Keywords: differential quadrature method, dam-reservoir interaction, non-prismatic beam, fluid-structure interaction, finite difference method.

Foundation-reservoir-structure interaction is a very important subject in engineering research and practice. Although sophisticated calculation tools based on general finite element codes are widely available, the availability of simplified methods is of great importance for obvious reasons. For most practical uses a linear analysis suffices for estimating the behavior of the system. A general approach in the literature is the application of a cantilever beam to model concrete gravity dams. As a result of the non-prismatic nature of the gravity dam's sections, conventional beam theory is insufficient but it seems adequate to use non prismatic beam theories and methods to model the dam. Various methods have been proposed to meet this requirement.

In this paper a numerical method is proposed for analyzing the interaction of the foundation-reservoir-structure for concrete gravity dams. The reservoir is assumed unbounded at the far end for incompressible and invicid fluid. The foundation is assumed elastic and is characterized by rotational and longitudinal springs. The structure is modeled as a cantilever beam with elastic support.

The partial differential equation of motion is discretized using differential quadrature method for spatial derivatives and the finite difference method for time derivatives. It is shown that using the differential quadrature method (DQM) with a few grid points in conjunction with the finite difference method (FDM) ensures good convergence. The comparison of the results obtained by the present method with those in the literature shows that the method is appropriate.

The accuracy of the quadrature solutions is dictated by the choice of the locations of the sampling grid points. However, the issue of the proper choice of the sampling grid points remains largely an unclear matter. Although it seems natural and convenient to choose sampling grid points with equal spacing, in a considerable number of papers, it has been reported that the Chebyshev (Gauss-Lobatto) sampling grid points performed consistently better than the equally spaced, Legendre and Chebyshev sampling grid points for a variety of problems. The formulation presented in this study seems promosing for closed form solutions and detailed formulations and relevant techniques are currently under investigation and will be published in near future.

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