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Surface Definition and Search Methods: Grid Search
In Slide, a user can define a grid (or multiple grids) of
centers for use in searching for the circular or composite failure
surface with the minimum factor of safety. The user can either define
the grid manually or have Slide automatically define the
grid. For each grid point a specified number of circular surfaces
are generated based on a minimum and maximum radius. The minimum and
maximum radius is determined from the model geometry. The analysis
then computes the factors of safety associated with all the surfaces
in the grid. In the Slide Interpreter, the grid is contoured
based on the surface with minimum factor of safety at each grid point.
Search parameters can be changed in the Surface Options dialog.
The surface options dialog for a Grid Search
The Surface Options dialog for a grid search lets the user define
the number of surfaces between the minimum and maximum radius (radius
increment). Whether the search also tries to locate composite surfaces
is also an option. In the case of reverse curvature circular surfaces,
the program has an option for extending the surface up to the ground
surface and automatically creating a tension crack.
A surface filter allows the user to put a limit on the elevation of the search, resulting in the search only looking for failure surfaces above a user-defined elevation. A minimum depth option also exists. Surfaces with a depth less than this value are filtered out of the analysis. This allows the user to ignore shallow failure surfaces.
Output from a grid search, the surface with the least factor of safety is displayed
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Surface Definition and Search Methods: Slope Search
A Slope Search is one of the Search Methods available in Slide
for locating the Global Minimum safety factor for CIRCULAR slip surfaces.
The Slope Search method in Slide allows the user to define
the search by defining areas of the slope which will be used to generate
slip circles. This is done by using the Slope Limits option.
1. The Slope Limits are used to randomly generate TWO points on the slope, which define the starting and ending points of the slip surface on the slope.
2. In order to define a slip circle, THREE points are needed. The third point, for each slip circle, is generated using the Initial Angle at Toe. If a focus object exists then the third point is generated using the focus object.
The surface options dialog for a Slope Search
The surface options dialog for a slope search lets the user define
the total number of surfaces to generate. The range of initial toe
angles can also be defined. The angle used is randomly selected
between these two limits. Whether the search also tries to locate
composite surfaces is also an option. In the case of reverse curvature
circular surfaces, the program has an option for extending the surface
up to the ground surface and automatically creating a tension crack.
A surface filter allows the user to put a limit on the elevation
of the search, resulting in the search only looking for failure
surfaces above a user-defined elevation. A minimum depth option
also exists. Surfaces with a depth less than this value are filtered
out of the analysis. This allows the user to ignore shallow failure
surfaces.
Output from a slope search, the surface with the least
factor of safety is displayed. All the surfaces generated are plotted
in a color representing their factor of safety.
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Surface Definition and Search Methods: Auto Refine Search
The Auto Refine Search is one of the Search Methods available in Slide
for locating the Global Minimum safety factor for CIRCULAR slip surfaces.
The Auto Refine Search method is different from other search methods
in Slide because the search for the lowest safety factor
is refined as the search progresses. An iterative approach is used
so that the results of one iteration are used to narrow the search
area on the slope, in the next iteration. The Auto Refine Search method
is a simple but effective algorithm for locating the Global Minimum
circular slip surface. In many cases, for an equal number of surfaces
generated, the Auto Refine method will locate lower safety factor
surfaces than a Grid Search or a Slope Search.
The Auto Refine Search method works as follows:
1. First, the slope surface, as defined by the Slope Limits, is
divided into a number of divisions.
2. Circles are then generated between each pair of divisions.
3. The safety factors are then calculated for these circles and
the lowest safety factor associated with each division along the
slope is recorded.
4. This constitutes one iteration of the Auto Refine Search method.
5. The divisions with the lowest recorded factors of safety are
then subdivided
and the process is repeated.
The surface options dialog for the Auto Refine search
A surface filter allows the user to put a limit on the elevation of the search, resulting in the search only looking for failure surfaces above a user-defined elevation. A minimum depth option also exists. Surfaces with a depth less than this value are filtered out of the analysis. This allows the user to ignore shallow failure surfaces.
