Environmental Engineering Reference
In-Depth Information
Table 11.1.
Shear strengths, pore pressures and unit weights for stability analysis (adapted from
Duncan 1992).
Condition
rapid draw-down and
Normal operating
End of construction
staged construction
(“steady seepage”)
Analysis procedure
Effective stress
Effective stress
Effective stress
and shear strength
analysis using c
,
analysis using c
,
analysis using c
,
for free draining
zones - filters,
rockfill, sand/gravel
in foundations
Analysis procedure
Total stress analysis
Total stress analysis using
Effective stress
(1)
or
(1)
for the dam
and shear strength
using S
u
and
S
u
and
analysis using c
,
,
for low permeability
effective stress analysis
prior to draw down or
unless soils are
contractive
(2)
in
zones
modelling partially
construction of the
saturated conditions
second stage
which case use Su
measured in the dam
Internal pore
No internal pore
No internal pore pressures
Pore pressures from
pressures
pressures (u) for total
(u) for total stress analysis;
seepage analysis
stress analysis; set u
set u equal to zero in these
and/or from
equal to zero in these
zones. Pore pressures from
piezometer readings
zones. Pore pressures
seepage analysis for
for effective stress
determined from
effective stress analysis
analysis
laboratory tests
for effective stress
analysis
Reservoir water
Include (usually as a
Include (usually as a zone
Include (usually as a
zone with c
0,
with c
0,
0,
zone with c
0,
9.8 kN/m
3
)
9.8 kN/m
3
)
9.8 kN/m
3
)
0,
0,
Unit weights
(3)
Total
Total
Total
Notes:
(1)
S
u
and
u
describe the undrained strength envelope, so the variation in undrained strength, with
increase in total stress, can be modelled in the analysis.
(2)
Contractive soils include poorly compacted saturated clay fill, normally and lightly over-consolidated
clays, and other situations described in Section 6.1.3. Effective stress analysis which ignores pore
pressures generated on shearing over-estimate the factor of safety.
(3)
For free draining zones use
dry
or
moist
for zones above water,
sat
below. For low permeability zones,
use
sat
or
moist
.
The analyses assume the factor of safety is uniform along the whole of the failure sur-
face and cannot directly allow for localised strain weakening or progressive failure effects.
The number of equations of equilibrium available is smaller than the number of
unknowns in limit equilibrium analysis, so assumptions are made to make the problem
determinate. This is what differentiates most of the methods in
Table 11.2
.
Of the meth-
ods listed, the ordinary (or Fellenius, 1927) method should not be used, because it gener-
ally underestimates the factor of safety. In force equilibrium methods the factor of safety
is affected significantly by the assumed inclination of the side forces between slices and are
therefore potentially not as accurate.
Most practitioners use the Bishop “modified” (or “simplified”) method for circular
analysis, which has been shown to be adequately accurate (Whitman and Bailey,
1967) and is stable computationally, but most methods give similar answers. For non-cir-
cular surfaces, the Morgenstern and Price (1965) and Spencer (1967) methods are widely
used.
Hungr (1997) has demonstrated that for non-circular surfaces the methods may give
different answers. The example is a simple bi-planar sliding block (
Figure 11.1
)
, defined
