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Journal articles on the topic 'Generalized Hoek-Brown criterion'

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Author: Grafiati

Published: 10 December 2022

Last updated: 29 January 2023

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1

Chen, H., H. Zhu, and L. Zhang. "Further modification of a generalized three-dimensional Hoek-Brown criterion – the GZZ criterion." Géotechnique Letters 12, no. 4 (December 1, 2022): 1–21. http://dx.doi.org/10.1680/jgele.21.00117.

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This paper presents a further modification of the generalized three-dimensional (3D) Hoek-Brown criterion - the GZZ (generalized 3D Zhang-Zhu) criterion. Specifically, a modification was made by introducing a 3D version of effective mean stress to replace the original 2D version of effective mean stress in the GZZ criterion. The modification overcomes the non-smoothness and non-convexity problems of the GZZ criterion and maintains a simple form of the criterion expression. The modified GZZ criterion can also reduce to the two-dimensional (2D) Hoek-Brown criterion under both triaxial compression and extension conditions and thus inherits the advantages of and uses the same parameters as the Hoek-Brown criterion. Eleven sets of true triaxial test data were collected from publications to evaluate the newly modified GZZ criterion. The results indicate that the newly modified GZZ criterion has the highest or at least the same accuracy for strength prediction among the various 3D versions of the Hoek-Brown criterion that can reduce to the Hoek-Brown criterion and are smooth and convex. Moreover, of the various 3D versions of the Hoek-Brown criterion that can reduce to the Hoek-Brown criterion and are smooth and convex, only the newly modified GZZ criterion can be expressed explicitly.

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2

Zou, Jin-feng, Song-qing Zuo, and Yuan Xu. "Solution of Strain-Softening Surrounding Rock in Deep Tunnel Incorporating 3D Hoek-Brown Failure Criterion and Flow Rule." Mathematical Problems in Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/7947036.

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In order to investigate the influence of the intermediate principal stress on the stress and displacement of surrounding rock, a novel approach based on 3D Hoek-Brown (H-B) failure criterion was proposed. Taking the strain-softening characteristic of rock mass into account, the potential plastic zone is subdivided into a finite number of concentric annulus and a numerical procedure for calculating the stress and displacement of each annulus was presented. Strains were obtained based on the nonassociated and associated flow rule and 3D plastic potential function. Stresses were achieved by the stress equilibrium equation and generalized Hoek-Brown failure criterion. Using the proposed approach, we can get the solutions of the stress and displacement of the surrounding rock considering the intermediate principal stress. Moreover, the proposed approach was validated with the published results. Compared with the results based on generalized Hoek-Brown failure criterion, it is shown that the plastic radius calculated by 3D Hoek-Brown failure criterion is smaller than those solved by generalized H-B failure criterion, and the influences of dilatancy effect on the results based on the generalized H-B failure criterion are greater than those based on 3D H-B failure criterion. The displacements considering the nonassociated flow rule are smaller than those considering associated flow rules.

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3

Han, Feng Shan. "Estimation of Strength of Massive Jointed Rock Mass Based on Generalized Hoek-Brown Criterion." Applied Mechanics and Materials 204-208 (October 2012): 259–62. http://dx.doi.org/10.4028/www.scientific.net/amm.204-208.259.

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The strength of massive jointed rock mass can be estimated based on Mohr-Coulomb criterion and Hoek-Brown criterion without making expensive experiment of massive jointed rock mass in site. Only using regression analysis, through transformation，Mohr-Coulomb criterion is compared with Hoek-Brown criterion, the strength of jointed rock mass can be economically obtained. In this paper, based on Geological Strength Index GSI and parameter Jv(Joint/m3), the strength of massive jointed rock mass can be obtained. As an example of GSI 24 for massive jointed rock mass is taken, generalized Hoek-Brown criterion is analyzed linearly and approximately using regression analysis, strength of jointed rock mass can be economically obtained That provide economical and effective method for practical engineering analysis

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4

Zhang, L. "A generalized three-dimensional Hoek–Brown strength criterion." Rock Mechanics and Rock Engineering 41, no. 6 (April 3, 2008): 893–915. http://dx.doi.org/10.1007/s00603-008-0169-8.

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5

Meng, Qingfeng, Xuyue Hu, Guanghui Chen, Peng Li, and Zhi Wang. "Estimation of the Critical Seismic Acceleration for Three-Dimensional Rock Slopes." Applied Sciences 11, no. 24 (December 7, 2021): 11625. http://dx.doi.org/10.3390/app112411625.

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An analytical approach for the estimating of critical seismic acceleration of rock slopes was proposed in this study. Based on the 3D horn failure model, the critical seismic acceleration coefficient of rock slopes was conducted with the modified Hoek–Brown (MHB) failure criterion in the framework of upper-bound theory for the first time. The nonlinear Hoek–Brown failure criterion is incorporated into the three-dimensional rotational failure mechanism, and a generalized tangent technique is introduced and employed to convert the nonlinear Hoek–Brown failure criterion into a linear criterion. The critical seismic acceleration coefficients obtained from this study were validated by the numerical simulation results based on finite element limit analysis. The agreement showed that the proposed method is effective. Finally, design charts were provided for exceptional cases for practical use in rock engineering.

