Environmental Engineering Reference
In-Depth Information
b
i
Resultant of all forces assumed
to act in this direction
W
i
h
i
N
is found by summing forces
in the direction
T
i
N
i
θ
i
U
i
∆
L
i
(a)
b
i
N
i
x
1
+1
x
i
W
i
E
i
+1
α
i
U
r
E
i
U
r
U
L
d
i
T
i
T
i
N
i
=
U
i
u
i
Dl
i
i
a
i
∆
L
i
(b)
b
i
Resultant of all side forces assumed
to act in the direction
W
i
N
i
found by summing forces in
this direction
FIGURE 9.78
Force systems acting on a slice assumed by
various analytical methods. (a) ordinary method
of slices; (b) complete force system assumed by
Bishop; (c) force system for modified Bishop.
(From Lambe, T.W. and Whitman, R.V.,
Soil
Mechanics,
Wiley, New York, 1969. Reprinted
with permission of John Wiley & Sons, Inc.)
T
i
N
i
U
i
i
(c)
FS
2
. Solutions converge rapidly. Parameters
d
and
L
are illustrated in
Figure 9.79a.
Janbu Equation 9.17 is similar to the modified Bishop,
except for the parameter
f
o
and the denominator, which in the Bishop equation is
and the procedure is repeated until FS
1
.
The Morgenstern and Price method:
This method (Morgenstern and Price, 1965)can be used
to analyze any shape of failure surface and satisfies all equilibrium conditions. It is based
on the Bishop method and requires a computer for solution. There are several theoretically
∑
W
sin
θ
