Generally, most waterpower plants have to function under energy system peak load operation. Thus, there is a relatively quick water level variation observed in water-storage reservoirs, which contributes to the problems, especially in case of high-pressure waterworks facilities. Swift reservoir draw-down enhances seepage volumetric forces acting from the rock mass, which may lead to rock mass cracking and eventually to the development of landslide processes. A rapid impoundment of the water-storage reservoir is no less damaging. In this case, seepage in the rock mass is progressing in non-steady conditions, there occurring, in the inception stage: - high magnitude seepage hydrodynamic forces at the rock mass surface, creating additional loads on the rock mass, causing deflection of its surface, which may promote dam-foundation contact opening; - with increased pore pressures and seepage gradients, there may occur suffusion and other undesirable processes in the rock mass. In the work is given a numerical analysis of some parameters of seepage mode given based on right-bank investigation admitting presence of break in the dam filling-up mode. Options of time-intervals for the two basic versions – in case of sudden rising of water level in the upstream and in case of slow filling-up and setting up steady-state seepage mode in the massive – are being discussed. Determination of seepage flow parameters (including gradients) requires nonstationary field task to be solved. Finite-elements approximation for time analysis of the task is solved by finite-difference scheme. Seepage calculations are carried out by cyclic-iteration scheme – where volumetric water content, hydraulic conductivity and elasticity module determined numerically by functional relations. The subject of research is Enguri waterpower plant arch dam, at present the highest in the world (Georgia, height 271.5m, fig. 1.1). Consideration is being given to a variety of cases: - canyon slope in the zone of major geological fracture; - foundation in the central part of the dam.

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