Nonlinear Shear-Strength Reduction Technique for Stability Analysis of Uniform Cohesive Slopes with a General Nonlinear Failure Criterion
Publication: International Journal of Geomechanics
Volume 21, Issue 1
Abstract
This paper develops a nonlinear shear-strength reduction technique for analyzing the stability of uniform slopes with the general nonlinear failure criterion. To incorporate the nonlinear power-law failure criterion into the finite-element slope stability analysis with the shear-strength reduction method (SSR-FEM), a general tangential approach is employed to obtain the instantaneous cohesive strength and internal friction angle from the power-law failure criterion iteratively. Therefore, the shear strength of the power-law criterion can be expressed by the instantaneous Mohr–Coulomb (MC) parameters related to stress within the slope soil. By this way, it is possible to use the linear MC failure criterion for the nonlinear slope stability analysis based on the conventional SSR-FEM. The proposed approach is applied to three typical examples including a homogenous 2D slope, a homogenous 3D slope, and a high rockfill embankment slope. The results show that the nonlinear shear-strength reduction technique presented in this paper can guarantee the accuracy and feasibility to determine the factor of safety (FOS) and provide an alternative way for stability analysis of simple uniform cohesive slopes with a general power-law criterion.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was financially supported by the National Natural Science Foundation of China (Nos. 51909224, 51979218, and 51679197), the Natural Science Foundation Research Project of Shaanxi province (Nos. 2020JQ-920, 2017JZ013, and 2018JM5118), the Natural science research project of Education Department of Shaanxi Provincial Government (No. 19JK0910), and Scientific Research Staring Foundation for Introduced Talents of Xijing University (No. XJ18T05). These supports are gratefully acknowledged.
References
Alcibiades, S., O. Claudio, and J. Rafael. 2016. “Analytical bearing capacity of strip footings in weightless materials with Power-Law failure criteria.” Int. J. Geomech. 16 (1): 04015010. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000465.
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).
Bishop, W. A. 1955. “The use of the slip circle in the stability analysis of slopes.” Géotechnique 5 (1): 7–17. https://doi.org/10.1680/geot.1955.5.1.7.
Collins, I. F., C. I. M. Gunn, M. J. Pender, and W. Yan. 1988. “Slope stability analyses for materials with nonlinear failure envelope.” Int. J. Numer. Anal. Methods Geomech. 12 (6): 533–550. https://doi.org/10.1002/nag.1610120507.
Dawson, E. M., W. H. Roth, and A. Drescher. 1999. “Slope stability analysis by strength reduction.” Géotechnique 49 (6): 835–840. https://doi.org/10.1680/geot.1999.49.6.835.
De Mello, V. F. B. 1977. “Reflections on design decisions of practical significance to embankment dams.” Géotechnique 27 (3): 281–355. https://doi.org/10.1680/geot.1977.27.3.281.
Drescher, A., and C. Christopoulos. 1988. “Limit analysis slope stability with nonlinear yield condition.” Int. J. Numer. Anal. Methods Geomech. 12 (4): 341–345. https://doi.org/10.1002/nag.1610120307.
Duncan, J. M. 1996. “State of the art: Limit equilibrium and finite-element analysis of slopes.” J. Geotech. Eng. 122 (7): 577–596. https://doi.org/10.1061/(ASCE)0733-9410(1996)122:7(577).
Duncan, J. M., P. M. Byrne, and K. S. Wong. 1978. Strength stress–strain and bulk modulus parameters for finite element analysis of stress and movements in soil masses. Berkeley: Berkeley Univ. of California.
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.
Gao, Y. F., 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.
Griffiths, D. V., and P. A. Lane. 1999. “Slope stability analysis by finite elements.” Géotechnique 49 (3): 387–403. https://doi.org/10.1680/geot.1999.49.3.387.
Griffiths, D. V., and R. M. Marquez. 2007. “Three-dimensional slope stability analysis by elasto-plastic finite elements.” Géotechnique 57 (6): 537–546. https://doi.org/10.1680/geot.2007.57.6.537.
Li, D., and Y. Cheng. 2012. “Lower bound limit analysis using nonlinear failure criteria.” Procedia Earth Planet. Sci. 5: 170–174. https://doi.org/10.1016/j.proeps.2012.01.030.
Li, X. 2007. “Finite element analysis of slope stability using a nonlinear failure criterion.” Comput. Geotech. 34 (3): 127–136. https://doi.org/10.1016/j.compgeo.2006.11.005.
Li, Y. X., and X. L. Yang. 2019. “Soil-slope stability considering effect of soil-strength nonlinearity.” Int. J. Geomech. 19 (3): 04018201. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001355.
