Abstract
The solution of a slope stability problem can be approached by its least upper-bound and maximum lower-bound with high accuracy. The limit equilibrium methods that employ vertical slices imply a lower bound of the factor of safety. It has been successfully extended to the area of active earth pressure analysis that accounts for different input of locations of earth pressure applications. Those methods that employ slices with inclined interfaces give an upper-bound approach to the stability analysis. It enjoys a sound mechanical background and is able to provide accurate solutions of soil plasticity. It has been successfully extended to the area of bearing capacity analysis in which various empirical coefficients are no longer necessary. The 3D upper-and lower-bound methods under this framework have been made possible and show great potential for solving various engineering problems.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bishop, A.W., 1955. The use of the slip circle in the stability analysis of slopes. Geotechnique, 5(1):7–17.
Chen, W.F., 1975. Limit Analysis and Soil Plasticity. Elsevier.
Chen, Z., 1992. Random trials used in determining global minimum factors of safety of slopes. Canadian Geotechnical Journal, 29(2):225–233.
Chen, Z., Morgenstern, N.R., 1983 Extensions to the generalized method of slices for stability analysis. Canadian Geotechnical Journal, 20(1):104–119.
Chen, Z., Shao, C., 1988. Evaluation of minimum factor of safety in slope stability analysis. Canadian Geotechnical Journal, 25(4):735–748.
Chen, Z.Y., Li, S.M., 1998. Evaluation of active earth pressure by the generalized method of slices. Canadian Geotechnical Journal, 35(4):591–599. [doi:10.1139/cgj-35-4-591]
Chen, Z., Wang, X., Haberfield, C., Yin, J., Wang, Y.A., 2001a. Three-dimensional slope stability analysis method using the upper bound theorem, Part I: Theory and methods. International Journal of Rock Mechanics and Mining Sciences, 38(3):369–378. [doi:10.1016/S1365-1609(01)00012-0]
Chen, Z., Wang, J., Yin, J., Wang, J., Haberfield, C.A., 2001b. Three-dimensional slope stability analysis method using the upper bound theorem, Part II: Numerical approaches, applications and extensions. International Journal of Rock Mechanics and Mining Sciences, 38(3):379–397. [doi:10.1016/S1365-1609(01)00013-2]
Chen, Z., Mi, H., Zhang, F., Wang, X., 2003. A simplified method for 3D slope stability analysis. Canadian Geotechnical Journal, 40(3):675–683. [doi:10.1139/t03-002]
Chen, Z.Y., Wang, X.G., Yang, J., Jia, Z., Wang, Y.J., 2005. Rock Slope Stability Analysis: Theory, Method and Computer Programs. China Water Resources Press, Beijing (in Chinese).
Donald, I.B., Giam, P., 1992. The ACADS Slope Stability Programs Review. Proc. 6th International Symposium on Landslides, 3:1665–1670.
Donald, I.B., Chen, Z.Y., 1997. Slope stability analysis by an upper bound plasticity method. Canadian Geotechnical Journal, 34(6):853–862. [doi:10.1139/cgj-34-6-853]
Duncan, J.M., 1996. State of the art: Limit equilibrium and finite element analysis of slopes. ASCE Journal of Geotechnical Engineering, 122(7):577–596. [doi:10.1061/(ASCE)0733-9410(1996)122:7(577)]
Huang, C.C., Tsai, C.C., 2000. New method for 3D and asymmetric slope stability analysis. ASCE Journal of Geotechnical and Environmental Engineering, 126(10):917–927. [doi:10.1061/(ASCE)1090-0241(2000) 126:10(917)]
Hungr, O., Salgado, F.M., Byrne, P.M., 1989. Evaluation of a three dimensional method of slope stability analysis. Canadian Geotechnical Journal, 26(4):679–686.
Janbu, N., 1973. Slope Stability Computations. In: Hirschfield, E., Poulos, S. (Eds.), Embankment Dam Engineering, Casagrande Memorial Volume. John Wiley, New York, p.47–86.
Lam, L., Fredlund, D.G., 1993. A general limit equilibrium model for three-dimensional slope stability analysis. Canadian Geotechnical Journal, 30:905–919.
Morgenstern, N.R., 1992. The Evaluation of Slope Stability—A 25 Year Perspective. Stability and Performance of Slopes and Embankments. ASCE Geotechnical Special Publications, p.1–26.
Morgenstern, N.R., Price, V., 1965. The analysis of the stability of general slip surface. Geotechnique, 15(1):79–93.
Peck, R., 1990. Fifty Years of Lateral Earth Pressure. Proc. of Conf. on Design and Performance of Earth Retaining Structures. Cornel University, Ithaca, New York. ASCE Geotechnical Special Publication, No. 25.
Sarma, K.S., 1979. Stability analysis of embankments and slopes. J. Geotech. Am. Soc. Civ. Engrs., 105(12):1511–1524.
Seed, R.B., Mitchell, J.K., Seed, H.B., 1990. Kettlemen Hills waste landfill slope failure, II: stability analysis. ASCE Journal of Geotechnical Engineering, 116(4):669–690.
Sokolovski, V.V., 1960. Statics of Soil Media (Translated by Jones D.H. and Scholfield A.N.). Butterworth, London.
Spencer, E., 1967. A method of analysis of embankments assuming parallel inter-slice forces. Geotechnique, 17:11–26.
Wang, Y.J., Yin, J.H., Chen, Z.Y., 2001. Calculation of bearing capacity of a strip footing using an upper bound method. International Journal for Numerical and Analytical Methods in Geomechanics, 25(8):841–851. [doi:10.1002/nag.151]
Zhang, X., 1988. Three-dimensional stability analysis of concave slopes in plan view. ASCE Journal of Geotechnical Engineering, 114(6):658–671.
Author information
Authors and Affiliations
Corresponding author
Additional information
The Zeng Guo-Xi Lecture, May 22, 2007; Project (Nos. 50539100, 50679035 and 50509027) supported by the National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Chen, Zy. The limit analysis in soil and rock: a mature discipline of geomechanics. J. Zhejiang Univ. - Sci. A 8, 1712–1724 (2007). https://doi.org/10.1631/jzus.2007.A1712
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.2007.A1712