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Optimization of Polygonal Slip Surface

The slip surface optimization proceeds such that the program changes subsequently locations of individual points of this surface and checks, which change of location of a given point results in the maximal reduction of the factor of slope stability SF. The end points of the optimized slip surface are moved on the ground surface, internal points are moved in the vertical and horizontal directions. The step size is initially selected as one tenth of the smallest distance of neighboring points along the slip surface. With every new run the step size is reduced by one half. Location of points of slip surface is optimized subsequently from the left to the right and it is completed when there was no point moved in the last run.

When optimizing the polygonal slip surface the iteration process may suffer from falling into the local minimum (with respect to gradual evolution of locations of nodal points) so not always the process is terminated by locating the critical slip surface. Especially in case of complex slope profile it is therefore advantageous to introduce several locations of the initial slip surface. Combination with the approach used for circular slip surfaces is also recommended. Therefore, the critical slip surface assuming circular shape is found first and the result is then used to define the initial polygonal slip surface. 

The optimization process can be restricted by various constraints. This becomes advantageous especially if we wish the searched slip to pass through a certain region or to bypass this region. The restriction on the optimization process can be performed in two different ways:

  1. Optimization restrictions are specified as a set of segments in a soil body. The optimized slip surface is then forced to bypass these segments during optimization.
  2. Another way of restricting the optimization process is to fix location of selected points along the optimized slip surface or allow for moving these points only in one of two directions, either vertically or horizontally.