How to Determine Co-efficient of Permeability of Soil? | Soil Engineering

Determination of Coefficient of Permeability in Laboratory:

1. Constant Head Permeability Test (Coarse Grained):

Water flows from the overhead tank consisting of three tubes – The inlet tube, the over-flow tube and the outlet tube. The constant hydraulic gradient i causing the flow is the head h (i.e., difference in water levels of the overhead and bottom tanks) divided by the length L of the sample.

If the length of the sample is large, the head lost over a length of specimen is measured by inserting piezometric tubes. If Q is the total quantity of flow in a time interval t, we have Darcy’s law.

Where A = total cross-sectional area of sample when steady state of flow is reached in time t.

2. Falling Head Permeability Test (Fine Grained):

Here discharge is small. The water level in the stand pipe constantly falls as water flows. Observations are started after steady state of flow has reached.

The head at any time instant t is equal to the difference in the water level in the stand pipe and the bottom tank.

Let h₁ and h₂ be heads at time intervals t₁ and t₂ (t₂ > t₁) respectively. Let h be head at any intermediate time interval t, and – dh be the change in the head in a smaller time interval dt (minus sign has been used since h decreases as t increases). Hence, from Darcy’s law, the rate of flow q is given by –

The laboratory observations consist of measurement of the heads h₁ and h₂ at two chosen time intervals t₁ and t₂.

Field Determination of Permeability:

Compared to laboratory tests, field permeability test are more reliable. They give the in situ value of permeability with minimum disturbance. In the pumping out test, drawdowns, corresponding to a steady discharge q, are observed at a number of observation wells.

The degree of disturbance and number of samples can affect the reliability of the average value of permeability obtained from laboratory tests, for the large soil mass in the field.

Two types of field tests for determining the coefficient of permeability are:

1. Pumping in tests

2. Pumping out tests.

These tests can be conducted in both unconfined aquifer and confined aquifer.

1. Pumping in Tests:

The US Bureau of Reclamation has devised two methods:

(a) Constant Water Level Method:

Figure 7.4 shows the arrangements for testing through the open end of a pipe casing which has been drilled to the desired depth and carefully cleaned out to the bottom of the casing. If the hole extends below the groundwater level, it should be kept filled with water to minimize squeezing of soil into the bottom of the casing.

The test is done by maintaining a constant head by adding clear water through a measuring device. The required data include the amount of head maintained during a constant rate of flow into the hole, diameter of the casing, and elevations of the top and bottom of the casing. Permeability is computed from the following relation –

k = q/5.5 rh

where k is coefficient of permeability; q the constant rate of flow into the hole; r the internal radius of casing, and n the differential head of water = gravity head – head loss due to friction.

(b) Packer Method:

A packer is an expandable cylindrical rubber sleeve. Packers are used as a means of sealing of a section borehole. Two types of packer methods are used.

They are:

i. Single Packer Method (Fig. 7.5a):

In single packer method the hole is drilled to the required depth. The packer is fixed at a desired level above the bottom of hole and the water pumped into the section below the packer. The constant rate of flow, q that is attained under an applied head, H is found.

ii. Double Packer Method (Fig 7b):

In the double packer method, the hole is drilled to the final depth and cleaned. Two packers are fixed at a distance apart equal to 5 times the diameter of borehole. Both packers are then expanded and water pumped into the section between the two packers, the constant rate of flow, q that is attained under an applied head, H is found. The coefficient of permeability, k is computed using the following equations –

Where, r = radius of borehole

H = differential head for maintaining a constant rate of flow in test section

q = constant rate of flow into the test section

L = length of the test section.

2. Pumping-Out Test:

a. Pumping-Out Test in Unconfined Aquifer:

For large engineering projects, it is usual practice to measure the permeability of soils by pumping out tests. The method is extremely useful for a homogeneous, coarse-grained deposit for which it is difficult to obtain undisturbed samples.

In an unconfined aquifer, a tube well is drilled as shown in Fig. 7.6. The tube used for the well is perforated so that water can enter the well. Water is pumped out of the test tube till a steady state is reached. At that stage, the discharge become constant and the water level in the well does not change.

The water table, which was originally horizontal before the pumping was started, is depressed near the well. The water table near the well forms an inverted cone, known as cone of depression. The maximum depression of the water table is known as the drawdown (s₁).

r = radius of main well

R = radius of zero drawdown known as maximum radius of influence

h = depth of water in the main well, during pumping

H = height of initial water table above impervious layer

q = rate at which water pumped out of well.

The slope of the hydraulic gradient line is small, and can be taken as tangent of the angle in place of the sine of angle, i.e.

i = dy/dx …(1)

From Darcy’s law q = kiA

Substituting the value of i from Eqn. (1) and A equal to 2πxy,

b. Pumping-Out Test in Confined Aquifer:

Let us consider the discharge thought a cylindrical surface at a radial distance x from the centre and of height b. From Darcy’s law –

Indirect Method:

(1) Computation Based on Grain Size:

Allen Hazen conducted a large number of tests on filter sands of particle size between 0.1 mm and 3.0 mm, having a coefficient of uniformity of less than 5, and gave the following relation –

K = C D²₁₀

Where k = coefficient of permeability (cm/sec)

D₁₀ = effective size (cm)

C = constant with a value between 100 and 150

If k and D₁₀ are taken in mm/sec and mm respectively, the value of the constant C lies between 10 and 15.

(2) From Consolidation Test Data:

The coefficient of permeability of fine-grained soil can be determined indirectly from the data obtained from a consolidation test conducted on the sample. It is given by –

K = C_v γ_w mv

Where k = coefficient of permeability (cm/sec)

C_v = coefficient of consolidation (cm²/sec)

γ_w = unit weight of water (gm/ml)

m_v = coefficient of volume compressibility (cm²/gm)

This method is suitable for very fine-grained soil conducted in the laboratory.