Path Search

A Path Search is one of two different Search Methods which can be used in SLIDE for locating the Global Minimum safety factor for NON-CIRCULAR slip surfaces. In order to perform a Path Search, the Surface Options dialog must be configured as follows:

Surface Type = Non-Circular
Search Method = Path Search

How Does the Path Search Work?

The Path Search in SLIDE generates random NON-CIRCULAR (piece-wise linear) slip surfaces as follows:

For each slip surface, a starting point is randomly generated on the slope surface. The allowable range for the starting point, is defined by the Slope Limits, as follows:

if a single set of Slope Limits is defined, then SLIDE will automatically divide the range in half, and use the range closest to the toe of the slope, to generate the slip surface starting points.
if a double set of Slope Limits is defined, then SLIDE will use the range closest to the toe of the slope to generate the slip surface starting points.

NOTE: a double set of Slope Limits is recommended for use with the Path Search in SLIDE, as it allows the user to more accurately define the initiation range for slip surfaces. See the Define Limits topic for information about how to customize the Slope Limits in SLIDE.

These two cases are illustrated below, for a Right to Left Failure Direction.

$image\path1.gif$

Possible range of Path Search Initiation points, for SINGLE set of Slope Limits.

$image\path2.gif$

Possible range of Path Search Initiation points, for DOUBLE set of Slope Limits.

Once a slip surface initiation point has been generated, SLIDE then generates the FIRST segment of the non-circular slip surface, according to the Initial Angle at Toe and the Segment Length specified in the Surface Options dialog for the Path Search. NOTE: See below for details about the Path Search Options.
The remainder of the slip surface is then generated according to the Segment Length, and the Path Search algorithm.
The endpoint of each slip surface must intersect the slope surface within the Slope Limits. The Slope Limits DO NOT influence the location of the endpoint, but are used as a filter, to ensure that the endpoint is within the Slope Limits. If the endpoint is NOT within the Slope Limits, the surface is discarded.
SLIDE will repeat steps 1 to 4, until the number of valid slip surfaces generated is equal to the Number of Surfaces specified in the Path Search Options.

NOTE:

the Path Search algorithm used in SLIDE is modeled after the "Irregular Surface Search" used in the slope stability program XSTABL. A few modifications have been made, but the basic methodology is the same.
Unlike the Grid Search (for Circular Surfaces) or the Block Search (Non-Circular Surfaces), the Path Search DOES NOT REQUIRE ANY SEARCH OBJECTS TO BE DEFINED. The Path Search is entirely defined by the Path Search Options specified in the Surface Options dialog, and the current Slope Limits.

Path Search Options

The following Path Search Options are defined in the Surface Options dialog.

Number of Surfaces

This is the total number of valid surfaces generated by the Path Search. NOTE: invalid surfaces generated by the Path Search are discarded, and are NOT included in this number. Invalid surfaces may occur if the slip surface endpoint does not intersect the slope within the Slope Limits, as described above, or other factors may be involved (e.g. incorrect Initial Angle at Toe).

Initial Angle at Toe

The Initial Angle at Toe is the orientation of the FIRST line segment of a slip surface generated by the Path Search.

Note: SLIDE ALWAYS generates slip surfaces for the Path Search, starting at the toe of the slope, and progressing towards the crest, regardless of the Failure Direction (Right to Left or Left to Right).

$image\path3.gif$

By default, SLIDE randomly generates the Initial Angle at Toe, for each slip surface, within the following angular limits:

Upper Angle – the default upper angular limit depends on the angle of the slope segment at the initiation point of the slip surface, and is equal to ( b – 5 ) degrees, where b is the angle of the slope segment.

Lower Angle – the default lower angular limit is 45 degrees below the horizontal.

$image\path4.gif$

Upper and lower angular limits for first segment of slip surface

User defined angular limits can be specified by selecting the Upper Angle or Lower Angle checkboxes, and entering the desired angular limits. NOTE that the angle measurement convention is the usual convention used in SLIDE, where a positive angle is measured in degrees COUNTER-CLOCKWISE from the positive horizontal axis.

NOTE: because of the angular measurement convention, the values of user defined angular limits will depend on the Failure Direction. For example: an Upper Angular Limit of 30 degrees for a Right to Left Failure Direction, is equivalent to an Upper Angular Limit of 150 degrees for a Left to Right Failure Direction. This is illustrated in the figure below.

$image\path5b.gif$

Example of equivalent angular limits for left and right facing slopes.

Segment Length

This is the length used by SLIDE for each segment of a non-circular surface generated by a Path Search. NOTE:

SLIDE automatically calculates a suitable default Segment Length, based on the extents of the model boundaries. It is NOT necessary for the user to specify a Segment Length, unless they wish to use a specific number.
A user-defined Segment Length can be specified, by selecting the Segment Length checkbox and entering a Segment Length in the edit box.

If the Segment Length is too small, invalid surfaces may result, if the surface becomes "too irregular" (i.e. kinematically inadmissible), or if the total number of segments generated for a surface exceeds the Number of Slices entered in the Project Settings dialog.
A recommended Segment Length which should generate valid slip surfaces in the majority of cases, is approximately 0.3H, where H is the maximum height of the slope.

Convex Surfaces Only

See the Block Search topic for a description of the Convex Surfaces Only option, as the effect on both the Block Search and the Path Search is the same.

Optimize Surfaces

A supplementary optimization can be applied to slip surfaces, after the initial analysis, in order to locate slip surfaces with an even lower factor of safety. See the Optimize Surfaces topic for details.

Minimum Elevation

The Minimum Elevation is the minimum allowable Y-coordinate for any slip surface generated by the Path Search. NOTE:

By default, SLIDE uses the lower limits of the External Boundary, as a limiting boundary which a slip surface cannot cross. It is NOT necessary for the user to specify a Minimum Elevation, unless they want to use a specific Y-coordinate ABOVE the lower limits of the External Boundary.

A user-defined Minimum Elevation can be specified, by selecting the Minimum Elevation checkbox, and entering a Minimum Elevation in the edit box. In this case, any slip surfaces generated by the Path Search, which go below the Minimum Elevation, will be discarded.

Minimum Depth

The Minimum Depth option, can be used to filter out shallow slip surfaces, which may be generated by a Path Search. The Minimum Depth option works as follows:

When a slip surface is generated, the slices are generated for the surface, and the MAXIMUM slice height is determined. The slice height is measured VERTICALLY, from the slip surface, to the ground surface.
If the Minimum Depth option is enabled, then the MAXIMUM slice height, for a slip surface, must be GREATER than the Minimum Depth value. If not, then the slip circle will not be analyzed.

If you do not wish to analyze shallow slip surfaces which may be generated by a Path Search, then use the Minimum Depth option to filter out these surfaces from the analysis.

Random Number Generation

The generation of slip surfaces by the Path Search is based on the generation of random numbers. For the Path Search, random numbers are used to generate:

the slip surface initiation points
the angle of the first slip surface segment
the angle of all subsequent slip surface segments

The method of generating random numbers is determined by the Random Numbers option in the Project Settings dialog. There are two methods available, Random or Pseudo-Random. Pseudo Random generation uses a constant seed value to generate random numbers. For a given model, this will generate exactly the same slip surfaces each time the analysis is run, and therefore the results will be reproducible. Random generation uses a variable seed value. This will generate DIFFERENT surfaces each time the analysis is run, and therefore results will be different each time Compute is selected. For details about the Random and Pseudo Random options, see the Random Numbers topic.