Environmental Engineering Reference
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2. Does the location of the critical slip surface change
location when negative pore-water pressures are taken
into account?
3. What is the percent change in calculated factor of
safety with and without consideration of the pore-water
pressures above the groundwater table?
4. What effect does the geometry (i.e., the steepness of the
slope) have on whether negative pore-water pressures
are taken into consideration?
5. Under what conditions can negative pore-water pres-
sures be considered to be semipermanent?
6. Under what conditions should negative pore-water
pressures be considered to be transient?
7. Does the trigger for instability of the slope lie in the
loss of matric suction? If so, under what rainfall con-
ditions over what period of time might the slope fail?
50
1.278
40
x
= 46.2 m
y
= 40.6 m
Radius = 32.0 m
30
Solution for
φ
b
= 0
°
g
= 18.5 kN/m
3
c
' = 20.0 kN/m
3
φ
-50 kPa
0 kPa
+50 kPa
+100 kPa
20
' = 24
°
10
0
10
20
30
40
50
60
70
Distance, m
Figure 12.109
Location of critical slip surface for relatively flat
slope when negative pore-water pressures are not taken into con-
sideration.
4.0
The effects of negative pore-water pressures should be
given consideration whether or not matric suctions are relied
upon in the slope stability analysis.
Slope stability modellers are quite familiar with the situa-
tion where the method-of-slices analysis yields a critical slip
surface that just touches the ground surface. The modeler
must decide whether or not to reject this analysis because it
seems unreasonable. The primary reason why the extremely
shallow slip surface has been selected is because the neg-
ative pore-water pressures were ignored. The influence of
negative pore-water pressures on shallow slip surfaces is
illustrated in the following example problems.
3.5
3.0
Morgenstern-Price method
f
b
= 0
°
2.5
2.0
1.5
1.0
10
15
20
25
30
35
40
45
Radius, m
12.7.4.1 Example 1 (Relatively Flat Slope with No
Suctions Considered)
Figure 12.109 shows a 20-m-high slope at an angle of 30
◦
.
The geometry consists of one soil type and has a water
table passing below the toe of the slope. The soil has a unit
weight of 18.5 kN/m
3
, an effective cohesion of 20 kPa, and
an effective angle of internal friction of 24
◦
. The slope is
first analyzed under the assumption that all negative pore-
water pressures are ignored (i.e.,
φ
b
Figure 12.110
Factor of safety for all grid centers for relatively
flat slope when negative pore-water pressures are ignored.
50
1.319
x
= 44.5 m
y
= 43.0 m
40
Radius = 34.5 m
b
= 15
30
Solution for
f
°
g
= 18.5 kN/m
3
c
' = 20.0 kN/m
3
φ
-50 kPa
0 kPa
+50 kPa
+100 kPa
0
.
0). All slopes were
analyzed using the Bishop simplified method of slices.
The grid of slip surface centers analyzed is shown in
Fig. 12.109. Figure 12.110 shows the computed factors of
safety versus the radius from the center of rotation to the
slip surface. The results show the minimum factor of safety
to be about 1.28. The results show that while the shortest
radii show an increased factor of safety the increase is rel-
atively small. The critical slip surface falls well below the
ground surface and even goes below the groundwater table.
=
20
' = 24
°
10
0
10
20
30
40
50
60
70
Distance, m
Figure 12.111
Location of critical slip surface for relatively
flat slope when negative pore-water pressures are taken into
consideration.
12.7.4.2 Example 2 (Relatively Flat Slope with Suctions
Considered)
The example problem described above (Fig. 12.109) was
reanalyzed with matric suction taken into consideration. The
φ
b
angle was assumed to be 15
◦
. Figure 12.111 shows the
location of the critical slip surface. The computed critical
factor of safety increased to 1.32, an increase of only 2.9%.
The location of the critical slip surface is now 1.5m lower
than in the example 1 analysis. In other words, negative
pore-water pressures tend to cause the critical slip surface
to move downward.
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