Author(s): S. Brambilla; F. Ferrari; D. Gatti; G. Testa; R. Pacheco
Linked Author(s): Yashemi Pacheco Rodriguez
Keywords: Lagrangian; Dam failure; Cascade dam
Abstract: The dam failures of multiple reservoirs cascade arranged along the same valley may generate macro flood which can result in enormous losses of lives and property damages. Several numerical schemes are available in the literature to evaluate the response of a chain of reservoirs to a catastrophic input, generated as a result of failure of an upstream dam or extreme floods. These include the following techniques: the characteristics method[Chen C. L., 1980]; finite difference method (FDM) [Garcia and Kahawita (1986), Fennema and Chaudhry (1990) ]and the finite elements method (FEM) [see, for example, Katapodes (1984), Alam and Bhuiyan (1994) ]. All the above mentioned schemes solve numerically the shallow water equations on Eulerian fixed grids. The major disadvantage implied in the Eulerian treatment of these problems is that the number of spatial grid points involved in the description of the free surface may constantly vary. This almost invariably requires interpolation or extrapolation procedures implying severe difficulties in computer coding. The obvious alternative, which also gives a more realistic representation of problems involving a moving waterline, is the use of a Lagrangian specification of the flow field. The present study deals with the mathematical modelling of flood waves resulting from successive dam failures using a finite element model that solves the governing equations of one-dimension free-surface flow in the Lagrangian form. The model, which is based on a technique proposed by Di Monaco and Molinaro[1]for the problem of propagation of a flooding wave on a dry riverbed, appears an excellent and effective tool for the numerical treatment of cascade dam failures. The way of dealing with cascade dam failure is discussed. In particular the paper shows a methodology that can be generalized when a Lagrangian approach for the solution of this type of problems is applied.
Year: 1999