An Analytical Solution for Confined Seepage Problem Beneath Hydraulic Structures

  • Ahmad-Reza Mohsenian
  • Mohammad Sedghi-AslEmail author
  • Hassan Rahimi
Research paper


A number of analytical methods have been proposed for solving two-dimensional problems of groundwater flow, which are concerned with functions which transform the problem from a geometric status where solution must be found to another status in which the solutions are known. Conformal mapping and its appropriate techniques allow us to change complex flow problems into regular geometric shapes. In this paper, an analytical solution is provided for calculating uplift pressure in alluvial foundations below dams. In the present study, velocity hodograph and Schwarz–Christoffel integrals are used to determine the uplift pressure in alluvial foundations for different depths and lengths of sheet pile and upstream blanket. An important point in this study is the asymmetric insertion of blanket relative to sheet pile along the longitudinal path. Finally, the results obtained from the employed analytical method and the results of laboratory studies are compared to evaluate the accuracy of analytical solution. The results of the studies indicate that in some cases, the present analytical method underestimates uplift pressure, while in some circumstances there is a good agreement between theoretical and laboratory methods.


Seepage Uplift pressure Coastal structures Schwartz–Christoffel integral 

List of symbols


Sheet pile depth


Finite layer depth


Upstream length of the blanket


Downstream length of the blanket


Upstream water depth


Uplift pressure


Length of the dike from sheet pile


Complete elliptic integral of the first kind


Length of blanket




Hydraulic conductivity or permeability)


Real number


Longitudinal coordinate of piezometers from sheet pile that varies 0.1–1.1 m for any row of piezometers


Real number


Imaginary unit


Auxiliary plane


Auxiliary plane


Mixed potential plane


Seepage discharge flowing per length


Potential function


Stream function

α1, α2



Complex variable


Variable between 1 and − 1

M, N

Complex constants


Constant value of integral


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Copyright information

© Shiraz University 2018

Authors and Affiliations

  • Ahmad-Reza Mohsenian
    • 1
  • Mohammad Sedghi-Asl
    • 2
    Email author
  • Hassan Rahimi
    • 3
    • 4
  1. 1.Islamic Azad University, Yasouj BranchYasoujIran
  2. 2.Department of Soil Science, Faculty of AgricultureYasouj UniversityYasoujIran
  3. 3.Department of Irrigation and ReclamationUniversity of TehranKarajIran
  4. 4.Geotechnical Group Leader, Geotechnical Services, Civil Section, ESI Maintenance Directorate, Sydney TrainsSydneyAustralia

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