• 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.

• 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.

• Geomechanics and Engineering
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• v.13 no.4
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• pp.585-600
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• 2017

This study deals with simple solutions for a spherical or circular opening excavated in elastic-brittle plastic rock mass compatible with a linear Mohr-Coulomb (M-C) or a nonlinear Hoek-Brown (H-B) yield criterion. Based on total strain approach, the closed-form solutions of stresses and displacement are derived simultaneously for circular and spherical openings using original H-B and M-C yield criteria. Two simple numerical procedures are proposed for the solution of generalized H-B and M-C yield criteria. Based on incremental approach, the similarity solution is derived for circular and spherical openings using generalized H-B and M-C yield criteria. The classical Runge-Kutta method is used to integrate the first-order ordinary differential equations. Using three data sets for M-C and H-B models, the results of the radial displacements, the spreading of the plastic radius with decreasing pressure, and the radial and circumferential stresses in the plastic region are compared. Excellent agreement among the solutions is obtained for all cases of spherical and circular openings. The importance of the use of proper initial values in the similarity solution is discussed.

• Tunnel and Underground Space
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• v.28 no.1
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• pp.59-71
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• 2018

Since the generalized Hoek-Brown (GHB) function predicts the strength of the jointed rock mass in a systematic manner by use of GSI index, it is widely used in rock engineering practices. In this study, a series of 2D elasto-plastic FE analysis, which adopts the GHB criterion as a yield function, was carried out to investigate the radial convergence characteristics of circular tunnel excavated in the GHB rock mass. The effect of the plastic potential function on the elasto-plastic displacement was also examined. In the analysis, the wide range of both the $K(={\sigma}_h/{\sigma}_v)$ and GSI values are considered. For each K value, the variation of the ratio of sidewall displacement to roof displacement was calculated with varying GSI values and the obtained displacement patterns were analysed. The calculation results show that the displacement ratio significantly depends not only on the K value but also on the range of GSI value. In particular, for lower range of GSI value, the displacement ratio pattern calculated in the elasto-plastic regime is opposite to that predicted by the elasticity theory. In addition, the variation of the radial displacement ratio with GSI value for different types of plastic potential function showed similar trend.

• Geomechanics and Engineering
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• v.32 no.1
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• pp.49-68
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• 2023

The three-dimensional failure criterion is essential for maintaining wellbore stability and sand production problem. The convenient factor for a stable wellbore is mud weight and borehole orientation, i.e., mud window design and selection of borehole trajectory. This study proposes a new three-dimensional failure criterion with linear relation of three in-situ principal stresses. The number of failure criteria executed to understand the phenomenon of rock failure under in-situ stresses is the Mohr-Coulomb criterion, Hoek-Brown criterion, Mogi-Coulomb criterion, and many more. A new failure criterion is the extended Mohr-Coulomb failure criterion with the influence of intermediate principal stress (σ₂). The influence of intermediate principal stress is considered as a weighting of (σ₂) on the mean effective stress. The triaxial compression test data for eleven rock types are taken from the literature for calibration of material constant and validation of failure prediction. The predictions on rock samples using new criteria are the best fit with the triaxial compression test data points. Here, Drucker-Prager and the Mogi-Coulomb criterion are also implemented to predict the failure for eleven different rock types. It has been observed that the Drucker-Prager criterion gave over prediction of rock failure. On the contrary, the Mogi-Coulomb criterion gave an equally good prediction of rock failure as our proposed new 3D failure criterion. Based on the yield surface of a new 3D linear criterion it gave the safest prediction for the failure of the rock. A new linear failure criterion is recommended for the unique solution as a linear relation of the principal stresses rather than the dual solution by the Mogi-Coulomb criterion.

• Geomechanics and Engineering
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• v.8 no.3
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• pp.323-359
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• 2015

This paper presents an elasto-plastic model for determination of the ground response curve of a circular underwater tunnel excavated in elastic-strain softening rock mass compatible with a nonlinear Hoek-Brown yield criterion. The finite difference method (FDM) was used to propose a new solution to calculate pore water pressure, stress, and strain distributions on periphery of circular tunnels in axisymmetric and plain strain conditions. In the proposed solution, a modified non-radial flow pattern, for the hydraulic analysis, is utilized. To evaluate the effect of gravitational loads and variations of pore water pressure, the equations concerning different directions around the tunnel (crown, wall, and floor) are derived. Regarding the strain-softening behavior of the rock mass, the stepwise method is executed for the plastic zone in which parameters of strength, dilatancy, stresses, strains, and deformation are different from their elasto-plastic boundary values as compared to the tunnel boundary values. Besides, the analytical equations are developed for the elastic zone. The accuracy and application of the proposed method is demonstrated by a number of examples. The results present the effects of seepage body forces, gravitational loads and dilatancy angle on ground response curve appropriately.

• Geomechanics and Engineering
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• v.22 no.4
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• pp.277-290
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• 2020

This paper presents an elastic-plastic solution for the circular tunnel of elastic-strain softening behavior considering the pressure-dependent Young's modulus and the nonlinear dilatancy. The proposed solution is verified by the results of the field measuring and numerical simulation from a practical project, and a published closed-form analysis solution. The influence of each factor is discussed in detail, and the ability of Young's modulus and dilatancy characterizing the mechanical response of surrounding rock is investigated. It is found that, in low levels of support pressure, adopting the constant Young's modulus model will seriously misestimate the surrounding rock deformation. Using the constant dilatancy model will underestimate the surrounding rock deformation. When adopting the constant dilatancy model, as the dilation angle increases, the range of the plastic region increases, and the surrounding rock deformation weakens. When adopting the nonlinear dilatancy, the plastic region range and the surrounding rock deformation are the largest. The surrounding rock deformation using pressure-dependent Young's modulus model is between those resulted from two constant Young's modulus models. The constant α of pressuredependent Young's modulus model is the main factor affecting the tunnel displacement. The influence of α using a constant dilatancy model is much more apparent than that using a nonlinear dilatancy model.