• Journal of the Korean Geotechnical Society
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• v.21 no.8
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• pp.37-43
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• 2005

Hoek-Brown model, which was developed in order to predict the behavior of rock mass, has widely been utilized and revised by many researchers to solve various problems encountered in tunnelling and slope stability analysis. However, there is no schematic investigation on the application of the Hoek-Brown model to numerical analysis including finite element simulations. In this paper the Hoek-Brown model was formulated as a constitutive model according to the procedure of generalized plasticity theory, and a Rounded Hoek-Brown model, which could overcome the numerical difficulties by modifying the edge part of the yield surface as a curve shape, was newly proposed. The new model could satisfy the requirements as an elasto-plastic constitutive soil model and follow the yield surface of the original Hoek-Brown model in the compression mode. The constitutive equation for the proposed model herein was established and presented to be applicable to the generalized nonlinear finite element analysis.

• Journal of the Korean Geotechnical Society
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• v.32 no.3
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• pp.15-27
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• 2016

In this study, a series of triaxial compressive strength tests were conducted for basaltic intact rocks sampled in the northeastern onshore and offshore, southeastern offshore and northwestern offshore of Jeju Island. Hoek-Brown constants $m_i$ were estimated from the results of the triaxial compression tests, and the properties of the Hoek-Brown constants $m_i$ were investigated. In addition, the cohesion and internal friction angle, strength parameters of Mohr-Coulomb failure criterion, obtained from the results of the triaxial compression tests were compared and analyzed with those estimated from Hoek-Brown failure criterion, respectively. As results, it was found that the Hoek-Brown constant $m_i$ is deeply related to the internal friction angle. As the internal friction grows, the Hoek-Brown constant $m_i$ increases exponentially. The cohesions estimated from the Hoek-Brown failure criterion, on average, are approximately 24% higher than those obtained from the Mohr-Coulomb failure criterion. The internal friction angles estimated from the Hoek-Brown failure criterion are similar to those obtained from the Mohr-Coulomb failure criterion.

• Journal of the Korean GEO-environmental Society
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• v.4 no.2
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• pp.77-91
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• 2003

The Hoek-Brown failure criterion for rock masses developed first in 1980 is widely accepted and has been applied in a variety of rock engineering problems including slope analyses. The failure criterion was modified over the years because rock mass strength by the original failure criterion in 1980 was overestimated. The modified failure criterion, named Generalized Hoek-Brown Failure Criterion, was proposed with a new classification called the Geological Strength Index(GSI) in 1994. Generally, Hoek-Brown failure criterion is applied in numerical analyses of rock mass behaviors using equivalent Mohr-Coulomb parameters estimated by linear regression method. But these parameters estimated by this method have some inaccuracies to be applied and to be incorporated into numerical models and limit equilibrium programs. The most important issue is that this method cannot take account of non-linear characteristics of Hoek-Brown criterion, therefore, equivalent Mohr-Coulomb parameters is used as constant values regardless of field stress distribution in rock masses. In this study, the numerical analysis on rock slope stability considering non-linear characteristics of Hoek-Brown failure criterion was carried out. Futhermore, by the latest Hoek-Brown failure criterion in 2002, the revised estimating method of equivalent Mohr-Coulomb parameters was applied and rock mass damage criterion is introduced to account for the strength reduction due to stress relaxation and blast damge in slope stability.

• Tunnel and Underground Space
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• v.24 no.1
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• pp.81-88
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• 2014

In the course of performing the stability analysis of rock structures, there are times when the strength of the Hoek-Brown rock mass needs to be understood in terms of the internal friction angle and cohesion. In this case, the original Hoek-Brown criteion, giving the relationship between ${\sigma}_1$ and ${\sigma}_3$ at failure, have to be transformed to the corresponding Mohr envelope. A new approach to derive the Mohr envelope of the Hoek-Brown criterion is suggested in this study. The new method is based on the Londe's transformation making the stress components dimensionless. The correctness of the derivation leading to the new ${\tau}-{\sigma}$ relationship is confirmed by comparing the calculation results with the Bray's solution through a verification example.

• Explosives and Blasting
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• v.26 no.2
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• pp.20-28
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• 2008

In the design stage of a tunnel, the wall convergence is commonly estimated through an elasto-plastic analysis of the tunnel, which has been a topic drawing many researcher's attention so far. Despite its importance, however, the elasto-plastic behavior of a circular tunnel excavated in a generalized Hoek-Brown rockmass is still poorly understood. In this study, a simple munerical method based on Lee & Pietruszczak (2008) for the elasto-plastic analysis of a circular tunnel surrounded by reinforced annulus is proposed. It is assumed that the tunnel is excavated in a strain-softening rockmass obeying the generalized Hoek-Brown failure condition. The commercial code FLAC is used for the verification of the proposed method. The influence of the Hoek-Brown strength parameter a and the thickness of the reinforcement annulus on the elasto-plastic behavior around the tunnel was discussed by conducting some example analyses. The results show that the influence of these two parameters on the distribution of stresses and displacements is substantial.

