Numerical Simulation for Determination of Sliding Type and Stability Factor of Safety in Finite Slopes with Limit Equilibrium Method

Document Type : Research Article


1 Associate Professor, Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz-Iran

2 PhD candidate, Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz-Iran


In this study, the effect of soil material parameters including soil specific weight (γ), cohesion (C) and angle of internal friction (∅) and geometric parameters of slope including angle with the horizontal (β) and slope height (H) on factor of safety (Fs) are investigated. Slope factor of safety is considered in two scenarios: (i) slope with dry condition and (ii) slope with steady-state saturated condition that comprises water level drawdown circumstances. In addition, the type of slip circle investigated. For this purpose, the limit of equilibrium method (LEM) is implemented. Results indicated that, decreasing of water level and omitting the hydrostatic pressure on the slope, would result in safety factor decrement such a way that with drawdown of 5.5 m water level, the factor of safety decreases about 41.42 % and also the type of slip circle is changed. Comparison of the plane and circular failure surfaces showed that plane failure method has good results for near-vertical slopes only. Determination of clip type showed that for β<60o each of the three types of slip (toe circle, midpoint circle and slope circle) occur, but for β>60o only toe circle can happen. Application of the LEM in Bishop’s method resulted the values of R2 and RMSE equal to 0.93 and 0.121, respectively that the error of this method is 1.3% respect to other methods, which can be neglected in comparison with the complex and accurate methods.


Main Subjects

[1] H.B. Wang, W.Y. Xu, R.C. Xu, Slope stability evaluation using back propagation neural networks, Engineering Geology, 80 (2005) 302–315.
[2] B.M. Das Principles of geotechnical engineering, Cenage Learning, Stamford, CT., (2010).
[3] W. Fellenius, Erdstatische Berechnungen, rev. ed., W. Ernst u. Sons, Berlin, (1927).
[4] A.W. Bishop, N. R. Morgenstern, Stability Coefficients for Earth Slopes, Geotechnique, 10(4) (1960) 129–147.
[5] J. Lowe, L. Karafiath, Stability of Earth Dams upon Drawdown, in:  Proceedings of the First PanAmerican Conference on Soil Mechanics and Foundation Engineering, Mexican Society of Soil Mechanics, Mexico D.F, (1960) 537-552.
[6] N. Janbu, Slope stability computations, New York, (1973).
[7] U.S.A.C.o. Engineers, Stability of Earth and Rock-Fill Dams, Vicksburg, MS, 1970.
[8] E. Spencer, A Method of Analysis of the Stability of Embankments Assuming ParallelInter-Slice Forces, Geotechnique, 17(1) (1967) 11–26.
[9] N.R. Morgenstern, V.E. Price, The analysis of the stability of general slip surfaces, Geotechnique, 15(1) (1965) 79– 93.
[10] S.K. Sarma, Stability analysis of embankments and slopes, Geotechnique, 23 (1973).
[11] Singh, Shear Strength and Stability of Man- Made Slope, Journal of the Soil Mechanics and Foundations Division, ASCE, 96(SM6) (1970) 1879–1892.
[12] B. Pradha, Use of GIS-based fuzzy logic relations and its cross application to produce landslide susceptibility maps in three test areas in Malaysia, Environ Earth Sci 63(2) (2011) 329–349.
[13] A.H. Alavi, A.H. Gandomi, Energy-based numerical models for assessment of soil liquefa ction, Geosci Front3(4)(2012)541-555.
[14] Kainthola, D. Verma, R. Thareja, T.N. Singh, A review on numerical slope stability analysis, Int J Sci Eng Technol Res, 2(6) (2013) Int J Sci Eng Technol Res.
[15] D. Ramakrishnan, T.N. Singh, A.K. Verma, A. Gulati , K.C. Tiwari, Soft computing and GIS for landslide susceptibility assessment in Tawaghat area, Kuman Himal aya, India. Nat Hazards, 65(1) (2013) 315–330.
[16] D. Verma, A. Kainthola, R. Thareja, T.N. Singh, Stability analysis of an open cut slope in Wardha valley coal field, J Geol Soc India, 81 (2013) 804–810.
[17] R.L. Michalowski, Stability Charts for Uniform Slopes, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 128(4) (2002) 351–355.
[18] T. Steward, N. Sivakugan, S.K. Shukla, B.M. Das, Taylor’s Slope Stability Charts Revisited, International Journal of Geomechanics, ASCE, 11(4) (2011) 348–352.
[19]Y. Erzin, T. Cetin, The prediction of the critical factor of safety of homogeneous finite slopes using neural networks and multiple regressions 51 (2013) 305-313.
[20] M.G. Sakellari ou, M.D. Fer entinou, A study of slope stability prediction using neural networks, Geotechnical and Geological Engineering, 23 (2005) 419–445.
[21] T. Gaopeng, Z. Lianheng, G. Liansheng , L. Wei, Stability charts for undrained clay slopes in overload conditions based on upper bound limit analysis Article in Electronic, Journal of Geotechnical Engineering,  (2014).
[22] Y. Luo, S. He, F.Z. Chen, X. Li , J.C. He, A physical model considered the effect of overland water flow on rainfallinduced shallow landslides, Geoenviron Disasters Springer J, 2(8) (2015) 1–11.
[23] F. Salmasi, F. Jafari, A Simple Direct Method for Prediction of Safety Factor of   Homogeneous Finite Slopes, Geotech Geol Eng 37, 3949–3959 (2019). s10706-019-00884-3
[24] Geo-Studio, Geo Slope International, in: V.U. manual (Ed.), Calgary, (2012).
[25] N.K. Sah, P.R. Sheorey, L.W. Upadhyama, Maximum likelihood estimation of slope stability, Maximum likelihood estimation of slope stability, 31 (1994) 47–53.
[26] E. Madzic, Stability of unstable final slope in deep open iron mine, In: Bonnard (ed.) Landslides , Balkema, 1 (1988) 455–458.
[27] SPSS, Statistical package for social science in:  software version 22.
[28] R.V. Witman, W.A. Baily, Use of computers for slope stability Analysis, Jr.Soil Mech. And Found . Eng. ASCE, 93(SM4) (1967).
[29] M., N. Arafati, A Comparison on Slope Stability Analysis of Aydoghmoosh Earth Dam by Limit Equilibrium, Finite Element and Finite Difference Methods, International Journal of Civil Engineering and Building Materials, 2(3) (2012).
[30] C. Culmann, Die Graphische Statik, Meyer and Zeller, Zurich, (1875).