THREE DIMENSIONAL FEM ANALYSIS OF SUB-SURFACE FLOW UNDER DRAINAGE BARREL

Abstract

Practically every hydraulic structure has to face the problem of seepage beneath it. The major works constructed in India on alluvial rivers in the 19th century were mainly designed on experience as no rational theory of seepage had been worked out by then. In the case of hydraulic structures constructed like weir and barrage across wide streams where the width of the floor is considerably greater than its length, flow pattern is two dimensional. In the case where the width/length ratio of the structure is small, the seepage flow will be markedly thee dimensional. The correct approach in the estimation of the uplift below the hydraulic structures built on the porous media appears to be the one that treat the seepage flow to be three dimensional. Seepage in a three dimensional flow net will occur in accordance with the Laplace Equation in three dimensions a20 a20 + ay 2 (— + — ax2 a2A = 0 ) with the imposed boundary conditions. There is no az- analytical solution for the 3-dimensional seepage for complex conditions of the boundary. A solution may be obtained by the method of relaxation but it is very laborious and intricate for the three dimensional case. For a reliable estimation of the seepage pressure under the floor, model studies of geometrically similar models or electrically analogy models are the only expeditious methods.