Geoscience Reference
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corresponding potential head is by definition
h =
z+u/
w
(
z
is chosen positive
downwards) and with
z =
cos
)
;
sin
)
, we find
h =
(
B
+ p
0
)/
w
cos
)
+
;
sin
.
The filter velocity components
q
;
and q
can be expressed by Darcy's law,
according to
q
;
=
)
. Anisotropic permeability (fissures
or layering in the subsoil) is accounted for by the ratio
k
;
h/
;
and
q
=
k
h/
= k
;
/k
. The resultant of
the flow components
q
;
and
q
pointing along flow direction
.
h
/
h
B
/
sin
cos
)
w
q
/q
;
=
tan(
)
+
)
=
=
(10.4)
/
;
)
Hence,
B =
w
cos
)
(
tan
)
tan(
)
+
) + 1), and the pore pressure field becomes
u =
(
B
+ p
0
)
=
w
cos
)
(
tan
)
tan(
)
+
) + 1
)
+ p
0
(10.5)
Next, the equilibrium of a small soil element is considered (see Fig 10.2a). A
plane uniform stress field is adopted. The general equilibrium condition, including
the effect of pore pressures and the soil weight
, is expressed in the
;
-
system as
follows
;
'
u
+
sin
)
=
0
(10.6a)
;
'
u
cos
)
=
0
(10.6b)
;
Because of 'infinite' symmetry of a long slope, (10.6) is independent of
;
, and
after integration, with condition at
=
0,
'
= 0, one obtains with (10.4)
=
sin
)
(10.7a)
' =
cos
)
u + p
0
=
cos
)
(1
(
w
/
)(
tan
)
tan(
)
+
)
+
1
))
(10.7b)
This shows that normal stress and shear stress increase with depth, and
consequently, there seems to be no specific potential slip surface. When the slope
fails, it may happen in many planes parallel to the slope surface, e.g. like a
mudflow. The condition
=
0 is valid for a submerged slope and the
effect of
p
0
cancels out. In the case of infiltration there could be a capillary
pressure:
p
0
=
'
= 0 at
w
h
c
, and then
'
=
h
c
at
=
0 holds, which gives an additional
term
h
c
in (10.7b), according to
' =
cos
)
(1
(
w
/
)(
tan
)
tan(
)
+
)
+
1
)) +
w
h
c
(10.7c)
. In fact,
as shown by a Mohr-circle in Fig 10.2b, one can define a slope stability factor,
according to
Finally, the stress state has to satisfy the failure criterion |
| <
'
tan
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