Civil Engineering Reference
In-Depth Information
Taylor concluded that the lower bound solution
provides a value of the factor of safety that is
sufficiently accurate for most practical problems
involving simple circular failure of homogeneous
slopes.
The basic principles of these methods of ana-
lyses are discussed in Section 8.6.
(e)
The locations of the tension crack and of
the slide surface are such that the factor of
safety of the slope is a minimum for the
slope geometry and ground water conditions
considered.
(f)
Ground water conditions vary from a dry
slope to a fully saturated slope under heavy
recharge; these conditions are defined in
Figure 8.4.
8.3 Derivation of circular failure charts
This section describes the use of a series of charts
that can be used to determine rapidly the factor of
safety of circular failures. These charts have been
developed by running many thousands of circular
analyses from which a number of dimensionless
parameters were derived that relate the factor of
safety to the material unit weight, friction angle
and cohesion, and the slope height and face angle.
It has been found that these charts give a reliable
estimate for the factor of safety, provided that the
conditions in the slope meet the assumptions used
in developing the charts. In fact, the accuracy in
calculating the factor of safety from the charts is
usually greater than the accuracy in determining
the shear strength of the rock mass.
Use of the stability charts presented in this
chapter requires that the conditions in the slope
meet the following assumptions:
(g)
Circular failure charts are optimized for a
rock mass density of 18.9 kN/m
3
. Densities
higher than this give high factors of safety,
densities lower than this give low factors
of safety. Detailed circular analysis may
be required for slopes in which the mate-
rial density is significantly different from
18.9 kN/m
3
.
The charts presented in this chapter corres-
pond to the lower bound solution for the factor
of safety, obtained by assuming that the normal
load is concentrated on a single point on the slide
surface. These charts differ from those published
by Taylor in that they include the influence of a
critical tension crack and of ground water.
8.3.1 Ground water flow assumptions
In order to calculate the forces due to water pres-
sures acting on the slide surface and in the tension
crack, it is necessary to assume a set of ground
water flow patterns that coincide as closely as pos-
sible with conditions that are believed to exist in
the field.
In the analysis of rock slope failures discussed
in Chapters 6, 7 and 9, it is assumed that most of
the water flow takes place in discontinuities in the
rock and that the rock itself is practically imper-
meable. In the case of slopes in soil or waste rock,
the permeability of the mass of material is gener-
ally several orders of magnitude higher than that
of intact rock and, hence, a general flow pattern
will develop in the material behind the slope.
Figure 5.10(a) shows that, within the rock mass,
the equipotentials are approximately perpendi-
cular to the phreatic surface. Consequently, the
flow lines will be approximately parallel to the
(a)
The material forming the slope is homogen-
eous, with uniform shear strength properties
along the slide surface.
(b)
The shear strength
τ
of the material is char-
acterized by cohesion:
c
and a friction angle
φ
, that are related by the equation
τ
=
+
c
σ
tan
φ
(see Section 1.4).
(c)
Failure occurs on a circular slide surface,
which passes through the toe of the slope.
2
(d)
A vertical tension crack occurs in the upper
surface or in the face of the slope.
2 Terzaghi (1943: 170), shows that the toe failure assumed
for this analysis gives the lowest factor of safety provided
that
φ>
5
◦
. The
φ
=
0 analysis, involving failure below the
toe of the slope through the base material has been discussed
by Skempton (1948) and by Bishop and Bjerrum (1960)
and is applicable to failures which occur during or after the
rapid construction of a slope.
