Technical Notes
Mar 7, 2024

Reliability Back Analysis of the Parameters of Rock Landslides with the Nonlinear Hoek-Brown Failure Criterion

Publication: International Journal of Geomechanics
Volume 24, Issue 5

Abstract

Landslides are frequent and devastating geological hazards that cause significant economic and human losses annually. The selection of appropriate shear strength parameters is crucial for evaluating and preventing landslide failure. Considering the nonlinear characteristics of rock-mass material, a rock slope stability analysis model was built using the nonlinear Hoek‒Brown failure criterion. A Geological Strength Index–material constant (GSI–mi) curve, based on a deterministic method, was proposed to back analyzed the Geological Strength Index (GSI), which is consistent with a trial-and-error method, but simpler to implement. The back analysis can be extended to other parameters in addition to the GSI. Furthermore, considering the randomness and uncertainty, a reliability-based back analysis method for nonlinear strength parameters of the sliding surface was proposed. The optimal parameter combination that corresponded to the minimum reliability index was determined, which could serve as reasonable values of the nonlinear strength parameters for landslides. A comparison of different failure criteria also suggested that the stress level at the sliding surface should be accounted for in landslides using the significant nonlinear characteristics of strength parameters.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

This study was financially supported by the Natural Science Foundation of Hunan Province (2023JJ40078), the Scientific Research Project of Hunan Provincial Education Department (No. 22C0573), the National Natural Science Foundation of China (No. 51978666), and the Guizhou Provincial Department of Transportation Foundation (No. 2018-123-040). All financial support is greatly appreciated.