• Tunnel and Underground Space
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• v.15 no.3 s.56
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• pp.228-235
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• 2005

Friction angle and cohesion of rock masses can be estimated from Hoek and Brown failure criterion and then plastic corrections can be applied using Mohr-Coulomb yield function. This study finds that this estimation procedure would not be appropriate for weak rock masses and for cases where low confining stress is expected to develop. A procedure is outlined in this paper for estimating plastic corrections directly from Hoek and Brown material model. Comparative study shows that direct procedure would simulate non-linear failure surface better than indirect procedure especially in the low confining stress regime.

• Geomechanics and Engineering
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• v.34 no.1
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• pp.69-86
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• 2023

To overcome the dilemma of the [BQ] method's inability to predict mountain tunnel support loads, this study is based on the Hoek-Brown criterion and previous results to obtain the connection equations from GSI scores to each parameter of the Hoek-Brown criterion and the link between the [BQ] scores and the GSI system. The equations were embedded in the Hoek-Brown criterion of FLAC6.0 software to obtain tunnel construction forecasts without destroying the in-situ stratigraphy. The feasibility of the secondary development of the Hoek-Brown criterion was verified through comparative analysis with field engineering measurements. If GSI > 45 with a confining pressure of less than 10 MPa, GSI has little effect on the critical softening factor while we should pay attention to the parameter of confining pressure when GSI < 45. The design values for each parameter are closer to the FLAC3D simulation results and the secondary development of the Hoek-Brown criterion meets the design objectives. If the Class V surrounding rock is thinned with shotcrete or the secondary lining is installed earlier, the secondary lining may act as the main load-bearing structure. The study may provide ideas for rapid prediction of mountainous tunnels in China.

• Journal of the Korean Geotechnical Society
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• v.36 no.10
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• pp.21-31
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• 2020

In this study, Hoek-Brown constants (m_i) were calculated through nonlinear regression analyses using the results of the triaxial compression tests for the basaltic intact rocks in Jeju Island. The relationships of the m_i with the uniaxial compressive strength (UCS), Brazilian tensile strength (BTS) and UCS/BTS of the Jeju basalts were investigated, respectively. In addition, a method that can be used in determining Hoek-Brown failure envelopes including the tensile and compressive failures of the Jeju basalts has been proposed. As results, the m_i values had no clear correlations with the UCS, BTS and UCS/BTS of the Jeju basalts, but there were two strong correlations between UCS and m_i/UCS, and between BTS and m_i/BTS of the Jeju basalts. In addition, it was found that the tensile strengths calculated by the Hoek-Brown failure criterion underestimate the tensile strengths of the Jeju basalts through the relationship between the m_i and UCS/BTS of the Jeju basalts. The method presented in this study is considered to be useful in determining the Hoek-Brown failure envelope for the tensile and compressive failures of the Jeju basalts.

• The Journal of Engineering Geology
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• v.19 no.2
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• pp.153-163
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• 2009

In this study, a series of triaxial tests on Jeju basalt were carried out and then rock strength parameters were estimated by the Mohr-Coulomb failure criterion and the Hoek-Brown failure criterion using the test results. The characteristics of both failure criterions were investigated through comparing the estimated rock strength parameters. As the result of the Mohr-Coulomb criterion, the cohesions and the internal friction angles are determined as 5.35 MPa and $50.25^{\circ}$ of Pyoseonri basalt, 16.99 MPa and $60.66^{\circ}$ of Trachy-basalt, and 2.33 MPa and $37.05^{\circ}$ of Scoria, respectively. The cohesions and internal friction angles were estimated by the Hoek-Brown failure criterion in the basis of the results of regression analysis. The cohesions and the internal friction angles are determined as 4.77 MPa and $52.47^{\circ}$ of Pyoseonri basalt, 14.69 MPa and $60.70^{\circ}$ of Trachy-basalt, and 2.22 MPa and $47.60^{\circ}$ of Scoria, respectively. As the result of comparison between the Mohr-Coulomb failure criterion and the failure envelope predicted by the Hoek-Brown criterion, the cohesion estimated by the Hoek-Brown criterion is usually lower than that obtained from the Mohr-Coulomb criterion, whereas the friction angle estimated by the Hoek-Brown criterion is higher than that obtained from the Mohr-Coulomb criterion.

• Tunnel and Underground Space
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• v.19 no.2
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• pp.158-166
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• 2009

As a basic study for investigating the development of the stress-induced crack in Hoek-Brown rock, a homogenization technique of elastic cracks is proposed. The onset of crack is monitored by Hoek-Brown empirical criterion, while the orientation of the crack is determined by the critical plane approach. The concept of volume averaging in stress and strain component was invoked to homogenize the representative rock volume which consists of intact rock and cracks. The formulation results in the constitutive relations for the homogenized equivalent anisotropic material. The homogenization model was implemented in the standard FEM code COSMOSM. The numerical uniaxial tests were performed under plane strain condition to check the validity of the propose numerical model. The effect of friction between the loading plate and the rock sample on the mode of deformation and fracturing was examined by assuming two different contact conditions. The numerical simulation revealed that the homogenized model is able to capture the salient features of deformation and fracturing which are observed commonly in the uniaxial compression test.