DESIGN OF WEIR ON PERMEABLE FOUNDATION

Abstract

In irrigation engineering, weirs are the most extensively used control structures for flow diversion and flow measurement. Type and shape of a weir differ from one place to other, depending on available materials, sub-soil condition and hydrology of the river. A modern designed weir is constructed with plain or reinforced concrete, and provided with one or more rows of sheet piles. The sub-surface structure of a weir generally consists of either a horizontal or a sloping floor with at least one end sheet pile. The weir with a sloping floor is preferred as it is efficient in dissipating the surplus flow energy. Design of weir on permeable foundation involves integration of diverse fields such as sub-surface flow, surface flow, economics and optimization. Although the methods of weir analysis were known, no attempt was made in the direction of the optimal design of weir. The main reason is being the complexity of the problem. A weir is built on a permeable foundation. Therefore, in addition to the drag forces on account of surface flow it is subjected to uplift forces due to seeping of water under the weir foundation. The provision of sheet piles plays an important role in the distribution of the uplift pressure. The stability of a weir demands an upstream sheet pile and a downstream sheet pile, to prevent slipping of the soil under the weir to the anticipated scour holes at the upstream and downstream reaches. Furthermore, the downstream sheet pile is recommended as a preventive device against undermining. However, provision of more than two sheet piles increases the degree of IV complexity of the floor geometry to such an extent that the usual methods of analysis can not be applied to evaluate the uplift pressure distribution. The present study was undertaken to develop an algorithm for optimal design of a weir with a sloping floor and having a number of sheet piles in various combinations. For this purposes a cost function of the weir was formed which involves its physical dimensions. The safety requirements were expressed in the form of constraints. The uplift pressure and the maximum exit gradient have been obtained using the Schwarz- Christoffel conformal mapping. The transformation parameters have been evaluated solving the implicit transformation equations using random search method. A design algorithm, using Random Search Method for minimizing the cost function subject to the constraints, was developed. For a given set of data the algorithm yields the optimum design which is safe and economical. The present study shows that provision of a downstream end sheet pile leads to increase the uplift pressure distribution under the floor which leads to increase the floor thickness. At the same time, it substantially reduces the required floor length. Therefore, a weir with end sheet pile is more economical than the weir without a sheet pile. In addition to the downstream sheet pile, provision of an upstream sheet pile slightly decreases the uplift pressure distribution under the floor but the cost of the weir increases due to the cost of the additional sheet pile. The provision of intermediate sheet piles is less important as they do not materially alter the pressure distribution. They are provided merely as an important second lines of defense. The present study indicates that, the cost of weir increases as a square root of the high flood discharge and it linearly increases with the ratio of unit cost of concrete/unit cost of earth work and it is inversely proportional to the median bed material size and the bed slope.