Upper-Bound Limit Analysis for Slope Stability Based on Modified Mohr–Coulomb Failure Criterion with Tensile Cutoff
Publication: International Journal of Geomechanics
Volume 21, Issue 10
Abstract
Using the classical (linear) Mohr–Coulomb (M–C) failure criterion, the failure mechanism of slopes is commonly treated as a completely shear failure. However, the tension failure mechanism has also been commonly observed in landslides, especially for those covered by cemented soils geometrical. Considering only the shear failure would overestimate the tensile capacity of geomaterial, which can lead to an optimistic result. In this paper, a modified M–C failure criterion with zero or low tensile strength (tension cutoff) was introduced that can characterize the shear–tension failure feature of slopes well. Combined with the limit upper bound theory, the expressions of stability factor (Ns) for slopes were derived considering (1) only soil self-weight; and two external conditions, (2) surcharge load, and (3) seismic load. Further, a detailed parametric analysis was conducted. The results show that the slope stability was greatly influenced by the surcharge coefficient (qt) and the horizontal seismic acceleration coefficient (kh). The influence of the degree of tension cutoff (ζ) on the slope stability strongly depends on the values of slope angle (β) and internal friction angle (φ). The difference in Ns under two extreme cases (ζ = 0 and ζ = 1) was significant, and the difference was more pronounced with the introduction of surcharge and seismic load.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The data used to support the findings of this study are available from the corresponding author upon request.
Acknowledgments
This research has been supported by the High-Speed Railway Joint Fund of National Natural Science Foundation of China (Grant No. U1934208), the Science and Technology Projects of Jiangxi Provincial Department of Transportation (Grant Nos. 2020Z0001 and 2021H0042), the Jiangxi Provincial Department of Communications Key Technology Foundation (Grant No. 2020Z0001), the Jiangxi Provincial Natural Science Foundation (Grant No. 20202BABL204067), and the Jiangxi Key Laboratory Foundation (Grant No. 20161BCD40010).
References
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., and S. Frydman. 1983. “Upper bound limit analysis of soil with non-linear failure criterion.” Soils Found. 23 (4): 34–42. https://doi.org/10.3208/sandf1972.23.4_34.
Bourne, S. J., and E. J. Willemse. 2001. “Elastic stress control on the pattern of tensile fracturing around a small fault network at Nash Point, UK.” J. Struct. Geol. 23 (11): 1753–1770. https://doi.org/10.1016/S0191-8141(01)00027-X.
Brace, W. F. 1960. “An extension of the Griffith theory of fracture to rocks.” J. Geophys. Res. 65 (10): 3477–3480. https://doi.org/10.1029/JZ065i010p03477.
Chen, W.-F. 1975. Limit analysis and soil plasticity. Amsterdam, Netherlands: Elsevier.
Collins, I. F., C. I. M. Gunn, M. J. Pender, and W. Yan. 1988. “Slope stability analyses for materials with a non-linear failure envelope.” Int. J. Numer. Anal. Methods Geomech. 12 (5): 533–550. https://doi.org/10.1002/nag.1610120507.
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-2014-0111.
Drescher, A., and C. Christopoulos. 1988. “Limit analysis slope stability with nonlinear yield condition.” Int. J. Numer. Anal. Methods Geomech. 12 (3): 341–345. https://doi.org/10.1002/nag.1610120307.
Duncan, J. M., S. G. Wright, and T. L. Brandon. 2014. Soil strength and slope stability. Hoboken, NJ: Wiley.
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.
Gipprich, T. L., R. K. Snieder, R. W. Jibson, and W. Kimman. 2008. “The role of shear and tensile failure in dynamically triggered landslides.” Geophys. J. Int. 172 (2): 770–778. https://doi.org/10.1111/j.1365-246X.2007.03681.x.
He, J., L. Xiao, W. Zhang, and W. Gao. 2016. “A method for calculating ultimate pull-out capacity of rock bolt based on modified Mohr–Coulomb failure criterion.” Rock Soil Mech. 37 (9): 2484–2488.
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.
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).
Michalowski, R. 2017a. “Stability of intact slopes with tensile strength cut-off.” Géotechnique 67 (8): 720–727. https://doi.org/10.1680/jgeot.16.P.037.
