2015 , Volume 20, № 4, p.45-55

In this article we develop a mathematical model for seismic fluctuations of a system consisting of schematized reservoirs, dams, base block and subbase layers of the soil massif. The model is a contact boundary value problem for a differential equation of the potential movement of water in the reservoir, the differential equation fluctuations cantilever beam (beam model of the dam), as well as differential equations of transverse (shear) oscillations of two layers subbase solid ground. These equations are interconnected through the boundary conditions at the contact surfaces. The boundary value problem is solved analytically. Initially we solve the hydrodynamic part of the initialboundary value problem. It consists of a differential equation of elliptic type with variable coefficients. The variability owes to factors due to the non prismatic configuration of the dam part of the reservoir, which is approximated by an exponential function of two spatial variables. With this approximation, an exact analytic solution of this differential equation with variable coefficients was found. In the process of solving the boundary problem we obtain an integral-differential equation of Fredholm type, which was solved using approximations. Numerical experiments have shown that the inclusion of the hydrodynamic water pressure at the upstream side of the dam significantly increases the amplitude of the displacement velocity and acceleration for oscillations of the dam. This effect must be considered when designing the construction. Results of the computational experiments allowed us to research and design the hydraulic structures and to properly choose the place of construction and dimensions of the structures that minimize the dynamic effects of the incident on the system of seismic waves.