• 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.

• Geomechanics and Engineering
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• v.10 no.1
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• pp.59-76
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• 2016

The non-linear Hoek-Brown failure criterion has been widely accepted and applied to evaluate the stability of rock slopes under plane-strain conditions. This paper presents a kinematic approach of limit analysis to assessing the static and seismic stability of three-dimensional (3D) rock slopes using the generalized Hoek-Brown failure criterion. A tangential technique is employed to obtain the equivalent Mohr-Coulomb strength parameters of rock material from the generalized Hoek-Brown criterion. The least upper bounds to the stability number are obtained in an optimization procedure and presented in the form of graphs and tables for a wide range of parameters. The calculated results demonstrate the influences of 3D geometrical constraint, non-linear strength parameters and seismic acceleration on the stability number and equivalent strength parameters. The presented upper-bound solutions can be used for preliminary assessment on the 3D rock slope stability in design and assessing other solutions from the developing methods in the stability analysis of 3D rock slopes.

• 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.

• 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.

• 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.

• 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.

• Geomechanics and Engineering
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• v.16 no.6
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• pp.569-575
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• 2018

The stability of shallow cavities with an arbitrary profile is a difficult issue in geotechnical engineering. This paper investigates this problem on the basis of the upper bound theorem of limit analysis and the Hoek-Brown failure criterion. The influence of pore pressure is taken into consideration by regarding it as an external force acting on rock skeleton. An objective function is constructed by equating the internal energy dissipation to the external force work. Then the Lagrange variation approach is used to solve this function. The validity of the proposed method is demonstrated by comparing the analytical solutions with the published research. The relations between shallow and deep cavity are revealed as well. The detaching curve of cavity roof with elliptical profile is obtained. In order to facilitate the application of engineering practice, the numerical results are tabulated, which play an important role in tunnel design and stability analysis of roof. The influential factors on potential collapse are taken into consideration. From the results, the impact of various factors on the extent of detaching is seen intuitively.

• Geomechanics and Engineering
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• v.31 no.5
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• pp.461-476
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• 2022

Research studies on the scale effect on triaxial strength of intact rocks are scarce, being more common those in uniaxial strength. In this paper, the authors present and briefly interpret the peak and residual strength trends on a series of triaxial tests on different size specimens (30 mm to 84 mm diameter) of an intact granitic rock at confinements ranging from 0 to 15 MPa. Peak strength tends to grow from smaller to standard-size samples (54 mm) and then diminishes for larger values at low confinement. However, a slight change in strength is observed at higher confinements. Residual strength is observed to be much less size-dependent. Additionally, this study introduces preliminary modelling approaches of these laboratory observations with the help of three-dimensional particle flow code (PFC3D) simulations based on bonded particle models (BPM). Based on previous studies, two modelling approaches have been followed. In the first one, the maximum and minimum particle diameter (D_max and D_min) are kept constant irrespective of the sample size, whereas in the second one, the resolution (number of particles within the sample or ϕ_v) was kept constant. Neither of these approaches properly represent the observations in actual laboratory tests, even if both of them show some interesting capabilities reported in this document. Eventually, some suggestions are provided to proceed towards improving modelling approaches to represent observed scale effects.