• 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.

• Magazine of the Korean Society of Agricultural Engineers
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• v.38 no.6
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• pp.64-73
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• 1996

The three-dimensional strength behavior of compacted decomposed granite soil was studied using cubical triaxial tests with independent control of the three principal stresses. All specimens were loaded under conditions of principal stress direction fixed and aligned with the directions of compacted plane. For comparable test conditions, the major principal strain and volume strain to failure were smallest when the major principal stress acted perpendicular to the compacted plane. The opposite extremes were obtained when the major principal stress acted parallel to the compacted plane. In cubical triaxial tests with same b values and with ${\theta}$ values in one of three sectors of the octahedral plane, independent of the range of ${\theta}$, higher friction angles are obtained in tests with b greater than in triaxial compression tests in which b 0.0, Comparison between the results of the drained cubical triaxial tests on lksan compacted decomposed granite soil and the cross section of the Mohr-Coulomb failure surface as well as the cross section of the Mohr-Coulomb failure surface were made. Lade's isotropic failure criterion based on vertical specimens overestimates the strengths for tests performed with values of 0 between 90˚ and 1 50˚ the Mohr-Coulomb criterion generally underestimates the strengths of tests performed with values of ${\theta}$ between $0^{\circ}$ and $180^{\circ}$ except around the $120^{\circ}$.

• Geotechnical Engineering
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• v.12 no.3
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• pp.5-16
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• 1996

Based on many experimental results on fine silica sands, the strength relation between triaxial and plane strain tests is expressed as a function of both density and mean effective principal stress at failure. Stress ratio of mean normal stress to deviatoric stress at failure is a well defined function of shear angle of friction, This ratio decreases with increasing shear angle of friction. Intermediate principal stress is also expressed in terms of major and minor principal stresses and a relatively good agreement between theoretical and observed angles of failure plane in plane strain test is confirmed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.3
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• pp.595-602
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• 1998

Specimens of 304 stainless steel were tested to failure at elevated temperatures under multiaxial stress states, uniaxial tension using smooth bar specimens, biaxial shearing using double shear bar specimens, and triaxial tension using notched bar specimens. Rupture times are compared for uniaxial, biaxial, and triaxial stress states with respect to the maximum principal stress, the von Mises effective stress, and the principal facet stress. The results indicate that the principal facet stress gives the best correlation for the material investigated, and this parameter can predict creep life data under multiaxial stress states with rupture data obtained with specimens under uniaxial stresses. The results also suggest that grain boundary cavitation, coupled with localized deformation processes such as grain boudary sliding, controls the lifetimes of the specimens.

• Journal of Mechanical Science and Technology
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• v.19 no.7
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• pp.1432-1440
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• 2005

High-temperature rupture behavior of 5083-Al alloy was tested for failure at 548K under multiaxial stress conditions: uniaxial tension using smooth bar specimens, biaxial shearing using double shear bar specimens, and triaxial tension using notched bar specimens. Rupture times were compared for uniaxial, biaxial, and triaxial stress conditions with respect to the maximum principal stress, the von Mises effective stress, and the principal facet stress. The results indicate that the von Mises effective and principal facet stresses give good correlation for the material investigated, and these parameters can predict creep life data under the multiaxial stress states with the rupture data obtained from specimens under the uniaxial stress. The results suggest that the creep rupture of this alloy under the testing condition is controlled by cavitation coupled with highly localized deformation process, such as grain boundary sliding. It is also conceivable that strain softening controls the highly localized deformation modes which result in cavitation damage in controlling rupture time of this alloy.

• Geotechnical Engineering
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• v.10 no.1
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• pp.103-118
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• 1994

A series of drained triaxial testis was performed on a Band by use of cubical triaxial apparatus, in which three principal stresses could be applied independently. The stress -strain behavior on the same stress path with cubical triaxial test was analyzed with application of the isotropic single hardening constitutive model presented by Lade. The behavior predicted by the constitutive model presented good coincidence with experimental results during poi mary loading. However, the predicted Mo윤ding and reloading behavior wan much different from results of cubical triaxial testy. That is, the softening part of the prediction might result in a rough approximation, since the plastic work parameters of single hardening model were based on the hardening portion of the data.