References

Akin, M. 2013. “Slope stability problems and back analysis in heavily jointed rock mass: A case study from Manisa, Turkey.” Rock Mech. Rock Eng. 46 (2): 359–371. https://doi.org/10.1007/s00603-012-0262-x.
Akin, M. 2017. “Reliability of shear strength parameters for a safe slope design in highly jointed rock mass.” In Advancing culture of living with landslides, edited by M. Mikoš, Ž. Arbanas, Y. Yin, and K. Sassa, 445–453. Cham: Springer International Publishing.
Baker, R. 2004. “Nonlinear Mohr envelopes based on triaxial data.” J. Geotech. Geoenviron. Eng. 130 (5): 498–506. https://doi.org/10.1061/(ASCE)1090-0241(2004)130:5(498).
Baker, R. 2006. “A relation between safety factors with respect to strength and height of slopes.” Comput. Geotech. 33 (4–5): 275–277. https://doi.org/10.1016/j.compgeo.2006.07.001.
Balmer, G. 1952. “A general analytical solution for Mohr’s envelope.” Proc. Am. Soc. Test Mater. 52: 1260–1271.
Cai, M., P. K. Kaiser, Y. Tasaka, and M. Minami. 2007a. “Determination of residual strength parameters of jointed rock masses using the GSI system.” Int. J. Rock Mech. Min. Sci. 44 (2): 247–265. https://doi.org/10.1016/j.ijrmms.2006.07.005.
Cai, M., H. Morioka, P. K. Kaiser, Y. Tasaka, H. Kurose, M. Minami, and T. Maejima. 2007b. “Back-analysis of rock mass strength parameters using AE monitoring data.” Int. J. Rock Mech. Min. Sci. 44 (4): 538–549. https://doi.org/10.1016/j.ijrmms.2006.09.012.
Cen, D. F., D. Huang, and F. Ren. 2016. “Shear deformation and strength of the interphase between the soil–rock mixture and the benched bedrock slope surface.” Acta Geotech. 12 (2): 391–413. https://doi.org/10.1007/s11440-016-0468-2.
Chen, W. F. 1990. Limit analysis in soil mechanics. Amsterdam, Netherlands: Elsevier.
Chen, Z. Y. 2003. Soil slope stability analysis: Theory, methods and programs. Beijing: China Water and Power Press.
Chen, Z. Y., X. G. Wang, J. Yang, Z. X. Jia, and Y. J. Wang. 2005. Rock slope stability analysis: Theory, methods and programs. Beijing: China Water and Power Press.
Chen, Z. Y., C. M. Zhan, H. L. Yao, L. H. Chen, and L. I. Xu. 2016. “Safety criteria and standards for stability analysis of gravity retaining walls.” Rock Soil Mech. 37 (8): 2129–2137.
Cui, Y., Y. Jiang, and C. Guo. 2019. “Investigation of the initiation of shallow failure in widely graded loose soil slopes considering interstitial flow and surface runoff.” Landslides 16 (4): 815–828. https://doi.org/10.1007/s10346-018-01129-9.
Deng, D. P., L. H. Zhao, and L. Li. 2015. “Limit equilibrium slope stability analysis using the nonlinear strength failure criterion.” Can. Geotech. J. 52 (5): 563–576. https://doi.org/10.1139/cgj-2013-0324.
Eid, H. T. 2014. “Stability charts for uniform slopes in soils with nonlinear failure envelopes.” Eng. Geol. 168: 38–45. https://doi.org/10.1016/j.enggeo.2013.10.021.
Gao, W. 2016. “Inversion of critical slip surface parameters for a landslide disaster using the bionics algorithm.” Int. J. Geomech. 16 (5): 06016001. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000556.
Gao, Y., D. Wu, and F. Zhang. 2015. “Effects of nonlinear failure criterion on the three-dimensional stability analysis of uniform slopes.” Eng. Geol. 198: 87–93. https://doi.org/10.1016/j.enggeo.2015.09.010.
Helgstedt, M. D. 1997. An assessment of the in-situ shear strength of rock masses and discontinuities. Luleå, Sweden: Lulea University of Technology.
Hoek, E. 1990. “Estimating Mohr–Coulomb friction and cohesion values from the Hoek–Brown failure criterion.” Int. J. Rock Mech. Min. Sci. Geomech. 27 (3): 227–229.
Hoek, E. 1998. “Reliability of Hoek–Brown estimates of rock mass properties and their impact on design.” Int. J. Rock Mech. Min. Sci. 35 (1): 63–68. https://doi.org/10.1016/S0148-9062(97)00314-8.
Hoek E., C. Carranza-Torres, and B. Corkum. 2002. “Hoek–Brown failure criterion––2002 edition.” Proc. NARMS-Tac. 1: 267–273.
Hoek, E. 2002. Practical engineering technology in rock mass. Kaifeng, China: The Yellow River Water Conservancy Press.
Hoek, E., and E. T. Brown. 1988. “The Hoek–Brown failure criterion –– A 1998 update.” J. Heuristics 16 (2): 167–188.
Hoek, E., and E. T. Brown. 1997. “Practical estimates of rock mass strength.” Int. J. Rock Mech. Min. Sci. 34 (8): 1165–1186. https://doi.org/10.1016/S1365-1609(97)80069-X.
Hoek, E., and E. T. Brown. 2019. “The Hoek–Brown failure criterion and GSI – 2018 edition.” J. Rock Mech. Geotech. Eng. 11 (3): 445–463. https://doi.org/10.1016/j.jrmge.2018.08.001.
Hoek, E., P. K. Kaiser, and W. F. Bawden. 1995. Support of underground excavations in hard rock. Abingdon, UK: Taylor and Francis.
Hoek, E., D. Wood, and S. Shah. 1992. “A modified Hoek–Brown failure criterion for jointed rock masses.” In Proc., Rock Characterization: ISRM Symp., Eurock’9. 209–214. London: British Geotechnical Society.
Jiang, J. C., and T. Yamagami. 2008. “A new back analysis of strength parameters from single slips.” Comput. Geotech. 35 (2): 286–291. https://doi.org/10.1016/j.compgeo.2007.09.004.
Jin, C., Y. Lu, T. Han, T. Chen, J. Cui, and D. Cheng. 2021. “Study on refined back-analysis method for stress field based on in situ and disturbed stresses.” Int. J. Geomech. 21 (8): 04021141. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002024.
