Curvilinear Slope Profile–Based Seismic Stability for Rock Slopes Using Stress Characteristics Method and Generalized Hoek–Brown Criterion
Publication: Journal of Engineering Mechanics
Volume 150, Issue 8
Abstract
This paper introduces a novel approach to analyze the seismic stability of rock slopes using the stress characteristics method (SCM). Based on a prescribed factor of safety (FS), the slope profile (SP) is forthrightly determined without involving any optimization technique. A theoretical model is developed to execute the seismic analysis by coupling the SCM with the modified pseudo-dynamic (MPD) approach. The SCM obliterates the necessity of predefined slope geometry and slip surfaces in the analysis, whereas the MPD approach captures more credible nonuniform seismic inertia forces during earthquake excitation. The generalized Hoek–Brown criterion is employed to model the nonlinear strength characteristics of the rock mass. With different recommended values of FS, chart solutions comprising SPs are presented to readily evaluate the seismic stability of rock slopes. A comprehensive parametric analysis is conducted to interpret the behavior of obtained SPs under the influence of various input parameters. The overall slope angle of the present curvilinear SPs is found to be in close agreement with that of traditional linear SPs reported in the literature. Moreover, the legitimacy of the current methodology for designing open pit mines and assessing the safety status of existing rock slopes is showcased through different case studies along with a numerical simulation of the derived SPs.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All the data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The first author acknowledges the Ministry of Education, Government of India, for the Prime Minister’s Research Fellowship (PMRF) grant [Grant No. PMRF-2301338].
References
Bellezza, I. 2014. “A new pseudo-dynamic approach for seismic active soil thrust.” Geotech. Geol. Eng. 32 (2): 561–576. https://doi.org/10.1007/s10706-014-9734-y.
Bellezza, I. 2015. “Seismic active earth pressure on walls using a new pseudo-dynamic approach.” Geotech. Geol. Eng. 33 (4): 795–812. https://doi.org/10.1007/s10706-015-9860-1.
Booker, J. R., and E. H. Davis. 1972. “A general treatment of plastic anisotropy under conditions of plane strain.” J. Mech. Phys. Solids 20 (4): 239–250. https://doi.org/10.1016/0022-5096(72)90003-8.
Carranza-Torres, C. 2021. “Computational tools for the analysis of circular failure of rock slopes.” IOP Conf. Ser.: Earth Environ. Sci. 833 (1): 012003. https://doi.org/10.1088/1755-1315/833/1/012003.
Chakraborti, S., H. Konietzky, and K. Walter. 2012. “A comparative study of different approaches for factor of safety calculations by shear strength reduction technique for non-linear Hoek–Brown failure criterion.” Geotech. Geol. Eng. 30 (4): 925–934. https://doi.org/10.1007/s10706-012-9517-2.
Chen, G., J. Zou, and R. Zhang. 2021. “Stability analysis of rock slopes using strength reduction adaptive finite element limit analysis.” Struct. Eng. Mech. 79 (4): 487–498. https://doi.org/10.12989/sem.2021.79.4.487.
Chen, J., J.-H. Yin, and C. F. Lee. 2004. “Rigid finite element method for upper bound limit analysis of soil slopes subjected to pore water pressure.” J. Eng. Mech. 130 (8): 886–893. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:8(886).
Choudhury, D., and S. Nimbalkar. 2005. “Seismic passive resistance by pseudo-dynamic method.” Géotechnique 55 (9): 699–702. https://doi.org/10.1680/geot.2005.55.9.699.
Deng, D., L. Li, J. Wang, and L. Zhao. 2016. “Limit equilibrium method for rock slope stability analysis by using the Generalized Hoek–Brown criterion.” Int. J. Rock Mech. Min. Sci. 89 (Jun): 176–184. https://doi.org/10.1016/j.ijrmms.2016.09.007.
Fang, H. W., Y. F. Chen, and Y. X. Xu. 2020. “New instability criterion for stability analysis of homogeneous slopes.” Int. J. Geomech. 20 (5): 04020162. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001665.
