• 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.23 no.3
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• pp.219-227
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• 2013

Although Mohr-Coulomb failure criterion has limitations in that it is a linear criterion and the effect of the intermediate principal stress on failure is ignored, this criterion has been widely accepted in rock mechanics design. In order to overcome these shortcomings, the Hoek-Brown failure criterion was introduced and recently a number of 3-D failure criteria incorporating the effect of the intermediate principal stress on failure have been proposed. However, in many rock mechanics designs, the possible failure of rock mass is still evaluated based on Mohr-Coulomb criterion and most of practitioners are accustomed to understanding the strength of rock mass in terms of the internal friction angle and cohesion. Therefore, if the equivalent Mohr-Coulomb strength parameters of the advanced failure criteria are calculated, it is possible to take advantage of the advanced failure criteria in the framework of the Mohr-Coulomb criterion. In this study, a method expressing the tangential Mohr-Coulomb strength parameters in terms of the stress invariant is proposed and it is applied to the generalized Hoek-Brown criterion and the HB-WW criterion. In addition, a new approach describing the geometric meaning of the ${\sigma}_2$-dependency of failure criteria in 3-D principal stress space is proposed. Implementation examples of the proposed method show that the influence of the intermediate principal stress on the tangential friction angle and cohesion of the HB-WW criterion is considerable, which is not the case for the 2-D failure criterion.

• Geomechanics and Engineering
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• v.9 no.1
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• pp.115-124
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• 2015

Determination of mobilized shear strength parameters (that identify stresses on the failure plane) is required for analyzing the stability by limit equilibrium method. Generalized Hoek-Brown (GHB) and Mohr-Coulomb (MC) failure criteria are usually used for obtaining stresses on the plane of failure. In the present paper, the applicability of these criteria for determining the stresses on failure plane is investigated. The comparison is based on stresses on the real failure plane which are obtained from the Mohr stress circle. To do so, 18 sets of data (consist of principal stresses and angle of failure plane) presented in the literature are used. In addition, the values account for (VAF) and the root mean square error (RMSE) indices were calculated to check the determination performance of the obtained results. Values of VAF and RMSE for the normal stresses on the failure plane evaluated from MC are 49% and 31.5 where for GHB are 55% and 30.5, respectively. Also, for the shear stresses on failure plane, they are 74% and 36 for MC, 76% and 34.5 for GHB. Results show that the obtained stresses and angles of failure plane for each criterion differ from real ones, but GHB results are closer to the empirical results. Also, it is inferred that results are affected by the failure envelope not real failure plane. Therefore, obtained shear strength parameters are not mobilized. Finally, a multivariable regressed relation is presented for determining the stresses on the failure plane.

• 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.23 no.5
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• pp.383-391
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• 2013

A number of true triaxial tests on rock samples have been conducted since the late 1960 and their results strongly suggest that the intermediate principal stress has a considerable effect on rock strength. Based on these experimental evidence, various 3-D rock failure criteria accounting for the effect of the intermediate principal stress have been proposed. Most of the 3-D failure criteria, however, are focused on the phenomenological description of the rock strength from the true triaxial tests, so that the associated strength parameters have little physical meaning. In order to confirm the likelihood that the intermediate principal stress dependency of rock strength is related to the presence of weak planes and their distribution to the preferred orientation, true triaxial tests are simulated with the transversely isotropic rock model. The conventional Mohr-Coulomb criterion is extended to its anisotropic version by incorporating the concept of microstructure tensor. With the anisotropic Mohr-Coulomb criterion, the critical plane approach is applied to calculate the strength of the transversely isotropic rock model and the orientation of the fracture plane. This investigation hints that the spatial distribution of microstructural planes with respect to the principal stress triad is closely related to the intermediate principal stress dependency of rock strength.

• Journal of Korean Tunnelling and Underground Space Association
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• v.9 no.3
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• pp.263-273
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• 2007

When a tunnel or an underground structure is excavated in deep geological environments, the failure process is affected and eventually dominated by stress-induced fractures growing preferentially parallel to the excavation boundary. This fracturing is generally referred to as brittle failure by spatting and slabbing. Continuum models with traditional failure criteria such as Hoek-Brown or Mohr-Coulomb criteria have not been successful in prediction of the extent and depth of brittle failure. Instead cohesion weakening and frictional strengthening (CWFS) model is known to predict brittle failure well. In this study, CWFS model was applied to predict the brittle failure around a circular opening observed in physical model experiments. To obtain the input parameters for CWFS model, damage-controlled tests were carried out. The predicted depth and extent of brittle failure using CWFS model were compared to the results of the physical model experiment and numerical simulation using traditional model.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.7
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• pp.529-535
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• 2016