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6

Lee, Youn-Kyou, and S. Pietruszczak. "Limit Equilibrium Analysis Incorporating the Generalized Hoek–Brown Criterion." Rock Mechanics and Rock Engineering 54, no. 9 (June 5, 2021): 4407–18. http://dx.doi.org/10.1007/s00603-021-02518-8.

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7

Yin, Nan. "Analysis on Surrounding Rock Mass Plastic Zone of Deep Underground Chamber Based on Hoek-Brown Criterion." Advanced Materials Research 838-841 (November 2013): 741–46. http://dx.doi.org/10.4028/www.scientific.net/amr.838-841.741.

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Generalized Hoek-Brown criterion is indicated as a dimensionless quantity, on this basis, elastic-plastic analytical method of circular underground chamber is presented based on generalized Hoek-Brown criterion in uniform stress field. Take into account a number of factors such as deep rock mass quality, rock strength, etc, surrounding rock mass plastic zone of deep underground chamber is analyzed by the analytical method. The results show that taking measures to improve the quality of rock mass can effectively control surrounding rock mass plastic zone for soft rock underground chamber, however, taking measures to improve the quality of rock mass can not appreciably control surrounding rock mass plastic zone for hard rock underground chamber.

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8

Lakirouhani, Ali, Mohammad Bahrehdar, Jurgis Medzvieckas, and Romualdas Kliukas. "COMPARISON OF PREDICTED FAILURE AREA AROUND THE BOREHOLES IN THE STRIKE-SLIP FAULTING STRESS REGIME WITH HOEK-BROWN AND FAIRHURST GENERALIZED CRITERIA." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 27, no. 5 (June 10, 2021): 346–54. http://dx.doi.org/10.3846/jcem.2021.15020.

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Breakout is a shear failure due to compression that forms around the borehole due to stress concentration. In this paper, the breakout theory model is investigated by combining the equilibrium elasticity equations of stress around the borehole with two Hoek-Brown and Fairhurst generalized fracture criteria, both of which are based on the Griffith criterion. This theory model provides an explicit equation for the breakout failure width, but the depth of failure is obtained by solving a quartic equation. According to the results and in general, in situ stresses and rock strength characteristics are effective in developing the breakout failure area, As the ratio of in-situ stresses increases, the breakout area becomes deeper and wider. Because in the shear zone, the failure envelope of the Fairhurst criterion is lower than the Hoek-Brown failure criterion, the Fairhurst criterion provides more depth for breakout than the Hoek-Brown criterion. However, due to the same compressive strength of the rock in these two criteria, the same failure width for breakout is obtained from these two criteria. Also, the results obtained for the depth of failure from the theoretical model based on the Fairhurst criterion are in good agreement with the laboratory results on Westerly granite.

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9

Zhang, Qi, Hehua Zhu, and Lianyang Zhang. "Modification of a generalized three-dimensional Hoek–Brown strength criterion." International Journal of Rock Mechanics and Mining Sciences 59 (April 2013): 80–96. http://dx.doi.org/10.1016/j.ijrmms.2012.12.009.

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10

Lee, Youn-Kyou. "Relationship between Tangential Cohesion and Friction Angle Implied in the Generalized Hoek-Brown Failure Criterion." Journal of Korean Society For Rock Mechanics 24, no. 5 (October 31, 2014): 366–72. http://dx.doi.org/10.7474/tus.2014.24.5.366.

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11

Deng, Xianghui, Yuncai Wang, Rui Wang, Daohong Xia, and Zhiqing Zhao. "Application of Modified Hoek–Brown Strength Criterion in Water-Rich Soft Rock Tunnel." Geofluids 2021 (June 7, 2021): 1–12. http://dx.doi.org/10.1155/2021/5552791.

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When a tunnel is excavated in the water-rich soft rock stratum, the strength of the soft rock is greatly reduced due to the seepage of groundwater. The condition may result in engineering accidents, such as large deformation, limit invasion, and even local collapse of the tunnel. Therefore, it is very important to research the stability of the surrounding rock in the water-rich soft rock tunnel. The water-rich disturbance factor considering the seepage influence of groundwater and blasting disturbance is proposed, and the generalized Hoek–Brown strength criterion is modified on the basis of the immersion softening test of soft rock. In accordance with the classical elastic–plastic mechanics theory, the stress, strain, and displacement calculation formulas of the tunnel surrounding rock are derived. The displacement of tunnel surrounding rock is analyzed using the derived formula and the modified Hoek–Brown strength criterion and then compared with the measured value. Results show that the displacement of surrounding rock, which is calculated by modified Hoek–Brown strength criterion considering water-rich disturbance factor and the displacement calculation formula, is close to the measured deformation of surrounding rock in water-rich soft rock tunnel, and the error is small. Therefore, the modified Hoek–Brown strength criterion can be applied to the water-rich soft rock tunnel, and the derived displacement calculation formula can accurately calculate the deformation of tunnel surrounding rock. It is of great significance to the study of surrounding rock stability of water-rich soft rock tunnel.

