Optimization of circular slip surface

The goal of the optimization process is to locate a slip surface with the smallest factor of slope stability FS. The circular slip surface is specified in terms of 3 points: two points on the ground surface and one inside the soil body. Each point on the surface has one degree of freedom while the internal point has two degrees of freedom. The slip surface is defined in terms of four independent parameters. Searching for such a set of parameters that yields the most critical results requires sensitivity analysis resulting in a matrix of changes of parameters that allows for fast and reliable optimization procedure. The slip surface that gives the smallest factor of slope stability is taken as the critical one. Parameters of individual slip surfaces and results from optimization runs can be displayed in output document.

This approach usually succeeds in finding the critical slip surface without encountering the problem of falling into a local minimum during iteration. It therefore appears as a suitable starting point when optimizing general slip surfaces such as the polygonal slip surface.  

The optimization process can be restricted by various constraints. This becomes advantageous especially if we wish the searched slip surface to pass through a certain region or to bypass this region. 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.