What is hydraulic conductivity?

Hydraulic conductivity is the measure of flowability of water inside the soil in the presence of a hydraulic gradient. The hydraulic gradient is defined as the difference in the water heads in the soil, which induces a water motion. In simple terms, a hydraulic gradient is the presence of a potential that induces a flow of water.

Soil is composed of pores at its upper surface and rocks, gravel, and sand particles beneath it. Water needs to travel through the soil to make itself available for the crops and plants. Measures of hydraulic conductivity are essential by civil engineers to determine the health of the soil and to predict and track flow paths of water throughout the soil. Constructional and agricultural decisions are based on the magnitudes of hydraulic conductivity.

In environmental engineering, this is the most crucial parameter to determine the amount of contamination of groundwater and is most of the time, difficult to analyze.

Basics of hydraulic conductivity and Darcy's law

The hydraulic conductivity of soil is given by the parameter $K$, which depends on the density, viscosity, permeability, and saturation degree of soil. The flowability of fluid through the soil not only depends on the nature and properties of soil, but also on the flowing fluid, or permeating fluid. It signifies that the soil will allow the passage of fluids depending upon the fluid properties. Hence, the value of hydraulic conductivity is different for different permeating fluids.

In mathematical terms, hydraulic conductivity is the coefficient of Darcy's law. Darcy's law relates the flow velocity of water (fluid) with the hydraulic gradient in the laminar flow regime. During laminar flow, the water articles have a smooth oriental motion having low Reynold's number. It is required by engineers to control groundwater.

As per Darcy's law, the rate of discharge of water is proportional to the head of the hydraulic gradient and hydraulic conductivity.

Consider the cylinder given in the diagram below. The cylinder has a cross-sectional area, $A$. The discharge through the cylinder is given by $Q$. Darcy's law is mathematically given by the equation,

$Q=-\frac{K}{\mu L}∆P$

Where $∆P$ denotes the pressure drop.

$L$ denotes the length of the cylinder.

$\mu$ denotes the dynamic viscosity of the fluid.

The negative sign indicates the flow of liquid towards the negative potential.

Laboratory techniques to determine hydraulic conductivity

There are varieties of experimental techniques and procedures used in the laboratory to determine the hydraulic conductivity of soil samples, a few of them are discussed below.

Constant head technique

In the constant head technique, there are different instruments used, they are:

• Permeameter mold
• Dummy plate
• Detachable collar
• Drainage base
• Porous drainage cap
• Proctor's reamer
• Water supply reservoir
• Vacuum pump
• Stopwatch
• Constant head collecting chamber
• Large funnel
• Thermometer
• Weighing balance and filter paper

After necessary specimen preparations, the soil specimen is collected through the top part of the constant head reservoir. The outlet at the bottom part of the constant head collecting chamber is kept open to maintain a steady flow. The amount of flow is collected for a particular time interval which is measured by a stopwatch. The difference in heads of the constant head reservoir and constant head collecting chamber is then measured. The procedure is repeated three times for the same time interval.

Falling head technique

This method is used for the determination of the hydraulic conductivity of fine-grained soils. The characteristic feature of this technique is that it makes use of a vertical standpipe with a small soil sample. The soil sample is made saturated before the start of the test. A specific quantity of de-aired water is inserted into the standpipe up to a certain lower limit. The time required by the water to fall from upper limit to lower limit is noted. This procedure is often repeated multiple times maintaining the same time interval.

Measurement by flow cells

Flow cells are specially designed cells through which liquids or samples flow desirably through a specified path. Measurements through flow cells are made on the field and then brought to the laboratory for measurements. These cells generally measure the undisturbed and disturbed soil samples. The amount of soil sample used typically decides the size of flow cells.

Determination of hydraulic conductivity through flow cells requires the soil sample to be tested, to be saturated before use. This sample is inserted into the flow cell with water, which is passed through the top of the flow cell maintaining a steady flow rate. The infiltration rates are then measured. Corrections need to be made based on the technique used in the analysis.

Using KSAT devices

KSAT (K stands for coefficient of hydraulic conductivity and SAT stands for saturation), or sometimes known as saturated hydraulic conductivity device, is an automated device, used for the determination of the hydraulic conductivity of saturated soil samples. Its functionality is similar to a flow cell but it is fast and has the capability of making both constant heads and falling head measurements. This device has a vertical water column, with an attached vertical burette to control the flow. This device makes use of small soil samples for experimental use. The water makes its way through the burette and reaches the bottom part of the soil sample. The pressure head associated with the water column is measured through a pressure sensor. The readings are passed into the computer software through which the parameters are measured and water viscosity values are corrected for a range of temperature values. The characteristic feature of this device is that all the processes are automatic using computer programs. This saves time and increases calculation accuracy.

Context and Applications

This topic is majorly taught in different Undergraduate and Postgraduate degree courses of:

• Bachelors of Technology (Civil engineering, Geotechnical engineering, Environmental engineering, Soil engineering)
• Masters of Technology (Civil engineering, Geotechnical engineering, Environmental engineering, Soil engineering)

Practice Problems

Q 1. Which of the following tests uses a vertical standpipe?

a. Falling head technique

b. Constant head technique

c. Both a and b

d. None of the above

Answer: Option a

Explanation: The falling head technique makes use of a vertical standpipe.

Q 2. Which of the following methods is automatic and uses computers?

a. KSAT technique

b. Falling head technique

c. Constant technique

d. None of these

Answer: Option a

Explanation: The KSAT technique is an automatic technique that uses computers.

Q 3. Which of the following instrument is used in the constant head technique?

a. Proctor's reamer

b. vacuum chamber

c. thermometer

d. all of these

Answer: Option d

Explanation: For measuring the hydraulic conductivity of soil using the constant head technique, a variety of instruments are used like Proctor's reamer, vacuum chamber, thermometer, and so on.

Q 4. Which of the following is true about Darcy's law?

a. The discharge varies inversely with dynamic viscosity.

b. The discharge varies inversely with pressure drop.

c. The discharge is proportional to the permeability coefficient.

d. both a and c

Answer: Option d

Explanation: As per Darcy's law, the discharge varies inversely with dynamic viscosity and it is proportional to the permeability coefficient.

Q.5 What does the negative sign in Darcy's equation indicate?

a. The flow is along the negative potential.

b. The flow is along the downstream.

c. The flow is along the negative pressure gradient.

d. Both a and c

Answer: Option a

Explanation: The negative sign in Darcy's equation indicates that the flow is along the negative potential or along the negative hydraulic gradient.

Related Concepts

• Use of flow cells for effective biosensing
• Use of standpipes in building construction
• Measuring volumetric flow rates using a flow meter
• Experimental determination of permeability using constant head reservoirs