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12

Shen, Jiayi, Murat Karakus, and Chaoshui Xu. "Chart-based slope stability assessment using the Generalized Hoek–Brown criterion." International Journal of Rock Mechanics and Mining Sciences 64 (December 2013): 210–19. http://dx.doi.org/10.1016/j.ijrmms.2013.09.002.

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13

Lee, Youn-Kyou, and Byung-Hee Choi. "Equivalent Friction Angle and Cohesion of the Generalized Hoek-Brown Failure Criterion in terms of Stress Invariants." Journal of Korean Society For Rock Mechanics 22, no. 6 (December 31, 2012): 462–70. http://dx.doi.org/10.7474/tus.2012.22.6.462.

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14

Lee, Youn-Kyou, and S. Pietruszczak. "Analytical representation of Mohr failure envelope approximating the generalized Hoek-Brown failure criterion." International Journal of Rock Mechanics and Mining Sciences 100 (December 2017): 90–99. http://dx.doi.org/10.1016/j.ijrmms.2017.10.021.

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15

Wang, Yalei, Jinming Xu, Junshuai Xu, and Chuanjiang Zhong. "Estimation of Rock Burst Grades Using Rock Mass Strength." Advances in Civil Engineering 2020 (July 18, 2020): 1–14. http://dx.doi.org/10.1155/2020/2517459.

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The traditional rock burst estimation method is usually based on the σc (rock strength) in practice, while the actual occurrence of rock burst depends more on the structure and strength of the rock mass. In this work, the actual rock bursts occurred in a railway tunnel project in Western China, and the σcm (rock mass strength) was calculated by the generalized Hoek–Brown criterion. According to the actual situation of rock bursts, a modified rock burst estimation criterion using the ratio of σcm to σmax (maximum geostress) was proposed. The influence of randomness on the reliability of rock burst estimation criterion was considered. The estimation results based on the traditional and modified method were furthermore compared with those of the actual rock bursts. The results show that σcm calculated by the generalized Hoek–Brown criterion may be considered well in the rock type and strength, construction condition, and structure features of the rock mass; the estimation results of rock burst using the ratio of σc to σmax are quite different from the actual situation, while those using the ratio of the σcm to σmax coincided relatively with the actual rock bursts; the ratios of σcm to σmax, which are greater than 0.167, 0.066 to 0.167, 0.012 to 0.066, and less than 0.012, are corresponded to the slight, medium, strong, and violent grades of the rock bursts, respectively; the randomness of data selection has certain influence on the rock burst estimation criterion, but the variation range is small; the modified estimation criterion of rock burst proposed in this work has a good reliability. The results presented herein are important for tunnel construction and the prevention of rock burst in the high geostress areas.

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16

Kang, K., O. V. Zerkal, A. A. Ponomarev, and I. K. Fomenko. "Probabilistic Slope Stability Assessment Under Seismic Conditions Based on the Generalized Hoek-Brown Criterion." Soil Mechanics and Foundation Engineering 58, no. 3 (July 2021): 223–29. http://dx.doi.org/10.1007/s11204-021-09732-0.

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17

Sofianos, A. I. "Tunnelling Mohr–Coulomb strength parameters for rock masses satisfying the generalized Hoek–Brown criterion." International Journal of Rock Mechanics and Mining Sciences 40, no. 3 (April 2003): 435–40. http://dx.doi.org/10.1016/s1365-1609(03)00017-0.

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18

Zhu, Hehua, Qi Zhang, Boqi Huang, and Lianyang Zhang. "A constitutive model based on the modified generalized three-dimensional Hoek–Brown strength criterion." International Journal of Rock Mechanics and Mining Sciences 98 (October 2017): 78–87. http://dx.doi.org/10.1016/j.ijrmms.2017.07.012.

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19

Saada, Z., S. Maghous, and D. Garnier. "Pseudo-static analysis of tunnel face stability using the generalized Hoek-Brown strength criterion." International Journal for Numerical and Analytical Methods in Geomechanics 37, no. 18 (April 4, 2013): 3194–212. http://dx.doi.org/10.1002/nag.2185.

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20

Pan, Qiujing, Daniel Dias, and Zhibin Sun. "A New Approach for Incorporating Hoek–Brown Failure Criterion in Kinematic Approach — Case of a Rock Slope." International Journal of Structural Stability and Dynamics 17, no. 07 (September 2017): 1771008. http://dx.doi.org/10.1142/s0219455417710080.

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This paper develops a novel approach to incorporate the generalized Hoek–Brown criterion in the kinematic approach. Two analytical expressions for the equivalent friction angle and the equivalent cohesion in the context of the Hoek–Brown criterion are derived as a function of the minimum principal stress. As an illustrative example, the stability of a rock slope is investigated. The spatial discretization technique is employed to generate a slope failure mechanism considering the spatial variation of the equivalent friction angle corresponding to the minimum principal stress. In order to simplify this problem, the minimum principal stress is taken as an additional parameter in the optimization process of the kinematical approach. For the numerical modeling, three kinds of stress distributions are considered in the optimization process. The proposed approach is validated by comparison with available numerical results with good agreement. It is also shown that with the uniform distribution of minimum principal stress, the proposed approach gives the same solutions as those by the classical tangential line technique, and with more complicated distributions, the proposed approach yields a better solution than the classical tangential line technique, especially for large values of geological strength index (GSI).

