Environmental Engineering Reference
In-Depth Information
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
Bishop's
Janbu
0.3
0.2
0.1
Morgenstern-Price
0.0
2
3
4
5
6789
2
3
4
5
1.0
Ratio R
Figure 11.2.
Comparison of the factors of safety obtained by four methods of analysis, for the bi-linear
surface shown in
Figure 11.1
.
The factors are normalized with respect to the Spencer's
Method. The abscissa is the ratio of strengths available on the two parts of the rupture
surface (Hungr, 1997).
tan
tan
′
′
B
A
R
(11.2)
The ordinate is a ratio between Factors of Safety determined by the various methods
and that obtained by Spencer's Method, which is used as a reference. All the methods are
shown to converge to the same value when R is low, i.e. when the flat basal plane is
weaker than the back scarp. On the other hand, the methods diverge by as much as 30%
in the case when the back scarp is weak and the sliding body is supported by the toe plane.
Under these conditions there is a significant difference even between Spencer's and
Morgenstern-Price methods.
Janbu's Simplified method produces a Factor of Safety which is consistently less than that
of Bishop's (with the Fredlund and Krahn modification). The Janbu correction factor is
required to compensate for this. All of these trends persist in equal measure for dry conditions
and with pore-pressure.
In practice, cases where R is low are fortunately more frequent than the opposite, as
Plane A often follows a thin weak layer in the stratigraphy, a bedding plane or a near-
horizontal pre-sheared surface. Under such conditions there is not much difference
between the four methods and the user is therefore justified in taking advantage of the
high efficiency of Bishop's Simplified Method in two or three dimensions.
On the other hand, in cases where the strongest element of the sliding surface is at the
toe, rigorous methods such as Morgenstern-Price should be used. Examples of this are
cases where the back scarp (Plane B) follows steeply inclined bedding, a fault surface or
similar and the sliding body is supported by a strong toe.
