Comparison of Factors of Safety Using a 3D Failure Mechanism with Kinematic Approach
Publication: International Journal of Geomechanics
Volume 18, Issue 9
Abstract
In slope stability analysis, there are two commonly used methods for calculating the factors of safety (FS). The first is the strength reduction method (SRM), which defines the FS as the ratio of the real material shear strength to the critical shear strength in the limit equilibrium state. The second is the gravity increase method (GIM), which defines the FS as the ratio of the critical increased gravity to the actual gravity. On the basis of a kinematically admissible three-dimensional (3D) failure mechanism, this paper develops a framework to compare these two kinds of FS. Earthquake effects are included in the study by using the quasi-static representation. By means of the kinematic approach of limit analysis, the GIM can give an explicit function about the FS, while the SRM can only provide an implicit equation on the FS. The lowest solutions for both two kinds of FS are obtained by optimizing the variables from the 3D failure mechanism. Numerical results are calculated and presented in the forms of graphs to show the difference between these two kinds of FS. It is shown that the FS calculated by the SRM is equal to that calculated by the GIM when the slope is in the limit state (FS = 1.0), that the FS by the SRM is greater than that by the GIM for an unstable slope (FS < 1.0), and that the FS by the SRM is smaller than that by the GIM for a safe slope (FS > 1.0). Finally, a power function is proposed to approximately express the relationship between these two kinds of FS.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Financial support was received from the National Natural Science Foundation of China (51378510) and the Innovation Foundation for Postgraduate of Central South University (2018zzts633) for the preparation of this manuscript. This financial support is greatly appreciated.
References
Ausilio, E., E. Conte, and G. Dente. 2001. “Stability analysis of slopes reinforced with piles.” Comput. Geotech. 28 (8): 591–611. https://doi.org/10.1016/S0266-352X(01)00013-1.
Azzouz, A. S., and M. M. Baligh. 1983. “Loaded areas on cohesive slopes.” J. Geotech. Eng. 109 (5): 724–729. https://doi.org/10.1061/(ASCE)0733-9410(1983)109:5(724).
Baligh, M. M., and A. S. Azzouz. 1975. “End effects on stability of cohesive slopes.” J. Geotech. Geoenviron. Eng. 101: 1105–1117.
Basudhar, P. K., Anubhav, and M. R. Lakshminarayana. 2017. “Three-dimensional limit-equilibrium stability analyses of slopes and effect of inclusion of soil nails.” Int. J. Geomech. 17 (9): 04017067. https://doi.org/10.1061/(ASCE)GM.1943-5622.0000932.
Cai, F., K. Ugai, A. Wakai, and Q. Li. 1998. “Effects of horizontal drains on slope stability under rainfall by three-dimensional finite element analysis.” Comput. Geotech. 23 (4): 255–275. https://doi.org/10.1016/S0266-352X(98)00021-4.
Chen, W. F. 1975. Limit analysis and soil plasticity. Rotterdam, Netherlands: Elsevier Science.
Chen, Z. Y., X. G. Wang, C. Haberfield, J. H. Yin, and Y. J. Wang. 2001. “A three-dimensional slope stability analysis method using the upper bound theorem: Part I: Theory and methods.” Int. J. Rock Mech. Min. Sci. 38 (3): 369–378. https://doi.org/10.1016/S1365-1609(01)00012-0.
Cheng, Y. M., T. Lansivaara, and W. B. Wei. 2007. “Two-dimensional slope stability analysis by limit equilibrium and strength reduction methods.” Comput. Geotech. 34 (3): 137–150. https://doi.org/10.1016/j.compgeo.2006.10.011.
Donald, I. B., and Z. Chen. 1997. “Slope stability analysis by the upper bound approach: Fundamentals and methods.” Can. Geotech. J. 34 (6): 853–862. https://doi.org/10.1139/t97-061.
Drescher, A. 1983. “Limit plasticity approach to piping in bins.” J. Appl. Mech. 50 (3): 549–553. https://doi.org/10.1115/1.3167089.
Farzaneh, O., and F. Askari. 2003. “Three-dimensional analysis of nonhomogeneous slopes.” J. Geotech. Geoenviron. Eng. 129 (2): 137–145. https://doi.org/10.1061/(ASCE)1090-0241(2003)129:2(137).
Gens, A., J. N. Hutchinson, and S. Cavounidis. 1988. “Three-dimensional analysis of slides in cohesive soils.” Geotechnique 38 (1): 1–23. https://doi.org/10.1680/geot.1988.38.1.1.
Griffiths, D. V., and R. M. Marquez. 2007. “Three-dimensional slope stability analysis by elasto-plastic finite elements.” Geotechnique 57 (6): 537–546. https://doi.org/10.1680/geot.2007.57.6.537.
Huang, C. C., and C. C. Tsai. 2000. “New method for 3D and asymmetrical slope stability analysis.” J. Geotech. Geoenviron. Eng. 126 (10): 917–927. https://doi.org/10.1061/(ASCE)1090-0241(2000)126:10(917).
Hungr, O., F. M. Salgado, and P. M. Byrne. 1989. “Evaluation of a three-dimensional method of slope stability analysis.” Can. Geotech. J. 26 (4): 679–686. https://doi.org/10.1139/t89-079.
Kalatehjari, R., A. Arefnia, A. S. A. Rashid, N. Ali, and M. Hajihassani. 2015. “Determination of three-dimensional shape of failure in soil slopes.” Can. Geotech. J. 52 (9): 1283–1301. https://doi.org/10.1139/cgj-2014-0326.
