Optimize Surfaces

The Optimize Surfaces option is available in the Surface Options dialog if Surface Type = Non-Circular.

The Optimize Surfaces option is a very powerful search technique, which allows you to search for lower safety factor slip surfaces, using the surfaces generated by a non-circular search or specific user-defined slip surfaces, as a starting point.

To enable the Optimize Surfaces option:

  1. Select the Optimize Surfaces checkbox in the Surface Options dialog.

  2. Various analysis options are available by selecting the Settings button beside the Optimize Surfaces checkbox. See below for details.

There are two optimization techniques available in Slide: Monte Carlo and Surface Altering. Surface Altering is recommended - it faster than Monte Carlo and able to find more critical surfaces.

Optimization Search: Monte Carlo

The Optimize Surfaces option is based on a Monte Carlo technique, often referred to as "random walking". For a detailed description of the algorithm, refer to Greco, 1996.

When used in conjunction with a non-circular search (e.g. Block Search or Path Search) the Optimize Surfaces option can be very effective at locating slip surfaces with lower safety factors.

NOTE: the Optimize Surfaces option is recommended for ALL NON-CIRCULAR SEARCH METHODS in Slide (i.e. Block Search, Path Search, Simulated Annealing, Auto Refine, Cuckoo), as it usually locates a lower safety factor surface, compared to the results without the optimization search.

Although the option is referred to as "optimization" in Slide, it can also be considered an additional Search Method. It does not require that a non-circular search be carried out. It can be used as an independent search method, starting with only a single, user-defined non-circular slip surface, as a starting point for the optimization search.

A simplified description of the algorithm follows:

  1. The factor of safety is calculated for the initial slip surface.

  2. The location of one vertex on the surface is randomly modified.

  3. The factor of safety is calculated for the new surface.

  4. If the factor of safety for the modified surface is lower than the factor of safety for the initial surface, the new surface replaces the original surface, and the location of another vertex is modified. The process is then repeated.

  5. If the factor of safety for the modified surface is higher than the factor of safety for the initial surface (or the change in the factor of safety is lower than some tolerance) the process ends.

This technique is known as "random walking", since a randomly generated number determines the direction that the vertices are moved. There is no complex underlying algorithm that is searching for the surface. The only data that is used to determine whether one surface is preferable to another, is the factor of safety.

As with many other optimization techniques, this method will become "trapped" in a local minimum, and is not guaranteed to find a global minimum for the factor of safety. However, notwithstanding the simplicity of the algorithm, the results typically compare very well with more complex methods of searching for global minimums (e.g. simplex, conjugate-gradient, etc).

The best application of the random walking optimization is to use it to optimize a surface that is already considered to be a good surface (i.e. already close to a local or global minimum, for example, determined by a non-circular search). Try the Optimize Surfaces option with the Non-Circular Surfaces Tutorial (Tutorial 03 on the Slide Tutorials page). Use the Global Minimum as the initial surface, and see how Optimize Surfaces determines the optimum location where the surface exits the weak layer.

A similar optimization algorithm is also described in Husein Malkawi et al. 2001 .

Optimization Search: Surface Altering

The Surface Altering Optimization (SA) option is a local search method which uses the results of the primary search method (e.g. Cuckoo search), converts this to a spline surface, and searches for a spline surface with a lower safety factor.

SA is a powerful tool to yield lower factors of safety by modifying geometry of a given slip surface. SA is a novel approach based on a derivative-free constrained nonlinear optimization*.

Unlike the metaheuristic method, SA is a local optimization method.

*Bound Optimization BY Quadratic Approximations (BOBYQA) developed by Powell in 2009.

Surface Optimization Settings

There are several options and settings associated with the Optimize Surfaces option, which may be customized by the user. They are available by selecting the Settings button beside the Optimize Surfaces checkbox in the Surface Options dialog. This will display the Optimize Surfaces Settings dialog, in which the following options are available.

Surfaces to Optimize

NOTE !!! – regardless of which Surfaces to Optimize option you select, the only result which will be displayed in the Slide Interpret program, is the (new) optimized Global Minimum surface. The program only keeps track of the slip surface with the lowest safety factor, during the optimization. All intermediate slip surfaces generated by the optimization, are NOT stored. In the Slide Interpret program, the original surfaces which existed BEFORE the optimization, will still be displayed – only the Global Minimum will be a new, lower safety factor surface.

Optimization Options

Snap Shallow Surfaces to Slope

In certain cases, the Optimization algorithm may generate a slip surface which "follows" the slope surface, at a very shallow depth beneath the surface. This usually occurs at either end of the slip surface, as illustrated in the following figure.

Very shallow slip surface at toe of slope

image\surf_opt_snap_to_slope1.gif

In the above example, very shallow slices have been created at the toe of the slope. You may not be able to see them without zooming in, however, if you turn on the slice numbers in Display Options, you can see the location of the slices. This is illustrated below.

Slice numbers displayed, indicating the location of shallow slices at toe of slope.

image\surf_opt_snap_to_slope2.gif

A slip surface such as this is clearly not kinematically feasible, and the calculated safety factor may be incorrect (usually too low). If you ever see results similar to this, after using the Optimization option, then you should select the Snap Shallow Surfaces to Slope checkbox and re-run the analysis. This will automatically "remove" very shallow portions at the ends of the slip surface, and the safety factor will be re-calculated for the slip surface.

For this example, if the analysis is re-run using the Snap Shallow Surfaces to Slope option, the resulting slip surface and safety factor are shown below. Notice that the safety factor is noticeably larger after re-running the analysis (1.658 vs. 1.644).

Analysis re-run using the Snap Shallow Surfaces to Slope option

image\surf_opt_snap_to_slope3.gif

Specify Distance

If you are using the Snap Shallow Surfaces to Slope option, then you may also specify the minimum distance allowed between the slip surface and the slope.

Use checks for depth, elevation, concave surfaces

This checkbox refers to the options in the Surface Options dialog. If this checkbox is selected in the Optimize Surfaces dialog, then the optimization search will use the settings for:

as specified in the Surface Options dialog (if applicable) for the search method.