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December 2006 |
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In this issue:
Soil Strength in SLOPE/W |
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Effect of Soil Strength on the Position of the Critical Slip Surface
One of the most misunderstood and perplexing issues
in slope stability analysis is the fact that the position of the critical slip surface is dependent on
the soil strength parameters. Once you have an understanding of how the shape
of the slip surface and the strength properties you have defined are connected,
you will then have an easier time interpreting your
SLOPE/W results, and less concern when faced with extreme cases.
Purely frictional case
When the cohesion of a soil is specified as zero, the minimum factor of
safety will always tend towards the infinite slope case where the factor of safety
is,
where
φ = the soil friction angle
α = the inclination of the slope.
Figure 1 shows a typical infinite slope situation. The critical slip surface is almost parallel to, and immediately next to the slope face. The slope inclination is 26.57 degrees and the friction angle is 30 degrees. The computed factor of safety is 1.203, which is just over the infinite slope factor of safety of 1.15.
Figure 1: Shallow slip for
purely frictional (c=0) case
The tendency to move towards the infinite slope case means the radius of the circle tends towards infinity. The minimum factor of safety is therefore usually on the edge of the grid of rotation centers, which is shown in Figure 2. The minimum is located on the grid edge, which represents the largest radius. Making the grid larger does not resolve the problem. The minimum occurs when the radius is at infinity, which cannot be geometrically specified. The Grid and Radius method appears to break down under these conditions, and the concept that the minimum factor of safety should be inside the grid is not achievable.
Figure 2 Minimum safety
factor on edge of grid when c is zero
Undrained strength case
The opposite situation occurs when the soil strength is defined purely by a constant undrained
strength; that is, φ is zero. For this case, as
shown in Figure 3, the critical slip surface will tend to go as deep as possible. In this
example the depth is limited by the geometry. If the problem geometry were to be extended,
the critical slip surface would progress even deeper.
Figure 3 Deep slip surface for
homogeneous undrained case
Figure 4 shows the resulting factor of safety contour plot on the search grid. Notice that the minimum factor of safety is located on the lower edge of the search grid. Once again, for this homogenous undrained case it is not possible to define a minimum center inside the search grid.
Figure 4 Minimum safety
factor on edge of grid when
φ is zero
Cause of unrealistic response
The reason for the unrealistic behavior in both the purely frictional case and the
homogeneous undrained case is that the specified strengths are unrealistic.
The purely frictional case is an academic exercise. Seldom, if ever, is the cohesion completely zero near the ground surface in reality. Almost always there is a desiccated layer near the surface that has a higher strength, or there is a root-zone near the surface, which manifests itself as an apparent cohesion. If the apparent cohesion component is considered, the soil strength increases, and the critical slip surface will be at some depth within the slope.
Shear strength can also be increased by considering the presence of negative pore-water pressures, which are discussed in the SLOPE/W Engineering Methodology book. The additional shear strength can be included in a SLOPE/W analysis by defining φb. If we make φb equal to 20 degrees, C equal to zero and φ equal to 30 degrees, then the position of the critical slip surface is as in Figure 5. Intuitively this seems more realistic and is likely more consistent with field observations. Moreover, the minimum factor of safety will now be located inside the grid.
Figure 5 Critical slip surface when
soil suction is considered
The problem with the undrained case is the assumption that undrained strength is the same everywhere. Once again, this is seldom, if ever, the case in the field. Usually there is an increase in strength with depth even for very soft soils. If the undrained strength is modeled more realistically with some increase with depth, the critical slip surface position no longer tends to go as deep as possible within the defined geometry. SLOPE/W has several soil models that can accommodate strength increase with depth.
Most realistic slip surface position
Someone once said that the main issue in a stability analysis is shear strength.
Actually, the main issue is more likely the pore-water pressure. It is relatively
easy to define effective strength parameters with considerable accuracy for most soils and rocks,
however it is not always as easy to define the pore-water pressures, particularly the correct
negative pore-water pressures. The difficulty with quantifying negative pore-water pressures
is that they can vary with both environmental conditions and time.
Shallow slip surfaces in purely frictional material do happen if the cohesion indeed goes to zero temporarily. This is why shallow slips often occur during periods of heavy rain. The precipitation causes the negative pore-water pressures near the surface to reduce and in turn the cohesion goes to zero. When this happens, the shallow slip surface predicted by SLOPE/W for the infinite slope case would be both realistic and appropriate for that moment in time.
Merry Christmas!
As we once again draw near to the end of another year, we at GEO-SLOPE
would like to take the time to thank you for your feedback and your continued interest
in our software. We would also like to take this opportunity to wish you a Merry
Christmas and a Happy New Year!
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