STUDY ON PIPING ON THE DOWNSTREAM OF A WEIR ON NON HOMOGENEOUS PERMEABLE SOIL

Abstract

The exit gradient theory up to 19th century that used for designing various irrigartion structures was empirical method based on experience and intuition. Some of the structures failed because of subsurface flow. The subsurface flow may cause the failure of the impervious floor either by piping or by uplift pressure. Bligh went a step forward and gave a creep theory. According to this theory, the percolating water creeps along the contact surface of the base structure with subsoil. As the water creeps from the upstream end to the downstream end, the head loss occurs. The head loss is proportional to the creep distance traveled. Lane brought out the deficiencies in Bligh's creep theory. The theory gives the vertical creep three times more weightage as compared to the horizontal creep. Koshla and his associates determined the flow pattern below the impervious base of hydraulic structures on permeable foundation. They started with potential flow theory and found the solution of Laplace's equation for different configuration of floors. From the flow pattern, the distribution of uplift pressure on the base of the hydraulic structures and exit gradient were found. Piping starts from the downstream side, when the hydraulic gradient at the exit end is greater than the critical gradient of the soil. To ensure that the piping does not occur, there must be a downstream pile and the exit gradient should be safe. A general method of determining the functional relationship for confined flow problem was first introduced by Pavlovsky. If the all boundaries of the flow domain are completely defined, such flow is said to be confined. All the flow characteristics could be obtained once the function w = f (z) was known. By Schwarz-Cristoffel transformation the flow region in each of iii these planes can be mapped conformally onto the same half on an auxiliary t plane, yielding the function z = 1, (t) and w = f2 (t) . In the present study, using methods of fragments and conformal mapping, confined flow under a weir with a downstream cut off founded on a porous medium of finite depth with a highly porous slit in the foundation soil, has been analysed and the distribution of exit gradient, which is the prime cause of the piping, has been studied. The presence of a slit changes the distribution of exit gradient. It shifts the place vulnerable to piping from the sheet pile to its own location.