Developing a mathematical framework for the cost of the river diversion works in dam construction, guides on the optimum diameter (Dopt) of the diversion tunnel are derived in both simple mathematical form and applied curves in terms of the design flood, tunnel length, valley width and tunnel support characteristics. Firstly, major components of the total cost were formulated to include tunnel excavation, pre-lining support, concrete lining and upstream cofferdam. Then assuming design discharge Q, tunnel length L and cofferdam length W are known, the cost function was determined using realistic unit prices. From the hydraulic equations describing the pressurized tunnel flow, the mathematical framework of the optimization is presented. In any given project, all four works involved (excavation, support, lining and cofferdam) can be expressed in terms of tunnel diameter, D. Therefore, D was adopted as the main variable in the minimization. The minimum construction cost of the diversion scheme, with or without lining, was derived in terms of D, Q, W and L. The use of realistic execution costs of the cofferdam and tunnel for a wide range of Q, W, L with various tunnel roughness coefficients provided for the required data to derive approximate formulas and curves to determine Dopt and the total cost in terms of the design flood. The curves can also be used to examine feasibility of twin tunnels as alternatives to single tunnel. It is found that Dopt and the total diversion cost are directly proportional to Q0.35 to 0.40 and Q0.52 to 0.62, respectively. It is also shown that Dopt is mainly a function of Q, W, L and the ratios (not the absolute values) of the unit prices and does not depend on the overall price levels in the respective country. Revision in design of the diversion schemes of some dams may lead to significant cost-effective changes.

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