Keywords: dam reservoir interaction, finite element method, truncating boundary, hydrodynamic pressure.

An important factor in the design of dams in seismic regions is the effect of hydrodynamic pressure exerted on the face of the dam as a result of earthquake ground motions. For an accurate analysis of hydrodynamic pressure on the dam having irregular geometries, the reservoir is generally treated as an assemblage of finite elements.

Zienkiewicz et al. [1] presented the finite element formulation for analyzing the coupled response of submerged structures assuming water to be incompressible. Nath [2] analyzed the problem using the method of finite differences but neglecting radiation damping. Chakrabarti and Chopra [3] have formulated the reservoir as a continuum of infinite length. Two dimensional problem of the added-mass effect of horizontal acceleration of a rigid dam with an inclined upstream face of constant slope was solved analytically by Chwang and Housner [4] using a momentum balance approach.

In the finite element formulation, unbounded domain of reservoir arise a problem in modeling. To achieve this difficulty, the unbounded domain should be truncated at a certain distance away from the structure. The most commonly used boundary condition along the truncation surface is the Sommerfeld radiation condition [5]. Since this boundary condition takes the form of that for a rigid stationary boundary, the behavior of the reservoir domain is not truly represented.

An another boundary condition along the truncating surface for an unbounded and incompressible fluid domain is developed by Sharan [6]. Although this boundary condition is better than the Sommerfeld radiation condition, it does not represent the behavior well when truncation surface is very near to dam surface.

A new boundary condition along the truncating surface of an unbounded reservoir domain is developed by approximating the analytical solution of the hydrodynamic pressure.

Solution of the hydrodynamic pressure is obtained by assuming that: 1) the fluid domain extends to infinity and its motions is two dimensional, 2) fluid-structure interface is vertical, 3) the submerged structure is rigid, 4) the bottom of fluid domain is rigid and horizontal.

A numerical study is carried out to compare the results of Sommerfeld's and Sharan's boundary conditions. It was seen that the proposed boundary condition is efficient and gives better results than the previous published results and this new boundary condition is extendable for compressible fluid domains.

1

O.C. Zienkiewicz, B. Irons, B. Nath, "Natural frequencies of complex free or submerged structures by the finite element method", Symp. Vibrations Civ. Engng, Butterworths, London, 1965.

2

B. Nath, "Coupled hydrodynamic response of gravity dam", Proc. Inst. Civ. Engng, 48, 245-257, 1971. doi:10.1680/iicep.1971.6462

3

P. Chakrabarti, A.K. Chopra, "Hydrodynamic effects in earthquake response of gravity dams" ASCE J. Stuct. Div., 100, 1211-1224, 1974.

4

A.T. Chwang, G.W. Hausner, "Hydrodynamic pressures on sloping dams during earthquakes. Part 1 : Momentum method", J. Fluid Mech. 87, 335-341, 1978. doi:10.1017/S0022112078001639

5

A. Sommerfeld, "Partial differential equations in physics", Academic Press, New York, 1949.

6

S.K. Sharan, "Finite element analysis of unbounded and incompressible fluid domains", Int. J. Numer. Meth, 21, 1659-1669, 1985. doi:10.1002/nme.1620210908

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