Determining three-dimensional non-spherical critical slip surface in earth slopes using an optimization method

Determination of the three-dimensional (3-D) critical slip surface with the minimum factor of safety in earth slopes is one of the important and difficult problems of the optimization methods. Counting the spherical slip surface in the stability analysis of 3-D slopes not only is easy, but also provides for a better understanding, although such slip surfaces cannot be adequately compatible with the actual slip surfaces found in nature. This paper is an attempt to obtain the non-spherical critical slip surface that is more consistent with the actual slip surface in nature by using the Three-Dimensional Alternating Variable Local Gradient (TDAVLG) optimization method. TDAVLG is a new approach in optimization process and it is based on the univariate method. The factor of safety is calculated using the limit equilibrium method. The optimization process can turn the initial slip surface into a non-spherical critical slip surface in all types of slopes with different soil properties. The resulting three-dimensional non-spherical slip surface not only has the minimum factor of safety, but is also the most compatible with respect to the actual slip surface emerging in nature. The non-spherical critical slip surface obtained in the examples proves the efficiency and precision of the suggested method.