Johari, A., A. Fazeli, and A. A. Javadi. 2013. “An investigation into application of jointly distributed random variables method in reliability assessment of rock slope stability.” Comput. Geotech. 47: 42–47. https://doi.org/10.1016/j.compgeo.2012.07.003.
Johari, A., and A. M. Lari. 2016. “System reliability analysis of rock wedge stability considering correlated failure modes using sequential compounding method.” Int. J. Rock Mech. Min. Sci. 82: 61–70. https://doi.org/10.1016/j.ijrmms.2015.12.002.
Johari, A., and Y. Peiro. 2022. “Determination of stochastic shear strength parameters of a real landslide by back analysis.” Int. J. Reliab. Risk Saf. Theory Appl. 4 (1): 7–16. https://doi.org/10.30699/IJRRS.4.1.2.
Kang, K. S., N. L. Hu, C. S. Sin, S. H. Rim, E. C. Han, and C. N. Kim. 2017. “Determination of mechanical parameters of rock mass based on GSI system and displacement back analysis.” J. Geophys. Eng. 14 (4): 939–948. https://doi.org/10.1088/1742-2140/aa6e78.
Kumar, V., A. Burman, N. Himanshu, and B. Gordan. 2021. “Rock slope stability charts based on limit equilibrium method incorporating generalized Hoek–Brown strength criterion for static and seismic conditions.” Environ. Earth Sci. 80 (6): 212.
Kumar, V., N. Himanshu, and A. Burman. 2019. “Rock slope analysis with nonlinear Hoek–Brown criterion incorporating equivalent Mohr–Coulomb parameters.” Geotech. Geol. Eng. 37 (6): 4741–4757. https://doi.org/10.1007/s10706-019-00935-9.
Kusumawardani, R., T. C. Upomo, and M. Faizal. 2016. “Back-analysis of Hoek–Brown criterion: Rock slide case in Manado.” Int. J. GEOMATE 11 (5): 2808–2814.
Lei, W., H. H. Jin, L. Zhe, C. H. Juang, and J. H. Xiao. 2013. “Probabilistic back analysis of slope failure – A case study in Taiwan.” Comput. Geotech. 51 (June): 12–23.
Li, A. J., M. J. Cassidy, Y. Wang, R. S. Merifield, and A. V. Lyamin. 2012. “Parametric Monte Carlo studies of rock slopes based on the Hoek–Brown failure criterion.” Comput. Geotech. 45: 11–18. https://doi.org/10.1016/j.compgeo.2012.05.010.
Li, Z., and S. D. Zhao. 2006. “Inverse analysis design in geotechnical engineering based on the reliability theory.” J. Xi’an Univ. Arch. & Tech. (Natural Science) 38 (2): 159–162.
Lianheng, Z., Z. Shuaihao, H. Dongliang, Z. Shi, and L. Dejian. 2018. “Quantitative characterization of joint roughness based on semivariogram parameters.” Int. J. Rock Mech. Min. Sci. 109: 1–8. https://doi.org/10.1016/j.ijrmms.2018.06.008.
Lim, K., A. J. Li, A. Schmid, and A. V. Lyamin. 2017. “Slope-stability assessments using finite-element limit-analysis methods.” Int. J. Geomech. 17 (2): 06016017. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000715.
Lin, H., and J. Y. Chen. 2017. “Back analysis method of homogeneous slope at critical state.” KSCE J. Civ. Eng. 21 (3): 670–675.
Low, B. K. 2007. “Reliability analysis of rock slopes involving correlated nonnormals.” Int. J. Rock Mech. Min. Sci. 44 (6): 922–935. https://doi.org/10.1016/j.ijrmms.2007.02.008.
Low, B. K. 2014. “FORM, SORM, and spatial modeling in geotechnical engineering.” Struct. Saf. 49: 56–64. https://doi.org/10.1016/j.strusafe.2013.08.008.
Lü, Q., and B. K. Low. 2011. “Probabilistic analysis of underground rock excavations using response surface method and SORM.” Comput. Geotech. 38 (8): 1008–1021. https://doi.org/10.1016/j.compgeo.2011.07.003.
Lv, Q. C., Y. R. Liu, and Y. Qiang. 2017. “Stability analysis of earthquake-induced rock slope based on back analysis of shear strength parameters of rock mass.” Eng. Geol. 228: 39–49. https://doi.org/10.1016/j.enggeo.2017.07.007.
Maksimovic, M. 1989. “Nonlinear failure envelope for soils.” J. Geotech. Eng. 115 (4): 581–586. https://doi.org/10.1061/(ASCE)0733-9410(1989)115:4(581).
Marinos, P., and E. Hoek. 2000. “GSI-A geologically friendly tool for rock mass strength estimation.” In Proc., GeoEng 2000 at the Int. Conf. on Geotechnical and Geological Engineering, 1422–1446. Lancaster, PA: Technomic.
Michalowski, R. L., and D. Park. 2020. “Stability assessment of slopes in rock governed by the Hoek–Brown strength criterion.” Int. J. Rock Mech. Min. Sci. 127: 104217. https://doi.org/10.1016/j.ijrmms.2020.104217.
Mostyn, G., and K. Douglas. 2000. “Strength of intact rock and rock masses.” In Proc., ISRM Int. Symp., 1–33. Washington, DC: The American Rock Mechanics Association (ARMA).
Ng, S. M., M. A. M. Ismail, and I. Abustan. 2014. “Back analysis of slope failure using finite element with point estimate method (FEM-PEM).” J. Civ. Eng. Res. 4 (3A): 31–35.
Park, H. J., J. Y. Jang, and J. H. Lee. 2019. “Assessment of rainfall-induced landslide susceptibility at the regional scale using a physically based model and fuzzy-based Monte Carlo simulation.” Landslides 16 (4): 695–713. https://doi.org/10.1007/s10346-018-01125-z.
Rackwitz, R., and B. Fiessler. 1978. “Structural reliability under combined random load sequences.” Comput. Struct. 9 (5): 484–494. https://doi.org/10.1016/0045-7949(78)90046-9.
