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Deformation of Dupuit's parabola in a dam with sheet piling

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Abstract

If the flow in an earth dam is plane and steady, the shape of the phreatic surface can be approximated by Dupuit's parabola. Thin sheet piling in the dam, deforms the phreatic surface in the vicinity of the sheet piling and at its tip the hydraulic gradient is singular. If the length of the sheet pile is much smaller than the thickness of the dam, the flux through the dam per sheet pile length is equal to the undisturbed flux, whereas if the length of the sheet pile is much larger than the thickness of the dam the corresponding flux is negligible.

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Abbreviations

a :

length of sheet pile

A :

auxiliary parameter

b :

thickness of dam

G :

Greens function

h :

height of phreatic surface

K :

hydraulic conductivity

Q :

flux per sheet pile length

Q 0 :

reference flux

r, ϑ :

auxiliary variables

r 0 :

auxiliary parameter

R :

half-strip in thex-y-plane with a cut

R 1 :

strip in thex-y-plane

R′1 :

half-strip in thex-y-plane

R 2 :

half space in theξ-η-plane

R :

radius of curvature of the tip of the sheet pile

z=x+iy :

complex variable inR,R 1 andR′1

w=ξ+iη :

complex in variable inR 2

φ≡h 2 :

potential

÷ :

unknown φ at a part of the boundary ofR 2

References

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Authors and Affiliations

  1. Department of Hydraulics, The Royal Institute of Technology, S-100 44, Stockholm, Sweden

    Göran Rehbinder

  2. The Swedish State Power Board, S-810 44, Älvkarleby, Sweden

    Anders Wörman

Authors
  1. Göran Rehbinder
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  2. Anders Wörman
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Rehbinder, G., Wörman, A. Deformation of Dupuit's parabola in a dam with sheet piling. Appl. Sci. Res. 52, 173–185 (1994). https://doi.org/10.1007/BF00868059

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  • DOI: https://doi.org/10.1007/BF00868059

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