dynamic response of embankment concrete- gravity and arch dams including hydrodynamic ...

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PNH-152324
REPORTNO.
UCB/EERC-80/39 EARTHQUAKE ENGINEERING RESEARCH CENTER
OCTOBER 1980
DYNAMIC RESPONSE OF
EMBANKMENT CONCRETE
GRAVITY AND ARCH DAMS
INCLUDING HYDRODYNAMIC
INTERACTION
by
JOHN F. HALL
ANIL K. CHOPRA
A Report on Research Conducted under
GrantsATA74-20554 and ENV76-80073
from the National Science Foundation.
COLLEGE OF ENGINEERING
UNIVERSITY OF CALIFORNIA . Berkeley, California
-IlEPllODUCEDBY
NATIONAL TECHNICAL
INFORMATION-SERVICE
u.s.DEPARTMENTOf COMMERCE
SPRIIIGfIElD.VA 22161
DISCLAIMER
Any opinions, findings, and conclusions or
recommendationsexpressedinthispublica
tion are those of the authors and do not
necessarilyreflecttheviewsoftheNational
Science Foundation or the Earthquake En
gineering Research Center, University of
California, Berkeley.
For sale by the National Technical Informa
tion Service, U.S. Department of Commerce,
Springfield, Virginia 22161.
See back of report for up to date listing of
EERC reports.
502n-l01
11.
REPORT DOCUMENTATION REPORT NO. 3. Recipient's Accession No.
PAGE NSF/RA-80 0298 PIIl1 1 I) 23 2 •
•• Title and Subtitle 5. Report Date
Dynamic Response of Embankment Concrete-Gravity and Arch Dams
October, 1980
Including Hydrodynamic Interaction
7. Author{s) 8. Performlna: Organization Rept. No.
John F. Hall and Anil K. Chopra UCB/EERC-80/39
9. Performing Organization Nameand Address 10. Proje<:t/TasklWork UnitNo.
Earthquake Engineering Research Center
University of California, Berkeley
11. Contract(C) OrGrant{G) No.
Richmond Field Station
(C)
47th Street &Hoffman Boulevard
Richmond, Calif. 94804 (G)
0'
12. SponsoringOrganizationNameandAddress 13.TyP4l Report & PeriodCovered
National Science foundation
1800 G. Street, N.W.
Washington, D.C. -20550 14.
15. Supplementary Notes
16. Abstract (Limit: 200 words)
An analysis procedure in the frequency domain is developed for determining the earth
quake response of a dam including hydrodynamic interaction and water compressibility
effects. Linear responses of idealized, two-dimensional gravity dams and three
dimensional dams, including arch dams, can be obtained. The dam and fluid domain are
treated as substructures and modeled with finite elements. The only geometric restriction
is that an infinite fluid domain must maintain a uniform cross-section beyond some point
in the upstream direction. For such an infinite uniform region, a finite element
discretization within the cross-section combined with a continuum representation in
the infinite direction provides for a proper transmission of pressure waves. The fluid
domain model approximately accounts for fluid-foundation interaction through a damping
boundary condition applied along the reservoir floor and sides. The dam foundation is
assumed rigid.
Hydrodynamic effects are shown to be equivalent to an added mass and added load in the
frequency domain equations of motion of the dam.
Hydrodynamic effects on the dam response are investigated for acceleration responses to
harmonic ground motions. Complex frequency response functions for-acceleration at the
dam crest are presented for two-dimensional concrete gravity and earth dams and for a
three-dimensional arch dam. Several reservoir shapes are included for the concrete
gravity dams. Water compressibility and fluid-foundation interaction significantly
influence the response of concrete gravity dams and are even more important for the arch
dam. One effect is a greatly increased importance for the vertical component of ground
motion. Hydrodynamic effects on the responses of earth dams are shown to be minor.
0'
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DYNAMIC RESPONSE OF EMBANKMENT, CONCRETE-GRAVITY AND ARCH DAMS
INCLUDING HYDRODYNAMIC INTERACTION
by
John F. Hall
Anil K. Chopra
A Report on Research Conducted Under
Grants ATA74-20554 and ENV76-80073
from the National Science Foundation
Report No. UCB/EERC-80/39
Earthquake Engineering Research Center
University of California
Berkeley, California
October 1980

ABSTRACT
An analysis procedure in the frequency domain is developed for
determining the earthquake response of a dam including hydrodynamic
interaction and water compressibility effects. Linear responses of
.idealized, two-dimensional gravity dams and three-dimensional dams,
including arch dams, can be obtained. The dam and fluid domain are
treated as substructures and modeled with finite elements. The only
geometric restriction is that an infinite fluid domain must maintain
a uniform cross-section beyond some point in the upstream direction.
For such an infinite uniform region, a finite element discretization
within the cross-section combined with a continuum representation in
the infinite direction provides for a proper transmission of pressure
waves. The fluid domain model approximately accounts for fluid
foundation interaction through a damping boundary condition applied
along the reservoir floor and sides. The dam foundation is assumed
rigid.
Hydrodynamic effects are shown to be equivalent to an added
mass and added load in the frequency domain equations of motion of the
dam. When water compressibility is considered, the added mass and
added load vary with excitation frequency, and factors influencing
the dam response include resonances of the added load and the radia
tion damping associated with the imagi~ary component of the added mass.
If fluid-foundation interaction is neglected, this damping occurs only
for infinite fluid domains, but occcurs for both infinite and finite
fluid domains if fluid-foundation interaction is included.
ii
Fluid-foundation interaction also reduces resonances of the added load
which can be very large if the foundation beneath the water is assumed
rigid.
Hydrodynamic effects on the dam response are investigated for
acceleration responses to harmonic ground motions. Complex frequency
.response functions for acceleration at the dam crest are presented for
two-dimensional concrete gravity and earth dams and for a three
dimensional arch dam. Several reservoir shapes are included for the
concrete gravity dams. Water compressibility and fluid-foundation
interaction significantly influence the response of concrete gravity
dams and are even more important for the arch dam. One effect is a
greatly increased importance for the vertical component of ground
motion. Hydrodynamic effects on the responses of earth dams are shown
to be minor.
iii
ACKNOWLEDGEMENT
This research investigation was supported by the National Science
Foundation under Grants ATA74-20554 and ENV76-80073. The authors are
grateful for this support.
This report also constitutes John F. Hall's doctoral dissertation
which has been submitted to the University of California, Berkeley.
The dissertation committee consisted of Professors A. K. Chopra
(Chairman), R. W. Clough and B. A. Bolt. Appreciation is expressed to
Professors Clough and Bolt for reviewing the manuscript.
iv