Renani, R. H., and C. D. Martin. 2020. “Slope stability analysis using equivalent Mohr–Coulomb and Hoek–Brown criteria.” Rock Mech. Rock Eng. 53 (1):13–21.
Saeidi, A., V. Maazallahi, and A. Rouleau. 2016. “Assessment of slide surface and pre-slide topography using site investigation data in back analysis.” Int. J. Rock Mech. Min. Sci. 88: 29–33. https://doi.org/10.1016/j.ijrmms.2016.07.008.
Sharifzadeh, M., M. Sharifi, and S. M. Delbari. 2010. “Back analysis of an excavated slope failure in highly fractured rock mass: The case study of Kargar slope failure (Iran).” Environ. Earth Sci. 60 (1): 183–192. https://doi.org/10.1007/s12665-009-0178-2.
Song, L., B. Xu, X. Kong, D. Zou, X. Yu, and R. Pang. 2021. “Reliability analysis of 3D rockfill dam slope stability based on the copula function.” Int. J. Geomech. 21 (3): 04021001. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001932.
Sonmez, H., R. Ulusay, and C. Gokceoglu. 1998. “A practical procedure for the back analysis of slope failures in closely jointed rock masses.” Int. J. Rock Mech. Min. Sci. 35 (2): 219–233. https://doi.org/10.1016/S0148-9062(97)00335-5.
Sun, L. C., H. X. Wang, N. Q. Zhou, and B. Y. Ning. 2012. “Application of reliability theory to back analysis of rocky slope wedge failure.” Chin. J. Rock Mech. Eng. 31 (S1): 2660–2667.
Sun, Z. B., B. W. Wang, C. Q. Hou, S. C. Wu, and X. L. Yang. 2022. “Pseudodynamic approach for rock slopes in Hoek–Brown media: Three-dimensional perspective.” Int. J. Geomech. 22 (11): 04022190. https://doi.org/10.1061/(ASCE)GM.1943-5622.0002553.
Tang, W. H., T. D. Stark, and M. Angulo. 1999. “Reliability in back analysis of slope failures.” J. Jpn. Geotech. Soc. Soils Found. 39 (5): 73–80. https://doi.org/10.3208/sandf.39.5_73.
Tarantola, A. 2009. Inverse problem theory and methods for model parameter estimation. Philadelphia, PA: Society for Industrial and Applied Mathematics.
Wei, Y. F., W. X. Fu, and F. Ye. 2021. “Estimation of the equivalent Mohr–Coulomb parameters using the Hoek–Brown criterion and its application in slope analysis.” Eur. J. Environ. Civ. Eng. 25 (4): 599–617. https://doi.org/10.1080/19648189.2018.1538904.
Wu, D., Y. Wang, F. Zhang, and Y. Qiu. 2021. “Influences of pore-water pressure on slope stability considering strength nonlinearity.” Adv. Civ. Eng. 2021: 1–16.
Wu, S. C., M. Zhang, S. H. Zhang, and R. H. Jiang. 2019. “Study on determination method of equivalent Mohr–Coulomb strength parameters of a modified Hoek–Brown failure criterion.” Rock Soil Mech. 40 (11): 4165–4177.
Xu, J., Q. Pan, X. L. Yang, and W. Li. 2018. “Stability charts for rock slopes subjected to water drawdown based on the modified nonlinear Hoek–Brown failure criterion.” Int. J. Geomech. 18 (1): 04017133. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001039.
Zhang, J., H. Fan, S. Zhang, J. Liu, and J. Peng. 2020a. “Back-calculation of elastic modulus of high liquid limit clay subgrades based on viscoelastic theory and multipopulation genetic algorithm.” Int. J. Geomech. 20 (10): 04020194. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001841.
Zhang, J., W. H. Tang, and L. M. Zhang. 2010. “Efficient probabilistic back-analysis of slope stability model parameters.” J. Geotech. Geoenviron. Eng. 136 (1): 99–109. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000205.
Zhang, Y., G. Su, Y. Li, M. Wei, and B. Liu. 2020b. “Displacement back-analysis of rock mass parameters for underground caverns using a novel intelligent optimization method.” Int. J. Geomech. 20 (5): 04020035. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001657.
Zhang, Y., J. Zhang, G. Chen, L. Zheng, and Y. Li. 2015. “Effects of vertical seismic force on initiation of the Daguangbao landslide induced by the 2008 Wenchuan earthquake.” Soil Dyn. Earthquake Eng. 73: 91–102. https://doi.org/10.1016/j.soildyn.2014.06.036.
Zhao, L. H., S. Zuo, J. Y. Chen, and Z. B. Wang. 2016a. “Reliability back analysis of shear strength parameters of landslide considering mutual-correlation between parameters.” J. South China Univ. Technol. 44 (6): 121–128.
Zhao, L. H., S. Zuo, Y. L. Lin, L. Li, and Y. B. Zhang. 2016b. “Reliability back analysis of shear strength parameters of landslide with three-dimensional upper bound limit analysis theory.” Landslides 13 (4): 711–724. https://doi.org/10.1007/s10346-015-0604-3.
Zheng, Y. R. 2010. Engineering treatment of slope and landslide. Beijing: China Communications Press.
Zhu, H. H., Q. Zhang, and L. Y. Zhang. 2013. “Review of research progresses and applications of Hoek–Brown strength criterion.” Chin. J. Rock Mech. Eng. 32 (10): 1945–1963.
Zuo, S., C. W. Hu, L. H. Zhao, K. F. Jiao, Z. B. Lei, D. L. Huang, and Z. H. Zhu. 2021. “Reliability back analysis of a 3D wedge slope based on the nonlinear Barton–Bandis failure criterion.” Eng. Fail. Anal. 128: 105601. https://doi.org/10.1016/j.engfailanal.2021.105601.
Zuo, S., L. H. Zhao, D. P. Deng, Z. B. Wang, and Z. G. Zhao. 2020. “Reliability back analysis of landslide shear strength parameters based on a general nonlinear failure criterion.” Int. J. Rock Mech. Min. Sci. 126: 104189. https://doi.org/10.1016/j.ijrmms.2019.104189.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 24Issue 5May 2024

