Design of hydraulic structures with two intermediate filters

The problem of steady-state seepage flow underneath two intermediate filter s located anywhere between two end cutoffs of a flat floor of a hydraulic s tructure on a permeable soil of a finite depth has not been previously solv ed. Conformal mapping has been applied in this paper to investigate the exa ct solution. Companion papers (M.I. Farouk, I.M. Smith, Journal of Hydrauli c Division, ASCE (2000), submitted for publication; M.I. Farouk, I.M. Smith , Proceedings of the European Geophysical Society on Millennium Conference on Earth, Planetary and Solar Systems Sciences, Nice, France, April 2000) u se numerical (finite element) techniques to study a wider range of practica l problems involving anisotropy, arbitrary geometries and so on. These solu tions are subject to idealization and discretization errors and it was of g reat value to have the exact results presented herein for comparison purpos es. Equations for pore water pressures at key points and hydraulic exit gra dient downstream of the hydraulic structure have been derived. Since these equations are not explicit, they are calculated numerically. Results are em ployed to create design charts in easy-to-use form. These charts indicate t hat potential heads along the entire floor and the hydraulic exit gradient downstream of the structure are considerably decreased by the provision of two filters even with very small length. Uplift pressures along the door be tween the two filters are controlled by the location of both filters. Poten tial heads along the upstream floor are controlled by the upstream filter l ocation and potential heads downstream, and the hydraulic exit gradient dow nstream by the downstream filter location. Potential heads downstream of th e second filter and the hydraulic exit gradient are decreased with decrease s in depth of the permeable strata. Pore water pressures upstream of the se cond filter are decreased with increases in depth of the upstream cut-off. The results clearly indicate that the use of more than one filter in these situations is worth practical consideration. (C) 2000 Elsevier Science Inc. All rights reserved.