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21

Meng, Qing Xiang, and Wei Wang. "A Novel Closed-Form Solution for Circular Openings in Generalized Hoek-Brown Media." Mathematical Problems in Engineering 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/870835.

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A novel closed-form solution is presented in this paper for the estimation of displacements around circular openings in a brittle rock mass subject to a hydrostatic stress field. The rock mass is assumed to be elastic-brittle-plastic media governed by the generalized Hoek-Brown yield criterion. The present closed-form solution was validated by employing the existing analytical solutions. Results of several example cases are analyzed to show that, with the simplified assumption, a novel closed-form solution is derived and found to be in an excellent agreement with those obtained by using the exact integration method with mathematical software. Parametric sensitivity analysis is carried out and the parameterartends to be the sensitive factor. As a closed-form solution that does not require transformation technique and the use of any numerical method, this work can provide a better choice in the preliminary design for circular opening.

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22

Wei, Yuan, Wang Liyan, Zhai Xing, Tan hanhua, Peng Shu, Xue Yanyu, Wang Wei, Sun Xiaoyun, and Niu Jiandong. "A rapid stability charts analysis method for rock slopes based on Generalized Hoek-Brown criterion." All Earth 33, no. 1 (January 1, 2021): 98–107. http://dx.doi.org/10.1080/27669645.2021.1959282.

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23

Dong-ping, Deng, Li Liang, Wang Jian-feng, and Zhao Lian-heng. "Limit equilibrium method for rock slope stability analysis by using the Generalized Hoek–Brown criterion." International Journal of Rock Mechanics and Mining Sciences 89 (November 2016): 176–84. http://dx.doi.org/10.1016/j.ijrmms.2016.09.007.

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24

Saada, Z., S. Maghous, and D. Garnier. "Seismic bearing capacity of shallow foundations near rock slopes using the generalized Hoek-Brown criterion." International Journal for Numerical and Analytical Methods in Geomechanics 35, no. 6 (April 6, 2011): 724–48. http://dx.doi.org/10.1002/nag.929.

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25

Zhang, Shiyue, Ruiyuan Gao, Qingxiang Meng, and Xiaohu Zhang. "Research on Rock Resistant Coefficient in Lining Tunnels Based on the Generalized Hoek-Brown Failure Criterion." Geofluids 2021 (January 29, 2021): 1–6. http://dx.doi.org/10.1155/2021/5554644.

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Rock resistant coefficient is a key parameter in rock engineering and can reflect the resistance of surrounding rocks. According to the load-structure method, there are many different formulas in the determination of rock resistant coefficient using elasticity or plasticity theory. Based on the generalized Hoek-Brown failure criterion, this paper develops a closed-form formula for calculating the rock resistant coefficient. The sensibility of different parameters on the rock resistant coefficient is also analyzed. The fact shows that the formula is sensitive to a , σ c , and K d comparing with m b and s especially when they are in a low value, laying a foundation for the determination of rock resistant coefficient in similar lining tunnels.

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26

Belghali, Mounir, and Zied Saada. "Seismic stability analysis of rock slopes by yield design theory using the generalized Hoek-Brown criterion." MATEC Web of Conferences 149 (2018): 02026. http://dx.doi.org/10.1051/matecconf/201814902026.

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The stability of rock slope is studied using the kinematic approach of yield design theory, under the condition of plane strain and by considering the last version of the Hoek-Brown failure criterion. This criterion, which is suitable to intact rock or rock mass highly fractured regarded as isotropic and homogeneous, is widely accepted by the rock mechanics community and has been applied in numerous projects around the world. The failure mechanism used to implement the kinematic approach is a log-spiral rotational mechanism. The stability analysis is carried out under the effects of gravity forces and a surcharge applied along the upper plateau of the slope. To take account of the effects of forces developed in the rock mass during the passage of a seismic wave, the conventional pseudo-static method is adopted. This method is often used in slope stability study for its simplicity and efficiency to simulate the seismic forces. The results found are compared with published numerical solutions obtained from other approaches. The comparison showed that the results are almost equal. The maximum error found is less than 1%, indicating that this approach is effective for analyzing the stability of rock slopes. The relevance of the approach demonstrated, investigations are undertaken to study the influence of some parameters on the stability of the slope. These parameters relate to the mechanical strength of the rock, slope geometry and loading.

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27

Belghali, Mounir, and Zied Saada. "Seismic stability analysis of rock slopes by yield design theory using the generalized Hoek-Brown criterion." MATEC Web of Conferences 149 (2018): 02026. http://dx.doi.org/10.1051/matecconf/201714902026.

