Analysis on Finite Element Grid Size and Discrete Error for Super-high Arch Dams

Abstract Compared with the world super-high arch dams with height more than 200 meters, the six super-high arch dams already built or under construction in China share the same special body shapes with higher ratios for both top/bottom width and thickness, and for top arch length with dam height. Also all of them are subjected to big top-level water pressures. In the paper, the computational formulation of thermal-coupled structure of hollow sphere similar to arch dam in shape and load-subjected is derived first and analysis of errors from the finite element method compared with the analytic solution is made. Then, a typical super-high arch dam is taken as the example of structure analysis including dam body mesh division, stress distribution, error estimation. Employing quadrilateral Coupled-field tetrahedral element with size decided by the bottom thickness multiple of arch crown beam, performance of mesh division and analysis for complex model is done conveniently and fast. Also, the paper investigates the error and convergence of results with different mesh density, discusses the special stress states of arch dam, and proposals acceptable dam body element size from calculation accuracy, convenient operation and elapsed time when performance is carried on with strong coupling on conmen personal computers. The research work indicates that errors of analysis results in most part of area are very small excepting those for the local singularity and concentration part when the dam body element size is decreased to 0.25 multiple of bottom thickness of arch crown beam, with dam body energy error norm less than 10% and consuming a couple of elapsed time. The conclusion should be common for the arch dams in China as they have similar shape.