Civil Engineering Reference
In-Depth Information
And the critical slope angle is given by
φ
c
1
φ
c
1
U
N
u
σ
tan
i
c
=
tan
−
=
tan
−
(21.28)
n
and, from Eq. (21.21)
φ
c
1
u
tan
i
c
=
tan
−
(21.29)
z
cos
2
i
c
γ
The value of the pore pressure
u
depends on the direction of the seepage near the slope,
as discussed in Sec. 21.5 and as shown in Fig. 21.8. For the case of seepage vertically
downwards, as shown in Fig. 21.8(a)
u
=
φ
c
and the critical slope angle is
the same as that in dry soil or in a submerged slope. For the case where the seepage is
parallel with the slope
u
=
0 and
i
c
w
z
cos
2
i
c
and
=
γ
φ
c
1
−
γ
w
γ
tan
i
c
=
tan
(21.30)
In many cases
γ
≈
2
γ
w
and
1
2
φ
c
i
c
≈
(21.31)
so, with seepage parallel to the slope, the critical slope angle is about half the critical
angle of a submerged or dry slope.
From Sec. 21.5 and Fig. 21.8 the pore pressure increases as the seepage firstly
becomes horizontal and then becomes inclined upwards and the critical slope angle
decreases as the pore pressure increases. From Fig. 21.8(d) the critical angle of the
slope below the water where the flowlines are inclined upwards will be less than
2
φ
c
.
This is one of the reasons why it is difficult to dig a hole in the beach below the
water table.
The solutions for the stability of infinite slopes given by Eqs. (21.28), (21.29) and
(21.30) are relatively simple. Notice that for the undrained slope the critical angle
i
c
is governed by the depth
H
of the slip surface; if this depth is relatively large the
mechanism cannot be approximated to sliding parallel to the surface and the solution
is no longer valid. For the drained case the critical angles for dry and submerged slopes
are the same,
i
c
=
φ
c
(because neither the unit weight nor the pore pressure appear
in the final solution), but if there is steady state seepage towards the slope the critical
slope angle is reduced. These results demonstrate the very significant influence of pore
pressures on slope stability.
21.8 Stability of vertical cuts
A simple experiment with dry sand or sugar demonstrates that you cannot make a
vertical cut in a drained soil. We can, however, make vertical cuts in soils that are
undrained where the negative pore pressures generate positive effective stresses.
