• 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.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.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.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.

• Geomechanics and Engineering
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• v.28 no.1
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• pp.35-48
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• 2022

The effect of discrete polypropylene fibre reinforcement on shear strength parameters, tensile properties and isotropic index of stabilized compacted residual subgrade was investigated. Composites of compacted subgrade were developed from polypropylene fibre dosage of 0%, 1%, 2.5% and 4% and 3% cement binder. Saturated compacted soil benefited from incremental fibre dosage, the mobilized friction coefficient increased to a maximum at 2.5% fibre dosage from 0.41 to 0.58 and the contribution due to further increase in fibre dosage was marginal. Binder stabilization increased the degree of isotropy for unreinforced soil at lower fibre dosage of 1% and then decreased with higher fibre dosage. Saturation of 3% binder stabilized soil decreased the soil friction angle and the degree of isotropy for both unstabilized and binder stabilized soil increased with fibre dosage. The maximum tensile stress of 3% binder stabilized fibre reinforced residual soil was 3-fold that of 3% binder stabilized unreinforced soil. The difference in computed and measured maximum tensile and tangential stress decreased with increase in fibre dosage and degree of stabilization and polypropylene fibre reinforced soil met local and international criteria for road construction subgrade.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.1 no.4
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• pp.265-275
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• 1989

An experimental study of decaying swirl air flow has been obtained by tangential inlet in a straight tube with Reynolds number range 20,000~40,000. The friction factor, swirl angle, velocity profiles and turbulent intensity are measured by using micro-manometer and hot-wire anemometer. It is found that the swirl flow behaviors depend on the swirl intensity along the test tube.

• Journal of the Korean Wood Science and Technology
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• v.18 no.4
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• pp.65-78
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• 1990

For the purpose of Improving the sounding boards for the conventional GAYAKUM, I was making approximately 202 specimens of radial board, 371 specimens of tangential board by cutting along the grain and the part of stem and 31 specimens of the disjointed traditional GAYAKUM made in Paulownia coreana. And it was conducted to measure specific gravity, dynamic Young's modulus, internal friction, resonant frequency, velosity of sound and width of annual ring by the method of the frexural vibration in a free-free bar in the audio frequency range. And it confirmed the juvenile wood by measuring wood fiber length of specimens. It was also conducted to investigate dynamic properties and moisture absorption by various heat-treatment and to test dynamic Young's modulus and internal friction for the disjointed conventional GAYAKUM. The results obtained were summarized as follow: 1. The Juvenile wood is located within about 7 annual rings from the pith in Paulownia coreana. 2. As increased with the specific gravity, the dynamic Young's modulus had more and more increased, but the internal friction had slightly decreased. 3. I think that radial board would be good for sounding board wood. because radial board is higher than tangential board in dynamic Young's mudulus and internal friction is lower than tangential board. 4. The value of mean dynamic Young's modulus on the conventional GAYAKUM, radial board and tangential board of 604 samples is $0.4283\pm0.037(\times10^{11}dyne/cm^2)$, $0.4316\pm(\times10^{11}dyne/cm^2)$ and $0.4234\pm0.112(\times10^{11}dyne/cm^2)$ respectively. The value of the radial board showed little higher than that of conventional GAYAKUM, but It had a similar tendency between conventional GAYAKUM and tangential board. 5. The annual ring width by four aspect is more narrow in north and west than that of others. 6. The values of specific gravity and dynamic Young's modulus in the mature wood showed higher than those of juvenile wood. 7. As the grain angle in the butt wood more increased to bark from pith, the dynamic Young's modulus were low. Then it was not good for sounding board. 8. It appeared that the heat-treatment for sounding board wood had a more effect to do the treatment of hotiron on surface after heat-treatment during 24 hours in $60^{\circ}C$ temperature. 9. As increased with the temperature, the rate of moisture absorption of heat-treatment wood had decreased. In conclusion, I thought that the sounding board wood for GAYAKUM would had the most effect to do the treatment of hotiron on surface after heat-treatment during 24 hours in $60^{\circ}C$ temperature using the radial board of mature wood.

• International Journal of Precision Engineering and Manufacturing
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• v.9 no.2
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• pp.3-7
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• 2008

Vibratory conveyors are widely used in industry to transport granular materials and products. A theoretical point mass model for vibratory conveying was studied. The results agreed well with experimental observations. The model theory included the resting, sliding and flight states of the material. Each state was considered separately when determining the equations of motion. For the coefficients of restitution, values of zero for the normal component and 0.8 for the tangential component were found to be appropriate for modeling the collisions of the granular particles with the conveying surface. The vibration angle had a large influence on the mode and rate of transport. There was an optimum vibration angle for a given set of conditions. The optimum vibration angle decreased and was better defined as the coefficient of friction increased. The results suggest the existence of an optimum dimensionless track acceleration (throw number), which does not support general industrial practice in which the track acceleration is limited when the feed cycle becomes erratic and unstable.

• 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.