Estimating resistance to percolation through beds of surface-water bodies

The influence of bed resistance (degree of imperviousness) at or near the lower boundary of a surface-water body is reflected in the ground-water flow conditions observable in the aquifer near that boundary.

In analysing the flow near such a hydraulic boundary one should differentiate between the following: the presence or absence of a hydraulic connexion through the boundary between the surface-water body and the flow system; the presence of a discontinuous hydraulic connexion (where an infiltration zone is formed under the boundary) charac- teristic of small perched water bodies and lined canals above a deeper-lying water table.

Hydraulic connexion between a body of surface water and a ground-water system is not uncommon, particularly in the vicinity of large rivers and lakes. The degree of hydraulic connexion across the perimeter of a surface-water body, in contact with an unconfined ground-water flow system, bears some relation to the distance, AL, out from the shore-line at which the projected water-table slope intersects the surface-water level;

the poorer the connexion the greater the value of AL (Fig. 6.4a).

FIG. 6.4a. Section view of parameters used in determining imperviousness of river bed.

The value AL is best determined from the observation data collected during a period of steady flow near the hydraulic boundary; records of fluctuations in surface-water stage and water-level fluctuations in two piezometers should be available. The piezo- meters should be located along a section normal to the shore-line, the nearest piezometer being at a distance not closer to the shore than the equivalent thickness of the aquifer (Fig. 6.4a).

The computation of AL is from the relation:

HI - H o

Hz

-

HI

AL = (xz - XI)

-

XI. 6.4(1)

During periods of filling or emptying the surface-water bodies the value AL can be determined using relationships derived from the theory of unsteady flow. The relationship between changes in water-level stage in the river and in the adjacent pervious material may vary, ranging through instantaneous, linear and non-linear forms. The process of filling or emptying reservoirs and canals may be considered virtually instantaneous ; the value AL can then be established, from variations in water level, AHo, in the surface- water body, and AH, in a piezometer located at a distance x from the shore, using the general relation

6.4 page I

6.4(2)

Grormd-water studies

where

A = - x . z =

JZ

A L d - x ’

2 \ 1 2

’

6.4(3) in which a is the hydraulic diffusivity of the aquifer; and t is the time interval over which the change in surface-water stage occurs.

A graph of the function 0 (A, z) is given in Figure 6.4b. The observation data yield a value for O = AH/AHo, for the time interval, t. Assuming the hydraulic diffusivity, a, has been previously established, the value of A may be computed from Equation 6.4 (3).

The value of z is then found from the graph (Fig. 6.4b) which permits computing the value AL from Equation 6.4 (3), rewritten in the form

-

x. 6.4(4)

AL ^=z

- J.t

z

FIG. 6.4b. Graph of the function 0 (- = 0 (A, z), -

- ^-

^{= O (log z)-for A = O).}

The ground-water flow régime on opposite sides of a surface-water reservoir may be analysed by the preceding technique provided that the reservoir width, B, is greater than 2.5AL. To determine bed resistances and effective distances (AL) it may be necessary to install lines of piezometers normal to the shore on each of the opposite sides (Fig.

6.4c), the nearest wells being placed no closer to the shore than the equivalent thicknesses of the flow régime.

The flow gradients i‘ and i” on the left- and right-hand sides of the surface-water body, and the heads H‘ and H“ at the left- and right-hand shores are determined from the water levels in the observation piezometers. These heads are established by rectilinear extrapolation of the water table (Fig. 6.4~) from the relations

G.4 page 2

Determining hydrodynamic parameters of ground-water flow

The value AL is computed for the steady state from the expressions

1' 1 2 2'

FIG. 6.4~. Observation piezometers for determining resistances to seepage through the bed of a canal.

All the computed relationships are given without considering the influence of infiltration or evaporation. For this reason when studying steady-state conditions a correction (wx2/2T) should be applied to the measured values, where x is distance from the obser- vation point to the water boundary; w is the rate of infiltration or evaporation; and T is the transmissivity of the aquifer. For infiltration this correction is deducted from the head value and for evaporation it is added.

4 2 6 ^t

*

. .

.

^0.

.

. .

* e.

.. .1'.'.+... . - . . . ' . .

.i///i/////////////////////////////////i

FIG. 6.4d. Section view with nomenclature for determining AL values for surface-water bodies in contact with two-layered ground-water reservoirs.

If the surface-water body is in contact with a two-layered ground-water reservoir (Fig. 6.4d), values of AL can be derived as follows:

1. For an expanse of water of infinite width, as for example an artificial reservoir or large river where B > 2.5 AL,

6.4(7) where b is the coefficient of leakage; B is the half width of the surface-water body, and KH, KB, mH, mb are the hydraulic conductivities and thicknesses respectively of the principal underlying aquifer and the overlying semi-pervious bed.

6.4 pnge 3

Ground-water studies

2. For an expanse of water of finite width:

AL =

-

cth b B

b ^6.4(8)

Both AL and Kb can be determined for these two equations, thus 1

Kb = mbTb2; b =

-

AL ^6.4(9) For an expanse of water of finite width, the coefficient of leakage, 6, and the value of Kb can be determined from Equations 6.4 (8) and 6.4 (9), if AL is known. The methods of determining values of bed resistance, and methods of their practical application, are discussed in detail by Shestakov (1965).

6.4 pagr 4

Determining lzyclvodynamic pavameters of ground-water flow

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G (ref.) page 4 Rev. 1 (1975)

7

7.1

Observations and

Dans le document Ground-water studiesl (Page 182-190)