• Tunnel and Underground Space
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• v.31 no.6
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• pp.480-493
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• 2021

Since the generalized Hoek-Brown criterion (GHB) provides an efficient way of identifying its strength parameter values with the consideration of in-situ rock mass condition via Geological Strength Index (GSI), this criterion is recognized as one of the standard rock mass failure criteria in rock mechanics community. However, the nonlinear form of the GHB criterion makes its mathematical treatment inconvenient and limits the scope of its application. As an effort to overcome this disadvantage of the GHB criterion, the explicit approximate analytical equations for the minimum principal stress, which is associated with the maximum principal stress at failure, are formulated based on the Taylor polynomial approximation of the original GHB criterion. The accuracy of the derived approximate formula for the minimum principal stress is verified by comparing the resulting approximate minimum principal stress with the numerically calculated exact values. To provide an application example of the approximate formulation, the equivalent friction angle and cohesion for the expected plastic zone around a circular tunnel in a GHB rock mass are calculated by incorporating the formula for the approximate minimum principal stress. It is found that the simultaneous consideration of the values of mi, GSI and far-field stress is important for the accurate calculation of equivalent Mohr-Coulomb parameter values of the plastic zone.

• Geomechanics and Engineering
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• v.22 no.1
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• pp.11-23
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• 2020

In this study, a new analytical-numerical procedure is developed to give the stresses and strains around a circular tunnel in rock masses exhibiting different stress-strain behavior. The calculation starts from the tunnel wall and continues toward the unknown elastic-plastic boundary by a finite difference method in the annular discretized plastic zone. From the known stresses in the tunnel boundary, the strains are calculated using the elastic-plastic stiffness matrix in which three dimensional Hoek-Brown failure criterion (Jiang and Zhao 2015) and Mohr-Coulomb potential function with proper dilation angle (i.e., non-associated flow rule) are employed in terms of stress invariants. The illustrative examples give ground response curve and show correctness of the proposed approach. Finally, from the results of a great number of analyses, a simple relationship is presented to find out the closure of circular tunnel in terms of rock mass strength and tunnel depth. It can be valuable for the preliminary decision of tunnel support and for prediction of tunnel problems.

• 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.

• Journal of the Korean GEO-environmental Society
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• v.10 no.7
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• pp.81-91
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• 2009

Recently, twin-tunnel is often designed in the aspects of disaster prevention and economical reasons. However, the design cases and the studies are relatively insufficient. By the twin-tunnel excavation, deviate stresses of pillar between tunnels are increased and the increased stresses induce the instability of the twin-tunnel. In this study, numerical analyses about the twin-tunnel behaviour were conducted with varying ground strength, width of pillar and depth of earth cover and a series of regression analyses were carried out by using the results of numerical analyses for the twin-tunnel. Based on the numerical analyses, an estimation method of derived stresses is suggested through the regression analyses. Also, based on the results of regression analyses, an quantitative estimation method considering the reinforcement effects is also suggested. Then various parametric studies were conducted to be considered the reinforcement type and various design parameters. Finally, the efficiency of the suggested method based on the Hoek-Brown Failure Criterion is verified through the results of parametric studies.

• Journal of the Korean Geotechnical Society
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• v.29 no.1
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• pp.61-70
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• 2013

This paper presents the results of a two-dimensional finite element analysis of end bearing capacity of single pile installed in fractured rock mass. A number of cases were analyzed using Hoek-Brown criterion that can consider the condition of rock joints. Considering a wide range of joint conditions in which the pile is embedded into the rock, GSI was set as a main parameter. And the effects of pile diameter, unconfined compressive strength of rock and Hoek-Brown constant $m_0$ were considered. Based on parameter study, end bearing load factor graphs were suggested.

• Geomechanics and Engineering
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• v.16 no.6
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• pp.655-667
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• 2018

To evaluate the stability of a rock slope with one pre-exiting vertical crack, this paper performs corresponding probabilistic stability analysis. The existence of cracks is generally ignored in traditional deterministic stability analysis. However, they are widely found in either cohesive soil or rock slopes. The influence of one pre-exiting vertical crack on a rock slope is considered in this study. The safety factor, which is usually adopted to quantity the stability of slopes, is derived through the deterministic computation based on the strength reduction technique. The generalized Hoek-Brown (HB) failure criterion is adopted to characterize the failure of rock masses. Considering high nonlinearity of the limit state function as using nonlinear HB criterion, the multivariate adaptive regression splines (MARS) is used to accurately approximate the implicit limit state function of a rock slope. Then the MARS is integrated with Monte Carlo simulation to implement reliability analysis, and the influences of distribution types, level of uncertainty, and constants on the probability density functions and failure probability are discussed. It is found that distribution types of random variables have little influence on reliability results. The reliability results are affected by a combination of the uncertainty level and the constants. Finally, a reliability-based design figure is provided to evaluate the safety factor of a slope required for a target failure probability.

• Geomechanics and Engineering
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• v.8 no.1
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• pp.97-111
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• 2015

The kinematical approach of limit analysis is used to estimate the three dimensional stability analysis of rock slopes with nonlinear Hoek-Brown criterion under earthquake forces. The generalized tangential technique is introduced, which makes limit analysis apply to rock slope problem possible. This technique formulates the three dimensional stability problem as a classical nonlinear programming problem. A nonlinear programming algorithm is coded to search for the least upper bound solution. To prove the validity of the present approach, static stability factors are compared with the previous solutions, using a linear failure criterion. Three dimensional seismic and static stability factors are calculated for rock slopes. Numerical results of indicate that the factors increase with the ratio of slope width and height, and are presented for practical use in rock engineering.

• Journal of the Korean GEO-environmental Society
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• v.9 no.7
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• pp.45-51
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• 2008

Triaxial compression tests on anisotropic rock specimens are carried out to investigate the failure strength characteristic of anisotropic rocks. The test core specimens were obtained in Daegu region. Test specimens are rock cores with the 7 different angles of bedding plane. The applied confining pressures were 5, 10, 20, 30, 40 MPa, and the rate of displacement was adopted 0.1%/min to fail the specimen within 5-15 min. The results were analyzed by using the failure criteria for anisotropic rocks proposed by Hoek & Brown (1980) and Jaeger (1960). The results of this study are summerised as follows: The results of inherent anisotropy show the shoulder type of anisotropy, and the effect of anisotropy is reduced as the confining pressure increases. The compressive strength of anisotropic rock shows the highest value at the ${\beta}$ (the angle of bedding plane) = $0^{\circ}$ and $90^{\circ}$ and the lowest value at $30^{\circ}$. The Hoek & Brown failure criterion for anisotropic rocks gives a relatively good agreement with the measured strength in all the range of ${\beta}$ angles, but the theory of Jaeger shows a reasonable agreement only in the range of ${\beta}=15^{\circ}$ and $45^{\circ}$.

• 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.

• 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.