Civil Engineering Reference
In-Depth Information
III.3 Analysis limitations
For the comprehensive stability analysis presen-
ted in this appendix there is one geometric
limitation related to the relative inclinations of
plane 3 and the line of intersection, and a specific
procedure for modifying water pressures. The
following is a discussion of these two limitations.
allows for the presence of a tension crack and
gives
u
1
γ
w
H
5w
/
3, where
H
5w
is the depth of the bottom vertex of the ten-
sion crack below the upper ground surface. The
water forces are then calculated as the product
of these pressures and the areas of the respective
planes.
To calculate stability of a partially saturated
wedge, the reduced pressures are simulated by
reducing the unit weight of the water,
γ
w
. That
is, if it is estimated that the tension crack is one-
third filled with water, then a unit weight of
γ
w
/
3
is used as the input parameter. It is considered
that this approach is adequate for most purposes
because water levels in slopes are variable and
difficult to determine precisely.
=
u
2
=
u
5
=
Wedge geometry.
For wedges with steep
upper slopes (plane 3), and a line of intersec-
tion that has a shallower dip than the upper slope
(i.e.
ψ
3
>ψ
i
), there is no intersection between
the plane and the line; the program will ter-
minate with the error message “Tension crack
invalid” (see equations (III.50) to (III.53)). The
reason for this error message is that the calcula-
tion procedure is to first calculate the dimensions
of the overall wedge from the slope face to the
apex (intersection of the line of intersection with
plane 3). Then the dimensions of a wedge between
the tension crack and the apex are calculated.
Finally, the dimensions of the wedge between the
face and the tension crack are found by subtract-
ing the overall wedge from the upper wedge (see
equations (III.54) to (III.57).
However, for the wedge geometry where (
ψ
3
>
ψ
i
), a wedge can still be formed if a tension crack
(plane 5) is present, and it is possible to cal-
culate a factor of safety using a different set of
equations. Programs that can investigate the sta-
bility wedges with this geometry include YAWC
(Kielhorn, 1998) and (PanTechnica, 2002).
Water pressure.
The analysis incorporates the
average values of the water pressure on the slid-
ing planes (
u
1
and
u
2
), and on the tension crack
(
u
5
). These values are calculated assuming that
the wedge is fully saturated. That is, the water
table is coincident with the upper surface of the
slope (plane 3), and that the pressure drops to
zero where planes 1 and 2 intersect the slope face
(plane 4). These pressure distributions are simu-
lated as follows. Where no tension crack exists,
the water pressures on planes 1 and 2 are given
by
u
1
III.4 Scope of solution
This solution is for computation of the factor of
safety for translational slip of a tetrahedral wedge
formed in a rock slope by two intersecting dis-
continuities (planes 1 and 2), the upper ground
surface (plane 3), the slope face (plane 4), and a
tension crack (plane 5 (Figure III.1)). The solu-
tion allows for water pressures on the two slide
planes and in the tension crack, and for differ-
ent strength parameters on the two slide planes.
Plane 3 may have a different dip direction to that
of plane 4. The influence of an external load
E
and a cable tension
T
are included in the ana-
lysis, and supplementary sections are provided for
the examination of the minimum factor of safety
for a given external load, and for minimizing the
anchoring force required for a given factor of
safety.
The
solution
allows
for
the
following
conditions:
(a)
interchange of planes 1 and 2;
(b)
the possibility of one of the planes overlying
the other;
(c)
the situation where the crest overhangs the
toe of the slope (in which case
η
=−
1); and
γ
w
H
w
/
6, where
H
w
is the ver-
tical height of the wedge defined by the two ends
of the line of intersection. The second method
=
u
2
=
(d)
the possibility of contact being lost on either
plane.
