• 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.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.29 no.3
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• pp.172-183
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• 2019

The generalized Hoek-Brown (GHB) failure criterion developed by Hoek et al. (2002) is a nonlinear function which defines a stress condition at failure of rock mass. The relevant strength parameter values are systematically determined using the GSI value. Since GSI index is a value quantifying the condition of in-situ rock mass, the GHB criterion is a practical failure condition which can take into the consideration of in-situ rock mass quality. Considering that most rock mechanics engineers are familiar with the linear Mohr-Coulomb criterion and that many rock engineering softwares incorporate Mohr-Coulomb criterion, the equations for the equivalent friction angle and cohesion were also proposed along with the release of the GHB criterion. The proposed equations, however, fix the lower limit of the minor principal stress range, where the linear best-fitting is performed, with the tensile strength of the rock mass. Therefore, if the tensile stress is not expected in the domain of analysis, the calculated equivalent friction angle and cohesion based on the equations in Hoek et al. (2002) could be less accurate. In order to overcome this disadvantage of the existing equations for equivalent friction angle and cohesion, this study proposes the analytical formula which can calculate optimal equivalent friction angle and cohesion in any minor principal stress interval, and verified the accuracy of the derived formula.

• Journal of the Korean Geotechnical Society
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• v.19 no.1
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• pp.209-220
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• 2003

Modification of general Hoek and Brown criterion is carried out to estimate the shaft resistance of drilled shaft socketed into rock mass. Since the general Hoek-Brown criterion can consider the in-situ state of the rock mass, the proposed method, estimating the unit shaft resistance of drilled shafts based on the Hoek-Brown criterion, has increased flexibility compared to other methods exclusively considering uniaxial compressive strength of intact rocks. The proposed method can form the upper and lower bounds, and most culled data (from 21 pile load tests) from the literature can be found between these two bounds. A comparison between the estimated and observed unit shaft resistances shows quite a good correlation even with crude assumptions for the input parameters. The best-fit line drawn from this analysis shows that at the lower strength of intact rocks (up to 10MPa), Horvath and Kenney's equation shows a good correlation with the measured values, and fur strong rocks Rosenberg and Journeaux's equation provides a close estimation with colleted data. The results of parametric studies for GSI and confining stress show that the normalized unit shaft resistance increases with these two factors. In addition, coefficient of the equational form of the estimation can vary with GSI and confining stresses.

• Tunnel and Underground Space
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• v.20 no.1
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• pp.49-57
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• 2010

For the elasto-plastic analysis of a circular tunnel driven in a strain-softening rock mass subjected to a hydrostatic in-situ stress condition, this study suggests a convenient elasto-plastic analysis scheme which takes the strain-softening of GSI index into account and demonstrates its potential as a numerical tool in designing a circular tunnel. The suggested numerical scheme was developed by modifying the previous elasto-plastic procedure proposed by Lee & Pietruszczak(2008). With the assumption that GSI index of rock mass adjacent to the tunnel surface may be degraded due to the damage caused by the blasting and excavation, the concept of the strain-softening of GSI index was invoked. The concept provides a useful tool considering the strain-softening of the strength parameters appearing in the generalized Hoek-Brown criterion because these parameters can be evaluated empirically by use of GSI. In order to check the validity of the proposed scheme, the elasto-plastic analyses for circular tunnels were performed in various analysis conditions and the results were discussed.

