Environmental Engineering Reference
In-Depth Information
50
b = 5
= 18 kN/m 3 ; E = 20,000 kPa
Cohesion = 20 kPa;
φ′
= 10
°
;
φ
°
;
γ
45
Method
DP (
X
Y
R
Factor of Safety
= 0.33)
DP ( μ = 0.48)
Enhanced method ( μ = 0.33)
Enhanced method (
μ
1.041
1.187
1.132
1.171
1.168
1.167
40
33.24 30.46 22.28
32.58 32.48 22.28
32.20 31.85 21.46
32.20 31.85 21.46
μ
= 0.48)
Morgenstern-Price
Simplified Bishop
35
30
Morgenstern-Price
Simplified Bishop
Enhanced method ( μ = 0.33)
Enhanced method ( μ = 0.48)
25
20
DP ( μ = 0.33)
15
DP ( μ = 0.48)
10
5
DP - Dynamic programming
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
Distance, m
Figure 12.84 Locations of critical slip surfaces obtained by various methods for slope with
phreatic line.
The dynamic programming results are presented for the
case of two Poisson's ratio values: 0.33 and 0.48. The cal-
culated factors of safety are compared to results from the
method of slices and the enhanced method (Fredlund and
Scoular, 1999; Fredlund et al., 1999). The enhanced method
of slope stability analysis uses the stress states calculated
from a linear elastic analysis along with assumed slip sur-
face shapes. In other words, the enhanced method is similar
to the method of slices, but the normal force at the base of
a slice is determined from a stress analysis.
The unit weight of the soil was 18 kN/m 3 .A φ b value of
5 was selected for all analyses. The location of the critical
slip surface is shown for each analysis. The computed fac-
tors of safety are quite similar for the dynamic programming
solution and the method-of-slices results. The shape of the
dynamic programming critical slip surface deviates slightly
from a circular shape for a homogeneous soil slope.
Figure 12.85 compares the factors of safety computed
using the dynamic programming method and the method
of slices for a range of soil parameters. Poisson's ratio was
0.33. Janbu's stability number was used as the basis for
comparison. In general, the dynamic programming method
appears to give slightly lower computed factors of safety.
When Poisson's ratio was increased to 0.48, the dynamic
programming factors of safety became slightly larger than
when Poisson's ratio was 0.33 (Fig. 12.86). The computed
factors of safety obtained from the dynamic programming
analyses appear to be similar to the results obtained from
the methods of slices for a homogeneous soil slope.
12.6.2.2 Nonhomogeneous Slope
The results of an analysis of a nonhomogeneous slope with
a weak soil layer (i.e., three- soil-layer system) are presented
in Fig. 12.87. The stress states were calculated using a linear
elastic model. The soil properties used for each soil layer
are shown on Fig. 12.87. Also shown is the location of the
critical slip surface determined from each of the analyses.
The computed factors of safety were slightly lower when
using the dynamic programming procedure. The shape and
location of the critical slip surfaces differed considerably
when a weak soil was incorporated into the non homoge-
neous soil cross section. The weak layer was used to force
the shape of the critical slip surface into a composite mode.
The factor of safety computed using the dynamic program-
ming method was about 14% lower than that obtained from
the Morgenstern-Price (1965) method. The critical slip sur-
face has a pronounced nonlinear shape enclosing the soil
mass. This example problem illustrates the advantage of
using the dynamic programming search technique to locate
the critical slip surface.
12.6.2.3 Transient Infiltration Analysis
Gitirana and Fredlund (2003) illustrated the use of the
dynamic programming method to simulate the infiltration
 
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