Technical Papers
Aug 22, 2022

Pseudodynamic Approach for Rock Slopes in Hoek–Brown Media: Three-Dimensional Perspective

Publication: International Journal of Geomechanics
Volume 22, Issue 11

Abstract

Pseudodynamic (PD) method is a novel method that has the merit of considering the temporal and spatial effects of earthquake input in seismic stability analysis. Currently, most PD analyses adopted the two-dimensional (2D) plane-strain assumption, which is inconsistent with the fact that many slope collapses have distinct three-dimensional (3D) features. To address that, a 3D PD method was proposed in this paper for rock slopes yielding Hoek–Brown criterion. The present method was established on the one-block mechanism in the kinematic analysis, since this mechanism has considerable efficiency in 3D safety factor computation. The details of the 3D PD method are elaborated herein, including failure mechanism, energy balance equation, and strategy of fining solutions. The effects of temporal–spatial variation of seismic input on slope stability are discussed using the proposed approach. The study reveals that phase change and acceleration amplification have contrary effects on rock slope stability, and which factor dominates determines whether PD analyses result in overestimated or underestimated safety factors than classical PS analyses. Finally, a parametric study is performed to investigate the influences of rock strength, slope geometry, and earthquake parameters in PD analysis.

Get full access to this article

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

Acknowledgments

The first author thanks the support of “the Fundamental Research Funds for the Central Universities” of China (JZ2020HGTB0042). The financial support of National Natural Science Foundation of China (51878074) is also greatly appreciated.

