How to Determine the Permeability of Aquifers? | Soil Engineering

The various types of in situ tests commonly used to determine the permeability of aquifers in the field are: 1. Pumping-out test. 2. Pumping-in Test.

Compared with laboratory methods, field methods give a more reliable value of permeability, since the soil is tested in situ without disturbing its structure and void ratio. The value of permeability thus obtained is an average for a large area. In situ methods are extremely useful for a homogeneous coarse-grained deposit for which it is difficult to obtain undisturbed samples. However, in situ tests are costly and can be justified only for large projects.

1. Pumping-Out Tests:

In the pumping-out test, a tubewell is drilled to penetrate the entire thickness of the aquifer up to the underly­ing impervious stratum. The tubewell is perforated in the aquifer portion so that the water can enter the well .The perforated tube is surrounded by screens to check the flow of soil particles into the well.

When the water is pumped from the well, the GWT gets lowered in the well and forms a cone of depression which is shown in Fig. 10.1. Pumping is continued and the rate of pumping is so adjusted as to reach a steady state.

The steady state is said to be reached when the discharge becomes constant and the water level in the well does not change. In this state, the groundwater level is observed at a number of observation wells.

The expression for the coefficient of permeability for unconfined and confined aquifers is derived in the following:

i. Unconfined Aquifer:

Figure 10.1 shows a well penetrating an unconfined aquifer to its full depth. When pumping is done at a steady state, the water from the circular area around the well flows radially toward the well. Consider the flow through a cylindrical surface of height z at a radial distance r from the center of the well. So –

Area of flow (A) = 2πrz

Hydraulic gradient is –

i = dz/dr

Applying Darcy’s law we get –

q = kiA = k(dz/dr).( 2πrz)

Rearranging the terms, we get –

Dr/r = 2πkz/q.dz

Integrating both sides between any row radial distances r₁ and r₂ on the same side of the well and their correspond­ing depth of flow z₁ and z₂, we have –

ii. Confined Aquifer:

In the case of a confined aquifer, the flow takes place only through the thickness, b, of the aquifer, as shown in Fig. 10.2. Let z be the depth of the piezometric level at any radial distance (r) from the center of the well. Then the area of flow will be –

Area of flow (A) = 2πrb

Hydraulic gradient will be –

i = dz/dr

Applying Darcy’s law, we get –

q = kiA = k(dz/dr).( 2πrb)

Rearranging the terms we get –

dr/r = 2πkb/q.dz

Integrating both sides between any two radial distances r₁ and r₂ on the same side of the well and their correspond­ing depth of flow z₁ and z₂, we have –

Equation (10.6a) may also be written as –

where s is the drawdown.

Assumptions:

The derivation of Eqs. (10.5) and (10.6a) is based on the following assumptions:

i. The slope of the hydraulic gradient line is so small that it can be represented by the tangent of the angle instead of its sine.

ii. The well penetrates and receives water from the entire thickness of the aquifer.

iii. The flow is steady and laminar and Darcy’s law is valid.

iv. The flow toward the well is radial and horizontal.

v. The soil mass (aquifer) is homogeneous and isotropic.

vi. The coefficient of permeability is uniform throughout the aquifer.

vii. The natural groundwater regime affecting the aquifer remains constant with time.

2. Pumping-In Tests:

Pumping-in tests are conducted to determine the permeability of an individual stratum of soil, through which a hole is drilled. The test gives the permeability of soil close to the bore hole and is more economical than the pumping-out test.

There are basically two types of pumping-in tests:

i. Open-End Test:

In this test, a casing pipe is inserted into the soil stratum and the soil in the casing pipe is removed up to the bottom of the casing. Clean water at a temperature slightly higher than that of groundwater is added under some pressure through a metering system. The test set-up for open-end test is shown in Fig. 10.3.

The added water seeps into the surrounding soil stratum through the bottom of the hole. The rate of the water added to the hole is adjusted in such a way that a constant head of water is maintained in the bore hole and thus steady state is reached.

The permeability of the soil close to the bottom of the casing is calculated from the following relation:

k = q {5.5r[h +(p/γ_w)]} …(10.7)

where q is the constant rate of the flow supplied into the bore hole, r is the inside radius of the casing, h is the difference in elevation between the water level in the bore hole and GWT, and p is the pressure at which the water is added to the bore.

The open-end test may also be conducted above GWT; in this case, h in Eq. (10.7) becomes the head of water in the bore hole.

ii. Packer Test:

Packer tests are performed in the uncased portion of a bore hole. Packer tests are more commonly used for testing of rocks than of soils. Figure 10.4 shows the schematic diagram of packer tests above and below GWT.

a. Single-Packer Test:

If the bore hole cannot stand without a casing pipe, the single-packer test is used. The packer is placed as shown in Fig. 10.4 and water is pumped from the hole, which comes out of the uncased portion of the hole below the casing. If the casing is used for the full depth of the stratum, it should have perforations in the portion of the stratum being tested. The lower end is plugged. When steady conditions are attained, the rate of flow is determined. Permeability is determined from the relation –

where r is the radius of the bore hole, l is the length of the bore hole, h is the difference in water level at entry and GWT if the test is conducted below GWT and it is the difference in water level at entry at middle of the tested length if the test is conducted above GWT, as shown in Fig. 10.4(b).

b. Double-Packer Test:

If the hole can stand without a casing, the double-packer test is used. A pipe fitted with two packers is placed in the bore hole and the bottom of the pipe is plugged. The test is conducted in the same way as a single-packer test and permeability is determined using Eqs. (10.8) and (10.9). The double-packer test is conducted first in the lowest portion near the bottom of the hole and later is repeated for upper layers. The packer tests give better results when conducted below the water table than above the water table.