Fu, W., and Y. Liao. 2010. “Non-linear shear strength reduction technique in slope stability calculation.” Comput. Geotech. 37 (3): 288–298. https://doi.org/10.1016/j.compgeo.2009.11.002.
Gray, D. 2013. “Influence of slope morphology on the stability of earthen slopes.” In Proc., Geo-Congress 2013: Stability and Performance of Slopes and Embankments, 1902–1911. Reston, VA: ASCE.
Hammah, R. E., T. E. Yacoub, B. Corkum, and J. H. Curran. 2005. “The shear strength reduction method for the generalized Hoek–Brown criterion.” In Proc., 40th US Symp. on Rock Mechanics. Alexandria, VA: ARMA.
Hoek, E., C. Carranza-Torres, and B. Corkum. 2002. “Hoek–brown failure criterion–2002 edition.” In Vol. 1 of Proc., 5th North American Rock Mechanics Symp. 17th Tunnelling Association of Canada Conf.: NARMS-TAC 2002, 267–273. Toronto: Univ. of Toronto.
ITASCA. 2021. FLAC/Slope 8.1 User’s manual. Minneapolis: ITASCA.
Jahanandish, M., and A. Keshavarz. 2005. “Seismic bearing capacity of foundations on reinforced soil slopes.” Geotext. Geomembr. 23 (1): 1–25. https://doi.org/10.1016/j.geotexmem.2004.09.001.
Jeldes, I. A., N. E. Vence, and E. C. Drumm. 2015. “Approximate solution to the Sokolovskiĭ concave slope at limiting equilibrium.” Int. J. Geomech. 15 (2): 04014049. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000330.
Jiang, X. Y., P. Cui, and C. Z. Liu. 2016. “A chart-based seismic stability analysis method for rock slopes using Hoek–Brown failure criterion.” Eng. Geol. 209 (Sep): 196–208. https://doi.org/10.1016/j.enggeo.2016.05.015.
Johari, A., S. M. Hosseini, and A. Keshavarz. 2017. “Reliability analysis of seismic bearing capacity of strip footing by stochastic slip lines method.” Comput. Geotech. 91 (Jun): 203–217. https://doi.org/10.1016/j.compgeo.2017.07.019.
Keshavarz, A., A. Fazeli, and S. Sadeghi. 2016. “Seismic bearing capacity of strip footings on rock masses using the Hoek–Brown failure criterion.” J. Rock Mech. Geotech. Eng. 8 (2): 170–177. https://doi.org/10.1016/j.jrmge.2015.10.003.
Keshavarz, A., and J. Kumar. 2018. “Bearing capacity of foundations on rock mass using the method of characteristics.” Int. J. Numer. Anal. Methods Geomech. 42 (3): 542–557. https://doi.org/10.1002/nag.2754.
Keshavarz, A., and J. Kumar. 2021. “Bearing capacity of ring foundations over rock media.” J. Geotech. Geoenviron. Eng. 147 (6): 04021027. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002517.
Kumar, J., and D. Mohapatra. 2017. “Lower-bound finite elements limit analysis for Hoek–Brown materials using semidefinite programming.” J. Eng. Mech. 143 (9): 04017077. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001296.
Latha, G. M., and A. Garaga. 2010. “Seismic stability analysis of a Himalayan rock slope.” Rock Mech. Rock Eng. 43 (6): 831–843. https://doi.org/10.1007/s00603-010-0088-3.
Li, A. J., A. V. Lyamin, and R. S. Merifield. 2009. “Seismic rock slope stability charts based on limit analysis methods.” Comput. Geotech. 36 (1–2): 135–148. https://doi.org/10.1016/j.compgeo.2008.01.004.
Liu, J., S. Xu, and X. L. Yang. 2022. “Modified pseudo-dynamic bearing capacity of strip footing on rock masses.” Comput. Geotech. 150 (Mar): 104897. https://doi.org/10.1016/j.compgeo.2022.104897.
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 (Sep): 104217. https://doi.org/10.1016/j.ijrmms.2020.104217.
