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

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## Abstract

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.

## Keywords

Case study Back analysis Analytic development Uncertainty## List of Symbols

- A
Quotient of the water inflow to the pressure difference in aquifer

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

- C
Tunnel edge

**c**Tunnel center with coordinates (d,-h)

- d
Distance of the tunnel to the reservoir

- ds
Infinitesimal arc length along a curve

- D
Drawdown of the water table relatively to the reservoir level

- G
Green function of the aquifer

- g
Auxiliary function

- h
Elevation of the reservoir level above the tunnel

- H
Elevation of the reservoir level above an impervious base

- k
Hydraulic conductivity of the rock mass

- k
_{s} Hydraulic conductivity of the sealed zone or lining

- n
Integer number 0, 1, 2 …

**n**Normal vector at the boundary

- p
Pressure

**q**Water flux or Darcy’s velocity

- Q
Flow rate or water inflow

- r
Radius of the tunnel or extrados of the sealing

- r
_{e} Radius at the extrados of the sealing

- r
_{i} Radius at the intrados of the sealing

- T
_{m} Tunnel meter

- u, \(\bar {u}\)
Under-pressure, mean under-pressure on tunnel edge

- u
_{e}, \(\bar {u}\)_{e} Under pressure, mean under-pressure on the extrados of the sealing

- u
_{i}, \(\bar {u}\)_{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**′- y(x)
Water table equation

- y
_{n}(x) *n*th iteration of the water table equation**z**,**z′**Points in the aquifer

- φ
Single layer

- φ
_{n}^{c} *n*th cosine coefficient of the single layer- φ
_{n}^{s} *n*th sine coefficient of the single layer- φ
_{0} Zero-order expansion of the single layer or φ

_{0}^{c}- π
Pi number

## Notes

### Acknowledgements

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

### Funding

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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