EP 1110-2-12
30 Sep 95
direction. This approach requires performing
(1) Standardized model. This type of model is
separate, independent dynamic analyses for the two
used in Chopra's Simplified Method. It is based on
orthogonal ground motion directions.
standardizing certain parameters that define the dam-
foundation-reservoir system. It recognizes the fact
(c) Conservative approach. Another more con-
that these parameters have little variation within the
servative approach accounts for both orthogonal com-
range of geometry common to gravity dams. For
ponents of ground motion. It is necessary to perform
example, the normalized fundamental mode shapes
the two dynamic analyses described above, but the
for six sample dam cross sections were studied and
first analysis includes the full magnitude design earth-
found to be almost identical. A standardized mode
quake ground motion component acting in an
shape was then developed for use in the calculation
assumed direction with a fraction of the design earth-
procedure.
quake ground motion acting orthogonally. The sec-
ond analysis includes the fractional part of the ground
(a) Factors considered. In the latest version, the
motion acting in the assumed direction and the full
standardized model considers dam-foundation rock
magnitude ground motion acting orthogonally. The
interaction, dam-reservoir effects, and reservoir bot-
fractional part of the design earthquake ground
tom absorption. All of these factors are based on
motion is usually assumed to be 30 percent of the
standard curves and formulae.
design earthquake ground motion. In a response
spectrum analysis, stresses produced by the two hori-
(b) Model limitations. The standardized model
zontal components of ground motion are added
is the simplest of the three types of models. A com-
directly to produce the resultant stress component for
puter is not required to formulate the model or even
horizontal ground motion. This resultant stress com-
to perform the dynamic analysis. However, standard-
ponent is then combined with the stress component
izing the mode shape, frequency, and other parame-
produced by the vertical component of ground motion
ters makes this an approximate method limited strictly
using SRSS.
to the typical nonoverflow monolith shape.
(d) Complexity of analysis. A 3-D analysis
(2) Finite element-substructure model. In this
requires considerably greater effort to create the 3-D
type of model, different techniques are used to repre-
model as compared to a 2-D model, and may require
sent the dam, foundation, and reservoir; however, by
a main frame computer and a substantial amount of
using common node points at the interfaces, a com-
computer time to perform the analysis. It also pro-
puter model is formulated that can be analyzed by
duces a large amount of output to evaluate and inter-
conventional matrix methods.
pret. However, the general purpose structural finite
element programs are continuously being improved
(a) Dam. The dam is modeled as an assembly
and are much more user oriented than they were in
of discrete finite elements. Either solid quadrilateral
the past. They have refined graphics capabilities
plane stress or plane strain elements are used for a
which help greatly in checking for errors in the com-
2-D model.
puter model input, and in displaying the stress output.
Also, specialized post-processors are being developed
(b) Foundation. The foundation is idealized as a
so that results can be evaluated much more effi-
viscoelastic half-plane. The elastic properties of the
ciently. These advances greatly enhance the practi-
foundation are formulated into a substructure matrix
cality of the 3-D analysis.
using the theory of elasticity. This matrix is com-
bined with the structural stiffness matrix developed
from the finite element representation of the dam.
d. Model configuration. This attribute of the
The substructure matrix introduces the foundation
dynamic analysis method is dependent on the type of
stiffness to the equations associated with the degrees-
model used to represent the dam-foundation-reservoir
of-freedom of the node points at the dam-foundation
system. The three types of models used for dynamic
interface. There is no finite element model of the
analysis of gravity dams are (1) the "standardized"
foundation. The dimensions of the structural stiffness
model developed by Chopra and used in his Simpli-
matrix are set by the finite element model of the dam.
fied Method of Analysis, (2) the finite element-
substructure model, and (3) the composite finite
element-equivalent mass system model.
8-2
Previous Page
