Civil Engineering Reference
In-Depth Information
Area of portion removed
=
1 5 3
.
× =
4 5
.
m
2
Weight of portion removed
=
4 5 19
.
× =
85 5
.
kN
3 3 1 5
2
.
+
.
Eccentricity from O
=
3 3
.
+
=
5 7
.
m
Relief of disturbing moment
=
5 7 85 5
.
×
.
=
488
kN m
2007
1579 488
⇒ =
F
=
1 84
.
−
13.2.3 The Swedish method of slices analysis
A more accurate assessment of the factor of safety can be gained using this method (also known as the
Fellenius method). In this method the sliding section is divided into a suitable number of vertical slices,
the stability of one such slice being considered in Fig.
13.11
(the lateral reactions on the two vertical sides
of the wedge, L
1
and L
2
, are assumed to be equal). By analysing the equilibrium of each slice and then
adding up the totals for all slices, we can establish the factor of safety of the slope.
The solution is solved graphically using a scale drawing or, more commonly, analytically using computer
software. Using a graphical approach, at the base of each slice set off its weight to some scale. Draw the
direction of its normal component, N, and by completing the triangle of forces determine its magnitude,
together with the magnitude of the tangential component T. Repeat for all slices.
Total stress analysis
The factor of safety is established by considering the moment equilibrium about the centre of
rotation, O:
Disturbing moment
=
R
Σ
T
Restoring moment
=
c
u
R
θ
Hence
c R
T
u
θ
F
=
∑
Fig. 13.11
The Swedish method of slices.