Mononobe, N., and H. Matsuo. 1929. “On the determination of earth pressure during earthquake.” In Vol. 9 of Proc., World Eng. Conf., 177–185. Tokyo: International Association of Earthquake Engineering.
Nandi, S., and P. Ghosh. 2023. “Seismic stability assessment of rock slopes using limiting slope face concept.” Rock Mech. Rock Eng. 56 (7): 5077–5102. https://doi.org/10.1007/s00603-023-03308-0.
Nandi, S., G. Santhoshkumar, and P. Ghosh. 2021a. “Determination of critical slope face in soil under seismic condition using method of stress characteristics.” Int. J. Geomech. 21 (4): 04021031. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001976.
Nandi, S., G. Santhoshkumar, and P. Ghosh. 2021b. “Development of limiting soil slope profile under seismic condition using slip line theory.” Acta Geotech. 16 (11): 3517–3531. https://doi.org/10.1007/s11440-021-01251-4.
Okabe, S. 1926. “General theory of earth pressure.” J. Jpn. Soc. Civ. Eng. 12 (6): 1277–1323.
Pain, A., D. Choudhury, and S. K. Bhattacharyya. 2017. “Seismic rotational stability of gravity retaining walls by modified pseudo-dynamic method.” Soil Dyn. Earthquake Eng. 94 (Sep): 244–253. https://doi.org/10.1016/j.soildyn.2017.01.016.
Santhoshkumar, G., P. Ghosh, and A. Murakami. 2019. “Seismic active resistance of a tilted cantilever retaining wall considering adaptive failure mechanism.” Int. J. Geomech. 19 (8): 04019086. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001470.
Serrano, A., and C. Olalla. 1994. “Ultimate bearing capacity of rock masses.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 31 (2): 93–106. https://doi.org/10.1016/0148-9062(94)92799-5.
Serrano, A., C. Olalla, and J. González. 2000. “Ultimate bearing capacity of rock masses based on the modified Hoek–Brown criterion.” Int. J. Rock Mech. Min. Sci. 37 (6): 1013–1018. https://doi.org/10.1016/S1365-1609(00)00028-9.
Shen, J., and M. Karakus. 2014. “Three-dimensional numerical analysis for rock slope stability using shear strength reduction method.” Can. Geotech. J. 51 (2): 164–172. https://doi.org/10.1139/cgj-2013-0191.
Shen, J., M. Karakus, and C. Xu. 2013. “Chart-based slope stability assessment using the Generalized Hoek–Brown criterion.” Int. J. Rock Mech. Min. Sci. 64 (Sep): 210–219. https://doi.org/10.1016/j.ijrmms.2013.09.002.
Shen, J., S. D. Priest, and M. Karakus. 2012. “Determination of Mohr-Coulomb shear strength parameters from generalized Hoek–Brown criterion for slope stability analysis.” Rock Mech. Rock Eng. 45 (1): 123–129. https://doi.org/10.1007/s00603-011-0184-z.
Shi, L., H. Wang, B. Bai, and X. Li. 2019. “Improved finite element–based limit equilibrium method for slope stability analysis by considering non-linear strength criteria and its application in assessing the anchoring effect.” Int. J. Numer. Anal. Methods Geomech. 43 (2): 578–598. https://doi.org/10.1002/nag.2879.
Sokolovski, V. V. 1960. Statics of soil media. London: Butterworths Scientific Publications.
Sonmez, H., and R. Ulusay. 1999. “Modifications to the geological strength index (GSI) and their applicability to stability of slopes.” Int. J. Rock Mech. Min. Sci. 36 (6): 743–760. https://doi.org/10.1016/S0148-9062(99)00043-1.
Steedman, R. S., and X. Zeng. 1990. “The influence of phase on the calculation of pseudo-static earth pressure on a retaining wall.” Géotechnique 40 (1): 103–112. https://doi.org/10.1680/geot.1990.40.1.103.
Sun, C., J. Chai, Z. Xu, Y. Qin, and X. Chen. 2016. “Stability charts for rock mass slopes based on the Hoek–Brown strength reduction technique.” Eng. Geol. 214 (Jun): 94–106. https://doi.org/10.1016/j.enggeo.2016.09.017.
