Environmental Engineering Reference
In-Depth Information
In the minds of most dam engineers today, the design and analysis of gravity dams for
earthquake loading would mean either the pseudo-static method or the more complex
approach of a finite element analysis.
16.9.2
Gravity dams on soil foundations
Generally speaking the foundations will be the critical factor in the design of these dams
for earthquake loading. The approach, therefore, to check these dams for earthquake
loading would logically be to follow the procedures outlined for embankment dams in
Chapter 12. For example, one would use SHAKE to determine the ground shaking
accelerogram for the soil deposit and then undertake a Newmark displacement analysis to
estimate the permanent displacements along a selected failure surface through the soil
foundations. As most of these dams would be low, stiff structures, the dam's response
effects could probably be ignored.
As will be clear from the discussion in Chapter 12, the net outcome could very well be sig-
nificant permanent displacements within the foundation that could, in turn, seriously com-
promise the dam. For a new dam, the object would be to design the dam such that its static
load factors of safety are high enough so that under earthquake loading the resultant per-
manent displacements would most likely be small. As well, the dam's details would need to
cope with potential differential movements between blocks. For an existing dam, unless con-
siderable strengthening works can be justified, an owner may simply have to live with the
inherent risk. Finally, for both new and existing dams, great care will be needed to assess the
risk of post-earthquake piping through the foundations.
In the case of concrete dam (or spillway structure) being founded on potentially lique-
fiable foundations measures will have to be taken to overcome the effects of liquefaction
such as removal or densification of the liquefiable material.
16.9.3
Gravity dams on rock foundations
16.9.3.1
General
The methods of analysis commonly used extend from the simple pseudo-static method first
suggested in Westergaard (1935), a method that treats the dam on a rigid body (natural
period
zero seconds) to complex finite element methods in which there are one or more
non-linear features, usually in the form of elements representing cracks. The pseudo-static
method was used as a matter of course well into the 1960s. With the advent of the readily
available computing facilities in the 1950s and 1960s, the finite element method (FEM)
became more and more available to design engineers, at first through developments at
Universities and later through specialist firms, and gradually these structural analysis pro-
grams began to be used for gravity dam analyses. The introduction of the desk-top com-
puter and the rapid increase in its computing power added to the spread of the gravity
dam analyses until now these FEM analyses have almost become “the thing to do”.
In between the two limits of the simple pseudo-static approach and the complex FEM
are pseudo-static methods such as the one developed by Fenves and Chopra (1987). This
method allows for the use of the first (the natural) period and, if needed, higher periods,
to assess the impact of the dams response to the ground shaking. The US Corps of
Engineers developed an approach that starts with this type of method and extends to lim-
ited FE analyses (Guthrie (1996)).
16.9.3.2
The Westergaard pseudo-static method
This method, which is usually applied in a 2-dimensional analysis, treats the dam as a
rigid structure on a rigid foundation. The hydrodynamic effects, which Westergaard