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28

Carranza-Torres, C. "Elasto-plastic solution of tunnel problems using the generalized form of the hoek-brown failure criterion." International Journal of Rock Mechanics and Mining Sciences 41 (May 2004): 629–39. http://dx.doi.org/10.1016/j.ijrmms.2004.03.111.

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29

Carranza-Torres, C. "Elasto-plastic solution of tunnel problems using the generalized form of the hoek–brown failure criterion." International Journal of Rock Mechanics and Mining Sciences 41, no. 3 (April 2004): 480–81. http://dx.doi.org/10.1016/j.ijrmms.2003.12.014.

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30

Shen, Jiayi, S. D. Priest, and M. Karakus. "Determination of Mohr–Coulomb Shear Strength Parameters from Generalized Hoek–Brown Criterion for Slope Stability Analysis." Rock Mechanics and Rock Engineering 45, no. 1 (September 14, 2011): 123–29. http://dx.doi.org/10.1007/s00603-011-0184-z.

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31

Wang, Rui, Jian-biao Bai, Shuai Yan, Zhi-guo Chang, Yuan-ba Song, Wei-guang Zhang, and Jun Xu. "The Elastoplastic Solutions of Deep Buried Roadway Based on the Generalized 3D Hoek-Brown Strength Criterion considering Strain-Softening Properties." Geofluids 2021 (April 6, 2021): 1–15. http://dx.doi.org/10.1155/2021/5575376.

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The deep underground roadways are widely used in the mining industries at present, but the relevant theoretical bases are not fully understood. In this paper, the numerical solutions for strain-softening surrounding rock under the generalized three-dimensional (3D) Hoek-Brown (GZZ) strength criterion are developed incorporating the confinement-dependent characteristics of ψ and η ∗ and their influences on the stress and displacement of equivalent circular roadway. On the basic of a finite difference, method for the strain-softening model is proposed to consider the variation of ψ and η ∗ in analyzing the strain-softening behavior of rock masses. Combining the equilibrium equation and strength criterion, the stress conditions for each annulus are calculated analytically. The displacement for each step is obtained analytically by solving the differential equation through invoking flow rule and Hooke’s law. The accuracy of the proposed method is verified through the comparison between the results and the previous studies. The effect of intermediate principal stress of GZZ strength criterion is considered; the rationality of the proposed method is verified by two aspects. First, by comparing with the two-dimensional narrow and generalized H-B strength criterion, the advantage of GZZ strength criterion that considers the effect intermediate main stress is highlighted. On the other hand, compared with the three-dimensional linear D-P criterion, the advantage of GZZ strength criterion in the theoretical research of deep underground roadway in coal mine is highlighted. The results show that the strain-softening of the surrounding rock in the plastic zone of the roadway can reduce the pressure of the surrounding rock, but it will greatly increase its deformation. In the high field stress areas, the strain-softening of surrounding rock is the key reason for the destruction of the roadway. It is suggested that in the design and calculation of the support system of the roadway, the strain-softening characteristics of the surrounding rock should be considered, which is very important to avoid large deformation and damage of roadway.

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32

Ou, Zhe, Cong Xin Chen, Hua Fu, and Yi Chao Zhou. "Study on the Value Range of Horizontal Ground Stress in Initial Geostress Field Based on the Generalized Hoek - Brown Criterion." Applied Mechanics and Materials 580-583 (July 2014): 334–37. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.334.

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On the conditions that assuming vertical ground stress and horizontal ground stress are both principal stress, a calculation model of horizontal ground stress value range with depth change in initial geostress field is built by formula derivation, according to the Generalized Hoek-Brown failure criterion, and the reasonability of the calculation model is verified by the geostress measured value. The results show that, there is a good consistency at the distribution range of horizontal ground stress calculated value and horizontal ground stress measured value, it is proved that the the calculation model is reasonable. The calculation model gives new methods and thinking for evaluation of the initial geostress field.

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33

Han, Jian Xin, Xing Hua Tong, Lei Wang, and Guo Fu Sun. "Study on Post-Failure Deformation and Residual Strength of Rock Mass Based on Hoek-Brown Criterion." Applied Mechanics and Materials 170-173 (May 2012): 121–24. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.121.

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In order to predict the stability of surrounding rock mass in geotechnical engineering, it is important to study the post-failure deformation property and residual strength of rock mass. Based on evolutional behavior of strength parameters, aiming at generalized Hoek-Brown strength criterion, selecting major principal strain as strain softening parameter, this paper presents the method of solving post-failure stress-strain curve . In numerical case, the effect of evolutional law of strength parameters ， and to deformation and residual strength is discussed and we can draw the following conclusions: the greater the residual values of ， are and the smaller the residual value of is, the post-failure strain softening curve falls more gently and the greater the residual strength is.

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34

Zou, Jin-feng, and Jia-min Du. "A Numerical Approach for the Quasi-Plane Strain-Softening Problem of Cylindrical Cavity Expansion Based on the Hoek-Brown Failure Criterion." Mathematical Problems in Engineering 2016 (2016): 1–10. http://dx.doi.org/10.1155/2016/3698525.

