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In the slope stability analysis, how to make the slip surface of the structure more precise and smoother has been the focus of research when fitting the slip surface with known numerical points. The study found that the logistic function has both advantages in fitting the slip surface. The related parameters (M, A, and K) are derived by the threshold, symmetry, and precision control of its function. Logistic function constructs the slip surface and compares it with the broken-line slip surface; the numerical results show that the slip points on the two slip surfaces are consistent, indicating that the logistic function fits the curve correctly; the logistic function smooths the original polyline curve, which facilitates solving the direction vector of the curve.