Lin, H., W. Xiong, and Z. M. Li. 2013. “Embedded program for slip surface by shear strain of slopes and parametric analysis.” [In Chinese.] Chin. J. Geotech. Eng. 35: 1–5.
Luan, M. T., Y. J. Wu, and T. K. Nian. 2003. “An alternating criterion based on development of plastic zone for evaluating slope stability by shear strength reduction FEM.” In Proc., SinaJapanese Symposium on Geotechnical Engineering, Beijing, China, 181–188.
Morgenstern, N. R., and V. E. Price. 1965. “The analysis of the stability of general slip surface.” Geotechnique 15 (1): 79–93. https://doi.org/10.1680/geot.1965.15.1.79.
Popescu, M., K. Ugai, and A. Trandafir. 2000. “Linear versus nonlinear failure envelopes in LEM and FEM slope stability analysis.” In Proc., 8th Int. Symp. on Landslides, edited by E. Bromhead et al., 1227–1234. London, UK: Thomas Telford Ltd.
Sun, C. W., J. R. Chai, Z. G. Xu, and Y. Qin. 2017. “3D stability charts for convex and concave slopes in plan view with homogeneous soil based on the strength-reduction method.” Int. J. Geomech. 17 (5): 06016034. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000809.
Sun, Y. J., E. X. Song, and J. Yang. 2016. “Finite element analysis of earth structure stability with general nonlinear failure criterion.” [In Chinese.] Eng. Mech. 33 (7): 84–91.
Tang, H. M., R. Yong, and M. A. M. Eldin. 2017. “Stability analysis of stratified rock slopes with spatially variable strength parameters: The case of Qianjiangping landslide.” Bull. Eng. Geol. Environ. 76 (3): 839–853. https://doi.org/10.1007/s10064-016-0876-4.
Ugai, K. 1989. “A method of calculation of total factor of safety of slopes by elastoplastic FEM.” Soils Found. 29 (2): 190–195. https://doi.org/10.3208/sandf1972.29.2_190.
Xu, J. S., Q. J. Pan, X. L. Yang, and W. T. 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.
Yang, X., and S. Chi. 2013. “Upper bound finite element analysis of slope stability using a nonlinear failure criterion.” Comput. Geotech. 54: 185–191. https://doi.org/10.1016/j.compgeo.2013.06.007.
Yang, X. L., and J. H. Yin. 2004. “Slope stability analysis with nonlinear failure criterion.” J. Eng. Mech. 130 (3): 267–273. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:3(267).
Yin, Y. P., B. L. Huang, Q. Zhang, G. Q. Yan, and Z. W. Dai. 2020. “Research on recently occurred reservoir-induced Kamenziwan rockslide in Three Gorges Reservoir, China.” Landslides 17 (8): 1935–1949. https://doi.org/10.1007/s10346-020-01394-7.
Yong, R., C. D. Li, J. Ye, M. Huang, and S. G. Du. 2016. “Modified limiting equilibrium method for stability analysis of stratified rock slopes.” Math. Probl. Eng. 76 (3): 839–853.
Zhang, X. J., and W. F. Chen. 1987. “Stability analysis of slopes with general nonlinear failure criterion.” Int. J. Numer. Anal. Methods Geomech. 11 (1): 33–50. https://doi.org/10.1002/nag.1610110104.
Zhang, X. L., E. X. Song, and M. Xu. 2010. “Influence of nonlinear strength of rockfill on slope stability of high fills in mountainous regions.” [In Chinese.] Ind. Constr. 40 (12): 65–69.
Zhao, L., F. Yang, Y. Zhang, H. Dan, and W. Liu. 2015. “Effects of shear strength reduction strategies on safety factor of homogeneous slope based on a general nonlinear failure criterion.” Comput. Geotech. 63: 215–228. https://doi.org/10.1016/j.compgeo.2014.08.015.
Zheng, H., G. H. Sun, and D. F. Liu. 2009. “A practical procedure for searching critical slip surfaces of slopes based on the strength reduction technique.” Comput. Geotech. 36 (1–2): 1–5. https://doi.org/10.1016/j.compgeo.2008.06.002.
Zienkiewicz, O. C., C. Humpheson, and R. W. Lewis. 1975. “Associated and nonassociated viscoplasticity in soil mechanics.” Géotechnique 25 (4): 671–689. https://doi.org/10.1680/geot.1975.25.4.671.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 21 • Issue 1 • January 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Nov 5, 2019
Accepted: Aug 12, 2020
Published online: Oct 23, 2020
Published in print: Jan 1, 2021
Discussion open until: Mar 23, 2021
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.