Behavior and selection of the composition of graded filters in the presence of a fluctuating flow

Abstract

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.

Stability of wide-graded granular filters under oscillatory flow

“…For semi-stable filter conditions, these processes are decelerated and in some cases unsteady under oscillatory flow. Similar processes were also observed and described by Belyashevskii et al (1972) For a better classification, a sieve analysis is performed for each specimen before and after the completed test series. The mixing of the two layers by contact erosion and internal erosion in the filter layer is observed as shown in Figure 11.…”

“…The results are in agreement with previous studies (cf. Belyashevskii et al, 1972;Molenkamp et al, 1979;de Graauw et al, 1983;Klein-Breteler et al, 1992;Köhler, 1993) in the sense that the stability of granular filters under oscillatory flow is lower compared to that under unidirectional flow. Geometrical filter criteria, developed for unidirectional flow, cannot be applied for oscillatory flow since the filter structure is affected by the cyclic pore pressure and associated effective stresses.…”

Use of a filterless antiwave revetment

“…E. A. Lubochkov is absolutely right in this regard, which is indicated also by certain other investigators [2,3,4]. 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 eliminated by construction measures --by suitable compaction and the quality of the earth being placed.In veiw of the fact that upon impact of the wave on the slab a surge of pore pressure occurs in the reverse filter in the under-slab space and a pronounced process of pulsating seepage flow arises, the cause of cavity formation under the slabs can be explained more nearly correctly only by settlement of the filter due to mixing of its particles along the contact with the sand particles at the embankment.As shown by extensive investigations of the contact stability of filters in the presence of pulsating seepage flows carried out under the author's supervision [7,8], for the coarse single-layer rubble filters usually placed under a revetment, contact mixing and additional compaction of the filter can readily occur and can acquire a character that threatens r_he strength of the slabs. 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.…”

“…As shown by extensive investigations of the contact stability of filters in the presence of pulsating seepage flows carried out under the author's supervision [7,8], for the coarse single-layer rubble filters usually placed under a revetment, contact mixing and additional compaction of the filter can readily occur and can acquire a character that threatens r_he strength of the slabs. Therefore, E. A. Lubochkov is right in asserting that rubble filters should be placed under revetment slabs.…”