EP 1110-2-12
30 Sep 95
Chapter 7
shape of these three spectra can be attributed to the
assumptions and techniques used in smoothing the
Factors Significantly Affecting
jagged spectra produced from the statistical combina-
Dynamic Response
tion of real earthquake records.
c. Spectral accelerations. Referring to
7-1.
Evaluation Procedure and Objectives
Figure 7-1, the range of interest of natural period
would be for periods of less than 1.0 second. This
There are many important factors in a dynamic stress
range would cover the mode shapes that produce
analysis that can greatly affect the response of a dam.
significant response. In this range the spectral accel-
The influence which the various material and strength
eration values for a given period vary between spectra
parameters and loads have on the final results must
up to as much as 65 percent. The ATC spectrum
be evaluated. This can be done by executing the
envelopes the other two design spectra, and is rec-
model using a typical dam cross-section and typical
ommended for use as the standard design response
material properties, then modifying the loads and
spectrum. In linear-elastic response spectrum analy-
parameters one-by-one to give an indication of the
ses, dynamic response of a particular system eval-
influence each factor has on the dynamic response.
uated by two different response spectra is directly
Once the important factors have been identified, the
proportional to the spectral ordinates taken from the
design effort should concentrate on the more critical
two spectra at the natural period of the system. Thus
factors that form the input to the dynamic analysis.
the shape of the design response spectrum greatly
Following is a discussion of the impact some of the
influences the results of the dynamic analysis.
parameters have on the response of a dam.
7-3.
Dam-Foundation Interaction, Damping
7-2.
Design Response Spectra
Effect
a. Spectral shape. Both the shape of the spec-
a. Properties of the foundation. The two prop-
trum and the PGA used to anchor the spectrum affect
erties of the foundation rock that have a significant
the dam response and should be established carefully.
influence on the dynamic response are the damping
The dynamic response in a linear-elastic analysis is
ratio and the deformation modulus. The damping
directly proportional to the PGA, but minor changes
characteristics of the foundation contribute signifi-
in the shape of the spectra may not result in propor-
cantly to the damping of the combined dam-
tional changes in the response.
foundation system and must be considered in the
analysis. When the foundation deformation modulus
is low, the damping ratio of the combined system is
b. Comparison of standard spectra. For com-
considerably higher than the damping ratio of the
parison purposes, three widely accepted standard
RCC dam structure alone.
design response spectra will be considered, each
representing the same site conditions. The design
spectra are: (1) Applied Technology Council spec-
b. Effective damping ratio. There are two
trum for rock of any characteristic whether shalelike
sources of damping for the foundation rock:
or crystalline in nature (ATC 1984), (2) H. B. Seed
(1) material (hysteretic) and (2) radiation. In contrast
spectrum for rock based on 28 records (Seed 1974),
to this type of damping is the viscous type of damp-
and (3) Newmark-Hall spectrum using recommended
ing (directly proportional to velocity) used in pro-
values for maximum ground velocity and displace-
ducing design response spectra. Therefore, it is
ment for competent crystalline rock (Newmark and
necessary to develop an effective viscous damping
Hall 1987). Figure 7-1 shows all three spectra nor-
ratio to represent the combined dam-foundation sys-
malized to 1.0 g PGA for the same rock foundation
tem in a response spectrum analysis. This is
site conditions. The Newmark-Hall spectrum is based
accomplished by using the curves provided in Fig-
on the median or 50th percentile cumulative probabil-
ure D-6 of Appendix D, and the following equation is
ity, where the other two spectra are based on the
for an empty reservoir condition which allows the
mean of the records used in their development. This
effects of foundation damping to be isolated. This
difference in probability level is reflected in the spec-
method, developed by A. K. Chopra, is based on the
tral shape. The primary cause for the difference in
7-1
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