Hydrodynamic pressure on arch dams—by a mapping finite element method

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Abstract
A novel Finite Element Method (FEM) is proposed for the analysis of the uncoupled hydrodynamic pressures generated on arch dams due to a steady‐state ground acceleration. In this method the equation governing hydrodynamic pressures and also the prescribed boundary conditions are all transformed from the Cartesian space to a logarithmically condensed cylindrical polar space; in this process the physical configuration of the reservoir‐dam is also mapped into an ‘image’ domain. The transformed governing equation is then solved in the image domain, subject to the transformed boundary conditions, using standard finite elements. Because physical dimensions are logarithmically condensed in the image space, the proposed method is particularly suitable for dealing with large or very large aspect‐ratio reservoir‐dam systems, economically and efficiently.The high degree of accuracy which the proposed method is capable of, and also the simple way in which it can be applied to complex reservoir‐dam shapes, have been demonstrated by means of examples. The method has also been applied to study the uncoupled hydrodynamic pressures on the upstream face of a cylindrical arch dam, generated by a steady‐state vertical ground acceleration.

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