Civil Engineering Reference
In-Depth Information
topography rises behind the slope. Even where
slopes are excavated into an inclined topography,
the stresses would flow around the excavation
to some extent, depending on the effective width
of the excavation perpendicular to the downhill
topographic direction.
A summary of the effects of boundary condi-
tions on analysis results is as follows:
concentrations near the toe of a slope, and slightly
over-predicts the pore pressure behind the toe by
ignoring the inclination of equipotential lines.
Seepage forces must also be considered in the
analysis. The hydraulic gradient is the difference
in water pressure that exists between two points
at the same elevation, and results from seepage
forces (or drag) as water moves through a porous
medium. Flow analysis automatically accounts
for seepage forces.
To evaluate the error resulting from specifying
a water table without doing a flow analysis, two
identical problems were run. In one case, a flow
analysis was performed to determine the pore
pressures. In the second case, the pressures were
determined using only a piezometric surface that
was assumed to be the phreatic surface taken from
the flow analysis. The material properties and
geometry for both cases are shown in Figure 10.2.
The right-hand boundary was extended to allow
the far-field phreatic surface to coincide with the
ground surface at a horizontal distance of 2 km
behind the toe. Hydraulic conductivity within the
model was assumed to be homogeneous and iso-
tropic. The error caused by specifying the water
table can be seen in Figure 10.4. The largest
errors, under prediction of up to 45%, are found
just below the toe, while over prediction errors
in pore pressure values behind the slope are gen-
erally less than 5%. The errors near the phreatic
surface are insignificant, as they result from the
relatively small pore pressures just below the
phreatic surface where small errors in small values
result in large relative errors.
For a phreatic surface at the ground surface
at a distance of 2 km, a factor of safety of 1.1
is predicted using circular failure chart number
3 (refer to Section 8.3). The factor of safety
determined by FLAC was approximately 1.15 for
both cases. The FLAC analyses give similar safety
factors because the distribution of pore pressures
in the area behind the slope where failure occurs
is very similar for the two cases. The conclusion
drawn here is that there is no significant differ-
ence in predicted stability between a complete
flow analysis and simply specifying a piezometric
surface. However, it is not clear if this conclusion
•
A fixed boundary causes both stresses and
displacements to be underestimated, whereas
a stress boundary does the opposite.
•
The two types of boundary condition
“bracket” the true solution, so that it is pos-
sible to conduct tests with smaller models
to obtain a reasonable estimate of the true
solution by averaging the two results.
A final point to be kept in mind is that all open pit
slope stability problems are three-dimensional in
reality. This means that the stresses acting in and
around the pit are free to flow both beneath and
around the sides of the pit. Therefore, it is likely
that, unless there are very low strength faults
parallel to the analysis plane, a constant stress
or following stress boundary will over-predict the
stresses acting horizontally.
10.3.6 Incorporating water pressure
The effect of water pressure in reducing effective
stresses and, hence, slope stability is well under-
stood. However, the effect of various assump-
tions regarding specification of pore pressure
distributions in slopes is not as well understood.
Two methods are commonly used to specify
pore pressure distributions within slopes. The
most rigorous method is to perform a complete
flow analysis, and use the resultant pore pres-
sures in the stability analyses. A less rigorous,
but more common method is to specify a water
table, and the resulting pore pressures are given
by the product of the vertical depth below the
water table, the water density and gravity. In this
sense, the water table approach is equivalent to
specifying a piezometric surface. Both methods
use similar phreatic surfaces. However, the water
table method under-predicts actual pore pressure
