Using Non-Linear Programming Techniques in Determination of the Most Probable Slip Surface in 3D Slopes
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Using Non-Linear Programming Techniques in Determination of the Most Probable Slip Surface in 3D Slopes

Authors: M. M. Toufigh, A. R. Ahangarasr, A. Ouria

Abstract:

Among many different methods that are used for optimizing different engineering problems mathematical (numerical) optimization techniques are very important because they can easily be used and are consistent with most of engineering problems. Many studies and researches are done on stability analysis of three dimensional (3D) slopes and the relating probable slip surfaces and determination of factors of safety, but in most of them force equilibrium equations, as in simplified 2D methods, are considered only in two directions. In other words for decreasing mathematical calculations and also for simplifying purposes the force equilibrium equation in 3rd direction is omitted. This point is considered in just a few numbers of previous studies and most of them have only given a factor of safety and they haven-t made enough effort to find the most probable slip surface. In this study shapes of the slip surfaces are modeled, and safety factors are calculated considering the force equilibrium equations in all three directions, and also the moment equilibrium equation is satisfied in the slip direction, and using nonlinear programming techniques the shape of the most probable slip surface is determined. The model which is used in this study is a 3D model that is composed of three upper surfaces which can cover all defined and probable slip surfaces. In this research the meshing process is done in a way that all elements are prismatic with quadrilateral cross sections, and the safety factor is defined on this quadrilateral surface in the base of the element which is a part of the whole slip surface. The method that is used in this study to find the most probable slip surface is the non-linear programming method in which the objective function that must get optimized is the factor of safety that is a function of the soil properties and the coordinates of the nodes on the probable slip surface. The main reason for using non-linear programming method in this research is its quick convergence to the desired responses. The final results show a good compatibility with the previously used classical and 2D methods and also show a reasonable convergence speed.

Keywords: Non-linear programming, numerical optimization, slope stability, 3D analysis.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1078162

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[1] Garret. N. Vanderplaats, Numerical Optimization Techniques for Engineering Design, New York: McGraw-Hill, 1984.
[2] M. Avriel, Nonlinear Programming: analysis and methods, Prentice Hall, Englewood cliffs, New Jersey, 1976.
[3] W. Hockand, K. Schittkowski, "The examples for nonlinear programming codes," Journal of Optimization Theory and Applications, vol. 30, 1980, pp. 127-129.
[4] J. C. Geromel, L. F. B. Baptistella, "Feasible direction method for large scale non-convex programs: decomposition approach," Journal of Optimization Theory and Applications, vol. 35, 1981, pp. 231-249.
[5] A. Ralston, A First Course in Numerical Analysis, New York: McGraw- Hill, 1965.
[6] J. Kowalik, M. R. Asborne, Methods for Unconstrained Optimization Problems, New York: American Elsevier, 1968.
[7] S. M. M. Shahidipour, Optimization-Theory and Applications, Mashhad: Ferdowsi University Press, 1994.
[8] M. J. Box, "A new method of constrained optimization and a comparison with other methods," Computer journal, vol. 8, No. 1, 1965, pp. 42-52.
[9] Z. Chen, H. Mi, F. Zhang, X. Wang, "A Simplified Method for 3D Slope Stability Analysis," Canadian Geotechnical journal, vol. 40, 2003, pp. 675-683.
[10] L. W. Abramson, T. S. Lee, S. Sharma, G. M. Boyce, "Slope Stability and Stabilization Methods," in Plastics, 2nd ed., John Willey & Sons, 2001.
[11] U.S. Army, Corps of Engineers, Slope Stability, Engineering Manual 1110-2-1902, 2003.
[12] M. M. Toufigh, S. Raees-Nia, "Determination of Critical Failure Surface in Embankments Based on Modified Displacement Vector," in Proc. 7th Australian New Zealand Conf. Geo Mechanics, Adelaide, 1996.
[13] Z. Chen, "Keynote lecture: The limit Analysis for Slopes: Theory, methods, and applications," in Proc. of the International Symposium on Slope Stability Analysis, Mastuyama, 1999, pp. 31-48.
[14] D.G. Fredlund, J. Krahn, "Comparison of Slope Stability Analysis" Canadian Geotechnical journal, vol. 14, 1977, pp. 429-439.
[15] X. Zhang, "Three-Dimensional Stability Analysis of Concave Slopes in Plan View," Journal of Geotechnical Engineering ASCE, vol. 114, 1988, pp. 658-671.
[16] O. Hunger, F. M. Salgado, P. M. Byrne, "Evaluation of a Three- Dimensional Method of Slope Stability Analysis," Canadian Geotechnical journal, vol. 26, 1989, pp. 679-686.