Keywords: acoustic cavitation, fluid-structure interaction, finite element method, nonlinear analysis, concrete arch dams.

The present research focuses on the development and verification of a computational procedure and relevant code capable of predicting the water cavitation effects on dynamic response of a coupled arch dam-reservoir system. One of the sources of nonlinear behavior in dam-reservoir systems is the formation and collapse of gaseous regions in the impounded water due to cavitation [1,2]. Cavitation occurs because of the reflection of the pressure wave from the free surface and, or wetted structure, which causes the pressure in the water decrease below its vapor pressure. The instantaneous bulk modulus of the cavitated water is smaller than that of uncavitated water, which produces nonlinear behavior [3].

The objective of this study is to provide the engineer with a set of tools to accurately and efficiently model the cavitation phenomenon with particular reference to the classic acoustic fluid-structure interaction problem of a dam experiencing seismic excitation. A one-fluid cavitation model [4] is used assuming the cavitating fluid to be a homogenous and barotropic mixture of vapor and liquid. An explicit staggered partitioned solution scheme [5] is employed for coupling the equations of motion of the fluid and the structural domains using the implicit (HHT-alpha) method [6] for the numerical time integration of the equations of motion. Based on the results presented in this paper the following conclusion can be drawn:

1. The coupling phenomena are found to have great significance in the case of dam-reservoir interaction analysis.
2. Once the cavitation takes place, the interaction process is quite different from what is predicted by a model that does not consider cavitation.
3. A parametric study of a typical arch dam- reservoir coupled system shows that water cavitation does not amplify the dynamic response of the arch dam but strongly changes the time history of the hydrodynamic pressure and crest displacement of the arch dam.

1

O.C. Zienkiewicz, D.K. Paul, E. Hinton, "Cavitation in fluid-structure response (with particular reference to dams under earthquake loading)", Earthquake Engineering and Structural Dynamics, 11, 463-481, 1983. doi:10.1002/eqe.4290110403

2

R.W. Clough, C. Chu-Han, "Seismic cavitation effects on gravity dam reservoirs", in R.W. Lewis et al., "Numerical methods in coupled systems", John Wiley and Sons, New York, 571-598, 1984.

3

G. Sandberg, "A new finite element formulation of shock-induced hull cavitation", Comput. Methods Appl. Mech. Engng., 120, 33-44, 1995. doi:10.1016/0045-7825(94)00050-W

4

D.P. Schmidt, C.J. Rutland, M.L. Corradini, "A fully compressible, two-dimensional model of small, high speed, cavitating nozzles", Atomization Sprays, 9, 255-276, 1999.

5

C.A. Felippa, K.C. Park, C. Farhat, "Partitioned Analysis of Coupled Mechanical Systems", Report No. CU-CAS-99-06, College of Engineering University of California, 1999.

6

H.M. Hilber, T.J.R. Heghes, R.T. Taylor, "Improved numerical dissipation for integration algorithms in structural dynamics", Earthquake Engineering and Structural dynamics, 5, 283-292, 1977. doi:10.1002/eqe.4290050306

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