Generating Slip Surfaces Using the Logistic Function Integral.

How to generate slip surfaces efficiently is crucial for the stability analysis of slopes. Traditional approaches for generating slip surfaces rely directly on the geometric features of slopes, which makes it complicated to generate arbitrary slip surfaces. Moreover, the resulting surfaces are usually not smooth in many cases. This study proposes a method for generating an arbitrary slip surface utilizing the superposition of the integral of the logistic function. This technique can transform the traditional geometry problem into a parameter selection one, in which three groups of parameters in the function determine the shape of the slip surface. The higher-order continuity and differentiable property of this function ensure the smoothness of the slip surfaces. The paper investigates the impact of relevant parameters on the slip surface's pattern and provides the upper and lower bounds of the control variables. This method further develops a procedure for producing arbitrary slip surfaces. The factor of safety and the critical slip surface are calculated using the Morgenstern–Price method and the biogeography-based optimization. After constructing the slip surfaces by this method, two cases in Association for Computer Aided Design show that this method is applicable and verify its calculation accuracy by comparing the factor of safety and the critical slip surface. The results indicate that this approach presents a new direction for the slip surface structure, which can be a general method extending from two to three dimensions. [ABSTRACT FROM AUTHOR]