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

• Tunnel and Underground Space
• /
• v.22 no.6
• /
• pp.462-470
• /
• 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.

• Tunnel and Underground Space
• /
• v.31 no.6
• /
• pp.480-493
• /
• 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
• /
• v.8 no.1
• /
• pp.97-111
• /
• 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.

• Geomechanics and Engineering
• /
• v.16 no.6
• /
• pp.655-667
• /
• 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
• /
• v.13 no.6
• /
• pp.907-928
• /
• 2017

The effects of seepage force and out-of-plane stress on cavity contracting and tunnel opening was investigated in this study. The generalized Hoek-Brown (H-B) failure criterion and non-associated flow rule were adopted. Because of the complex solution of pore pressure in an arbitrary direction, only the pore pressure through the radial direction was assumed in this paper. In order to investigate the effect of out-of-plane stress and seepage force on the cavity contraction and circular tunnel opening, three cases of the out-of-plane stress being the minor, intermediate, or major principal stress are assumed separately. A method of plane strain problem is adopted to obtain the stress and strain for cavity contracting and circular tunnel opening for three cases, respectively, that incorporated the effects of seepage force. The proposed solutions were validated by the published results and the correction is verified. Several cases were analyzed, and parameter studies were conducted to highlight the effects of seepage force, H-B constants, and out-of-plane stress on stress, displacement, and plastic radius with the numerical method. The proposed method may be used to address the complex problems of cavity contraction and tunnel opening in rock mass.

• Tunnel and Underground Space
• /
• v.32 no.5
• /
• pp.312-326
• /
• 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
• /
• v.11 no.3
• /
• pp.439-455
• /
• 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.

• Geomechanics and Engineering
• /
• v.18 no.3
• /
• pp.225-234
• /
• 2019

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass is investigated, which is compatible with Mohr-Coulomb and generalized Hoek-Brown failure criteria. Based on finite difference method, plastic region is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium and compatibility equations, the material parameters of the rock or soil mass are assumed to be the same in each ring. For the strain-softening behavior, the strength parameters are assumed to be a linear function of deviatoric plastic strain (${\gamma}p^*$) for each ring. Increments of stress and strain for each ring are calculated with the finite difference method. Assumptions of large-strain for soil mass and small-strain for rock mass are adopted, respectively. A new numerical stepwise approach for limited pressure and plastic radius are obtained. Comparisons are conducted to validate the correctness of the proposed approach with Vesic's solution (1972). The results show that the perfectly elasto-plastic model may underestimate the displacement and stresses in cavity expansion than strain-softening coefficient considered. The results of limit expansion pressure based on the generalised H-B failure criterion are less than those obtained based on the M-C failure criterion.