Assessment of Slope Stability by Continuum and Discontinuum Methods

Authors: Taleb Hosni Abderrahmane, Berga Abdelmadjid

Abstract:

The development of numerical analysis and its application to geomechanics problems have provided geotechnical engineers with extremely powerful tools. One of the most important problems in geotechnical engineering is the slope stability assessment. It is a very difficult task due to several aspects such the nature of the problem, experimental consideration, monitoring, controlling, and assessment. The main objective of this paper is to perform a comparative numerical study between the following methods: The Limit Equilibrium (LEM), Finite Element (FEM), Limit Analysis (LAM) and Distinct Element (DEM). The comparison is conducted in terms of the safety factors and the critical slip surfaces. Through the results, we see the feasibility to analyse slope stability by many methods.

Keywords: Comparison, factor of safety, geomechanics, numerical methods, slope analysis, slip surfaces.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1124517

References:

[1] Chen, Z. Y.: Stability analysis of soil slope—Theory, Method and Programs. Chinese Water Press, Beijing, 2003.
[2] Kim, J. Y., Lee, S. R.: An improved search strategy for the critical slip surface using finite element stress fields. Computers and Geotechnics, 1997.
[3] Kentli, B., Topal, T.: Assessment of rock slope stability for a segment of the Ankara-Ppzant1 motorway, Turkey. Engineering Geology, 2004, 74, 73–90.
[4] Fellenius W. Calculation of stability of earth dams. Transactions, 2nd Congress on Large Dams, Washington, DC, 1936, vo1445-462.
[5] Bishop A.W. The use of slip circle in the stability analysis of slopes. Geotechnique, 1955, 5(1):7-17.
[6] Morgenstern, N. R., and Price, V. E. The analysis of the stability of general slip surfaces. Geotechnique, London, 1965, 15(1), 79-93.
[7] Spencer, E. A method of analysis of the stability of embankments assuming parallel interslice forces. Geotechnique. London, 1967, 17(1), 11-26.
[8] Sarma S K. Stability Analysis of Embankment and Slopes”. Geotechnique, 1973, 23:423‐33.
[9] Janbu, N. Slope Stability Computations, Embankment-Dam Engineering, Casagrande Volume, Hirschfeld, R.C. and Poulos. J. (ed.), John Wile and Sons, New York, USA, 1973, 47-86.
[10] Zhu, D. Y., Lee, C. F., Jiang, H. D. Generalized framework of limit equilibrium methods for slope stability analysis (J). Geotechnique, 2003, 53(4): 377-395.
[11] Abramson L W; Lee T S; Sharma S; Boyce G M. Slope Stability Concepts. Slope Stabilisation and Stabilisation Methods, Second Edition, published by John Wiley & Sons, Inc., 2002, pp. 329-461.
[12] Duncan J. M. State of the art: limit equilibrium and finite-element analysis of slopes. J Geotech Eng, 1996, 122(7):577–96.
[13] O. C. Zienkiewicz, R. L. Taylor, 4th edition, The Finite Element Method, vol. 2, McGraw-Hill, London, 1991.
[14] M. A. Crisfield, Non-linear Finite Element Analysis of Solids and Structures, John Wiley, Chichester, 1991.
[15] E. Hinton, D. R. J. Owen, Finite Elements in Plasticity: Theory and Practice, Pineridge Press, Swansea, Wales, 1980.
[16] K. J. Bathe, Finite Element Procedures, Prentice-Hall, New Jersey. 1996.
[17] Griffiths D. V., Lane P. A. Slope stability analysis by finite elements. Géotechnique, 1999, (3):387–403.
[18] L.C. Li, C. A. Tang, W. C. Zhu, Z. Z. Liang; Numerical analysis of slope stability based on the gravity increase method, journal of Computers and Geotechnics, 2009.
[19] Rabie, M. «Comparison study between traditional and finite element methods for slopes under heavy rainfall» Housingand Building National Research Center, 2014, 9.
[20] Abramson LW, Lee TS, Sharma S, et al. Slope stability and stabilization methods. New York: Springer, 1996.
[21] Zheng H., Tham L. G., Liu D. F. On two definitions of the factor of safety commonly used in the finite element slope stability analysis. Comput Geotech, 2006, 33: 188–95.
[22] Dawson E. M., Roth W. H., Drescher A. Slope stability analysis by strength reduction. Geotechnique, 1999, 49(6):835–40.
