As is known, proper drainage of spillway aprons considerably or even completely relieves the apron from uplift under the slabs as a resuk of the large pressure reduction in the surface flow in the region of the hydraulic jump [1,2]. Moreover, surcharging of the apron by the surface flow can be attained by the appropriate arrangement of drain holes and by blocking off free access of water under the apron on the downstream side. This allows a considerable reduction of the thickness and volume of spillway aprons.The effect of relieving the apron from uplift is used widely in design and, in particular, in the design of the apron of the Kanevsk hydroeleotric station.The installation of drain holes in the apron in the region of the hydraulic jump creates the possibility of occurrence under the apron of large fluctuating pressure pulses, causing the filter under a drained apron to operate in a fluctuating-flow regime.Problems of the calculation of a fluctuating flow in coarse-grained material and its effect on graded filters with consideration of inertia forces and other circumstances were investigated in detail by N. N. Belyashevskii and N. G. Bugai [3][4][5]. Their studies developed formulas for finding the scouring gradient in the case of contact scour by longitudinal steady and fluctuating flows for materials of different grain size for interlayer coefficients K = (Ds0/ds0) < 40 and scouring gradients ~s -< 1.0. These design relationships were obtained on the basis of experiments with quite uniform compositions of the rabble for ~ = (Ds0/D10) __< 5. Such rubble formed a rigid undeformable filter skeleton.The maximum pressure gradient in the fluctuating flow ~m depends on the distance between drain wells and the parameters of the filter itself and also on the magnitude of the fluctuating press~e pulses in the surface flow. G.A. Yuditskii's generalizing study is devoted to pressure fluctuations in the surface flow [6]. When calcuiating fm it is also necessary to take into account that the probability of the maximum pulses of opposite sign occurring simultaneously over adjacent drain wells is extremely small [7].Thus, exhaustive data were obtained for a well-founded calculation of the fraotional composition of a graded filter under a drained apron operating in a fluctuating-flow regime. However, these investigations pertained to rather uniform rubble materials with no intermixing of the contacting layers, wNch imposed limitations on the selection of the fractional composition of the multilayered graded filter and especially its first layer contacting the sand foundation.

The problem of constructing a concrete revetment on the upstream slopes of earth dams without placing a reverse filter under it, which was raised by Lubochkov [i], deserves great attention, since the wide introduction of this revetment into practice would effect a considerable economy. Unfortunately, the problem raised has been covered insufficiently from the viewpoint of the physics of the processes occurring, although a revetment on constructed experimental sections operated completely satisfactorily.As shown by investigations and full-scale observations of the operation of reinforcedconcrete revetments on the upstream slopes of earth dams, the main cause of the disturbance and destruction of such revetments is the formation of cavities under the slabs on the wavebreaking section from the settlement of the rubble filter and transformation of the slab from one supported on an elastic foundation, as specified by the calculation, to one with two supports, or operating as a cantilever. E. A. Lubochkov is absolutely right in this regard, which is indicated also by certain other investigators [2,3,4]. Let us examine the cause of such cavity formation. In investigations [2, 3, 4] the authors were inclined to regard the case of cavity formation under the slab due to liquefaction and sliding of the earth in the slope on the wave-breaking section due to the dynamic wave loads, which cause in the under-slab space pressure pulses with high accelerations. The graph of the maximum accelerations =max occurring in the under-slab space upon impact of a wave on the slab as a function of the wave height and size of the slab is shown in Fig. 1 according to the investigations [4].As is easy to see from Fig. i, for slabs 0.2-0.25 m thick and large planar dimensions with a side of 15-20 m, at wave heights of 2-3 m we can expect ~max = 500-1000 mm/sec 2, i.e., accelerations that are equivalent in magnitude to accelerations during intensi~y 8-9 earthquakes. It would seem, actually, that there are grounds to fear for the dynamic stability of the earth embankment. To Judge this, we turn to Fig. 2, where, according to the data of the author and Sukhorukov [3, 6], the graph acr = f(D) is plotted for sandy soils of different types and grain size. Here ~cr is the critical acceleration at which liquefaction of the sand occurs and D is the coefficient of its relative density.It follows from the graph that all sands, from coarse-grained to flne-gralned rounded, at a relative density D > 0.4-0.6, i.e., a density easily attained when constructing an embankment by the hydraulic or dry method, cannot be liquefied at The values of Umax indicated above. The exceptions are the fine-grained silty sands, distinguished by pronounced thixotrophy, which are easily liquefied even in the most dense structure. But such soils should, as a rule, never be placed on a dam slope. It follows from the above that the conditions for formation of cavities under slabs due to liquefaction of the embankment earth are generally absent and, in any event, they are easily eli...

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In hydraulic construction practice there are frequent cases in which it is necessary to construct reservoirs or railings ponds on highly pervious foundations. In such cases the complex of hydraulic structures has, as integral parts, the antiseepage and drainage elements which are intended not only to reduce substantially the seepage losses but also to lessen as much as possible the harmful effects of the seepage on the adjacent zones. However, the substantiation of the type and size of these elements involves significant methodological difficulties, since the existing analytical, analog, and numerical methods of seepage analysis and investigation have been developed for comparatively simple conditions. For this reason, the use of these methods under real conditions characterized by unsteady and three-dimensional seepage, nonhomogeneity of the porous medium, presence of several feeding regions, relief of the seepage flow. etc. may lower the reliability of the results. Nevertheless, experience with seepage investigations carried out by the Institute of Hydromechanics of the Academy of Sciences of the UkrainianSSR for different railings ponds and reservoirs in the Ukraine [3, 4, 7, and 8] has shown that the existing methods may be used even for comparatively complex hydrogeologic conditions. It is recommended that the analysis be carried out in two stages.In the first stage, the water losses are ealcuiated for the free seepage phase, when the seepage from the railings pond has not yet been merged with the ordinary ground water level. It should be pointed out that the existing methods of analysis of free seepage [1, 5, 6] have been worked out basically for irrigation canals which are filled nearly instantaneousiy and have a very small longitudinal slope. Tailings ponds are characterized by prolonged filling, considerable slope, and variable bottom width (in railings ponds of the gully and plain-gully type), which do not permit using the existing methods of analysis in their pure form. A modification proposed for these methods is described below.The entire railings pond depression is divided, by area, into separate portions within whose limits free seepage occurs simultaneously. Within these portions the bottom is eousidered to be horizontal. The size of these portions depends on the wetting time of the pervious mass, the bottom slope, and the rate of rise of the water at the upstream side. In the ease of uniform permeability of the mass, the wetting time of this mass and the seepage flows for each of the portions are determined by applying formulas presented in the literature [5. 6]. The analysis is made by the method of successive approximations, during which, on the basis of the filling graph for the tailings pond, the acting heads, the areas of the portions, and the wetting time of the pervious mass are linked with each other.In the ease of highly pervious soils covered by far less pervious soils or by an antiseepage facing made from soils of low permeability, initially for each of the analytical portions the wet...