A three‐dimensional Hoek–Brown failure criterion based on an elliptical Lode dependence

Jiang, Hua; Yang, Yang

doi:10.1002/nag.3125

Cited by 11 publications

(3 citation statements)

References 40 publications

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“…The plots in the p-q plane shown in Figures 11-13 provide a good evaluation of the stress states along lines C5 and D6 by comparing the upper-and lower-bound strength envelopes. However, these plots do not show the ultimate strength corresponding to each stress point since the ultimate strengths are dependent on both mean pressure and Lode angle, as explained in the material model in Section 3 [34,35]. Therefore, in order to evaluate more accurately, an additional plot showing the stress state in the octahedral plane is necessary.…”

Section: Stressesmentioning

confidence: 99%

Numerical Parametric Studies on the Stress Distribution in Rocks around Underground Silo

Kim

Kim²

2022

Applied Sciences

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The underground silo was constructed as a facility for the disposal of low- and intermediate-level radioactive waste. It is divided into three parts: the upper-dome core, the lower-dome core, and the cylindrical-space core. Numerical parametric studies on the stress distribution occurring in the surrounding rocks around the underground silo are presented in this paper. It is assumed that the soil layer was distributed to a depth of −4.3 m from the ground level, the weathered rocks were distributed to a depth of −9.5 m from the bottom of the soil layer, and the rocks were distributed in the lower part of the weathered rocks. A 2D axial symmetric finite element model was considered for the numerical analysis of the underground silo. A 3D finite element model was used to verify the reliability of the 2D axial symmetric model. Finite element analysis was carried out under various ratios of in situ horizontal stress to vertical stress (Ko). The numerical results obtained through these analyses include detailed stress states in the p–q and octahedral planes at key locations of finite element models around an underground silo. Contours of safety factor distributions are also presented to evaluate the overall structural safety of the surrounding rock mass, which is the main supporting body of the underground silo.

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Section: Stressesmentioning

confidence: 99%

Numerical Parametric Studies on the Stress Distribution in Rocks around Underground Silo

Kim

Kim²

2022

Applied Sciences

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“…Mohr-Coulomb and Hoek-Brown's failure criterion does not consider the effect of intermediate principal stress, so the rock failure prediction under the triaxial stress condition is unreliable. These lead to developing several three-dimensional Hoek-Brown criteria given by Pan and Hudson (1988); Priest (2005); Zhang and Zhu (2007); Zhang (2008); Jiang and Yang (2020). Singh et al (2011) and Mahetaji et al, (2023) developed a modified non-linear Mohr-Coulomb criterion considering the effect of intermediate principal stress on strength behavior.…”

Section: Introductionmentioning

confidence: 99%

Multivariable Regression 3D Failure Criteria for In-Situ Rock

Mahetaji,

Brahma,

Kumar Vij

2023

Earth sci. res. j.

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Wellbore stability problems increase with the exploration and development of oil and gas reservoirs. A new 3D non-linear failure criterion is proposed as a trigonometric function considering the intermediate principal stress (2) on the triaxial compression test data. Mohr-Coulomb and Hoek-Brown are well-known failure criteria, but they do not consider the influence of (2) on rock strength. This new criterion produces a concave surface on the principal stress space (1,2, 3) with the influence of intermediate principal stress. In this study, sensitivity analysis for the variable is also done to understand the significant influence of parameters on the accuracy of the proposed criterion. Further validation of this non-linear criterion on three principal stresses (1,2, 3) was done compared with linear regression and second-degree polynomial regression results. It has been observed that the new non-linear 3D criterion with five material parameters reveals a good fit compared to linear regression and second-degree polynomial regression, which have four and six material parameters, respectively. The new non-linear criterion was further validated by comparison with existing criteria like the Priest, Drucker-Prager, and Mogi-Coulomb. It has been observed that the new 3D non-linear criterion shows a more accurate result than these existing criteria as certain rock types exhibit coefficient of determination (DC) values near one, precisely 0.95 for inada granite, 0.94 for orikabe monzonite, and 0.91 for KTB amphibolite. In contrast, other rock types have DC values ranging from 0.7 to 0.9. The new 3D non-linear criterion also yields lower root means square error (RMSE) values than the Mogi-Coulomb criterion for seven rock types. Specifically, the RMSE values by the new criterion are as follows: KTB amphibolite - 40.03 MPa, Dunham dolomite - 15.16 MPa, Shirahama sandstone - 9.08 MPa, Manazuru andesite - 22.14 MPa, Inada granite - 35.47 MPa, and Coconino sandstone - 19.047 MPa. This new 3D criterion gave precise predictions of the failure of the formation under in-situ stresses and was further helpful for the simulation of the wellbore in the petroleum industry. The variable in the new 3D criterion should be calculated from triaxial compression test data for each formation rock before applying this criterion to the wellbore stability problem and the sand production problem.

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“…ey divided each isotropic modern strength theory into shear stress, octahedral, and principal stress strength theories, and they discussed, compared, and reviewed these theories using relevant triaxial test data obtained from China and other countries. Jiang and Yang [8] proposed a three-dimensional Hoek-Brown failure criterion by introducing additional coefficients to explore failure in rock and concrete under multiaxial stress states. In addition, Wu et al [9] studied the instantaneous equivalent Mohr-Coulomb parameters used to modify the Hoek-Brown criterion.…”

Section: Introductionmentioning

confidence: 99%

Three-Parameter Twin τ2 Strength Theory for Brittle Materials under Multiaxial Stress State and Its Application

Meng

Chen

Meng

et al. 2022

Mathematical Problems in Engineering

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The strength failure of brittle materials under complex stress is an important problem. Herein, we propose a novel three-parameter twin τ2 strength theory considering the influence of hydrostatic pressure and normal stress on the principal shear-stress surface, derive a mathematical expression for the strength theory, and compare the theoretical predictions under several stress states with existing experimental data. The results show that different ultimate stress ratios, α and β, correspond to different strength theories for brittle materials. The principal stress σ1 increases gradually with an increase in σ2 (=σ3) under the stress state σ1 > σ2 = σ3; σ1 (=σ2) increases gradually with an increase in σ3 under the stress state σ1 = σ2 > σ3. Furthermore, the biaxial compressive strength is considerably higher than the uniaxial compressive strength under the biaxial compressive stress for σ1 > 0, σ2 > 0, and σ3 = 0. When σ3 is fixed and σ2 is relatively small under the stress states of σ1 > 0, σ2 > 0, and σ3 > 0, the maximum principal stress σ1 increases with the increasing σ2. When σ2 is relatively large and as σ1 gradually decreases with the increasing σ2, the effect law of intermediate principal stress σ2 is obtained.

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A three‐dimensional Hoek–Brown failure criterion based on an elliptical Lode dependence

Cited by 11 publications

References 40 publications

Numerical Parametric Studies on the Stress Distribution in Rocks around Underground Silo

Numerical Parametric Studies on the Stress Distribution in Rocks around Underground Silo

Multivariable Regression 3D Failure Criteria for In-Situ Rock

Three-Parameter Twin τ2 Strength Theory for Brittle Materials under Multiaxial Stress State and Its Application

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