Abstract
In the slope stability analysis, the interslice force calculated by the method of slices is the internal force of the slope in the limit equilibrium state, which is vital to the design of reinforcement. However, none of the existing methods can guarantee a priori the interslice force is reasonable. Starting from the global analysis procedure, an optimization problem for maximizing the factor of safety is posed under the constraints that the system of forces in the sliding body is physically admissible. In the problem, both the factor of safety and the normal stress along the slip surface are taken as the independent variables. With weak nonlinearity and no numerical problems inherent in the methods of slices, the optimization problem can be solved by those conventional optimization techniques. No assumption is made regarding the interslice forces, but the system of forces from the optimization problem is physically admissible. To bracket the factor of safety, meanwhile, the minimum of the factor of safety is calculated through a minimization process under the same constraints as the maximization process. It is illustrated that for smooth slip surfaces, the solutions to the maximum and the minimum almost coincide, and for non-smooth slip surfaces, the interval of the solution is very narrow.
Similar content being viewed by others
References
Abramson LW, Lee TS, Sharma S et al (1996) Slope stability and stabilization methods. Wiley, New York
Baker R (1980) Determination of the critical slip surface in slope stability computations. Int J Numer Anal Meth Geomech 4(4):333–359
Baker R, Garber M (1978) Theoretical analysis of the stability of slopes. Géotechnique 28(4):395–414
Bell JM (1968) General slope stability analysis. J Soil Mech Found Div ASCE 94(SM6):1253–1270
Chen ZY (2004) A generalized solution for tetrahedral rock wedge stability analysis. Int J Rock Mech Min Sci 41(4):613–628
Chen ZY, Morgenstern NR (1983) Extensions to the generalized method of slices for stability analysis. Can Geotech J 20(1):104–109
Cheng YM, Zhao ZH, Sun YJ (2010) Evaluation of interslice force function and discussion on convergence in slope stability analysis by the lower bound method. J Geotech Geoenviron Eng 136(8):1103–1113
Chugh AK (1981) Multiplicity of numerical solutions for slope stability problems. Int J Numer Anal Meth Geomech 5(3):313–322
Di Maio C, Vassallo R (2011) Geotechnical characterization of a landslide in a Blue Clay slope. Landslides 8(1):17–32
Donald IB, Giam P (1992) The ACADS slope stability programs review. In: Proceedings of the 6th international symposium on landslides, Christchurch, vol 3. New Zealand, pp 1665–1670
Duncan JM (1996) State of the art: limit equilibrium and finite element analysis of slopes. J Geotech Eng 122(7):577–596
Fan K, Fredlund DG, Wilson GW (1986) An interslice force function for limit equilibrium slope stability analysis. Can Geotech J 23(3):287–296
Fredlund DG, Krahn J (1977) Comparison of slope stability methods of analysis. Can Geotech J 14(3):429–439
Krahn J (2003) The 2001 R. M. Hardy lecture: the limits of limit equilibrium analyses. Can Geotech J 40(3):643–660
Martin JB (1975) Plasticity: fundamentals and general results. MIT Press, Massachusetts
Pan JZ (1980) Stability analyses of structures and landslides. Water Resources and Hydropower Press, Beijing (in Chinese)
Sarma SK, Tan D (2006) Determination of critical slip surface in slope analysis. Géotechnique 56(8):539–550
Singh TN, Gulati A, Dontha L, Bhardwaj V (2008) Evaluating cut slope failure by numerical analysis—a case study. Nat Hazards 47(2):263–279
Sun GH, Zheng H, Liu DF (2011) A three-dimensional procedure for evaluating the stability of gravity dams against deep slide in the foundation. Int J Rock Mech Min Sci 48(3):421–426
Tinti S, Manucci A (2006) Gravitational stability computed through the limit equilibrium method revisited. Geophys J Int 164(1):1–14
Whitman RV, Bailey WA (1967) Use of computers for slope stability analysis. J Soil Mech Found Div Proc of ASCE 93(SM4):4754–4798
Xu QJ, Zhang LM (2010) The mechanism of a railway landslide caused by rainfall. Landslides 7(2):149–156
Yang HJ, Wang JH, Liu YQ (2001) A new approach for the slope stability analysis. Mech Res Commun 28(6):653–669
Yu HS, Salgado R, Sloan SW, Kim JM (1998) Limit analysis versus limit equilibrium for slope stability. J Geotech Geoenviron Eng 124(1):1–10
Zheng H (2009) Eigenvalue problem from the stability analysis of slopes. J Geotech Geoenviron Eng ASCE 135(5):647–656
Zheng H, Tham LG (2009) Improved Bell’s method for the stability analysis of slopes. Int J Numer Anal Meth Geomech 33(14):1673–1689
Zheng H, Zhou CB, Liu DF (2009) A robust solution procedure for the rigorous methods of slices. Soils Found 49(4):537–544
Zhu DY, Lee CF (2002) Explicit limit equilibrium solution for slope stability. Int J Numer Anal Meth Geomech 26(15):1573–1590
Acknowledgments
This study is supported by the National Basic Research Program of China (973 Program), under the Grant No. 2011CB013505, and the National Science Fund of China, under the Grant No. 11172313.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zheng, H., Yang, Z.L. & Sun, G.H. Extremum solutions to the limit equilibrium method subjected to physical admissibility. Nat Hazards 65, 79–96 (2013). https://doi.org/10.1007/s11069-012-0345-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11069-012-0345-8