Li, L. C., C. A. Tang, W. C. Zhu, and Z. Z. Liang. 2009. “Numerical analysis of slope stability based on the gravity increase method.” Comput. Geotech. 36 (7): 1246–1258. https://doi.org/10.1016/j.compgeo.2009.06.004.
Li, T. Z., and X. L. Yang. 2018. “Reliability analysis of tunnel face in broken soft rocks using improved response surface method.” Int. J. Geomech. 18 (5): 04018021. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001129.
Matsui, T., and K. C. San. 1992. “Finite element slope stability analysis by shear strength reduction technique.” Soils Found. 32 (1): 59–70. https://doi.org/10.3208/sandf1972.32.59.
Michalowski, R. L. 1989. “Three-dimensional analysis of locally loaded slopes.” Geotechnique 39 (1): 27–38. https://doi.org/10.1680/geot.1989.39.1.27.
Michalowski, R. L., and A. Drescher. 2009. “Three-dimensional stability of slopes and excavations.” Geotechnique 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.
Mononobe, N., and H. Matsuo, 1929. “On the determination of earth pressures during earthquakes.” In Vol. 9 of Proc., World Engineering Congress, 179–187. Tokyo: Nihon Kogakkai (Engineering Society of Japan).
Nadukuru, S. S., and R. L. Michalowski. 2013. “Three-dimensional displacement analysis of slopes subjected to seismic loads.” Can. Geotech. J. 50 (6): 650–661. https://doi.org/10.1139/cgj-2012-0223.
Nian, T. K., R. Q. Huang, S. S. Wan, and G. Q. Chen. 2012. “Three-dimensional strength-reduction finite element analysis of slopes: Geometric effects.” Can. Geotech. J. 49 (5): 574–588. https://doi.org/10.1139/t2012-014.
Okabe, S. 1924. “General theory on earth pressure and seismic stability of retaining wall and dam.” J. Jpn. Soc. Civil Eng. 10 (6): 1277–1323.
Pan, Q. J., and D. Dias. 2017. “Upper-bound analysis on the face stability of a non-circular tunnel.” Tunnelling Underground Space Technol. 62: 96–102. https://doi.org/10.1016/j.tust.2016.11.010.
Pan, Q. J., and D. Dias. 2018. “Three dimensional face stability of a tunnel in weak rock masses subjected to seepage forces.” Tunnelling Underground Space Technol. 71: 555–566. https://doi.org/10.1016/j.tust.2017.11.003.
Saada, Z., S. Maghous, and D. Garnier. 2012. “Stability analysis of rock slopes subjected to seepage forces using the modified Hoek-Brown criterion.” Int. J. Rock Mech. Min. Sci. 55: 45–54. https://doi.org/10.1016/j.ijrmms.2012.06.010.
Seo, Y. K., and C. C. Swan. 2001. “Load-factor stability analysis of embankments on saturated soil deposits.” J. Geotech. Geoenviron. Eng. 127 (5): 436–445. https://doi.org/10.1061/(ASCE)1090-0241(2001)127:5(436).
Shen, H., and S. M. Abbas. 2013. “Rock slope reliability analysis based on distinct element method and random set theory.” Int. J. Rock Mech. Min. Sci. 61: 15–22. https://doi.org/10.1016/j.ijrmms.2013.02.003.
Swan, C. C., and Y. K. Seo. 1999. “Limit state analysis of earthen slopes using dual continuum/FEM approaches.” Int. J. Numer. Anal. Methods Geomech. 23 (12): 1359–1371. https://doi.org/10.1002/(SICI)1096-9853(199910)23:12%3C1359::AID-NAG39%3E3.0.CO;2-Y.
Ugai, K., and D. Leshchinsky. 1995. “Three-dimensional limit equilibrium and finite element analyses: A comparison of results.” Soils Found. 35 (4): 1–7. https://doi.org/10.3208/sandf.35.4_1.
Wei, W. B., Y. M. Cheng, and L. Li. 2009. “Three-dimensional slope failure analysis by the strength reduction and limit equilibrium methods.” Comput. Geotech. 36 (1–2): 70–80. https://doi.org/10.1016/j.compgeo.2008.03.003.
Xu, J. S., and X. L. Yang. 2018. “Three-dimensional stability analysis of slope in unsaturated soils considering strength nonlinearity under water drawdown.” Eng. Geol. 237: 102–115. https://doi.org/10.1016/j.enggeo.2018.02.010.
Yang, X. L., and Z. W. Li. 2018. “Kinematical analysis of 3D passive earth pressure with nonlinear yield criterion.” Int. J. Numer. Anal. Methods Geomech. 42 (7): 916–930. https://doi.org/10.1002/nag.2771.
Yang, X. L., and S. Zhang. 2018. “Risk assessment model of tunnel water inrush based on improved attribute mathematical theory.” J. Cent. South Univ. 25 (2): 379–391. https://doi.org/10.1007/s11771-018-3744-5.
Zienkiewicz, O. C., C. Humpheson, and R. W. Lewis. 1975. “Associated and non-associated visco-plasticity and plasticity in soil mechanics.” Geotechnique 25 (4): 671–689. https://doi.org/10.1680/geot.1975.25.4.671.
Information & Authors
Information
Published In
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Oct 16, 2017
Accepted: Mar 14, 2018
Published online: Jun 28, 2018
Published in print: Sep 1, 2018
Discussion open until: Nov 28, 2018
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.