- Rapid drawdown.Values of ruin the range of 0.30–0.60 may occur
immediately after initial drawdown. Transient values of uwmay be esti-
mated from flownets drawn for intermediate positions of the drawdown
phreatic surface. (The complex response of an old embankment dam
during drawdown is described in Holton, Tedd and Charles (1989))
Values of Fmindetermined in a comprehensive stability analysis must
always be regarded as relative and not as absolute. The expressions deter-
miningFare of varying rigour and are inexact, a reflection of the complex-
ity of the stability problem, where measured shear strength parameters
can be subject to a variance of up to 30–40%. Economic considerations
require acceptance of relatively low values of Ffor embankment slopes.
The factors of safety for embankment dam slopes are time depend-
ent, varying significantly in accordance with changes in loading corres-
ponding to construction and the subsequent operational cycle. This is
illustrated schematically in Fig. 2.14. Representative guideline values of
Fmincorresponding to the major loading conditions are presented in Table
2.7. Values considered acceptable must always reflect the confidence
attaching to geotechnical data and design parameters.
The expressions for Fcorresponding to the analytical methods most
commonly employed are as follows.
(a) Swedish circle (Fellenius) solution: circular arc surface
F (2.25)
whereLais the overall length of the failure surface, Wandlare, respec-
tively, the weight and base length of the slices into which the active mass is
subdivided for analysis and is the angle of inclination of the slice base to
cLatan∑(Wcos uwl)
∑WsinSTABILITY AND STRESS 85
Table 2.7 Guideline factors of safety: effective stress stability analysis
Design loading condition Factor of safety, Fmin
Downstream slope Upstream slope(1) Under construction; end of 1.25 1.25
construction
(2) Long-term operational; reservoir full 1.5 1.5
(3) Rapid drawdown – 1.2
(4) Seismic loading with 1, 2 or 3 above 1.1 1.1
- The above values mustbe interpreted in the context of the particular case considered, e.g.
uncertainties regarding any of the principal parameters, uw,cand. - Higher design minima are appropriate for analyses based on total stress parameters or on
peak strengths in the case of more brittle soils.