History

Received: May 21, 2023
Accepted: Nov 6, 2023
Published online: Mar 7, 2024
Published in print: May 1, 2024
Discussion open until: Aug 7, 2024

Permissions

Request permissions for this article.

Authors

Affiliations

Lecturer, College of Civil Engineering, Changsha Univ., Changsha, Hunan 410022, China. Email: [email protected]
Zhiying Dai [email protected]
Senior Engineer, Shenzhen Transportation Design and Research Institute, Shenzhen 518003, China. Email: [email protected]
Professor, College of Civil Engineering, Central South Univ., Changsha, Hunan 410075, China; Key Laboratory of Heavy-Haul Railway Engineering Structure, Ministry of Education, Central South Univ., Changsha, Hunan 410075, China; Hunan Provincial Key Laboratory for Disaster Prevention and Mitigation of Rail Transit Engineering Structure, Central South Univ., Changsha, Hunan 410075, China (corresponding author). ORCID: https://orcid.org/0000-0002-8406-5973. Email: [email protected]
Ph.D. Student, College of Civil Engineering, Central South Univ., Changsha, Hunan 410075, China. Email: [email protected]
Ph.D. Student, College of Civil Engineering, Central South Univ., Changsha, Hunan 410075, China. ORCID: https://orcid.org/0000-0001-7612-9175. Email: [email protected]
Ph.D. Student, College of Civil Engineering, Central South Univ., Changsha, Hunan 410075, China. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share