Practical Formulas for Frequency Domain Analysis of Earthquake-Induced Dam-Reservoir Interaction
Publication: Journal of Engineering Mechanics
Volume 136, Issue 1
Abstract
Dam-reservoir dynamic interactions are complex phenomena requiring advanced mathematical and numerical modeling. Although available sophisticated techniques can handle many aspects of these phenomena, simplified procedures are useful and still needed to globally evaluate the dynamic response of dam-reservoir systems. This paper presents and validates an original practical procedure to investigate earthquake induced dam-reservoir interaction in the frequency domain, including the effects of dam flexibility, water compressibility, and reservoir bottom wave absorption. The procedure relates hydrodynamic pressure due to any deflected modal response of a two-dimensional gravity dam on a rigid foundation to hydrodynamic pressure caused by a horizontal rigid body motion. New analytical expressions that can be easily programmed in a spreadsheet package or implemented in a dam structural analysis program are also proposed to conduct simplified fundamental mode earthquake analysis of gravity dams. The techniques presented can be efficiently used to provide valuable insight into the effects and relative importance of the various parameters involved in the dynamic response of dam-reservoir systems. Although the mathematical derivations and closed-form expressions developed were applied to dam-reservoir systems herein, they can be easily adapted to other fluid-structure interaction problems.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writers acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Quebec Fund for Research on Nature and Technology (FQRNT).
References
ADINA R&D, Inc. (2009). “Theory and modeling guide, Volume I: ADINA solids and structures.” Rep. No. ARD 09-7, Watertown, Mass.
Bouaanani, N., Paultre, P., and Proulx, J. (2002). “Two-dimensional modelling of ice-cover effects for the dynamic analysis of concrete gravity dams.” Earthquake Eng. Struct. Dyn., 31(12), 2083–2102.
Bouaanani, N., Paultre, P., and Proulx, J. (2003). “A closed-form formulation for earthquake-induced hydrodynamic pressure on gravity dams.” J. Sound Vib., 261(3), 573–582.
Chakrabarti, P., and Chopra, A. K. (1973). “Earthquake analysis of gravity dams including hydrodynamic interaction.” Earthquake Eng. Struct. Dyn., 2(2), 143–160.
Chopra, A. K. (1968). “Earthquake behavior of reservoir-dam systems.” J. Engrg. Mech. Div., 94(6), 1475–1500.
Chopra, A. K. (1970). “Earthquake response of concrete gravity dams.” Rep. No. UCB/EERC-70/01, Univ. of California, Berkeley, Calif.
Chopra, A. K. (1978). “Earthquake resistant design of concrete gravity dams.” J. Struct. Div., 104(6), 953–971.
Clough, R. W., and Penzien, J. (1975). Dynamics of structures, McGraw-Hill, New York.
Fenves, G., and Chopra, A. K. (1984). “EAGD-84, a computer program for earthquake analysis of concrete gravity dams.” Rep. No. UCB/EERC-84/11, Univ. of California, Berkeley, Calif.
Fenves, G., and Chopra, A. K. (1985). “Simplified earthquake analysis of concrete gravity dams: Separate hydrodynamic and foundation interaction effects.” J. Eng. Mech., 111(6), 715–735.
Fenves, G., and Chopra, A. K. (1987). “Simplified earthquake analysis of concrete gravity dams.” J. Struct. Eng., 113(8), 1688–1708.
Fok, K. L., Hall, J. F., and Chopra, A. K. (1986). “EACD-3D, a computer program for three-dimensional earthquake analysis of concrete dams.” Rep. No. UCB/EERC-86/09, Univ. of California, Berkeley, Calif.
Hall, J. F., and Chopra, A. K. (1980). “Dynamic response of embankment, concrete-gravity and arch dams including hydrodynamic interaction.” Rep. No. UCB/EERC-80/39, Univ. of California, Berkeley, Calif.
Humar, J. L., and Jablonski, A. M. (1988). “Boundary element reservoir model for seismic analysis of gravity dams.” Earthquake Eng. Struct. Dyn., 16(8), 1129–1156.
Liu, Ph., and Cheng, A. (1984). “Boundary solutions for fluid-structure interaction.” J. Hydraul. Eng., 110(1), 51–64.
Maeso, O., Aznarez, J. J., and Dominguez, J. (2004). “Three-dimensional models of reservoir sediment and effects on the seismic response of arch dams.” Earthquake Eng. Struct. Dyn., 33(10), 1103–1123.
Proulx, J., Paultre, P., Rheault, J., and Robert, Y. (2001). “An experimental investigation of water level effects on the dynamic behaviour of a large arch dam.” Earthquake Eng. Struct. Dyn., 30(8), 1147–1166.
Saini, S. S., Bettess, P., and Zienkiewicz, O. C. (1978). “Coupled hydrodynamic response of concrete gravity dams using finite and infinite elements.” Earthquake Eng. Struct. Dyn., 6(4), 363–374.
Tsai, C. S., and Lee, G. C. (1987). “Arch dam-fluid interactions: by FEM-BEM and substructure concept.” Int. J. Numer. Methods Eng., 24(12), 2367–2388.
Westergaard, H. M. (1933). “Water pressure on dams during earthquakes.” Trans. Am. Soc. Civ. Eng., 98(1850), 418–472.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 136 • Issue 1 • January 2010
Pages: 107 - 119
Copyright
© 2010 ASCE.
History
Received: Jun 28, 2008
Accepted: Jun 4, 2009
Published online: Jun 6, 2009
Published in print: Jan 2010
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.