• 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.

• Tunnel and Underground Space
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• v.21 no.2
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• pp.93-102
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• 2011

In spite of being unable to take into the effect of intermediate principal stress, Mohr-Coulomb and Hoek-Brown criteria are very popular as rock failure criteria. The recent researches reveal that the influence of intermediate principal stress on the failure strength of rock is substantial, so that 3-D failure criteria in which the intermediate principal stress could be considered is necessary for the safe design of the important rock structures. In this study, the likely application of the 3-D failure criterion proposed by Jiang & Pietruszczak (1988) to the prediction of the true triaxial strength of rock materials is discussed. The failure condition is linear in the meridian plane of principal stress space and it is represented by the smooth surface contacting the corners of the Mohr-Coulomb surface. The performance of the Jiang & Pietruszczak's criterion is demonstrated by simulating the actual true triaxial tests on the rock samples of three different rock types.

• Geomechanics and Engineering
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• v.12 no.2
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• pp.313-326
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• 2017

Based on the reliability theory and limit analysis method, the roof stability of a shallow tunnel is investigated under the condition of surface settlement. Nonlinear Hoek-Brown failure criterion is adopted in the present analysis. With the consideration of surface settlement, the internal energy and external work are calculated. Equating the rate of energy dissipation to the external rate of work, the expression of support pressure is derived. With the help of variational approach, a performance function is proposed to reliability analysis. Improved response surface method is used to calculate the Hasofer-Lind reliability index and the failure probability. In order to assess the validity of the present results, Monte-Carlo simulation is performed to examine the correctness. Sensitivity analysis is used to estimate the influence of different variables on reliability index. Among random variables, the unit weight significantly affects the reliability index. It is found that the greater coefficient of variation of variables lead to the higher failure probability. On the basis of the discussions, the reliability-based design is achieved to calculate the required tunnel support pressure under different situations when the target reliability index is obtained.

• Tunnel and Underground Space
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• v.9 no.3
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• pp.221-229
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• 1999

Parameters of failure criteria, compressive strength and elastic modulus are most important for design and stability analysis of rock structure using numerical analysis. In this study, it suggests that the application of input data for numerical analysis by the literature study and the result of the 150 sets of triaxial compressive test. There was much different between parameters of failure criterion suggested by Hoek-Brown and parameters resulted from the analysis using 150 sets of triaxial compressive test. But the converting equations of compressive strength have had an interrelation with RMR. However, the converting of elastic of elastic modulus were different as chosen of equation, and the equation by Nicholson et at was more useful than others.

• Tunnel and Underground Space
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• v.27 no.1
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• pp.39-49
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• 2017

The factor of safety (FOS) is commonly used as an index to quantitatively state the degree of safety of various rock structures. Therefore it is important to understand the definition and characteristics of the adopted FOS because the calculated FOS may be different according to the definition of FOS even if it is estimated under the same stress condition. In this study, four local factors of safety based on maximum shear stress, maximum shear strength, stress invariants, and maximum principal stress were defined using the Mohr-Coulomb and Hoek-Brown failure criteria. Then, the variation characteristics of each FOS along five stress paths were investigated. It is shown that the local FOS based on the shear strength, which is widely used in the stability analysis of rock structures, results in a higher FOS value than those based on the maximum principal stress and the stress invariants. This result implies that the local FOS based on the maximum shear stress or the stress invariants is more necessary than the local FOS based on the shear strength when the conservative rock mechanics design is required. In addition, it is shown that the maximum principal stresses at failure may reveal a large difference depending on the stress path.