Utili, S., A. Agosti, N. Morales, C. Valderrama, R. Pell, and G. Albornoz. 2022. “Optimal pitwall shapes to increase financial return and decrease carbon footprint of open pit mines.” Min. Metall. Explor. 39 (2): 335–355. https://doi.org/10.1007/s42461-022-00546-8.
Vahedifard, F., S. Shahrokhabadi, and D. Leshchinsky. 2016. “Optimal profile for concave slopes under static and seismic conditions.” Can. Geotech. J. 53 (9): 1522–1532. https://doi.org/10.1139/cgj-2016-0057.
Vo, T., and A. R. Russell. 2017a. “Interaction between retaining walls and unsatured soils in experiments and using slip line theory.” J. Eng. Mech. 143 (4): 04016120. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001187.
Vo, T., and A. R. Russell. 2017b. “Stability charts for curvilinear slopes in unsaturated soils.” Soils Found. 57 (4): 543–556. https://doi.org/10.1016/j.sandf.2017.06.005.
Vo, T., and A. R. Russell. 2020. “Contours of saturated and unsaturated overhanging slopes at limiting equilibrium condition.” Int. J. Numer. Anal. Methods Geomech. 44 (1): 93–116. https://doi.org/10.1002/nag.3008.
Wang, B., T. Li, Z. Sun, Y. Li, and C. Hou. 2022. “A pseudo-dynamic approach for seismic stability analysis of rock slopes in Hoek–Brown media.” Geotech. Geol. Eng. 40 (7): 3561–3577. https://doi.org/10.1007/s10706-022-02120-x.
Wijesinghe, D. R., A. Dyson, G. You, M. Khandelwal, C. Song, and E. T. Ooi. 2022. “Simultaneous slope design optimization and stability assessment using a genetic algorithm and a fully automatic image-based analysis.” Int. J. Numer. Anal. Methods Geomech. 46 (15): 2868–2892. https://doi.org/10.1002/nag.3431.
Yang, X. L., L. Li, and J. H. Yin. 2004. “Stability analysis of rock slopes with a modified Hoek–Brown failure criterion.” Int. J. Numer. Anal. Methods Geomech. 28 (2): 181–190. https://doi.org/10.1002/nag.330.
Yang, X. L., and J. F. Zou. 2006. “Stability factors for rock slopes subjected to pore water pressure based on the Hoek–Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 43 (7): 1146–1152. https://doi.org/10.1016/j.ijrmms.2006.03.010.
Yang, X.-L., and J.-H. Yin. 2004. “Slope stability analysis with non-linear failure criterion.” J. Eng. Mech. 130 (3): 267–273. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:3(267).
Yuan, W., J. Li, Z. Li, W. Wang, and X. Sun. 2020. “A strength reduction method based on the Generalized Hoek–Brown (GHB) criterion for rock slope stability analysis.” Comput. Geotech. 117 (Apr): 103240. https://doi.org/10.1016/j.compgeo.2019.103240.
Zhong, J. H., and X. L. Yang. 2022. “Pseudo-dynamic stability of rock slope considering Hoek–Brown strength criterion.” Acta Geotech. 17 (6): 2481–2494. https://doi.org/10.1007/s11440-021-01425-0.
Zienkiewicz, O. C., C. Humpheson, and R. W. Lewis. 1975. “Associated and non-associated viscoplasticity in soil mechanics.” Géotechnique 25 (4): 671–689. https://doi.org/10.1680/geot.1975.25.4.671.
Zuo, J. Y., B. T. Wang, W. W. Li, and H. X. Zhang. 2022. “Upper-bound solution for the stability analysis of layered slopes.” J. Eng. Mech. 148 (3): 04022007. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002087.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 150 • Issue 8 • August 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Oct 18, 2023
Accepted: Mar 18, 2024
Published online: Jun 3, 2024
Published in print: Aug 1, 2024
Discussion open until: Nov 3, 2024
ASCE Technical Topics:
Authors
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.