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October 2005 |
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In this issue:
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Display of Most Critical Slip Surfaces
In the early days of limit equilibrium stability analyses, the only
way to graphically portray a summary of all the computed safety factors was to
contour the factors of safety on a grid of rotation centers as illustrated in
Figure 1.
With today's sophisticated software, there are now other more convenient and meaningful
ways to display a summary of the trial slip surfaces which can help with interpreting
slope stability results.
The historic approach of developing contours of safety factors does provide a visual picture of the extent of the trial slip surfaces analyzed, but more importantly, the contours can also be used to determine if the most critical slip surface has been found. The ideal solution occurs when the minimum factor of safety falls inside a closed contour like the 1.23 contour.
The technique of contouring safety factors on the grid of rotation centers has become deeply entrenched in slope stability analyses. This approach became popular partly because of early developments within the method of limit equilibrium itself and presentations that were given of resulting solutions. In addition, most related textbooks present this approach as an inherent requirement of slope stability analysis.
Figure 1 – Display of Factor
of Safety Contours on Grid Centers
However, with today's sophisticated software tools, there are other more convenient and meaningful ways to display and analyze the trial slip surfaces developed from a limit equilibrium analysis.
One way is to show some or all of the trial slip surfaces, including the most critical, simultaneously on the ground profile as illustrated in Figure 2. In this particular figure, we have presented the 20 most critical slip surfaces with the lowest factors of safety from the 228 slip surfaces available. The most critical slip surface with its resulting mass is also presented, and you can see that the location of this slip surface falls within the boundaries defined by other displayed surfaces, graphically depicting that the minimum has been located. Selecting all trial slip surfaces to view usually tends to blur the picture too much, but it can be used to reveal the extent of the trial slip surfaces if this is something you would be interested in assessing.
Figure 2 – Display of
Multiple Trial Slip Surfaces
Another way to summarize and view slip surfaces is to have the software draw a colored zone which depicts a particular range of safety factors. The factor of safety band may show, for example, a range between 1.20 to 1.25 where 1.20 is the lowest factor of safety value. The critical slip surface (the white line as shown in Figure 3) should fall within the factor of safety band, indicating the minimum is within this band.
Figure 3 – Display of
Safety Map (Potential failure zone)
The factor of safety band visually conveys the concept that there is a failure zone as opposed to one distinct slip surface. It can be argued that it depicts a more realistic picture of how well the input parameters can actually be defined. It is also a pictorial way of rounding-off the computed factor of safety, removing the tendency to view factors of safety to the 3rd decimal. Furthermore, there likely really is a failure zone in reality, not just one distinct perfectly paper-thin slip surface.
A disadvantage of the historic approach of contouring grid of rotation centers is that it is difficult to know where to specify the grid at the start of the analysis, such that the critical slip surface will fall nicely within the grid. It is not always possible to achieve the objective of having the minimum fall within the grid center. Sometimes, such as the case of purely frictional (c = 0) or purely cohesive (phi = 0), the minimum will always tend to fall on the edge of the grid. Using one of the alternative display methods outlined in this article overcomes the frustration of trying to specify a grid which simply cannot meet the traditional objective of needing the minimum to exist in the middle of the grid.
We have found that showing multiple slip surfaces simultaneously or developing a factor of safety zone is much more meaningful than the traditional way of developing factor of safety contours. We believe you will agree with us once you start using these new features in the latest version of SLOPE/W.
Calgary Geotechnical Modeling Workshop Wrap-Up
On September 28 - 30th, 2005, fifty-one numerical modelers traveled to
Calgary, Canada from five different
countries, including South Africa, Australia, Kazakhstan, the USA and Canada to participate
in the 5th Annual Geotechnical Numerical Modeling workshop. The
three day workshop encompassed a combination of hands-on numerical modeling sessions,
group discussions and classroom-style presentations.
Special modeling lectures were also given by
Dr. S. Lee Barbour from the University of Saskatchewan and
Dr. James Blatz from the University of Manitoba and Blatz Engineering.
We would like to thank all those who participated in this year's workshop. If you are interested in attending a future workshop in Calgary, please visit our Calgary workshop page for further details, or to have your name added to a workshop email notification list.
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