In this theoretical study, the strength parameters of the Drucker-Prager yield criterion and Mohr-Coulomb yield criterion were set to equal values, in order to analyze the correlation among the parameters. The Drucker-Prager strength parameters ${\alpha}$ and k were represented by the Mohr-Coulomb strength parameters c and ${\phi}$. Specifically it can be seen that k is function of c, ${\phi}$ and ${\alpha}$ is function of ${\phi}$ alone. Drucker-Prager strength parameter ${\alpha}$ increases as the internal friction angle of soil increases. ${\alpha}_{av}$ which is the average of ${\alpha}_c$ and ${\alpha}_i$ was proportional to internal friction angle in which ${\alpha}_c$ and ${\alpha}_i$ are ${\alpha}$ values corresponding to the circles of the Drucker-Prager yield cirteria circumscribes and inscribes the Mohr-Coulomb yield criterion respectively. The values of the ${\alpha}_{av}$ was 0.07 and 0.29 which correspond to the internal friction angle of $10^{\circ}$ and $45^{\circ}$ respectively. In addition, value of ${\alpha}_c/{\alpha}_i$ was proportional to internal friction angle of soil and the values of ${\alpha}_c/{\alpha}_i$ 1.12 and 1.62 which corresponds to internal friction angle of $10^{\circ}$ and $45^{\circ}$ respectively.The influence of the Mohr-Coulomb strength parameters on the Drucker-Prager strength parameter k was investigated and it was found that k was mainly influenced by the cohesion of the soil, except in the case of the minimum assumed value of c of 10kPa. The deviator stresses, $S_{c0}$ and $S_{t0}$, which correspond to the cases of the Mohr-Coulomb yield criterion under uniaxial compression and uniaxial tension, respectively, and $S_{0(ave)}$, which is the average value of $S_{c0}$ and $S_{t0}$, decrease as the internal friction angle increases. Furthermore, the hexagon, which represents the Mohr-Coulomb yield locus, becomes more irregular, and the deviations of $S_{c0}$ and $S_{t0}$ from $S_{0(ave)}$ also increase, as the internal friction angle increases.

• The Journal of Engineering Geology
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• v.10 no.3
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• pp.225-236
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• 2000

We conducted laboratory simulations of deep vertical drilling into the earth's crust to induce borehole breakouts and investigated their potential use for estimating in situ stress magnitudes in Westerly granite and Berea sandstone. Our experiments consisted of two major stages, a series of triaxial tests and borehole-breakout formation tests under a wide range of far-field stresses. We derived the Mohr-Coulomb, Nadai and Mogi failure criteria from the triaxial test results. Each criterion was compared with the stress condition at breakout boundaries. We concluded that the well known Mohr-Coulomb criterion is not compatible with the stress condition at breakout failure. On the other hand, polyaxial (truly triaxial) failure criteria such as the Nadai criterion for Berea sandstone and the Mogi criterion for Westerly granite were much more suitable for predicting breakout failure zone. Such failure criteria appeared to enable the reliable estimation of the magnitude of one of two horizontal principal stresses if the other one is known.

• Tunnel and Underground Space
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• v.22 no.1
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• pp.12-21
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• 2012

Although the Mohr-Coulomb and Hoek-Brown failure criteria have been adopted widely in rock mechanics, they neglect the ${\sigma}_2$ effect. The result of true triaxial tests on rock samples, however, reveals that the ${\sigma}_2$ effect on strength of rocks is considerable, so that rock failure criteria taking into account the influence of ${\sigma}_2$ are necessary for the precise stability evaluation of rock structures. In this study, a new nonlinear 3-D failure criterion has been suggested by combining the Hoek-Brown criterion with the smooth octahedral shape function taken from Jiang & Pietruszczak (1988). The performance of the new criterion was assessed by comparing the strength predictions from both the suggested criterion and the corresponding linear 3-D criterion. The resulting fit of the new criterion to the true triaxial test data for six rock types taken from the literature shows that the criterion fits the experimental data very well. Furthermore, for the data sets having data taken in the low ${\sigma}_3$ range, the nonlinear failure criterion works better than the linear criterion.

• Structural Engineering and Mechanics
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• v.60 no.5
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• pp.809-828
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• 2016

In deep open pit mines, slope stability is very important. Particularly, increasing the depths increase the risks in mines having weak rock mass. Blasting operations in this type of open pits may have a negative impact on slope stability. Several or combination of methods can be used in order to enable better analysis in this type of deep open-pit mines. Numerical modeling is one of these options. Many complex problems can be integrated into numerical methods at the same time and analysis, solutions can be performed on a single model. Rock failure criterions and rock models are used in numerical modeling. Hoek-Brown and Mohr-Coulomb terms are the two most commonly used rock failure conditions. In this study, mine planning and discontinuity conditions of a lignite mine facing two big landslides previously, has been investigated. Moreover, the presence of some damage before starting the study was identified in surrounding structures. The primary research of this study is on slope study. In slope stability analysis, numerical modeling methods with Hoek-Brown and Mohr-Coulomb failure criterions were used separately. Preparing the input data to the numerical model, the outcomes of patented-blast vibration minimization method, developed by co-author was used. The analysis showed that, the model prepared by applying Hoek-Brown failure criterion, failed in the stage of 10. However, the model prepared by using Mohr-Coulomb failure criterion did not fail even in the stage 17. Examining the full research field, there has been ongoing production in this mine without any failure and damage to surface structures.