Environmental Engineering Reference
In-Depth Information
The pseudo-static method of analysis, despite its earlier popularity, was based on a num-
ber of restrictive assumptions. For instance, it assumed that the seismic coefficient acting
on the potential unstable mass is permanent and in one direction only. In reality, earth-
quake accelerations are cyclic, with direction reversals. Also, the concept of failure used in
the approach was influenced by that used in static problems where a factor of safety of less
than one cannot be permitted, as the stresses producing this state will exist until large
deformations change the geometry of the structure. However, under seismic conditions, it
may be possible to allow the FOS to drop below one, as this state exists only for a short
time. During this time, earthquake induced inertia forces cause the potentially unstable
masses to move down the slope. However before significant movement takes place, the
direction of the earthquake loading is reversed and the movement of the soil masses stop
as, once again, the FOS rises above one. In fact, experience shows that a slope may remain
stable despite having a calculated FOS less than one and, on the other hand, it may fail at
FOS
1, depending on the dynamic characteristics of the slope-forming material.
The authors have in the past recommended the US Corps of Engineers (1984) method
as a screening method to select dams which need more detailed assessment. We are how-
ever now of the view that screening is best done using the simplified deformation analy-
ses described below, and do not believe pseudo-static analyses are useful, because they do
not model the actual load condition.
12.6.3
Simplified methods of deformation analysis for dams where liquefaction and
significant strain weakening do not occur
There are a number of approaches for estimating the deformations of a dam which may
occur during an earthquake. These include:
(a) Empirical methods based on recorded deformations, dam geometry and earthquake
loading e.g. Swaisgood (1998), Pells and Fell (2002, 2003) extended this to include an
empirical method to assess whether cracking would occur;
(b) Integration of the displacements which occur when the earthquake loading exceeds
the available strength e.g. Newmark (1965) and developments of that approach using
simplified numerical analyses programs such as SHAKE;
(c) Developments of the Newmark (1965) approach to allow for dynamic response of the
embankment e.g. Makdisi and Seed (1978).
The following gives an outline of these methods. Readers will need to refer to the ref-
erences given, or engage the services of a person experienced in these methods to apply all
but the empirical methods.
12.6.3.1
Swaisgood (1998) empirical method for estimating crest settlements
Swaisgood (1998) gathered data on crest settlement, dam height, dam type, depth of allu-
vium in the foundation, earthquake magnitude and peak ground acceleration, and the
focal distance of the dam to the earthquake.
Figure 12.34
shows relative crest settlement (settlement/{dam height
thickness of
alluvium in the foundation}) versus peak ground acceleration (bedrock).
Swaisgood (1998) recommended the following equations to predict settlement:
CS
SEF
RF
(12.29)
where CS is the vertical crest settlement expressed as a percentage of the dam height plus
the alluvium thickness. SEF is the seismic energy factor and RF is the resonance factor.
These factors are calculated from:
e
(0.72 M
6.28 PGA-9.1)
SEF
(12.30)
