Civil Engineering Reference
In-Depth Information
s
b
(a)
Tension crack in upper
surface of slope
Face
z
z
w
V
H
U
Slide plane
W
f
p
(b)
Tension crack in face
Face
z
z
w
H
V
U
Slide plane
W
f
p
Figure 6.3
Geometries of plane slope failure: (a) tension crack in the upper slope; (b) tension crack in the face.
moments that would tend to cause rotation
of the block, and hence failure is by slid-
ing only. While this assumption may not
be strictly true for actual slopes, the errors
introduced by ignoring moments are small
enough to neglect. However, in steep slopes
with steeply dipping discontinuities, the pos-
sibility of toppling failure should be kept in
mind (see Chapter 9).
at
the
lateral
boundaries
of
the
failing
rock mass (Figure 6.2(b)).
(g)
In analyzing two-dimensional slope prob-
lems, it is usual to consider a slice of unit
thickness taken at right angles to the slope
face. This means that on a vertical section
through the slope, the area of the sliding sur-
face can be represented by the length of the
surface, and the volume of the sliding block
is represented by the cross-section area of the
block (Figure 6.2(c)).
(e)
The shear strength
τ
of the sliding surface
is defined by cohesion
c
and friction angle
φ
that are related by the equation
τ
=
c
σ
tan
φ
, as discussed in Chapter 4. In
the case of a rough surface or a rock mass
having a curvilinear shear strength envelope,
the apparent cohesion and apparent friction
angle are defined by a tangent that takes into
account the normal stress acting on the slid-
ing surface. The normal stress
σ
acting on a
sliding surface can be determined from the
curves given in Figure 6.4.
+
The factor of safety for plane failure is calcu-
lated by resolving all forces acting on the slope
into components parallel and normal to the slid-
ing plane. The vector sum of the shear forces,
S
acting down the plane is termed the
driving
force
. The product of the total normal forces,
N
and the tangent of the friction angle
φ
, plus
the cohesive force is termed the
resisting force
(see Section 1.4.2). The factor of safety FS of the
sliding block is the ratio of the resisting forces to
(f)
It is assumed that release surfaces are present
so that there is no resistance to sliding
