Abstract: How to generate a slip surface is one of the key issues in slope stability analysis, and to construct a slip surface with a complex shape is quite challenging. The curve based on the integral of a Logistic function or other basis functions can take the place of the traditional slip surface generated using non-circular curves, which not only improves the smoothness of the slip surface but reduces its degree of freedom. Slip surface generating methods based on basis functions are sorted out in this paper. They are divided into the superposition method of continuous functions and the integral operation method. The characteristics of the Logistic function and its integral are examined carefully, and the influence of different parameters on the curve shape is obtained to narrow parameter ranges. This provides a basis to reduce the degree of freedom of slip surfaces. And a method is presented to determine the initial parameter values of a given slip surface. The calculations of two slope examples show our method is tolerably good in slope stability analysis.

Key words: slope, slip surface, safety factor, Logistic curve, degree of freedom