• Magazine of the Korean Society of Agricultural Engineers
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• v.37 no.2
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• pp.64-72
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• 1995

A series of cubical triaxial tests with three independent principal stresses was per- formed on Baekma river sand( # 40~100). It was found that the major principal strain at failure remained approximately constant for b values larger than about 0.3 for both the drained and undrained condition, and thereafter increased as b value decreased. The test results showed that the direction of the strain increment at failure form acute angles with the failure surfaces for both the drained and undrained condition. The results were thus not in agreement with the normality condition from classic plasticity theory. Howev- er, it was found that the projections of the plastic strain increment vectors on the octahe- dral plane were perpendicular to the failure surface in that plane. Failure strength in terms of effective stress anlaysis was greatly influenced by the variation of intermediate principal stress and so was failure criterion. The effective stress failure surfaces for both the drained and undrained condition were estimated quite well by use of Lade's failure criterion.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.8 no.2
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• pp.99-107
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• 1988

A limited number of cubical triaxial tests with independent control of the three principal stresses were performed on an overconsolidated clay. The cubical undisturbed specimens with overconsolidation ratio of 5 were prepared in triaxial chamber after sampling in field. It was found that the intermediate principal stress influences on the stress-strain, undrained strength effective strength, effective friction angle and pore pressure of the overconsolidated clay. When the magnitude of the intermediate principal stress is not same as the minimum principal stress, the failure strength of the overconsolidated clay is underestimated by use of Mohr-Coulomb failure criterion while it can be estimated quite well by use of Lade failure criterion. And the undrained strength of the overconsolidated clay does not coincide with that obtained by Tresca failure criterion.

• Geomechanics and Engineering
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• v.11 no.5
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• pp.639-655
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• 2016

The effect of particle breakage and intermediate principal stress ratio on the behaviour of crushable granular assemblies under true triaxial stress conditions is studied using the discrete element method. Numerical results show that the increase of intermediate principal stress ratio $b(b=({\sigma}_2-{\sigma}_3)/({\sigma}_1-{\sigma}_3))$ results in the increase of dilatancy at low confining pressures but the decrease of dilatancy at high confining pressures, which stems from the distinct increasing compaction caused by breakage with b. The influence of b on the evolution of the peak apparent friction angle is also weakened by particle breakage. For low relative breakage, the relationship between the peak apparent friction angle and b is close to the Lade-Duncan failure model, whereas it conforms to the Matsuoka-Nakai failure model for high relative breakage. In addition, the increasing tendency of relative breakage, calculated based on a fractal particle size distribution with the fractal dimension being 2.5, declines with the increasing confining pressure and axial strain, which implies the existence of an ultimate graduation. Finally, the relationship between particle breakage and plastic work is found to conform to a unique hyperbolic correlation regardless of the test conditions.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.1
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• pp.153-166
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• 1991

In an attempt to investigate the effect of intermedate principal stresses which are related to the stress-strain behavior of standard sands, a series of three-Principal stress control tests were conducted for individual stress paths. The results have shown that shear strengths of sands vary with the stress paths. The variations in internal friction angle are accorded with the Habibs stress parameter, b which represents Stress paths, showing on abropt increase at the values between 0.0 and 0.268, a moderate level between 0.268 and 0.682, and a slight decrease between 0.682 and 1.0 However, the friction angles under a triaxial extention state, were found relatively larger than under a triaxial compression state. In general, such veriations were found to have the same tendency without any relevant relation with the density of specimens and confining pressures. Therefore, it is concluded, that the shear strength of sands are positively influeced by the intermediate principal stresses present in the media. And the influnce of intermediate principal stresses on shear strengths of sands found from the present study are well compared with the previous studies by Lade-Duncan and Matsuoka-Nakai revealing a similar tendency within the failure criteria proposed by them.