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This paper focuses on a novel approach for the quasi-plane strain-softening problem of the cylindrical cavity expansion based on generalized Hoek-Brown failure criterion. Because the intermediate principal stress is deformation-dependent, the quasi-plane strain problem is defined to implement the numerical solution of the intermediate principal stress. This approach assumes that the initial total strain in axial direction is a nonzero constant (ε0) and the plastic strain in axial direction is not zero. Based on 3D failure criterion, the numerical solution of plastic strain is given. Solution of the intermediate principal stress can be derived by Hooke’s law. The radial and circumferential stress and strain considering the intermediate principal stress are obtained by the proposed approach of the intermediate principal stress, stress equilibrium equation, and generalized H-B failure criterion. The numerical results can be used for the solution of strain-softening surrounding rock. In additional, the validity and accuracy of the proposed approach are verified with the published results. At last, parametric studies are carried out using MATLAB programming to highlight the influences of the out-of-plane stress on the stress and displacement of surrounding rock.

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35

Yang, X. L., and Z. X. Long. "Seismic and static 3D stability of two-stage rock slope based on Hoek–Brown failure criterion." Canadian Geotechnical Journal 53, no. 3 (March 2016): 551–58. http://dx.doi.org/10.1139/cgj-2015-0147.

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Two-stage slope is beneficial to improve slope stability in comparison with single-stage slope. Based on nonlinear Hoek–Brown criterion, a three-dimensional failure mechanism is employed to estimate the stability of two-stage rock slope, with the effect of seismic inertia force being taken into account. A generalized tangential technique is used to formulate the stability factor problem as a classical optimization problem corresponding to the dissipated energy. The upper-bound solutions are obtained by minimizing the objective function with respect to the location of sliding body center and the location of tangency point. The seismic inertia force is considered and incorporated into the objective function. In comparison with previously published solutions using the linear Mohr–Coulomb criterion, the validity of the present solutions is shown. The analytical expressions for two-stage slope are derived to estimate the seismic stability of slopes. Numerical results for different types of rocks are presented for practical use in engineering, and the effects of different parameters on slope stability are discussed.

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36

Zhang, Xutao, Mingyang Ren, Zhaobo Meng, Baoliang Zhang, and Jinglong Li. "Experimental Study on the Mechanical Behavior of Yunnan Limestone in Natural and Saturated States." Advances in Civil Engineering 2021 (February 28, 2021): 1–16. http://dx.doi.org/10.1155/2021/6614412.

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Rock material is a kind of mineral assemblage with complex structural heterogeneity, whose mechanical behavior is strongly affected by water or moisture content. In this work, we carried out a series of laboratory tests to investigate the mechanical response (e.g., deformation, strength, and failure characteristics) of Yunnan limestone in natural and saturated states. Our test results show that (1) after saturation, the stiffness and strength of Yunnan limestone degenerate considerably. Compared with the natural condition, the elastic modulus, deformation modulus, and tensile modulus decrease by about 30% on average, and uniaxial compressive strength and tensile strength also decrease by about 15% and 20%, respectively. While Poisson’s ratio is less affected by water content, it can be regarded as a constant; (2) the elastic modulus and deformation modulus of Yunnan limestone are significantly affected by confining pressure, and the relationship between them and confining pressure satisfies the law of hyperbolic function; (3) the peak strength envelope of Yunnan limestone has significant nonlinear characteristics, which can be well described by generalized Hoek-Brown strength criterion. However, the generalized Hoek-Brown criterion does not apply to the residual strength, which shows a linearly increasing trend with the increasing confining pressure; (4) the failure modes of Yunnan limestone are significantly dependent on confining pressure but insensitive to water content. With the increasing confining pressure, the failure modes of Yunnan limestone transform from splitting failure, tension-shear mixed failure, single inclined plane shear failure to Y-shaped or X-shaped conjugated shear failure. The test results can provide important experimental data for the establishment of the constitutive model of Yunnan limestone, which will contribute to obtain more reliable results for stability assessment of Xianglu Mountain Tunnel.

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Du, Dianchun, and Zhentao Liu. "Seismic Bearing Capacity of Strip Foundation on Rock Mass Obeying Modified Hoek-Brown Failure Criterion." Buildings 12, no. 12 (November 28, 2022): 2083. http://dx.doi.org/10.3390/buildings12122083.

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The kinematic method of limit analysis theory was adopted in this paper to calculate the seismic bearing capacity of the shallow strip foundation on a rock mass obeying the non-linear modified Hoek-Brown failure criterion. The generalized Prandtl failure mechanism was chosen, which is different from the multi-wedge failure mechanism assumption commonly used in previous research. Three angle parameters were used to control the mechanism shapes, and the equivalent friction angle and equivalent cohesive were adopted to faithfully reflect the shape characteristics of the failure mechanism. The seismic action was considered using the pseudo-static method, which is simplified to the inertial force determined by the horizontal seismic coefficient. The validation of the present method was carried out by comparing with previous analytical results and the finite element model. Subsequently, the influences of the surface overload, the properties of the rock mass, and the seismic action on the shape and ultimate bearing capacity of the failure mechanism were investigated. For the convenience of practical engineering, this paper gives the ultimate bearing capacity of strip foundations on five representative rock foundations, and the variation trend of bearing capacity with the unit weight of rock mass, surface overload, and horizontal seismic coefficient.

