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An Analytical Solution for Confined Seepage Problem Beneath Hydraulic Structures

  • Ahmad-Reza Mohsenian
  • Mohammad Sedghi-Asl
  • Hassan Rahimi
Research paper
  • 20 Downloads

Abstract

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.

Keywords

Seepage Uplift pressure Coastal structures Schwartz–Christoffel integral 

List of symbols

S

Sheet pile depth

T

Finite layer depth

L1

Upstream length of the blanket

L2

Downstream length of the blanket

h1

Upstream water depth

p

Uplift pressure

L

Length of the dike from sheet pile

K

Complete elliptic integral of the first kind

LB

Length of blanket

λ

Modulus

k

Hydraulic conductivity or permeability)

x

Real number

X

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

y

Real number

i

Imaginary unit

W1

Auxiliary plane

W2

Auxiliary plane

wr

Mixed potential plane

qr

Seepage discharge flowing per length

φr

Potential function

ψr

Stream function

α1, α2

Points

ζ

Complex variable

σ

Variable between 1 and − 1

M, N

Complex constants

C

Constant value of integral

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Copyright information

© Shiraz University 2018

Authors and Affiliations

  • Ahmad-Reza Mohsenian
    • 1
  • Mohammad Sedghi-Asl
    • 2
  • 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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