Civil Engineering Reference
In-Depth Information
where the forces
T
=
τ
l
,
N
=
σ
l
and
U
=
ul
, where
l
is the length of the base FJ.
Summing for all the slices gives
T
(
N
φ
=
−
U
) tan
(20.19)
The interslice forces such as
F
may be decomposed into horizontal and vertical com-
ponents
E
and
X
. In the slip circle method the boundaries between adjacent slices are
not slip surfaces and so nothing can be said at present about the magnitude, direction
or point of application of the force
F
in Fig. 20.10. Considering the forces on the block
FGHJ in Fig. 20.10(b), the magnitudes, direction and points of application are known
for
W
and
U
, the directions and points of application are known for
T
and
N
, but
nothing is known about the force
F
. Thus there are five unknowns:
T
,
N
,
F
,
a
and
.
We can obtain three equations by resolution of forces and by taking moments follow-
ing the usual rules of statics. These, together with Eq. (20.18), lead to a possible total
of four equations and each slice is statically indeterminate. To obtain a solution for the
method of slices for drained loading we are obliged to make at least one simplifying
assumption in order to make the problem statically determinate. There are a number
of such solutions, each based on a different simplifying assumption. For the present
I will consider the two commonest of these solutions.
θ
(a) The Swedish method of slices (Fellenius, 1927)
Here it is assumed that the resultant
F
of the interslice forces is zero for each slice and
thus
F
,
a
and
θ
vanish. Each slice is then statically determinate, and from Fig. 20.11
Figure 20.11
Slip circle method for drained loading - Swedish method.
