On filtration schemes occurring in the problem of flow over a Zhukovskii sheet pile

Abstract

Consideration is given to fi ltration under a Zhukovskii sheet pile through a ground layer underlain by a highly permeable head horizon the left semiinfi nite part of whose roof is modeled by an impermeable base. A study is made of the case of fl ow where the velocity at the end of the sheet pile is equal to infi nity and the fl ow rate takes on extremum values on both water-permeable portions of the boundary of the region of motion. Limiting cases of fl ow associated with the absence of upthrust and of an impermeable inclusion alike are noted, as is an adjacent scheme due to the absence of the two indicated extremum points. Solutions are given for two schemes of motion in a semiinverse formulation, with the classical Zhukovskii problem being the limiting case of one scheme. Distinctive features of such models are noted. For investigation of these fl ows, use is made of a Polubarinova-Kochina method which allows exact analytical representations for motion elements. Results of numerical calculations and the analysis of the infl uence of all physical factors on fi ltration characteristics are given.