Output from an auto refine search, the surface with the least factor of safety is displayed. The multi-colored dots are the centers of rotation for the generated surfaces. All the surfaces generated are plotted in a color representing their factor of safety.
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Surface Definition and Search Methods: Block Search
A Block 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. A Block Search requires one or more
Block Search objects to be defined by the user. A Block Search object
can be a window (arbitrary quadrilateral), a line (defined by two
points), a single point, or a special polyline object which allows
you to easily and automatically generate a search along a linear or
arbitrary weak layer.
The Block Search method works as follows:
1. For EACH Block Search object, a point is randomly generated (ie.
within a window object or along a line object. If a polyline object
is used, then two points are generated on the polyline. If a point
search object is used, then the exact point is used).
2. The points generated by the search objects are then joined by
straight line segments (if a polyline object is used, the surface
will follow the polyline between the two points generated on the
polyline).
3. The Left and Right Projection Angles (entered in the Surface
Options dialog, see below) are then used to project the slip surface
up to the ground surface from the leftmost and rightmost points
generated by the Block Search objects.
4. Steps 1 to 3 are repeated, for the Number of Surfaces specified
in the Surface Options dialog.
The surface options dialog for a Block Search
Output from a block search, the surface with the least
factor of safety is displayed. The block search objects (windows)
are the red rectangular objects.
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Surface Definition and Search Methods: 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. 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. The algorithm is a brute-force
method which basically uses some simple restraints to randomly create
large numbers of slip surfaces in the slope.
The Path Search method works as follows:
1. For each slip surface, a starting point is randomly generated
on the slope surface.
2. 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. The default Segment
Length is a function of the slope height.
3. Further segments of the slip surface are then generated according
to a Segment Length and randomly generated angles.
4. The endpoint of each slip surface must intersect the slope surface
within the Slope Limits.
5. 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 Surface Options dialog.
The surface options dialog for a Path Search
Output from a Path Search, the surface with the least
factor of safety is displayed.
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Surface Definition and Search Methods: Slope Limits
Slope limits (green triangular markers in the following figures) allow
the user to define where the slip surfaces can be generated. Both
the entry and exit points of the slip surface must lie between the
slope limits.
With Slide, you can define two sets of slope limits, if desired.
The entry point of the slip surface must lie within one set of limits
while the exit point must lie within the other set.
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Surface Definition and Search Methods: Search Focus
Search focus objects are used to help the user define where circular
slip surfaces should be generated. A focus object can be a point,
line, window or tangent line. The slip surfaces are generated in such
a way as to always intersect or pass through the focus object.
A window focus (dark red square), all surfaces pass through the window
A line focus (dark red line), all surfaces intersect the line
A point focus (dark red point at toe of slope), all surfaces pass through this point
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Surface Definition and Search Methods:
Non-circular surface optimization
During the computation, Slide can now automatically optimize
the location of vertices on a non-circular surface in order to automatically
search for the surface with the lowest factor of safety. Using the
feature is as simple as checking the "Optimize Surfaces" checkbox
and computing your model. The location of the surface is adjusted
during computation, in an effort to find a more critical surface.
The algorithm is based on the method proposed by Greco (1996) and
uses simple Monte-Carlo techniques to locate the slip surface with
the lowest factor of safety.
The new surface optimization lets you spend less time searching
for a critical surface, so your search takes less effort and you
will be more likely to find the minimum surface in your model. In
addition to saving time, you will also have more confidence that
you have found the minimum surface, thus giving you more confidence
that you have come up with a suitable design for your slope.
The Optimize Surfaces option can be used in conjunction with either
the Block Search or the Path Search. In this case, the Optimization
will start with the Global Minimum slip surface determined by the
Block Search or Path Search. However, the Optimize Surfaces option
can be considered as a search method in its own right. For example,
Optimize Surfaces can start with a single user-defined non-circular
slip surface, and begin the optimization search using this surface.
The Surface Options dialog - Optimize Surfaces option
selected for Path Search
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Reference
Greco, Venanzio R. (1996), Efficient Monte Carlo Technique for Locating Critical
Slip surface, Journal of Geotechnical Engineering, July, No.517.
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