usage of this criterion. Accordingly, many attempts have been made to understand the generalized H-B condition in the framework of the M-C function. This study presents the closed-form expression relating the tangential cohesion to the tangential friction angle, which is derived by the non-dimensional stress transformation of the generalized H-B criterion. By use of the derived equation, it is investigated how the relationship between the tangential cohesion and friction angle of the generalized H-B criterion varies with the quality of rock masses. When only the variation of GSI value is considered, it is found that the tangential friction angle decreases with the increase of GSI, while the tangential cohesion increases with GSI value.

• Tunnel and Underground Space
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• v.23 no.3
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• pp.219-227
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• 2013

Although Mohr-Coulomb failure criterion has limitations in that it is a linear criterion and the effect of the intermediate principal stress on failure is ignored, this criterion has been widely accepted in rock mechanics design. In order to overcome these shortcomings, the Hoek-Brown failure criterion was introduced and recently a number of 3-D failure criteria incorporating the effect of the intermediate principal stress on failure have been proposed. However, in many rock mechanics designs, the possible failure of rock mass is still evaluated based on Mohr-Coulomb criterion and most of practitioners are accustomed to understanding the strength of rock mass in terms of the internal friction angle and cohesion. Therefore, if the equivalent Mohr-Coulomb strength parameters of the advanced failure criteria are calculated, it is possible to take advantage of the advanced failure criteria in the framework of the Mohr-Coulomb criterion. In this study, a method expressing the tangential Mohr-Coulomb strength parameters in terms of the stress invariant is proposed and it is applied to the generalized Hoek-Brown criterion and the HB-WW criterion. In addition, a new approach describing the geometric meaning of the ${\sigma}_2$-dependency of failure criteria in 3-D principal stress space is proposed. Implementation examples of the proposed method show that the influence of the intermediate principal stress on the tangential friction angle and cohesion of the HB-WW criterion is considerable, which is not the case for the 2-D failure criterion.

• Tunnel and Underground Space
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• v.22 no.6
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• pp.462-470
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• 2012

Implementing the generalized Hoek-Brown failure criterion in the framework of the Mohr-Coulomb criterion requires the calculation of the equivalent friction angle and cohesion. In the conventional method based on the Balmer (1952)'s theory, the tangential instantaneous friction angle and cohesion are expressed in terms of the minimum principal stress ${\sigma}_3$, which does not provide the information about the dependency of the equivalent parameters on the hydrostatic pressure and the stress path. In this study, this defect of the conventional method has been overcome by representing the equivalent parameters in terms of stress invariants. Through the example implementation of the new method, the influence of the magnitude of the hydrostatic pressure and the Lode angle on the tangential instantaneous friction angle and cohesion is investigated. It turns out that the tangential instantaneous friction angle is maximum when the stress condition is triaxial extension, while the tangential cohesion is maximum when the stress condition is triaxial compression. The dependency of the equivalent Mohr-Coulomb strength parameters on the hydrostatic pressure and the Lode angle tends to be more substantial for the favorable rockmass of larger GSI value.

• Tunnel and Underground Space
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• v.25 no.3
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• pp.284-292
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• 2015

The generalized Hoek-Brown failure criterion, the strength parameters of which are determined by using the GSI index, is an empirical nonlinear failure criterion of rock mass and has been widely employed in various rock engineering practices. Many rock engineering practitioners, however, are still familiar with the description of the strength of rock mass in terms of friction angle and cohesion. In addition, almost all rock mechanics softwares incorporate the simple linear Mohr-Coulomb function. Therefore, it is necessary to provide a tool to implement the Hoek-Brown function in the framework of the Mohr-Coulomb criterion. In this study, the use of upper-bound solution of limit analysis for bearing capacity of a strip footing resting on the ground surface is proposed for the estimation of the equivalent friction angle and cohesion of rock mass incorporating the generalized Hoek-Brown failure criterion. The upper-bound bearing capacity is expressed in terms of friction angle by use of the relationship between tangential friction angle and tangential cohesion implied in the generalized Hoek-Brown function. The friction angle minimizing the upper-bound bearing capacity is taken as the equivalent friction angle. Through the illustrative implementations of the proposed method, the influences of GSI, $m_i$ and D on the equivalent friction angle and cohesion are investigated.

• Tunnel and Underground Space
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• v.32 no.5
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• pp.312-326
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• 2022

The generalized Hoek-Brown (GHB) criterion, which is recognized as one of the standard failure conditions for rock mass, is specialized for rock engineering applications and covers a wide range of rock mass conditions. Accordingly, many research efforts have been devoted to the incorporation of this criterion into the stability analysis of rock structures. In this study, the slip-line analysis method, which is a kind of elastoplastic analysis method, is combined with the GHB failure criterion to derive analytical equations that can easily calculate the plastic radius and stress distribution in the vicinity of the circular tunnel. In the process of derivation of related formulas, it is assumed that the behavior of rock mass after failure is perfectly plastic and the in-situ stress condition is hydrostatic. In the formulation, it is revealed that the plastic radius can be calculated analytically using the two respective tangential friction angles corresponding to the stress conditions at tunnel wall and elastic-plastic boundary. It is also shown that the plastic radius and stress distribution calculated using the derived analytical equations coincide with the results of Lee & Pietruszczak's numerical method published in 2008. In the latter part of this paper, the influence of the quality of the rock mass on the size of the plastic zone, the stress distribution, and the change of the tangential friction angle was investigated using the derived analytical equations.

