• 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.

• Geomechanics and Engineering
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• v.9 no.5
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• pp.619-629
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• 2015

Influenced by various mining activities, fractures in rock masses have different densities, set numbers and lengths, which induce different mechanical properties and failure modes of rock masses. Therefore, precisely expressing the failure criterion of the fractured rock influenced by coal mining is significant for the support design, safety assessment and disaster prevention of underground mining engineering subjected to multiple mining activities. By adopting PFC2D particle flow simulation software, this study investigated the propagation and fractal evolution laws of the micro cracks occurring in two typical kinds of rocks under uniaxial compressive condition. Furthermore, it calculated compressive strengths of the rocks with different confining pressures and box-counting dimensions. Moreover, the quantitative relation between the box-counting dimension of the rocks and the empirical parameters m and s in Hoek-Brown strength criterion was established. Results showed that with the increase of the strain, the box-counting dimension of the rocks first increased slowly at the beginning and then exhibited an exponential increase approximately. In the case of small strains of same value, the box-counting dimensions of hard rocks were smaller than those of weak rocks, while the former increased rapidly and were larger than the latter under large strain. The results also presented that there was a negative correlation between the parameters m and s in Hoek-Brown strength criterion and the box-counting dimension of the rocks suffering from variable mining activities. In other words, as the box-counting dimensions increased, the parameters m and s decreased linearly, and their relationship could be described using first order polynomial function.

• 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.

• 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.

• 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 $45^{\circ}$.

• Geomechanics and Engineering
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• v.37 no.4
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• pp.323-339
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• 2024

If the pressure exerted on the face of a tunnel excavated by TBM exceeds a threshold, it leads to failure of the soil or rock masses ahead of the tunnel face, which results in heaving the ground surface. In the current research, the upper bound method of limit analysis was employed to calculate the blow-out pressure of tunnels excavated in rock masses obeying the Hoek-Brown nonlinear criterion. The results of the proposed method were compared with three-dimensional finite element models, as well as the available methods in the literature. The results show that when σ_ci, m_i, and GSI increase, the blow-out pressure increases as well. By doubling the tunnel diameter, the blow-out pressure reduces up to 54.6%. Also, by doubling the height of the tunnel cover and the surcharge pressure exerted on the ground surface above the tunnel, the blow-out pressure increased up to 74.9% and 5.4%, respectively. With 35% increase in the unit weight of the rock mass surrounding the tunnel, the blow-out pressure increases in the range of 14.8% to 19.6%. The results of the present study were provided in simple design graphs that can easily be used in practical applications in order to obtain the blow-out pressure.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.1C
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• pp.25-31
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• 2006

It is common to use the unconfined compressive strength (UCS) of intact rock to estimate the shaft resistance of rock socketed drilled shaft. Therefore the most design manuals give a guide to use the UCS of rock core to estimate the shaft resistance of rock-socketed drilled shaft. Recently, however the design manuals for highway bridge (KSCE, 2001) and of AASHTO (2000) were revised to use the UCS of rock mass with RQD instead of the UCS of rock core so that the estimated resistance could be representative of field conditions. Questions have been raised in application of the new guide to the domestic main bed rock types. The intrinsic drawbacks in terms of RQD were comprised in the questions, too. As the results, in 2002 the new guide in the design manual for highway bridge (KSCE, 2001) were again revised to use the UCS of rock core to estimate the shaft resistance of rock-socketed drilled shafts. In this paper, various methods which can estimate the UCS of rock mass from intact rock core were reviewed. It seems that among those, the Hoek-Brown method is very reliable and practical for the estimation of the UCS of rock mass from rock cores. As the results, using the Hoek-Brown failure criterion a modified guide for the estimation of the shaft resistance of rock-socketed drilled shafts was suggested in this paper. Through a case study it is shown that the suggested method gives a good agreement with the measured data.

• 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.

• Journal of the Korean Geotechnical Society
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• v.22 no.7
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• pp.23-35
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• 2006

Shear load transfer characteristics of rock-socketed drilled shafts were analyzed. The constant normal stiffness (CNS) direct shear tests were performed to identify the major influencing factors of shaft resistance, i.e., unconfined compressive strength, borehole roughness, normal stiffness, initial confining stress, and material properties. Based on the CNS tests, shear load transfer function of drilled shafts in rocks is proposed using borehole roughness and the geological strength index (GSI), which indicates discontinuity and surface condition of rock mass in Hoek-Brown criterion (1997). The proposed load-transfer function was verified by the load test results of seven rock-socketed drilled test shafts subjected to axial loads. Through comparisons of the results of load tests, it is found that the load-transfer function by the present study is in good agreement with the general trend observed by in situ measurements, and thus represents a significant improvement in the prediction of load transfer of drilled shafts.

• Journal of the Korean GEO-environmental Society
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• v.20 no.5
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• pp.13-21
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• 2019

There are many cuts or natural rock slopes that remain stable for a long time in the natural environment with steep slopes ($65^{\circ}$ to $85^{\circ}$). In terms of design practice, the rock mass consisting of similar rock condition and geological structures is defined as a good continuum rock slope, and during the process of decision making angle of this rock slope, it will be important to establish the geotechnical properties estimating method of the continuum rock on the process of stability analysis in the early stages of design and construction. In this study, the stability analysis of a good continuum rock slope that can be designed as a steep slope proposed a practical method of estimating the shear strength by induced from the Hoek-Brown failure criterion, and in addition, the design applicability was evaluated through the stability analysis of steep rock slope. The existing method of estimating the shear strength was inadequate for practical use in the design, as the equivalent M-C shear strength corresponding to the H-B envelope changes sensitively, even with small variations in confining stress. To compensate for this problem, it was proposed to estimate equivalent M-C shear strength by iso-angle division method. To verify the design applicability of the iso-angle division method, the results of the safety factor and the displacement according to the change in angle of the cut slope constructed at the existing working design site were reviewed. The safety factor is FS=16~59 on the 1:0.5 slope, FS=12~52 on the 1:0.3 slope, most of which show a 10~12 percent reduction. Displacement is 0.126 to 0.975 mm on the 1:0.5 slope, 0.152 to 1.158 mm on the 1:0.3 slope, and represents an increase of 10 to 15%. This is a slightly change in normal proportion and is in good condition in terms of stability. In terms practical the working design, it was confirmed that applying the shear strength estimated by Iso-angle division method derived from the H-B failure criterion as a universal shear strength for a good continuum rock mass slope was also able to produce stable and economic results. The procedure for stability analysis using LEM (Limit Equilibrium Analysis Method) and FEM (Finite Element Analysis Method) will also be practical in the rock slope where is not distributed fault. The study was conducted by selecting the slope of study area as a good rock condition, establishing a verification for which it can be applied universal to a various rock conditions will be a research subject later on.