References

Assefa, S., A. Graziani, and A. Lembo-Fazio. 2017. “A slope movement in a complex rock formation: Deformation measurements and DEM modelling.” Eng. Geol. 219: 74–91. https://doi.org/10.1016/j.enggeo.2016.10.014.
Baker, R., R. Shukha, V. Operstein, and S. Frydman. 2006. “Stability charts for pseudostatic slope stability analysis.” Soil Dyn. Earthquake Eng. 26 (9): 813–823. https://doi.org/10.1016/j.soildyn.2006.01.023.
Basha, B. M., and G. Babu. 2009. “Computation of sliding displacements of bridge abutments by pseudo-dynamic method.” Soil Dyn. Earthquake Eng. 29 (1): 103–120. https://doi.org/10.1016/j.soildyn.2008.01.006.
Camones, L., E. D. Vargas, R. P. de Figueiredo, and R. Q. Velloso. 2013. “Application of the discrete element method for modeling of rock crack propagation and coalescence in the step-path failure mechanism.” Eng. Geol. 153: 80–94. https://doi.org/10.1016/j.enggeo.2012.11.013.
Cattoni, E., D. Salciarini, and C. Tamagnini. 2019. “A Generalized Newmark Method for the assessment of permanent displacements of flexible retaining structures under seismic loading conditions.” Soil Dyn. Earthquake Eng. 117: 221–233. https://doi.org/10.1016/j.soildyn.2018.11.023.
Cattoni, E., and C. Tamagnini. 2020. “Critical accelerations for propped diaphragm walls in sand by finite-element limit analysis.” J. Earthquake Eng. 24 (3): 403–420. https://doi.org/10.1080/13632469.2018.1452805.
Chehade, H. A., D. Dias, M. Sadek, O. Jenck, and F. H. Chehade. 2019. “Seismic analysis of geosynthetic-reinforced retaining wall in cohesive soils.” Geotext. Geomembr. 47 (3): 315–326. https://doi.org/10.1016/j.geotexmem.2019.02.003.
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.
Di Filippo, G., V. Bandini, G. Biondi, and E. Cascone. 2019. “A two-wedge approach for the evaluation of seismic-induced rock-slides dams.” In Proc., 7th Int. Conf. on Earthquake Geotechnical Engineering for Protection and Development of Environment and Constructions, 2128–2135. Boca Raton, FL: CRC Press.
Drescher, A. 1983. “Limit plasticity approach to piping in bins.” J. Appl. Mech. 50 (3): 549–553. https://doi.org/10.1115/1.3167089.
FHWA (Federal Highway Administration). 2011. Seismic analysis and design of transportation geotechnical features and structural foundations. Geotechnical Engineering Circular 03-LRFD. FHWA-NHI-11-032. Washington, DC: FHWA.
Gazetas, G., E. Garini, I. Anastasopoulos, and T. Georgarakos. 2009. “Effects of near-fault ground shaking on sliding systems.” J. Geotech. Geoenviron. Eng. 135 (12): 1906–1921. https://doi.org/10.1061/40975(318)186.
Gens, A., J. N. Hutchinson, and S. Cavounidis. 1988. “Three-dimensional analysis of slides in cohesive soils.” Géotechnique 38 (1): 1–23. https://doi.org/10.1680/geot.1988.38.1.1.
Hoek, E. 1983. “Strength of jointed rock masses.” Géotechnique 33 (3): 187–223. https://doi.org/10.1680/geot.1983.33.3.187.
Hoek, E. 1990. “Estimating Mohr-Coulomb friction and cohesion values from the Hoek-Brown failure criterion.” Int. J. Rock. Mech. Min. Sci. Geomech. Abstr. 27 (3): 227–229. https://doi.org/10.1016/0148-9062(90)94333-O.
Hoek, E., and J. W. Bray. 1981. Rock slope engineering. 3rd ed. London: Institution of Mining and Metallurgy.
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., C. Carranza-Torres, and B. Corkum. 2002. “Hoek–Brown Failure criterion-2002 edition.” In Vol. 1 of Proc., NARMS-TAC Conf., 267–273. Toronto: University of Toronto Press.
Hoek, E., and M. S. Diederichs. 2006. “Empirical estimation of rock mass modulus.” Int. J. Rock Mech. Min. Sci. 43 (2): 203–215. https://doi.org/10.1016/j.ijrmms.2005.06.005.
Hou, C. Q., T. T. Zhang, Z. B. Sun, D. Dias, and M. Shang. 2019. “Seismic analysis of nonhomogeneous slopes with cracks using a discretization kinematic approach.” Int. J. Geomech. 19 (9): 04019104. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001487.
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: 196–208. https://doi.org/10.1016/j.enggeo.2016.05.015.
Kalourazi, A. F., A. Izadi, and R. J. Chenari. 2019. “Seismic bearing capacity of shallow strip foundations in the vicinity of slopes using the lower bound finite-element method.” Soils Found. 59 (6): 1891–1905. https://doi.org/10.1016/j.sandf.2019.08.014.
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.
Li, A. J., R. S. Merifeld, and A. V. Lyamin. 2008. “Stability charts for rock slopes based on the Hoek–Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 45 (5): 689–700. https://doi.org/10.1016/j.ijrmms.2007.08.010.
Ling, H. I., and A. H. D. Cheng. 1997. “Rock sliding induced by seismic force.” Int. J. Rock Mech. Min. Sci. 34 (6): 1021–1029. https://doi.org/10.1016/S1365-1609(97)80011-1.