• Proceedings of the KIEE Conference
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• 2005.07c
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• pp.1986-1988
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• 2005

V-형 선형 초음파 모터를 설계하고 유한 요소 해석 소프트웨어인 ANSYS9.0을 사용하여 모터를 해석하고 그 결과를 도출하였다. 이 모터의 기본적인 구조는 압전 세라믹을 V-형 모터 stator 에 부착한 형태이다. 모터의 동작을 위해서 90도 위상차가 있는 2개의 교류전원을 각각 세라믹에 인가하였다. 그러면 각 세라믹은 압전 역효과와 위상의 차이에 의해 모터 arm을 대칭-비대칭 운동을 하게 만든다. 그리고 이 운동이 타원 제적을 발생시킨다 즉 모터와 슬라이드의 접선에서 이 타원궤적 운동의 마찰력으로 모터가 동작하게 된다. 최적의 조건을 찾기 위해 ANSYS를 이용하여 모터의 구조에 여러 가지 변수-고정점, stator의 재질, arm-body에 부착한 세라믹의 위치, 위상차, arm의 결합각 차, arm-body와 세라믹의 크기 변화, arm의 크기 변화-를 주어 선형 초음파 모터 구조의 최적 조건을 찾아 설계를 하였다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.34 no.2
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• pp.515-527
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• 2014

This study conducted experiment for understanding engineering characteristics of domestic sands by examining standard sand and sand from Yokji Island and Nakdong River in terms of confining pressure, $K_0$, over consolidation and relative density factors through triaxial compression test. The test showed that deviator stress by strain positively changed as confining pressure and relative density grow while $K_0$ and over consolidation factors do not directly correlated with it. Angle of internal friction decreases as confining pressure increases which strengthens contact force between particles, and declines as relative density drops, whereas $K_0$ and over consolidation factors hardly affect the results. When it comes to volumetric strain, volume expansion decreases as confining pressure increase due to crushability and rearrangement of particles while $K_0$ and over consolidation shows same movement unconditionally, and relative density appears compressed as it grows at the beginning however it expands as axial strain increases. Modulus of elasticity ($E_{sec}$) by strain has tendency into convergence resulting in initial secant modulus of elasticity ($E_{ini}$) > secant modulus of elasticity($E_{sec}$) > tangent modulus of elasticity ($E_{tan}$). On the other hand, it grows as confining pressure and relative density increase while indicating similar modulus of elasticity ($E_{sec}$) regarding on $K_0$ and over consolidation. Slope of critical line (M) tended to decrease as confining pressure increases, follow same line according to $K_0$, confining pressure and relative density, and increase as relative density grows.

• Journal of the Korean Institute of Gas
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• v.19 no.5
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• pp.13-19
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• 2015

This paper presents a hydraulic fracture propagation model to describe propagation more realistically. In propagating the hydraulic fractures, we have used two criteria: maximum tangential stress to determine the fracture initiation angle and whether a hydraulic fracture intersects a natural fracture. The model was validated for the parameters relevant to fracture propagation, such as initiation angle and crossing ability through natural fracture. In order to check whether a hydraulic fracture crosses a natural fracture, the model results on crossing state excellently matched with the experimental data. In the sensitivity analysis for direction of maximum horizontal stress, frictional coefficient of fracture interface, and natural fracture orientation, the results show that hydraulic fracture intersects natural fracture, and then, propagated suitably with theoretical results according to fracture interaction criterion. In comparison of this model against vertical fracture approach, it was ascertained that there are discrepancies in fracture connectivity and stimulated reservoir volume.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.22 no.6
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• pp.460-468
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• 2021

This study investigated the enhanced combustion efficiency of an "air-cooled combustion system" with single F.D. fan, and performed a numerical analysis for the operation and design conditions to increase the combustion efficiency. The combustion efficiency in an actual combustor was compared before and after the structure modification. Numerical analysis for application of a single fan revealed the difficulty of forming a turbulence for circular combustion conditions. This is because the supply ratio of combustion air supplied into 2 flow paths becomes irregular in the combustion furnace due to a change in friction force and pressure in each flow path. Subsequently, two methods of supplying air into the combustion furnace were analyzed numerically to obtain the optimal combustion conditions of an air-cooled combustion system. The first method involved injecting the preheated combustion air after a 180~360 degree rotation from the outer wall, whereas in the second method, the combustion air was injected into the combustion furnace in a tangential direction after primary heat exchange outside the combustion furnace, by applying a rotatable vane structure in the combustion furnace. Results reveal that application of a single F.D. fan to the air injection into a rotatable combustion furnace is desirable for optimization of the combustion conditions for applying a duct structure having a dual cooling wall for the cooling of the outer wall of the combustion furnace, and for maintaining perfect mixing in the combustion furnace. We therefore confirmed enhanced combustion efficiency by comparing the actual combustion efficiency before and after structure modification.