Environmental Engineering Reference
In-Depth Information
lower bound strengths for earthfill, not allowing for the high friction angles of rockfill
at low confining stresses.
(b) The lower minimum factors of safety for the construction condition is based on the
consequences of failure usually being lower than for a dam under steady state seepage.
However the uncertainties in the shear strength are often high, so unless there is good
monitoring of pore pressures and displacements, high factors of safety should be used.
(c) The lower factors of safety for rapid drawdown are again predicated on the assump-
tion that the dam is unlikely to breach under a drawdown failure but it should be rec-
ognized that, by adopting a lower factor of safety, there is a higher chance of failure.
(d) It should be recognised that by adopting lower factors of safety for the construction
and drawdown conditions there is an acceptance of a higher probability of instability.
(e) The factors of safety apply to non-trivial failure surfaces. Failure surfaces passing only
through free draining rockfill may acceptably have lower factors of safety, because
provided the slope can be constructed, there is no possible change in conditions which
will cause instability. If realistic (high) effective friction angles are used for rockfill at
low confining stresses, this problem will generally not arise.
(f) The greater uncertainty in undrained strengths than in effective stress strengths means
that higher factors of safety should be used where undrained strengths control stability.
11.5.2
Post failure deformation assessment
It is recommended that as a matter of routine the potential post failure deformation of the
dam be assessed using the simplified method of Khalili et al. (1996).
The Khalili et al. (1996) model considers two modes of failure defining the upper and
lower bounds of post-failure deformation:
-A “rapid model” based on the principle of conservation of energy, where the potential
energy of the slide mass is resisted by the frictional forces along the surface of rupture,
and approximated using the residual shear strength;
-A “slow model” based on equations of equilibrium between the driving force of the slide
mass and resisting forces along the surface of rupture and approximated using the
residual shear strength, i.e. assuming the rate of movement would be so slow that the
effect of inertia forces of the sliding mass is negligible.
The failure model is shown in
Figure 11.23
and is based on the assumptions of a circular
slide surface, the failure is plane strain, the failing mass moves as a rigid body and energy
losses during failure is only due to the frictional forces acting along the slip surface.
Approximate solutions for the rapid model are calculated using Equation 11.20 and for the
slow model using Equation 11.21, where FS
residual
is the factor of safety calculated using
residual strengths along the surface of rupture, and
i
and
f
are the initial and final positions
of the centre of gravity as defined in Figure 11.23.
Rapid Model
2
(FS
0.5)
(11.20)
f
i
residual
Slow Model sin
FS
sin
(11.21)
f
residual
i
Khalili et al. (1996) found that for most cases analysed the rapid model gave the best
estimate of deformations.
In this manner, the consequences of the dam “failing” (reaching a factor of safety
1)
can be determined. It will become apparent that in many cases, either the factor of safety
using residual strengths is
1.0, in which case failure is virtually impossible, or it is only a
little less than 1.0, because the materials in the dam are not significantly strain weakening.
