GRAVITY DAM ANALYSIS 151
at all node points. The approach is detailed in USBR (1976), but has now
largely been displaced by more powerful and flexible finite element tech-
niques.
(b) Finite element analysis (FEA)
The finite element approach considers the dam and that portion of the
supporting foundation lying within the structural zone of influence of the
dam as an assemblage of distinct elements, interconnected at node points
at their vertices. A mathematical model is constructed based on determin-
ing the nodal displacements which, in turn, define the state of strain, and
therefore of stress, within each element. An acceptable mathematical
representation of the load response of the concrete and the foundation
strata is therefore important, accuracy of representation being balanced
against computational workload. The quality of the output is a function of
element type, mesh configuration and mesh size. Accuracy is enhanced by
a finer mesh, but the computational effort is greatly increased and may be
unacceptably high. A compromise between mesh fineness and the accu-
racy of the solution is therefore necessary.
Analysis of problems which can be considered in terms of plane
stress or plane strain, as with the gravity dam, can be conducted using a
two-dimensional mesh of quadrilateral elements. Where a simplification
to plane stress or plane strain conditions is not justifiable, a three-
dimensional analysis is necessary, e.g. for an arch or cupola dam. Three-
dimensional analysis is frequently based on the use of isoparametric
hexahedronal elements having eight node points, and the computing
power required is considerable. The finite element approach is an elegant,
flexible and extremely powerful analytical tool. Secondary loads, e.g. tem-
perature effects, deformation, etc., can be introduced and the method is, in
principle, well suited to parametric studies. As examples, the effect of rock
stiffness on structural response, or the influence of a major crack or
opening in the dam can be studied. The method is particularly suited to
analysing the complex shape of arch or cupola dams.
A comprehensive introduction to finite element methods is given in
Zienkiewicz (1977). The application of the technique to the analysis of
dams is reviewed in Clough and Zienkiewicz (1978). The effort and spe-
cific computational skills necessary for setting up an FEA application are
such that many analyses are conducted using commercially available soft-
ware suites. Preparation of the mathematical model using such software is
nevertheless a task requiring particular expertize and considerable care in
the selection of input parameters and data.