Keywords: concrete arch dam, shell buckling, shell structure, thin shell, hydrostatic pressure loading, linear elastic buckling.

The research on arch dams that has been reported in the literature has mostly comprised case studies of actual dams constructed worldwide to date. Although important lessons can be learnt from such studies, the data upon which the observations are based is very site-specific, making it difficult to apply the results to new designs that may be required elsewhere. New forms of arch dams have been explored both experimentally and via numerical simulations [1]. Good arch-dam design consists in minimising bending actions and ensuring that the state of stress is near-membrane, but bending effects will be inevitable in the vicinity of the edges [2].

It is acknowledged that attempting to generalise design situations which are generally all different from each other results in loss of design precision and the optimization that goes with it. However, such an approach can have merit in the preliminary stages of the design process, where the objective is simply to establish which alternatives are viable, and details are not too important. Real arch dams with irregular boundaries and non-uniform support conditions can be idealised as simpler models with straight-sided boundaries and support conditions that remain uniform over a given edge. By combining the simplified valley shapes with all possible surface geometries of the arch dam (singly-curved and doubly-curved shells), and with all practical thickness variations of the concrete shell, we can assemble a comprehensive set of arch-dam options. These can then be studied individually to extract important characteristics like buckling strength and buckling modes, critical stresses for material failure in tension and compression, natural frequencies of vibration, etc. A database of basic characteristics of each type of arch dam can thus be assembled.

In this preliminary study, we consider horizontally-curved arches of circular and parabolic profile, where the projection of the dam wall on a vertical plane is a rectangle of width a and depth b, and the horizontal bulge of the shell relative to the vertical plane connecting the left and right abutments (which we will call the rise of the shell) is h. The concrete shell of the dam is assumed to be of constant thickness t. Based on the load case of full hydrostatic water pressure, a numerical investigation of the dependence of the critical buckling pressure on the parameters a, t, h/a and b/a is carried out. The results are presented in the form of design curves, which allow a safe combination of design parameters to be chosen, at the same time providing an indication of the factor of safety associated with a particular design.

Ongoing studies are considering more complicated valley shapes, arch dams in the form of shells of double curvature (elliptic paraboloids and toroidal surfaces), walls of varying thickness (linear and parabolic), effect of vertical rib stiffeners, nonlinear material behaviour, and postbuckling response of the arch dam.

1

V.D. da Silva, E.N.B.S. Julio, "Computation of membrane shapes and analysis of arch dams", Computers & Structures, 64(1-4), 849-855, 1997. doi:10.1016/S0045-7949(96)00420-8

2

A. Zingoni, "Shell Structures in Civil and Mechanical Engineering", Thomas Telford Publishing, London, 1997.

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