There are several laboratories and in situ tests that can be done to estimate the permeability of the soil and every test has its own advantages and disadvantages. The two most common are “the constant head permeability method” and “the falling head permeability method”.

Permeability testing is done to determine the **coefficient of permeability** (K) of a sample, which is defined as the rate of flow of water under laminar flow conditions through a porous medium area of unit cross section under unit hydraulic gradient.

However, it is hard to estimate the coefficient of permeability, since its value can vary even by a small order of magnitude.

This document examines the concept behind permeability (Darcy’s Law), why the coefficient of permeability is important, and explains the **Constant Head Permeability Testing Method**, which is the Test method supported by VJ Tech’s Clisp Studio Software.

**1.1 Why is the Coefficient of Permeability important?**

Permeability can be expressed as the ease with which water can flow through soils. Coefficient of permeability helps in solving issues related to the:

- Yield of water bearing strata
- Stability of earthen dams
- Embankments of canal banks
- Seepage in earthen dams
- Settlement Issues

**1.2 Darcy’s Law**

The coefficient of permeability is based on Darcy’s Law. In 1856, Henry Darcy published a report where he described his experiment on the flow of water through a porous media. The end result was a mathematical equation which describes the fluid motion in porous media, stating that the rate of fluid flow through a porous medium is proportional to the potential energy gradient within that fluid.

i v = k

where K is the constant of proportionality, which is known as Darcy’s permeability (or hydraulic conductivity (m/s)), and i is the hydraulic gradient.

**2. The Constant Head Permeability Testing Method**

This method is recommended when we have a coarse granular soil such as sand, where the quantity of discharge of liquid through the sample is large. It is possible to test disturbed and undisturbed samples. This test is carried out using an instrument called the Constant Head Permeameter as shown in the Figure 1.

There is a contact water reservoir and water is released into the sample. The first step is to completely saturate the soil until a constant flow (Q) is coming from the bottom of the permeameter.

It is important to leave the water flowing for some time so that a stable rate of flow Q can be achieved. When the water has been released and the sample is saturated, the water will rise to a certain height in the burettes. The difference in height (∆h) represents the difference of the energy of water at two different levels, also called “Head Loss”. The difference in the energy also drives the flow.

It is crucial to keep the head loss constant during this test, so that the hydraulic gradient is constant, and to achieve this, the water level supply must be constant. Please note, L is the flow path and not necessarily the length of the soil sample.

**3. Falling Head Method**

This method, also called the Variable Head Permeability test, is suitable for fine grain soils with intermediate-low permeability such as clays and silts.

Figure 2 shows a schematic representation of the test which basically works the same as the constant head permeability test, the only difference being that the water head will not be constant but diminishing over time.

This test involves the flow of water through a soil sample. At the top of the sample is a standpipe which provides the water head and allows measurement of the volume of water passing through the sample. The diameter of the standpipe depends on the permeability of the soil. This type of test can be carried out in an oedometer cell, or in a specific Falling Head permeability cell.

**Test procedure**

The first step is to completely saturate the soil until a constant flow (Q) is coming from the bottom of the permeameter (please note the water has to be de-aired). Once the sample is saturated and a steady flow of water is achieved, you can close the bottom valve (stopping the flow), refill the standpipe with de-aired water, open the bottom valve and start the test. Water will flow while the water head will be diminishing over time. The test will be considered complete when the water in the standpipe reaches a lower predefined level.

During the test, the time for the water in the standpipe to drop from the higher level to the lower level is recorded. This operation is usually done a couple of times, and the time taken for the water to drop from the higher level to the lower level should be approximately the same (within 10% error). If the error in the time taken is bigger than 10%, then the test has to be considered as failed.

According to this test, the permeability value can be computed as follows:

Where a is the cross-section area of the standpipe, L is the height of the soil sample, A is the sample cross section area, ∆t is the recorded time and hU & hL are the upper and lower standpipe levels.

**4. Testing Procedure for Permeability in a Triaxial cell using Clisp Studio**

This test refers to the Constant head permeability method.

At the time of writing, VJ Tech complies to **BS1377-6:1990, EN ISO 17892-11 and D5484-16 (Method A).**

**a. ****Sample Preparation**

The preparation of the soil specimen should be made according to the testing standard. Special consideration should be given to the state properties of the sample, such as the initial density, water content, compaction method etc. as all these factors affect the results. The sample is sealed within a rubber membrane to avoid direct contact between the soil and the confining fluid. Two saturated porous discs are inserted at the top and bottom of the sample, in contact with the Top Cap and Base Pedestal, respectively. Please note, the porous discs do not change the permeability results.

**b. ****Saturation**

To saturate the soil specimen in a Triaxial cell, we follow the same procedure as in static Triaxial tests, i.e. by gradually elevating the Back pressure so that pore air is dissolved into pore water. Saturation checks are performed by elevating the confining pressure to the specimen and keeping the drainage valve closed. The B-value is then calculated as the change in the Pore Water Pressure to the change in the Confining Pressure:

where *Δ**U* is the change in the Pore Water Pressure of the specimen which is caused when the Confining Pressure changes by *Δ**CP*.

Usually, when the B-value is greater than **0.95** the soil is considered fully saturated, though for some soils lower values are considered acceptable.

**c. ****Consolidation**

Consolidation of the soil specimen is necessary to establish the desired stress state and apply the correct effective stresses prior to the permeability stage. During the isotropic consolidation, the drainage valve remains open to allow drainage and dissipation of the excess Pore Water Pressure.

During Isotropic consolidation, the change in sample volume will be equal to the volume of water that was removed from the sample, since this was already saturated in the previous stage. Therefore, the volume of water that drains out of the sample is recorded and is plotted against the square root of time (Figure 3a). Moreover, the dissipation of the excess Pore Water Pressure can be plotted against time (Figure 3b). Consolidation is considered complete, when either the excess Pore Water Pressure has been dissipated by 95% or when the volume change has ceased.

**a. ****Permeability**

After setting up your Starting, Logging and Stopping conditions, we can start setting up the pressures (Cell, Back and Drain) in order to achieve the required effective pressure and the gradient pressure. Once the test is complete, a graphical representation is available to analyse the data and actively find the Flow in ml/min as shown in Figure 4.

For more details on test procedure please refer to the** Permeability Test (csPermeability) User Guide**.

If you have any questions or want to learn more about Permeability Testing and our equipment range, please contact us.