Optimal hydraulic structures profiles under uncertain seepage head

Most of the hydraulic structures are founded on permeable foundation. There is, however, no procedure to fix the basic barrage parameters, which are depth of sheet piles/cutoffs and the length and thickness of floor, in a cost-effective manner. Changes in hydrological and climatic factors may alter the design seepage head of the hydraulic structures. The variation in seepage head affects the downstream sheet pile depth, overall length of impervious floor, and thickness of impervious floor. The exit gradient, which is considered the most appropriate criterion to ensure safety against piping on permeable foundations, exhibits non linear variation in floor length with variation in depth of downstream sheet pile. These facts complicate the problem and increase the non linearity of the problem. However, an optimization problem may be formulated to obtain the optimum structural dimensions that minimize the cost as well as satisfy the exit gradient criteria. The optimization problem for determining an optimal section for the weirs or barrages normally consists of minimizing the construction cost, earth work, cost of sheet piling, length of impervious floor etc. The subsurface seepage flow is embedded as constraint in the optimization formulation. Uncertainty in design, and hence cost from uncertain seepage head are quantified using fuzzy numbers. Results show that an uncertainty of 15 percent in seepage will result in 22 percent of uncertainty in design represented by overall design cost. The limited evaluation show potential applicability of the proposed method.