Optimal design of trapezoidal lined channel with least cost: Semi-theoretical approach powered by genetic programming

Abstract

In this paper the effects of the aspect ratio (width to depth ratio, b/d) on the cost of a trapezoidal concrete-lined channel (either power channel or irrigation channel) are analysed. The recommended b/d ratios given in the literature and their limitations are also discussed. Efforts are made to derive an equation for determining the optimal depth of the water from known parameters such as discharge, velocity and bed slope for concrete-lined channels. An equation for finding the minimum possible discharge within a specific velocity and bed slope is developed based on a semi-theoretical approach. The same approach is followed to obtain another formula for finding the maximum possible velocity for a specific discharge and bed slope. The obtained equations eliminate the iteration process commonly involved in finding the dimensions of a trapezoidal channel. A relation is developed for finding the aspect ratio in response to a given discharge and bed slope by using linear genetic programming techniques. The results show that the proposed model can be successfully applied in the design of lined channels as an alternative to existing methods.