TECHNICAL PAPERS
Oct 1, 1990

Method for Transient Analysis of Three‐Dimensional Dam‐Reservoir Interactions

Publication: Journal of Engineering Mechanics
Volume 116, Issue 10

Abstract

The nonlinear behavior of dam‐reservoir interactions is not well understood, especially when the system is formulated as a three‐dimensional problem. One of the major difficulties is a lack of time‐domain transmitting boundary for the far field (extending to infinity in the fluid domain). An efficient time‐domain analysis procedure for a three‐dimensional fluid‐structure system based on a semianalytical method is developed, which takes into consideration the radiated waves in the far field. The cross section of the far field, which may have an arbitrary shape, is assumed to extend uniformly to infinity in the upstream direction. The irregular near field with arbitrary geometrical shape and boundary conditions is modeled using the conventional finite element method. Accuracy of the proposed method is established by comparing the numerical results with piecewise exact form of analytical solutions for a vertical rigid dam with vertical valleys subjected to actual earthquake and ramp loadings. In the proposed method, all of the procedures are processed directly in the time domain, which is efficient for nonlinear analyses of dams with infinite reservoirs formulated as a three‐dimensional problem.

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References

1.
Antes, H., and Von Estorff, O. (1987). “Analysis of absorption effects on the dynamic response of dam reservoir systems by boundary element methods.” Earthquake Engrg. Struct. Dyn., 15(8), 1023–1036.
2.
Bathe, K. J. (1982). Finite element procedures in engineering analysis. Prentice‐Hall Inc., Englewood Cliffs, N.J.
3.
Chakrabarti, P., and Chopra, A. K. (1973). “Earthquake analysis of gravity dams including hydrodynamic interaction.” Earthquake Engrg. Struct. Dyn., 2(2), 143–160.
4.
Chopra, A. K. (1967). “Hydrodynamic pressures on dams during earthquakes.” J. Engrg. Mech., ASCE, 93(6), 205–223.
5.
Chopra, A. K., and Gupta, S. (1982). “Hydrodynamic and foundation interaction effects in frequency response functions for concrete dams.” Earthquake Engrg. Struct. Dyn., 10(1), 89–106.
6.
Chwang, A. T., and Housner, G. W. (1978). “Hydrodynamic pressures on sloping dams during earthquakes. Part 1. Momentum method.” J. Fluid Mech., 87, Part 2, 335–341.
7.
Dowling, M. J., and Hall, J. F. (1989). “Nonlinear seismic analysis of arch dams.” J. Engrg. Mech., ASCE, 115(4), 768–789.
8.
El‐Aidi, B., and Hall, J. F. (1989a). “Non‐linear earthquake response of concrete gravity dams part 1: Modelling.” Earthquake Engrg. Struct. Dyn., 18(6), 837–851.
9.
El‐Aidi, B., and Hall, J. F. (1989b). “Non‐linear earthquake response of concrete gravity dams part 2: Behavior.” Earthquake Engrg. Struct. Dyn., 18(6), 853–865.
10.
Erdelyi, A. (1953). Higher transcendental functions, Vol. II, McGraw‐Hill Book Co., New York, N.Y.
11.
Fenves, G., and Chopra, A. K. (1985). “Earthquake analysis of concrete gravity dam including reservoir bottom absorption and dam‐water‐foundation rock interaction.” Earthquake Engrg. Struct. Dyn., 13(1), 13–31.
12.
Fenves, G., and Vargas‐Loli, L. M. (1988). “Nonlinear dynamic analysis of fluidstructure ystems.” J. Engrg. Mech., ASCE, 114(2), 219–240.
13.
Fok, K.‐L., and Chopra, A. K. (1986). “Earthquake analysis of arch dams including dam‐water interaction, reservoir boundary absorption and foundation flexibility.” Earthquake Engrg. Struct. Dyn., 14(2), 155–184.
14.
Hall, J. F. (1986). “Study of the earthquake response of pine flat dam.” Earthquake Engrg. Struct. Dyn., 14, 281–295.
15.
Hall, J. F., and Chopra, A. K. (1980). “Dynamic response of embankment, concrete gravity and arch dams including hydrodynamic interaction.” Report No. EERC. 80‐39, Oct., Earthquake Engrg. Res. Ctr., Univ. of California, Berkeley, Calif.
16.
Hall, J. F., and Chopra, A. K. (1982). “Two‐dimensional dynamic analysis of concrete gravity and embankment dams including hydrodynamic effects.” Earthquake Engrg. Struct. Dyn., 10(2), 305–332.
17.
Hanna, Y. G., and Humar, J. L. (1982). “Boundary element analysis of fluid domain.” J. Engrg. Mech., ASCE, 108(2), 436–450.
18.
Hung, T.‐K., and Wang, M. H. (1987). “Nonlinear hydrodynamic pressure on rigid dam motion.” J. Engrg. Mech., ASCE, 113(4), 482–499.
19.
Liu, P. L.‐F., and Cheng, A. H.‐D. (1984). “Boundary solutions for fluid‐structure interaction.” J. Hydr. Engrg., ASCE, 110(1), 51–64.
20.
Liu, P. L.‐F., and Liggett, J. A. (1984). “Boundary element formulations and solutions for some non‐linear water wave problems.” Developments in boundary element methods‐3, P. K. Banerjee and S. Mukherjee, eds., Elsevier Applied Science Publishers, New York, N.Y.
21.
Lotfi, V., Roesset, J. M., and Tassoulas, J. L. (1987). “A technique for the analysis of the response of dams to earthquake.” Earthquake Engrg. Struct. Dyn., 15(4), 463–490.
