Civil Engineering Reference
In-Depth Information
Figure 21.8
Seepage towards a slope.
In Fig. 21.8(d) the seepage is inclined upwards at an angle
α
. From the geometry of
the figure
w
z
1
=
γ
=
γ
u
w
h
w
(21.5)
1
−
tan
α
tan
i
90
◦
and the expressions in Eqs. (21.3) and (21.4)
Equation 21.5 gives
u
=
0 for
α
=−
with the appropriate values for
. Notice that as the direction of the seepage rotates
from downwards to inclined upwards the pore pressure at a depth
z
increases. This will
mean that the limiting slope angle
i
c
will decrease as the direction of seepage rotates
and this will be discussed later in Sec. 21.6.
α
21.6 Stability of infinite slopes
From now on I will examine the limiting stability of slopes with the critical state
strengths
s
u
or
φ
c
; to apply a factor of safety you can do the same calculations using
φ
s
obtained from Eqs. (21.1) and (21.2). For slope stability calculations you can
use the upper and lower bound method described in Chapter 19 or the limit equilibrium
method described in Chapter 20. A simple but very useful case is for shallow sliding on
a slip surface parallel to the slope, as illustrated in Fig. 21.3(b). The depth to the slip
surface will be controlled by geological or groundwater conditions; a common case is
s
us
or
