• Proceedings of the Korean Geotechical Society Conference
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• 2008.03a
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• pp.963-971
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• 2008

Unsaturated soil mechanics has been often used to find out a cause of failure (tensile failure) of retaining walls and hill slopes containing sandy soils. Checking shear strength is a popular method by considering suction stress developed form pore water menisci among the grains and saturated pockets of pore water under negative pressure. Linear Mohr-Coulomb failure criterion is generally adopted as a failure criterion. However, depending on relative density, stress history, and the magnitude of stress, the failure behavior of sand may not follow linear M-C frictional behavior. For stress in the large compressive ranges, say from tens to hundreds of kPa, the linear M-C criterion is an adequate representation for the shear strength behavior of sand. However, less than tens of kPa, the M-C criterion often can not be accurately represented. Depending on failure criterion, the uniaxial tensile strength is different over 100% relative error. For sand behavior under small compression regimes, therefore, such as under low or zero gravity, or under undergoing tensile failure in the crest area of hill slopes or behind retaining walls, it is important to consider the non-linear behavior.

• Journal of the Korean Geotechnical Society
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• v.30 no.3
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• pp.73-85
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• 2014

The strength parameters used in rock mass design are mainly estimated by equations using Hoek-Brown failure criterion because the tests to obtain the values are limited and expensive. To estimate the strength parameters, the Hoek-Brown failure criterion should be transformed to the Mohr-Coulomb failure criterion. But the processes are more or less cumbersome due to the several stages including the computation and the analyzing steps. In this study, several rock states of various conditions were modeled and then the strength parameters were estimated using the Hoek-Brown failure criterion. Thereafter by analyzing the results, some charts and equations estimating the strength parameters through only one step or easily in the field using the values of RMC, the uniaxial compressive strength and the rock constant ($m_i$), were suggested. And then the suggested method was compared and discussed with the existing method.

• Tunnel and Underground Space
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• v.29 no.3
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• pp.172-183
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• 2019

The generalized Hoek-Brown (GHB) failure criterion developed by Hoek et al. (2002) is a nonlinear function which defines a stress condition at failure of rock mass. The relevant strength parameter values are systematically determined using the GSI value. Since GSI index is a value quantifying the condition of in-situ rock mass, the GHB criterion is a practical failure condition which can take into the consideration of in-situ rock mass quality. Considering that most rock mechanics engineers are familiar with the linear Mohr-Coulomb criterion and that many rock engineering softwares incorporate Mohr-Coulomb criterion, the equations for the equivalent friction angle and cohesion were also proposed along with the release of the GHB criterion. The proposed equations, however, fix the lower limit of the minor principal stress range, where the linear best-fitting is performed, with the tensile strength of the rock mass. Therefore, if the tensile stress is not expected in the domain of analysis, the calculated equivalent friction angle and cohesion based on the equations in Hoek et al. (2002) could be less accurate. In order to overcome this disadvantage of the existing equations for equivalent friction angle and cohesion, this study proposes the analytical formula which can calculate optimal equivalent friction angle and cohesion in any minor principal stress interval, and verified the accuracy of the derived formula.

• Fibers and Polymers
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• v.7 no.3
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• pp.276-285
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• 2006

Development and numerical implementation for an elastoplastic constitutive model for anisotropic and asymmetric materials are presented in this paper. The Coulomb-Mohr yield criterion was modified to consider both the anisotropic and asymmetric properties. The modified yield criterion is an isotropic function of the principal values of a symmetric matrix which is linearly transformed from the Cauchy stress space. In addition to the constitutive equation, the numerical treatment for the singularity in the vertex region of yield surface and stress integration algorithm based on elastoplasticity were presented. In order to assess the accuracy of numerical algorithm, isoerror maps were considered. Also, extension of a strip with a circular hole was simulated and results compared with those obtained using the (smooth) Mises yield criterion to validate stress output for a complex stress state.

• 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.

• 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.

• 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.

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1999.10c
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• pp.556-561
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• 1999

The real strength evvelope for soils without cemetation goes through the origin and is curved. The Mohr -Coulomb failure criterion with the strength parameters c' and ø' from conventional tests overestimates the shear strength available at low normal stresses. The results of laboratory tests interpreted in terms of the Mohr-Coulomb failure criterion are not appropriate for evaluation of surficial slope stability , because the range of effective normal stresses in the field are not used in the laboratory tests.

• Journal of Industrial Technology
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• v.24 no.A
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• pp.139-155
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• 2004

A room and pillar mining method has been adopting at the Jeungsun limestone mine. To check stability of pillar with multiple and irregular openings, the size, shape and spacing of rib pillar were first designed using some empirical suggestions. The Finite Difference Method(FDM)was used to analyze the pillar stability. Twelve different cases with the variation of K(horizontal/vertical stress)values, different height and different spacing of pillar were used in this study. Finally Mohr-Coulomb criterion was adopted to calculate the safety factors. Horizontal and vertical displacement, maximum and minimum principal stresses, range of plastic zone and safety factors were calculated at each case. As a result of analysis, the size of one block is 160m long, 70m wide, 40m high with 20m wide rib pillar and 20m square column pillar. The overall recovery at this case can be estimated about 40%.