Civil Engineering Reference
In-Depth Information
The same result can be obtained using a part analytical approach. We can see from the triangle of forces,
that:
N
=
W cos
α
T
=
T = W sin
α
where
α
is the angle between the normal, N and the vertical.
From the above relationship, we have:
c R
W
θ
u
F
=
∑
sin
α
A tension crack can be allowed for in the analysis.
Effective stress analysis
As time passes after the construction of an embankment or cutting, the slope will no longer be in the
undrained state and any slope stability analysis must be done considering the drained strength parameters
c
′
and tan
φ
′
and the pore pressure, u acting along the slip surface. The approach used in the undrained
analysis can be adapted to cover this case:
Taking moments about the centre of rotation, O:
Disturbing moment
=
R
Σ
T
Restoring moment
=
R(c
′
R
θ
+
Σ
N
′
tan
φ
′
)
Hence
′
+
′
′
=
′
+
′
c R
θ
∑
∑
N
T
tan
φ
c R
θ
∑
(
N u
−
) tan
φ
F
=
∑
T
where u
=
pore pressure at base of slice.
The effect of a tension crack can again be allowed for, and in this case:
′
′
2
c
φ
h
c
=
tan
45
°+
γ
2
Example 13.3:
Swedish method of slices
An embankment made from clay is to be constructed upon the ground surface as shown
in Fig.
13.12.
The completed embankment can be assumed to be homogenous and thus
will possess constant density and shear strength throughout its mass. Determine the
factor of safety in the short-term (undrained state).
Solution:
Draw the slope to scale using CAD software or on graph paper and split the sliding
section up into a suitable number of slices; 4 or 5 is a typical amount.
Calculate the weight of each slice, and set off this value as a vertical line from the
mid-point of the base of the slice:
