An analytical solution for dynamic response of water barrier subjected to strong shock waves caused by an underwater explosion to dams

Shock waves arriving at a dam site are close to plane waves when the center of an underwater explosion is far from the dam site. In general, the wave pressure is calculated with COLE empirical formula. The COLE formula is a negative exponential function with respect to time. In this paper, a new analytical solution algorithm is proposed, which does not require the use of step-by-step time integration. In Comparison with the step-by-step time integration, the proposed algorithm requires relatively less calculation and avoids high-frequency oscillation. Furthermore, the vertical upstream surface and the sloping upstream surface in two types of the dams are analyzed in this paper. The research results indicate that the analytical solution can be applied for a dam with a vertical upstream surface. However, because the upstream face of a dam is inclined, the analytical solution can be obtained only for dams that are at lower height. Whenever the height of a dam is higher, then no analytical solution can be obtained, and only the use of step-by-step time integration can obtain a solution.