NURBS Surface-Altering Optimization for Identifying Critical Slip Surfaces in 3D Slopes

The evaluation of slope stability of a three-dimensional slope requires identifying the critical slip surface with the minimum factor of safety, which is a complex optimization problem. Failure to identify the critical slip surface can lead to unconservative conclusions about the stability of a slope. This paper proposes a novel 3D surface-altering optimization method, which iteratively alters the geometry of a 3D slip surface to find the critical slip surface representing the minimum factor of safety in a slope. The geometry of the slip surface is defined via nonuniform rational basis spline (NURBS) curves formed over a plan grid of control points. The proposed method includes a series of five subroutines that apply various forms of transformations to the control points. These subroutines include minimization problems, which determine the optimal transformation parameters for minimizing the obtained factor of safety of the resulting slip surfaces. Given that any geometrically defined slip surface can be approximated using an equivalent series of NURBS control points, the proposed method can be used in efforts to further reduce the global factor of safety first obtained via conventional search methods, such as those involving spherical or ellipsoidal slip surfaces. To demonstrate its effectiveness, the proposed method was applied to further optimize the critical ellipsoidal slip surfaces reported in some numerical examples. Comparing the results with those limited to ellipsoidal slip surfaces, the proposed method was consistently able to identify slip surfaces with significantly lower factors of safety. The postaltered slip surfaces also matched closely with finite element shear strength reduction results. As such, the proposed method is effective in searching for critical slip surfaces and can be used as a final step in the critical surface searching routine.