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Antoniou, A., and I. Spyropoulos. "The influence of rockmass properties at the plastic zone around a circular tunnel." Bulletin of the Geological Society of Greece 47, no. 4 (September 5, 2013): 1674. http://dx.doi.org/10.12681/bgsg.11032.

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The influence of rockmass properties at the plastic zone around a circular tunnel. Tunneling in weak rock has to be carefully designed since the overestimation of weak rock mass properties or the underestimated design and behaviour of the support system can lead to increased cost or even to failure. Based on the generalized Hoek-Brown failure criterion this paper presents relation between geometrical parameters (tunnel's radius, depth, etc) and rock's mass parameters (GSI, mi, etc) with the extension of plastic zone around a circular tunnel, as well as the wall displacement of an unsupported circular tunnel. All the analyses were executed considering hydrostatic stress field and isotropic behaviour of the surrounding rock mass

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Kang, K., I. K. Fomenko, J. Wang, and O. V. Nikolskaya. "PROBABILISTIC ASSESSMENT OF ROCK SLOPE STABILITY IN OPEN PIT MINE CHAARAT USING THE GENERALIZED HOEK–BROWN CRITERION." Journal of Mining Science 56, no. 5 (September 2020): 732–40. http://dx.doi.org/10.1134/s1062739120057068.

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Belghali, Mounir, Zied Saada, Denis Garnier, and Samir Maghous. "Pseudo-static stability analysis of rock slopes reinforced by passive bolts using the generalized Hoek–Brown criterion." Journal of Rock Mechanics and Geotechnical Engineering 9, no. 4 (August 2017): 659–70. http://dx.doi.org/10.1016/j.jrmge.2016.12.007.

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Wei, Yuan, Li Jiaxin, Li Zonghong, Wang Wei, and Sun Xiaoyun. "A strength reduction method based on the Generalized Hoek-Brown (GHB) criterion for rock slope stability analysis." Computers and Geotechnics 117 (January 2020): 103240. http://dx.doi.org/10.1016/j.compgeo.2019.103240.

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Shen, Jiayi, Murat Karakus, and Chaoshui Xu. "Direct expressions for linearization of shear strength envelopes given by the Generalized Hoek–Brown criterion using genetic programming." Computers and Geotechnics 44 (June 2012): 139–46. http://dx.doi.org/10.1016/j.compgeo.2012.04.008.

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43

Lee, Youn-Kyou, and S. Pietruszczak. "A New Discrete Form of Hoek–Brown Criterion and Its Application to Limit Equilibrium Analysis of Rock Slope Stability." Sustainability 14, no. 19 (September 25, 2022): 12113. http://dx.doi.org/10.3390/su141912113.

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The generalized Hoek–Brown criterion (GHB) is recognized as one of the standard failure criteria in rock engineering and its validity extends to a wide range of rock mass quality. A drawback of this criterion is the difficulty of transforming it into an explicit form defining the Mohr failure envelope when its strength parameter a is not equal to 0.5. The information on the functional form of the Mohr envelope for the full range of rock mass conditions enables the implementation of classical engineering approaches, such as the limit equilibrium method and limit analysis, in the framework of the GHB criterion. Knowing that for a≠0.5 the exact closed-form representation of the Mohr envelope is not feasible, an alternative is to express it in an approximate analytical form. The main purpose of this study is to propose a new improved method to define an approximate Mohr envelope of the GHB criterion that is much more accurate compared with the recently published approximations. The idea behind the formulation is to expand the Balmer’s equation, which defines the relationship between the normal stress and minor principal stress at failure, by invoking the finite Taylor series centered at the known solution for a=0.5. The formulation is then completed by substituting this solution into another Balmer’s equation, defining the relationship between the shear strength and the minor principal stress. The Taylor polynomial approximations of up to third degree are considered in the formulation. The accuracy of the shear strength prediction is shown to be much better than that of the approximate formula of Lee and Pietruszczak proposed in 2021. An illustrative example of limit equilibrium analysis of rock slope stability, incorporating the new approximate expression for the Mohr envelope, is provided. The analysis incorporates a modified version of the Bishop approach, which is simpler and more rigorous than the original nonlinear expression. The study confirms that the new approximate representation of the Mohr failure envelope can facilitate the application of the GHB criterion to a range of practical rock engineering calculations.

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Rojat, Fabrice, Vincent Labiouse, and Philippe Mestat. "Improved analytical solutions for the response of underground excavations in rock masses satisfying the generalized Hoek–Brown failure criterion." International Journal of Rock Mechanics and Mining Sciences 79 (October 2015): 193–204. http://dx.doi.org/10.1016/j.ijrmms.2015.08.002.

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Saeidi, Ali, Côme Cloutier, Abbas Kamalibandpey, and Alireza Shahbazi. "Evaluation of the Effect of Geomechanical Parameters and In Situ Stress on Tunnel Response Using Equivalent Mohr-Coulomb and Generalized Hoek-Brown Criteria." Geosciences 12, no. 7 (June 28, 2022): 262. http://dx.doi.org/10.3390/geosciences12070262.