Michalowski, R. L. 2017b. “Failure potential of infinite slopes in soils with tensile strength cut-off.” Can. Geotech. J 55 (4): 477–485.
Mollon, G., D. Dias, and A. H. Soubra. 2011. “Rotational failure mechanisms for the face stability analysis of tunnels driven by a pressurized shield.” Int. J. Numer. Anal. Methods Geomech. 35 (12): 1363–1388. https://doi.org/10.1002/nag.962.
Park, D., and R. L. Michalowski. 2018. “A cone surface in 3D analyses of slopes with tension cut-off.” Geotech. Res. 5 (2): 1–48.
Park, D., Z. Wang, and R. L. Michalowski. 2017. “Consequences of seismic excitation on slopes in soils with a tensile strength cutoff.” In Geotechnical Frontiers, Geotechnical Special Publication 278, edited by T. L. Brandon and R. J. Valentine, 304–313. Reston, VA: ASCE.
Perazzelli, P., and G. Anagnostou. 2017. “Uplift resistance of strip anchors in cohesive frictional mediums of limited tensile strength.” Int. J. Geomech. 17 (9): 04017042. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000901.
Stead, D., E. Eberhardt, and J. Coggan. 2006. “Developments in the characterization of complex rock slope deformation and failure using numerical modelling techniques.” Eng. Geol. 83 (1–3): 217–235. https://doi.org/10.1016/j.enggeo.2005.06.033.
Tang, G.-p., L.-h. Zhao, L. Li, and F. Yang. 2015. “Stability charts of slopes under typical conditions developed by upper bound limit analysis.” Comput. Geotech. 65: 233–240. https://doi.org/10.1016/j.compgeo.2014.12.008.
Tang, G., L. Zhao, L. Liang, S. Zuo, and R. Zhang. 2017. “Stability design charts for homogeneous slopes under typical conditions based on the double shear strength reduction technique.” Arab. J. Geosci. 10 (13): 280. https://doi.org/10.1007/s12517-017-3071-4.
Yang, X.-g., and S.-c. 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).
Yang, X., and Z. Li. 2018. “Kinematical analysis of 3D passive earth pressure with nonlinear yield criterion.” Int. J. Numer. Anal. Methods Geomech. 42 (7): 916–930.
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, Y. 2017. Earthquake-induced landslides: Initiation and run-out analysis by considering vertical seismic loading, tension failure and the trampoline effect. Berlin: Springer.
Zhang, Y., G. Chen, J. Wu, L. Zheng, and X. Zhuang. 2012. “Numerical simulation of seismic slope stability analysis based on tension–shear failure mechanism.” Geotech. Eng. 43 (2): 18–28.
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.
Zhou, J.-W., W.-Y. Xu, X.-G. Yang, C. Shi, and Z.-H. Yang. 2010. “The 28 October 1996 landslide and analysis of the stability of the current Huashiban slope at the Liangjiaren Hydropower Station, Southwest China.” Eng. Geol. 114 (1–2): 45–56. https://doi.org/10.1016/j.enggeo.2010.04.001.
Information & Authors
Information
Published In
International Journal of Geomechanics
Volume 21 • Issue 10 • October 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Dec 28, 2020
Accepted: May 29, 2021
Published online: Jul 29, 2021
Published in print: Oct 1, 2021
Discussion open until: Dec 29, 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.
Cited by
- Pingping Rao, Peihao Ouyang, Jian Wu, Peinan Li, Sanjay Nimbalkar, Qingsheng Chen, Seismic Stability of Heterogeneous Slopes with Tensile Strength Cutoff Using Discrete-Kinematic Mechanism and a Pseudostatic Approach, International Journal of Geomechanics, 10.1061/(ASCE)GM.1943-5622.0002578, 22, 12, (2022).
- Dejian Li, Wentao Jia, Lianheng Zhao, Xiao Cheng, Yingbin Zhang, Haiying Fu, Bin Ye, Lu Zheng, Upper-Bound Limit Analysis of Rock Slope Stability with Tensile Strength Cutoff Based on the Optimization Strategy of Dividing the Tension Zone and Shear Zone, International Journal of Geomechanics, 10.1061/(ASCE)GM.1943-5622.0002366, 22, 5, (2022).