Piped water cooling of concrete dams

Charpin, J. and Myers, T. and Fitt, A.D. and Fowkes, N. and Ballim, Y. and Patini, A.P. (2006) Piped water cooling of concrete dams. Mathematics in Industry Study Groups in South Africa > MISGSA 2006: University of the Witwatersrand (23rd - 27th January 2006).

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Abstract/Summary

Piped water is used to remove hydration heat from concrete dams during construction. By examining simple models we obtain an estimate for the temperature rise along the pipe network and within the concrete. To leading order, for practically useful networks, the temperature distribution is quasi-steady, so that exact analytic solutions are obtained. The temperature in the water increases linearly with distance along the pipe and varies logarithmically with radial distance from the pipe in the concrete. Using these results we obtained estimates for the optimal spacing of pipes and pipe length. Some preliminary work on optimal network design has been done. This is work in progress.

Problem Statement

At the first (South African) Mathematics in Industry Study Group a mathematical model was developed to analyse the temperature, moisture content and maturity in concrete dams. Maturity describes the degree of hydration which occurs when water and cement are combined. By considering heat conservation, hydration chemistry and water conservation, three coupled nonlinear partial differential equations for the temperature, moisture content and maturity were derived. Since the moisture diffusivity of concrete depends on the moisture content, the moisture content satisfies a nonlinear diffusion equation. The Study Group is asked to investigate analytical and numerical solutions of this system of equations subject to suitable boundary and initial conditions for models of hydration of concrete dams.

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