22.
Lysmer, J., and Wass, G. (1972). “Shear waves in plane infinite structures.” J. Engrg. Mech., ASCE, 98(1), 85–105.
23.
Mei, C. C., Foda, M. A., and Tong, P. (1979). “Exact and hybrid‐element solutions for the vibration of a thin elastic structure seated on the sea floor.” Appl. Ocean Res., 1(2), 79–88.
24.
O'Connor, J. P. F., and Boot, J. C. (1988). “A solution procedure for the earthquake analysis of arch dam‐reservoir systems with compressible water.” Earthquake Engrg. Struct. Dyn., 16(5), 757–773.
25.
Porter, C. S., and Chopra, A. K. (1982). “Hydrodynamic effects in dynamic response of simple arch dams.” Earthquake Engrg. Struct. Dyn., 10(3), 417–431.
26.
Shiojiri, H., and Taguti, T. (1988). “Nonlinear dynamic analysis of structures including hydrodynamic and foundation interaction effects.” Proc. Ninth World Conf. on Earthquake Engrg., VI, Japan Assoc. of Earthquake Disaster Prevention, Aug., 1988, 271–276.
27.
Sommerfeld, A. (1949). Partial differential equations in physics. Academic Press, New York, N.Y.
28.
Tsai, C. S., and Lee, G. C. (1987a). “Arch dam‐fluid interactions: by FEM‐BEM and substructure concept.” Int. J. Numer. Methods Engrg., 24, Dec., 2367–2388.
29.
Tsai, C. S., and Lee, G. C. (1987b). “Analyses of infinite reservoir using the boundary element method with particular integrals.” Boundary Elements IX, Proc., Ninth Int. Conf., Stuttgart, West Germany, Sep., 1, 143–164.
30.
Tsai, C. S., and Lee, G. C. (1987c). “Analyses of infinite reservoir.” ASCE Engrg. Mech. Specialty Conf., May.
31.
Tsai, C. S., Lee, G. C., and Ketter, R. L. (1988). “Solution of the dam‐reservoir interaction problem using a combination of FEM, BEM with particular integrals, modal analysis and substructuring.” Tech. Report NCEER‐88‐0036, National Center for Earthquake Engrg. Res., State Univ. of New York, Buffalo, N.Y.
32.
Tsai, C. S., and Lee, G. C. (1989). “Hydrodynamic pressure on gravity dams subjected to ground motion.” J. Engrg. Mech., ASCE, 115(3), 598–617.
33.
Tsai, C. S., Lee, G. C., and Ketter, R. L. (1990). “A semi‐analytical method for time‐domain analyses of dam‐reservoir interactions.” Int. J. Numerical Methods in Engrg., 29, 913–933.
34.
Vargas‐Loli, L. M., and Fenves, G. L. (1988). “Nonlinear response of concrete gravity dams.” Proc. Ninth World Conf. on Earthquake Engrg., VI, Aug., 1988, 343–348.
35.
Vargas‐Loli, L. M., and Fenves, G. L. (1989). “Effects of concrete cracking on the earthquake response of gravity dams.” Earthquake Engrg. Struct. Dyn., 18, 575–592.
36.
Von Karman, T. (1933). “Discussion of water pressures on dams during earthquakes.” Trans., ASCE, 98, 434–436.
37.
Wepf, D. H., Wolf, J. P., and Bachmann, H. (1988). “Hydrodynamic‐stiffness matrix based on boundary elements for time‐domain dam‐reservoir‐soil analysis.” Earthquake Engrg. Struct. Dyn., 16, 417–432.
38.
Westergaard, H. M. (1933). “Water pressures on dams during earthquakes.” Trans., ASCE, 98, 418–433.
39.
Zangar, C. N., and Haefeli, R. J. (1952). “Electric analog indicates effect of horizontal earthquake shock on dams.” Civ. Engrg., Apr., 54–55.
40.
Zienkiewicz, O. C., and Nath, B. (1963). “Earthquake hydrodynamic pressures on arch dams—an electric analogue solution.” Proc. Inst. Civ. Engrg., 25, 165–176.
41.
Zienkiewicz, O. C., Bettess, P., and Kelly, D. W. (1978). “The finite element method for determining fluid loadings on rigid structures two‐ and three‐dimensional formulations.” Numerical Methods in Offshore Engineering, O. C. Zienkiewicz, R. W. Lewis, and K. G. Stagg, eds., John Wiley and Sons, New York, N.Y.
42.
Zienkiewicz, O. C., and Bettess, P. (1978a). “Dynamic fluid‐structure interaction. Numerical modeling of the coupled problem.” Numerical Methods in Offshore Engineering, O. C. Zienkiewicz, R. W. Lewis, and K. G. Stagg, eds., John Wiley and Sons, New York, N.Y.
43.
Zienkiewicz, O. C., and Bettess, P. (1978b). “Fluid‐structure dynamic interaction and wave forces. An introduction to numerical treatment.” Int. J. Numer. Methods in Engrg., 13, 1–16.
44.
Zienkiewicz, O. C., Paul, D. K., and Hinton, E. (1983). “Cavitation in fluid‐structure response (with particular reference to dams under earthquake loading).” Earthquake Engrg. Struct. Dyn., 11, 463–481.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 116Issue 10October 1990
Pages: 2151 - 2172

History

Published online: Oct 1, 1990
Published in print: Oct 1990

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Authors

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Chong‐Shien Tsai, Associate Member, ASCE
Res. Asst. Prof., Dept. of Civ. Engrg., 412 Bonner Hall, Univ. of Buffalo, Buffalo, NY 14260
George C. Lee, Member, ASCE
Prof., Dean of Engrg. and Appl. Sci., 412 Bonner Hall, Univ. of Buffalo, Buffalo, NY

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