Similar articles

Abstract: The method of nonlinear finite element reliability analysis (FERA) of slope stability using the technique of slip surface stress analysis (SSA) is studied. The limit state function that can consider the direction of slip surface is given, and the formulations of FERA based on incremental tangent stiffness method and modified Aitken accelerating algorithm are developed. The limited step length iteration method (LSLIM) is adopted to calculate the reliability index. The nonlinear FERA code using the SSA technique is developed and the main flow chart is illustrated. Numerical examples are used to demonstrate the efficiency and robustness of this method. It is found that the accelerating convergence algorithm proposed in this study proves to be very efficient for it can reduce the iteration number greatly, and LSLIM is also efficient for it can assure the convergence of the iteration of the reliability index.

[1] Auvinet, G., Gonzalez, J.L., 2000. Three dimensional reliability analyses of earth slopes. Computers and Geotechnics, 26(3-4):247-261.

[2] Bhattacharyya, B., Chakraborty, S., 2002. NE-MCS technique for stochastic structural response sensitivity. Computer Methods in Applied Mechanics and Engineering, 191(49-50):5631-5645.

[3] Bhattacharya, G., Jana, D., Ojha, S., Chakraborty, S., 2003. Direct search for reliability index of earth slopes. Computers and Geotechnics, 30(6):455-462.

[4] Bishop, A.W., 1955. The use of slip circle in the stability analysis of slopes. Géotechnique, 1(1):7-17.

[5] Chen, Z.Y., 2003. Soil Slope Stability Analysis—Theory Method and Programs. China Water Power Press, Beijing, China, p.299-302 (in Chinese).

[6] Chugh, A.K., 2003. On the boundary conditions in slope stability analysis. International Journal for Numerical and Analytical Methods in Geomechanics, 27(11):905-926.

[7] Duncan, J.M., 1996. State of the art: limit equilibrium and finite-element analysis of slope. Journal of Geotechnical and Geoenvironmental Engineering, 122(7):577-596.

[8] Gong, J.X., 2003. Computational Methods for Reliability of Engineering Structures. Dalian University of Technology Press, Dalian, China, p.123-138 (in Chinese).

[9] Griffiths, D.V., Fenton, G.A., 2004. Probabilistic slope stability analysis by finite elements. Journal of Geotechnical and Geoenvironmental Engineering, 130(5):507-518.

[10] Griffiths, D.V., Lane, P.A., 1999. Slope stability analysis by finite element. Géotechnique, 49(3):387-403.

[11] Hasofer, A.M., Lind, N.C., 1974. An exact and invariant first order reliability format. Journal of Engineering Mechanics Division, 100:111-121.

[12] Imai, K., Frangopol, D.M., 2000. Geometrically nonlinear finite element reliability analysis of structural systems. I: theory. Computers and Structures, 77(6):677-691.

[13] Kim, J.Y., Li, S.R., 1997. An improved search strategy for the critical slip surface using finite element stress fields. Computer and Geotechnics, 21(4):295-313.

[14] Koduru, S.D., Haukaas, T., 2006. Uncertain reliability index in finite element reliability analysis. International Journal of Reliability and Safety, 1(1/2):77-101.

[15] Manzari, M.T., Nour, M.A., 2000. Significance of soil dilatancy in slope stability analysis. Journal of Geotechnical and Geoenvironmental Engineering, 126(1):75-80.

[16] Mellah, R., Auvinet, G., Masrouri, F., 2000. Stochastic finite element method applied to non-linear analysis of embankments. Probabilistic Engineering Mechanics, 15(3):251-259.

[17] Rackwitz, R., Fiessler, B., 1978. Structural reliability under combined random load sequences. Computers and Structures, 9(5):489-494.

[18] Swan, C.C., Seo, Y.K., 1999. Limit state analysis of earthen slopes using dual continuum/FEM approaches. International Journal for Numerical and Analytical Methods in Geomechanics, 23(12):1359-1371.

[19] Tan, X.H., 2007. Nonlinear Finite Element Reliability Analysis of Slope Stability. PhD Thesis, Hefei University of Technology, Hefei, China (in Chinese).

[20] Wang, X.C., Shao, M., 1988. Basic Principle of Finite Element Method and Numerical Method (3rd Ed.). Tsinghua University Press, Beijing, China (in Chinese).

[21] Yamazaki, F., Shinozuka, M., 1988. Neumann expansion for stochastic finite element analysis. Journal of Engineering Mechanics, 114(8):1335-1354.

[22] Zheng, H., Liu, D.F., 2005. Properties of elasto-plastic matrix D_ep and a criterion on limiting state of slope stability by FEM. Chinese Journal of Rock Mechanics and Engineering, 24(7):1099-1105 (in Chinese).