Flooding Probability Constrained Optimal Design of Trapezoidal Channels

Abstract

Trapezoidal open channels are designed for specified slope, specific lining materials, and for a specified design flow. These input design parameters are prone to uncertainties. The freeboard is used to confine the flow within the limits of the channel cross section and to accommodate the uncertainty effects. Because of the size of uncertainty, the flow can overtop the freeboard with a “flooding probability.” To design an optimum channel cross section for safety against overtopping, the flooding probability constrained optimum channel design concept is introduced. An optimization model was developed which has two objective functions of minimizing the total cost of the channel and minimizing the flooding probabilities subject to uniform flow equation as constraint. The constraint method of multiobjective optimization is used in which the objective of minimizing the flooding probability is converted to a constraint, and the resulting single objective optimization problem is solved. The flooding probability constraint is developed by using the first order analysis. The final single objective optimization model is highly nonlinear and requires the use of the projected augmented Lagrangian technique. The optimization model is applied for two cases, namely, channels having composite roughness and channels having uniform roughness. The solution results of the analysis established the potential of the model.