Analytic Assessment of the Water Table Drawdown, Seepage, and Back Pressure at Rudbar PSPP

  • Mohamed El TaniEmail author
  • Abbas Kamali
  • Mohamed Ali Gholami
Original Paper


The impoundment of the Rudbar dam raised underground water level. On the right bank, the elevation of the water table is monitored in exploratory boreholes. The water table has remained below the level of the reservoir. The lower level of the water table is due to underground tunnels and galleries that behave as drains. Special analytic developments have been carried out to analyze the behavior of the water table during impoundment. The peculiarity of the model is that it considers a draining tunnel in an open aquifer with a free water table. Two new equations are obtained: one for inflow of water and the other for the water table drawdown. These equations are used to assess the water table elevation in the exploratory boreholes, calculate the hydraulic conductivity of the rock mass from the measured seepage in the conveyance tunnel, and determine the efficiency of the sealing from the measured back pressure on the extrados of the drainage gallery. The comparison of the calculated hydraulic conductivity with the available information from measurements with packer tests and DFN predictions will reveal the importance of scale effects and uncertainties.


Case study Back analysis Analytic development Uncertainty 

List of Symbols


Quotient of the water inflow to the pressure difference in aquifer


Quotient of the water inflow to the pressure difference in an annular sealing


Tunnel edge


Tunnel center with coordinates (d,-h)


Distance of the tunnel to the reservoir


Infinitesimal arc length along a curve


Drawdown of the water table relatively to the reservoir level


Green function of the aquifer


Auxiliary function


Elevation of the reservoir level above the tunnel


Elevation of the reservoir level above an impervious base


Hydraulic conductivity of the rock mass


Hydraulic conductivity of the sealed zone or lining


Integer number 0, 1, 2 …


Normal vector at the boundary




Water flux or Darcy’s velocity


Flow rate or water inflow


Radius of the tunnel or extrados of the sealing


Radius at the extrados of the sealing


Radius at the intrados of the sealing


Tunnel meter

u, \(\bar {u}\)

Under-pressure, mean under-pressure on tunnel edge

ue, \(\bar {u}\)e

Under pressure, mean under-pressure on the extrados of the sealing

ui, \(\bar {u}\)i

Under pressure, mean under-pressure on the intrados of the sealing

x, x′

Horizontal coordinate of point z, z

y, y′

Vertical coordinate of point z, z


Water table equation


nth iteration of the water table equation

z, z′

Points in the aquifer


Single layer


nth cosine coefficient of the single layer


nth sine coefficient of the single layer


Zero-order expansion of the single layer or φ0c


Pi number



The authors acknowledge IWPCO, Iran, and Water and Power Resources Development Company, for the approval to submit and publish this manuscript.


The research paper has not been funded by any public, academic, industrial, or financial entity.

Compliance with Ethical Standards

Conflict of interest

The authors declare no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Rockgro ConsultingBeirutLebanon
  2. 2.Mahab-Ghodss Consulting EngineersTehranIran

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