Long, Z. X., and X. L. Yang. 2016. “Seismic and static 3D stability of two-stage rock slope based on Hoek–Brown failure criterion.” Can. Geotech. J. 53 (3): 551–558. https://doi.org/10.1139/cgj-2015-0147.
Mánica, M., E. Ovando, and E. Botero. 2014. “Assessment of damping models in FLAC.” Comput. Geotech. 59: 12–20. https://doi.org/10.1016/j.compgeo.2014.02.007.
Michalowski, R. L. 2010. “Limit analysis and stability charts for 3D slope failures.” J. Geotech. Geoenviron. Eng. 136 (4): 583–593. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000251.
Michalowski, R. L., and A. Drescher. 2009. “Three-dimensional stability of slopes and excavations.” Géotechnique 59 (10): 839–850. https://doi.org/10.1680/geot.8.P.136.
Michalowski, R. L., and T. Martel. 2011. “Stability charts for 3D failures of steep slopes subjected to seismic excitation.” J. Geotech. Geoenviron. Eng. 137 (2): 183–189. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000412.
Qin, C. B., and S. C. Chian. 2018. “Kinematic analysis of seismic slope stability with a discretisation technique and pseudo-dynamic approach: A new perspective.” Géotechnique 68 (6): 492–503. https://doi.org/10.1680/jgeot.16.P.200.
Sharma, S., T. K. Raghuvanshi, and R. Anbalagan. 1995. “Plane failure analysis of rock slopes.” Geotech. Geol. Eng. 13 (2): 105–111. https://doi.org/10.1007/BF00421876.
Shukha, R., and R. Baker. 2008. “Design implications of the vertical pseudostatic coefficient in slope analysis.” Comput. Geotech. 35 (1): 86–96. https://doi.org/10.1016/j.compgeo.2007.01.005.
Silvestri, V. 2006. “A three-dimensional slope stability problem in clay.” Can. Geotech. J. 43 (2): 224–228. https://doi.org/10.1139/t06-001.
Steedman, R. S., and X. Zeng. 1990. “Influence of phase on calculation of pseudostatic earth pressure on a retaining wall.” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 27 (5): 307. https://doi.org/10.1016/0148-9062(90)93144-B.
Xu, J. S., and X. L. Yang. 2018. “Seismic stability analysis and charts of a 3D rock slope in Hoek–Brown media.” Int. J. Rock Mech. Min. Sci. 112: 64–76. https://doi.org/10.1016/j.ijrmms.2018.10.005.
Yang, X. L. 2007. “Seismic displacement of rock slopes with nonlinear Hoek–Brown failure criterion.” Int. J. Rock Mech. Min. Sci. 44 (6): 948–953. https://doi.org/10.1016/j.ijrmms.2007.01.002.
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.
Zhang, Z., J. A. Fleurisson, and F. Pellet. 2018. “The effects of slope topography on acceleration amplification and interaction between slope topography and seismic input motion.” Soil Dyn. Earthquake Eng. 113: 420–431. https://doi.org/10.1016/j.soildyn.2018.06.019.
Zhao, L., X. Cheng, L. Li, J. Chen, and Y. Zhang. 2017. “Seismic displacement along a log-spiral failure surface with crack using rock Hoek–Brown failure criterion.” Soil Dyn. Earthquake Eng. 99: 74–85. https://doi.org/10.1016/j.soildyn.2017.04.019.
Zhao, L. H. 2009. “Energy analysis method for slope stability and reinforcement design.” [In Chinese.] Ph.D. thesis, Central South Univ., Changsha, Hunan.
Zhong, J. H., and X. L. Yang. 2020. “Kinematic analysis of the three-dimensional stability for tunnel faces by behavior approach.” Comput. Geotech. 128: 103802. https://doi.org/10.1016/j.compgeo.2020.103802.
Zhou, X. P., and H. Cheng. 2013. “Analysis of stability of three-dimensional slopes using the rigorous limit equilibrium method.” Eng. Geol. 160: 21–33. https://doi.org/10.1016/j.enggeo.2013.03.027.
Zhou, X. P., Y. Zhao, and Q. H. Qian. 2015. “A novel meshless numerical method for modeling progressive failure processes of slopes.” Eng. Geol. 192: 139–153. https://doi.org/10.1016/j.enggeo.2015.04.005.

Information & Authors

Information

Published In

Go to International Journal of Geomechanics
International Journal of Geomechanics
Volume 22Issue 11November 2022

History

Received: Nov 18, 2021
Accepted: Jun 4, 2022
Published online: Aug 22, 2022
Published in print: Nov 1, 2022
Discussion open until: Jan 22, 2023

Permissions

Request permissions for this article.

Authors

Affiliations

School of Automotive and Transportation Engineering, Hefei Univ. of Technology, Hefei 230009, China. ORCID: https://orcid.org/0000-0002-3607-8825. Email: [email protected]
School of Automotive and Transportation Engineering, Hefei Univ. of Technology, Hefei 230009, China. Email: [email protected]
School of Automotive and Transportation Engineering, Hefei Univ. of Technology, Hefei 230009, China (corresponding author). Email: [email protected]
School of Automotive and Transportation Engineering, Hefei Univ. of Technology, Hefei 230009, China. Email: [email protected]
School of Civil Engineering, Central South Univ., Changsha 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