Mathematical Modeling of Filtration Flows from Foundation Pits Fenced with Zhukovskii Sheet Piles

Consideration is given to the filtration of water from foundation pits fenced with Zhukovskii sheet piles through a ground layer underlain by a well-permeable confined aquifer on whose roof there is a water-impermeable portion. A mixed multiparametric boundary-value problem of the theory of analytical functions is formulated, which is solved with the Polubarinova-Kochina method. Based on this model, an algorithm of calculation of the filrtation characteristics is developed for situations where, in water motion from the foundation pits, one has to take into account the joint influence of such important factors, as seepage onto the free surface, upthrust from the water of the underlying highly permeable aquifer, and the presence of the impermeable inclusion on the roof of the latter, on the pattern of the phenomenon. Limiting cases of the model are considered which are related to the absence of one factor characterizing the modeled process (upthrust, an impermeable inclusion, seepage) and to the degeneration of the foundation pits into a submergence band semiinfinite on the left. A solution of the problem is given for the scheme under the assumption of a finite value of the flow velocity at the end of a sheet pile; it is a certain analog of the Zhukovskii classical problem.