• Geomechanics and Engineering
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• v.9 no.1
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• pp.115-124
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• 2015

Determination of mobilized shear strength parameters (that identify stresses on the failure plane) is required for analyzing the stability by limit equilibrium method. Generalized Hoek-Brown (GHB) and Mohr-Coulomb (MC) failure criteria are usually used for obtaining stresses on the plane of failure. In the present paper, the applicability of these criteria for determining the stresses on failure plane is investigated. The comparison is based on stresses on the real failure plane which are obtained from the Mohr stress circle. To do so, 18 sets of data (consist of principal stresses and angle of failure plane) presented in the literature are used. In addition, the values account for (VAF) and the root mean square error (RMSE) indices were calculated to check the determination performance of the obtained results. Values of VAF and RMSE for the normal stresses on the failure plane evaluated from MC are 49% and 31.5 where for GHB are 55% and 30.5, respectively. Also, for the shear stresses on failure plane, they are 74% and 36 for MC, 76% and 34.5 for GHB. Results show that the obtained stresses and angles of failure plane for each criterion differ from real ones, but GHB results are closer to the empirical results. Also, it is inferred that results are affected by the failure envelope not real failure plane. Therefore, obtained shear strength parameters are not mobilized. Finally, a multivariable regressed relation is presented for determining the stresses on the failure plane.

• Proceedings of the Korean Geotechical Society Conference
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• 2009.03a
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• pp.434-443
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• 2009

Slope stability analysis is an essential part of rock slope design. For highly fractured rock, the limit equilibrium method (LEM) based slope stability analysis with a circular failure surface is often carried out assuming the rock mass behaves more or less as a continuum. This paper examines first, the applicability of the finite-element method (FEM) based shear strength reduction (SSR) technique for highly fractured rock slope, and second the use of Mohr-Coulomb (MC) failure criterion in conjunction with generalized Hoek-Brown (HB) failure criterion. The numerical results on a number of cases are compared in terms of the factor of safety (FS). The results indicated that the FEM-based SSR technique yields almost the same FSs from LEM, and that the MC and HB failure criteria yield almost identical FSs when the strength parameters for MC failure criterion are obtained based on the modified HB failure criterion if and only if value of the Hoek-Brown constant $m_i$ is smaller than 10 and slope angle is smaller than 1:1, otherwise MC failure criteria over-estimate the factor of safety.

• Proceedings of the Korean Geotechical Society Conference
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• 2000.11a
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• pp.713-720
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• 2000

The directional response of strength and deformation on the rocks acting by external loads is called by strength and deformability anisotropy, respectively. Peak strength and its failure criteria of anisotro rocks have been studied and reported. Many authors have investigated in detail the behavior of triaxial peak strength of anisotropic rocks(Jaeger 1960, McLamore & Gray 1967, Hoek & Brown 1980, Ramamurthy & Rao 1985). They concluded that the triaxial strength of anisotropic rocks varies according to the inclination of discontinuity in specimens. And, the minimun triaxial strength occurs in the specmen with 60° of inclination angle ; and specimens with 0° or 90° inclination have maximum triaxial strength. Based on the experimental result, the behavior triaxial strength is investigated. The triaxial compression tests due to the angle bedding plane have been conducted and the material constants, 'm' and 's', cohesion and angle of friction and nonlinear strength parameters to fit for the failure criterion were derived from the regression analysis. And, the experimental date are employed to examine three existing failure criteria for peak strength, provided by Jaeger, McLamore and Hoek & Brown and Ramamurthy & Rao. For a shale, the suitability of the failure criteiria of triaxial peak strength for anisotropic rocks is discussed.

• 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.

• Geomechanics and Engineering
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• v.15 no.6
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• pp.1183-1191
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• 2018

Reliability analysis is generally regarded as the most appropriate method when uncertainties are taken into account in slope designs. With the help of limit analysis, probability evaluation for three-dimensional rock slope stability was conducted based upon the Mote Carlo method. The nonlinear Hoek-Brown failure criterion was employed to reflect the practical strength characteristics of rock mass. A form of stability factor is used to perform reliability analysis for rock slopes. Results show that the variation of strength uncertainties has significant influence on probability of failure for rock slopes, as well as strength constants. It is found that the relationship between probability of failure and mean safety factor is independent of the magnitudes of input parameters but relative to the variability of variables. Due to the phenomenon, curves displaying this relationship can provide guidance for designers to obtain factor of safety according to required failure probability.