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The generalized Hoek-Brown (GHB) failure criterion can estimate the rock mass parameters required for rock mechanics–related analyses such as numerical modeling in geomechanics. The determination of GHB parameters has been developed in the field of rock mechanics. Due to the wide use of the Mohr-Coulomb criterion and the lack of an existing relationship for determining its parameters for a rock mass, equivalent Mohr-Coulomb parameters (EMC) can be derived from the GHB. To determine the differences in the use of these two criteria, we analyzed the behavior of a deep circular tunnel in nine stress states for three metamorphic rocks recovered from the Canadian Shield from rock masses that present a very blocky structure. We carried out 241 simulations using the finite element code RS2 to assess the effect of the geological strength index (GSI), in situ stress, and rock type on the deviation of wall displacement, the number of yielded elements, and the differential stress obtained by the GHB and EMC parameters. A combination of low in situ stress and high GSI yielded similar results when using both failure criteria.

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Kumar, Jyant, and Obaidur Rahaman. "Lower Bound Limit Analysis Using Power Cone Programming for Solving Stability Problems in Rock Mechanics for Generalized Hoek–Brown Criterion." Rock Mechanics and Rock Engineering 53, no. 7 (April 11, 2020): 3237–52. http://dx.doi.org/10.1007/s00603-020-02099-y.

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Fischer, C. P., and M. S. Diederichs. "Explicit numerical models for the prediction of plastic and weakening rockmass behaviour around a circular tunnel in isotropic and anisotropic stress conditions." IOP Conference Series: Earth and Environmental Science 1124, no. 1 (January 1, 2023): 012061. http://dx.doi.org/10.1088/1755-1315/1124/1/012061.

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Abstract The Geological Strength Index, GSI, is an assessment system for rockmass structure conditions (blockiness and discontinuity condition) based on the visual examination of exposed rockmass surfaces. The Generalized Hoek-Brown failure criterion is widely used with GSI to estimate the strength and stiffness of jointed rockmasses in traditional continuum numerical modelling. Modern numerical analysis tools allow networks of discrete structure to be represented with assigned properties based on site investigation data. In this paper, models with defined explicit structure are shown to yield similar results to implicit GSI-based models and provide more detailed information on the spatial variability of tunnel response when reasonable rockmass input parameters are estimated and calibrated. Once plastic explicit models are calibrated to give similar response to plastic implicit GSI-based models, explicit models using weakening joint and intact rock elements are used to determine appropriate post-yield strength and dilation parameters for use in implicit GSI-based modelling.

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Ma, Lin-jian, Xin-yu Liu, Qin Fang, Hong-fa Xu, Hui-min Xia, Er-bing Li, Shi-gang Yang, and Wen-pei Li. "A New Elasto-Viscoplastic Damage Model Combined with the Generalized Hoek–Brown Failure Criterion for Bedded Rock Salt and its Application." Rock Mechanics and Rock Engineering 46, no. 1 (May 10, 2012): 53–66. http://dx.doi.org/10.1007/s00603-012-0256-8.

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Zhao, Xingdong, Yangyang Li, Jingyu Shi, and Qingdong Qu. "A numerical algorithm for ground reaction curves of circular openings in strain-softening rock masses satisfying the generalized Hoek-Brown criterion." Tunnelling and Underground Space Technology 134 (April 2023): 104925. http://dx.doi.org/10.1016/j.tust.2022.104925.

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Wang, Mingnian, Xiao Zhang, Jianjun Tong, Wenhao Yi, Zhilong Wang, and Dagang Liu. "A New Semi-Analytical Method for Elasto-Plastic Analysis of a Deep Circular Tunnel Reinforced by Fully Grouted Passive Bolts." Applied Sciences 10, no. 12 (June 26, 2020): 4402. http://dx.doi.org/10.3390/app10124402.

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The use of fully grouted passive bolts as a reinforcement technique has been widely applied to improve the stability of tunnels. To analyze the behaviors of passive bolts and rock mass in a deep circular tunnel, a new semi-analytical solution is presented in this work based on the finite difference method. The rock mass was assumed to experience elastic–brittle–plastic behavior, and the linear Mohr–Coulomb criterion and the nonlinear generalized Hoek–Brown criterion were employed to govern the yielding of the rock mass. The interaction and decoupling between the rock mass and bolts were considered by using the spring–slider model. To simplify the analysis process, a bolted tunnel was divided into a bolted region and an unbolted region, while the contact stress at the bolted–unbolted interface and the rigid displacement of the bolts were obtained using two boundary conditions in combination with the bisection method. Comparisons show that the results obtained using the proposed solution agree well with those from the commercial numerical software and the in situ test. Finally, parametric analyses were performed to examine the effects of various reinforcement parameters on the tunnel’s stability. The proposed solution provided a fast but accurate estimation of the behavior of a reinforced deep circular tunnel for preliminary design purposes.

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