[23] Zienkiewicz O. C., Humpheson C., Lewis R. W. Associated and non-associated visco-plasticity and plasticity in soil mechanics. Geotechnique, 1975, 25(4): 671–89.
[24] Naylor D. J. Finite elements and slope stability. Proceedings of the NATO Advanced Study Institute, Lisbon, Portugal, 1981. Numer. Methods Geomech, 1982, 229–44.
[25] Donald I. B., Giam S. K. Application of the nodal displacement method to slope stability analysis. In: Proceedings of the 5th Australia–New Zealand conference on geomechanics, Sydney, Australia, 1988, p. 456–60.
[26] Matsui T., San K. C. Finite element slope stability analysis by shear strength reduction technique. Soils Foundations, 1992, 32(1):59–70.
[27] Ugai K. A method of calculation of total factor of safety of slopes by elastoplastic FEM. Soils Foundations, 1989, 29(2):190–5.
[28] Song E. Finite element analysis of safety factor for soil structures. Chinese J Geotech Eng, 1997.
[29] Dawson EM, Roth WH, Drescher A. Slope stability analysis by strength reduction. Geotechnique, 1999.
[30] Zheng Y. R., Zhao S. Y., Kong W. X., Deng C. J. Geotechnical engineering limit analysis using finite element method. Rock Soil Mech 2005, 26(1):163–8.
[31] Colby, C. Swan and Young-Kyo Seo. Slope stability analysis using finite element techniques. 13 th Iowa ASCE Geotechnique Conference, USA. 1999.
[32] Drucker, D. C., Greenberg, W. and Prager, W., The safety factor of an elastic plastic body in plane strain, Transactions of the ASME, Journal of Applied Mechanics, 1951, 73, 371.
[33] Drucker D. C. and Prager W., Soil mechanics and plastic analysis or limit design, Quarterly of Applied Mathematics, 1952, 10, 157–165.
[34] Chen, J., Yin, J. H., and Lee, C. F. Upper bound limit analysis of slope stability using rigid finite elements and nonlinear programming. Can. Geotech. J., 2003, 40: 742-752.
[35] Chen, J., Yin, J. H., and Lee, C. F. A three-dimensional upper-bound approach to slope stability analysis based on RFEM. Geotechnique, 2005.
[36] Donald, I.B., and Chen, Z.Y. Slope stability analysis by the upper bound approach: fundamentals and methods. Can. Geotech. J., 1997, 34: 853-862.
[37] Michalowski, R. L. Three-dimensional analysis of locally loaded slopes. Geotechnique, 1989, 39(1): 27-38.
[38] Michalowski, R. L. Stability charts for uniform slopes. Journal of Geotechnical and Geo-environmental Engineering, ASCE, 2002, 128(4): 351-355.
[39] Viratjandr, C.., and Michalowski, R. L. Limit analysis of submerged slopes subjected to water drawdown. Can. Geotech. J., 2006, 43: 802-814. (b) (a)
[40] Cundall P.A. and Strack O.D.L. The distinct numerical model for granular assemblies. Géotechnique, 1979, 29: 47–65.
[41] Thorn ton C. Numerical simulation of deviatoric shear deformation of granular media. Geotechnique, 2000, 50(1): 43–53.
[42] Anandarajah A. On influence of fabric anisotropy on the stress-strain behaviour of clays.Computers and Geotechnics, 2000, 27: 1–17.
[43] Bardet J. P. and Proubet J. A numerical investigation of the structure of persistent shear bands in granular media. Géeotechnique, 1991, 41: 599–613.
[44] Iwashita K.and Oda M.. Rolling resistance at contacts in simulation of shear band development by DEM. Journal of Engineering Mechanics, ASCE, 1998.
[45] Kiyama H., Nishimura T.and Fujimura H..Adv anced distinct element model coupling with pore water. Dob oku Gakkai Rombun-Hokokushu/Proceedings of the Japan Society of Civil Engineers, 1994, 499 (III-28), pp.31–39.
[46] Ng T. T.and Dobry R., A nonlinear numerical model for soil mechanics. Journal of Geotechnical Engineering, ASCE, 1994, 120(2): 388–403.
[47] O. C. Zienkiewicz, C. Humpheson & R. W. Lewis, Associated and non-associated visco-plasticity and plasticity in soil mechanics, Géotechnique 25, No 4, 1975, pp. 671-689.
[48] A. Preh, Modellierung des verhaltens von massenbewegungen bei großen verschiebungen mit hilfe des Particle Flow Codes (PFC), Thèse de doctorat, Université de technologie, Vienne, 2004.
[49] R. Hamza-Cherif. Étude des mouvements de pentes par le code de calcul PFC2D, mémoire de Magister, Tlemcen, Algérie, 2009.