Finite Elements In Combination With InfiniteBoundary Elements For Concrete ArchDam-foundation Analysis

Abstract

This paper suggests a scheme of analysis for arch dam-foundation problems. For the arch dam part the thick shell finite elements had been used while the foundation part is modelled by the general quadratic boundary elements and the infinite boundary elements. In order to implement the coupling of this different type of element a sort of shell-coupling finite element is developed. Thus an effective procedure for the interaction of foundation-dam system had been proposed. Some computational results are given. INTRODUCTION The interaction of foundation and dam is one of the key factors for accurrate analysis of the safety of dams. Boundary element method is particularly suitable for the infinite nature of the foundation. Coupling of finite element and boundary element will preserve the advantages of high accuracy in computations and the reduction of the dimensions of the problem for boundary element treatment while the procedure of the finite elements will still keep its versatility. A situation to be easily accommodated is the case for more than one element type is employable to the simulating the structure. For example, in three dimensional analysis the solid finite element may have a shell finite element associated with it. This is particularly useful in the analysis of reinforced concrete structures such as prestressed concrete reactor vessels, tunnel construction and the design of important dams, where the concrete structure is modelled by shell finite elements and the foundation is modelled by solid finite elements or infinite boundary elements. In the solid finite element or boundary element there are three degrees of freedom at each node while in the shell finite element the shape of element is prescribed by the nodal coordinates in the middle plane of the shell, each node is of five degrees of freedom. In order to implement the coupling of these different element types it is desirable that a sort of shell-coupling finite element is developed. In this paper, an effective scheme of analysis for the arch dam-foundation problems has been proposed. Transactions on Modelling and Simulation vol 7, © 1994 WIT Press, www.witpress.com, ISSN 1743-355X 586 Boundary Element Method XVI A VARIABLE NODE BOUNDARY ELEMENT A 4-8 node boundary element for general quadratic boundary element or infinite boundary element is shown in Fig. 1 . For a finite boundary element the coordinate, displacement and traction components can be interpolated in the following manner( isoparametric interpolation): z,= 7V'X, M,: = 7VX f, = 7V . (c=l,2,--.,8) (1) where the shape functions can be written as following