• Tunnel and Underground Space
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• v.22 no.5
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• pp.354-364
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• 2012

In order to evaluate the physical properties of rock which might serve as a database for both mining and civil works, a lot of laboratory tests for Jecheon limestones were conducted to find unit weight, absorption ratio, porosity, elastic wave velocity, uniaxial compressive strength, Young's modulus, poisson's ratio, tensile strength, shore hardness, friction angle and cohesion. On investigation of the mechanical properties of both the gray limestone and the clayey limestone distributed in the studied region, the clayey limestone turned out to have more weak mechanical properties which might come from low unit weight, high absorption ratio and high porosity of rocks. The failure criteria of Jecheon limestones were discussed by means of both Mohr-Coulomb criterion and Hoek-Brown criterion. Regression analyses of the physical properties obtained from a lot of laboratory tests were also conducted by means of both linear and multiple regression analyses.

• Tunnel and Underground Space
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• v.25 no.3
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• pp.231-243
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• 2015

In this study, both in-situ stress measurements and a lot of laboratory rock tests were conducted at a metal mine in Jeongseon, Korea. The stress ratio obtained from in-situ stress measurements showed a tendency to decrease according to depth below surface and its average value was 1.10. The mechanical properties such as unit weight, absorption ratio, porosity, elastic wave velocity, uniaxial compressive strength, Young's modulus, Poisson's ratio, tensile strength, shore hardness, friction angle and cohesion were investigated for the four different rocks mainly distributed at a studied mine, which were dolomite, felsite, granite and magnetite. The mechanical properties of the four different rocks were compared by means of statistical analyses, whereupon the felsite and the granite turned out to have more strength characteristics than the magnetite. The correlation of mechanical properties was also investigated, whereupon a few results against the general correlation were found out. The failure criteria of the four different rocks were finally discussed by means of both Mohr-Coulomb criterion and Hoek-Brown criterion.

• Geomechanics and Engineering
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• v.16 no.6
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• pp.569-575
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• 2018

The stability of shallow cavities with an arbitrary profile is a difficult issue in geotechnical engineering. This paper investigates this problem on the basis of the upper bound theorem of limit analysis and the Hoek-Brown failure criterion. The influence of pore pressure is taken into consideration by regarding it as an external force acting on rock skeleton. An objective function is constructed by equating the internal energy dissipation to the external force work. Then the Lagrange variation approach is used to solve this function. The validity of the proposed method is demonstrated by comparing the analytical solutions with the published research. The relations between shallow and deep cavity are revealed as well. The detaching curve of cavity roof with elliptical profile is obtained. In order to facilitate the application of engineering practice, the numerical results are tabulated, which play an important role in tunnel design and stability analysis of roof. The influential factors on potential collapse are taken into consideration. From the results, the impact of various factors on the extent of detaching is seen intuitively.

• Geomechanics and Engineering
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• v.11 no.3
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• pp.439-455
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• 2016

This paper presented solutions of displacement and stress for a circular opening which is reinforced with grouted rock bolt. It satisfies the Mohr-Coulomb (M-C) or generalized Hoek-Brown (H-B) failure criterion, and exhibits elastic-brittle-plastic or strain-softening behavior. The numerical stepwise produce for strain-softening rock mass reinforced with grouted rock bolt was developed with non-associative flow rules and two segments piecewise linear functions related to a principle strain-dependent plastic parameter, to model the transition from peak to residual strength. Three models of the interaction mechanism between grouted rock bolt and surrounding rock proposed by Fahimifar and Soroush (2005) were adopted. Based on the axial symmetrical plane strain assumption, the theoretical solution of the displacement and stress were proposed for a circular tunnel excavated in elastic-brittle-plastic and strain-softening rock mass compatible with M-C or generalized H-B failure criterion, which is reinforced with grouted rock bolt. It showed that Fahimifar and Soroush's (2005) solution is a special case of the proposed solution for n = 0.5. Further, the proposed method is validated through example comparison calculated by MATLAB programming. Meanwhile, some particular examples for M-C or generalized H-B failure criterion have been conducted, and parametric studies were carried out to highlight the influence of different parameters (e.g., the very good, average and very poor rock mass). The results showed that, stress field in plastic region of surrounding rock with considering the supporting effectiveness of the grouted rock bolt is more than that without considering the effectiveness of the grouted rock bolt, and the convergence and plastic radius are reduced.