## What is Hydraulic Conductivity?

Hydraulic conductivity is one of the hydraulic properties of soil defined as a measurement of the ability of a porous medium to permit water movement or fluid flow through it. It is denoted by the letter K. It is influenced by the density and viscosity of the fluid. It is also called permeability. Hydraulic conductivity is defined as the ratio of velocity to the hydraulic gradient. The different methods used to determine the hydraulic conductivity are laboratory methods (constant head permeability tests and falling head tests), in-situ field methods (pumping in and pumping out tests), small scale field tests (infiltration tests and slug tests), and indirect methods such as estimation from grain size, consolidation test data, and horizontal capillary test. The pedotransfer function (PTF) method is a specific empirical estimating approach employed in the soil sciences is also used to determine the hydraulic conductivity of the soil.

The hydraulic conductivity of the soil can also be computed from different relations, and the most used relation for the computation is the Kozeny-Carman equation.

$K=\left(\frac{g\times {\rho}_{w}}{{C}_{s}\times \mu \times {S}^{2}\times {T}^{2}}\right)\times \frac{{e}^{3}}{1+e}\phantom{\rule{0ex}{0ex}}where,\phantom{\rule{0ex}{0ex}}e=voidsratio\phantom{\rule{0ex}{0ex}}T=Tortuosity\phantom{\rule{0ex}{0ex}}S=SurfaceArea\phantom{\rule{0ex}{0ex}}\mu =Dynamicvis\mathrm{cos}ity\phantom{\rule{0ex}{0ex}}g=Accelerationduetogravity\phantom{\rule{0ex}{0ex}}{C}_{s}=Cons\mathrm{tan}t$

The K values indicates the coefficient of permeability or hydraulic conductivity.

## Factors influencing hydraulic conductivity

- The hydraulic conductivity of the soil is proportional to the square of the particle size of the soil.
- The permeability of the soil increases with the increase of the pores present in the soil.
- The degree of saturation of soil has a significant effect on hydraulic conductivity. The partially saturated soil has low permeability as the path of water is blocked by gases, while field-saturated soils are more permeable to water than this.
- The adsorbed particles surrounding the soil particles have fixed positions in the soil and hence decrease the permeability of the soil.
- The presence of any foreign particles like dust also decreases the permeability of the soil.
- The permeability will decrease when a particular surface area increases. Particles with a rounded form will have higher permeability than those with an angular shape. It's because angular particles have a larger specific surface area than rounded ones.
- The permeability of the soil is also affected by the surrounding temperature, the higher the temperature, the higher will be the permeability of the soil.

## Applications of Hydraulic conductivity

### Rate of settlement

Primary consolidation is a function of hydraulic conductivity. In fine-grained, due to fewer pores present the flow rate of water is low resulting in low hydraulic conductivity, so the rate of settlement is less. In coarse-grained, the voids are high, so the conductivity of water is also high and hence the settlement of soil is also high.

### Construction of hydraulic structures

The construction of structures such as dams depends on the hydraulic conductivity of the soil. The soil on which the dam structures are constructed should be impermeable or less permeable to water. If the subsurface soil is more pervious, it may lead to piping failure of the dam structure. Seepage flow beneath the foundation of hydraulic structures built on permeable soils puts upward pressure on the base of the structure, lowering frictional resistance and increasing the susceptibility to slide.

### Stability of slopes

The design of slopes and retaining structures depend on the saturated hydraulic conductivity of the soils.

### In agriculture

Aeration, water holding capacity, and drainage capacity of the soil are all affected by pore size and distribution. Soil with lesser voids or soil of impermeable nature lower waters capacity to penetrate the soil vertically, increasing surface runoff and the danger of floods.

### Calculation of groundwater flow

The hydraulic head and the permeability determine the rate of groundwater movement. Permeability enables the water to flow through the rock or unconsolidated sediment and also indicates the ease with which the water can be extracted from the well.

### Filters

The saturated hydraulic conductivity (Ksat) of porous filters used in water treatment methods is crucial for maximizing nutrient and contaminant retention.

### Soil Drainage

The materials used to create soil drainage systems should have a high hydraulic conductivity. The drainage material must not only have a high hydraulic conductivity when it is first installed, but it must also maintain that conductivity overtime to resist clogging of the contaminants. The hydraulic conductivity of drainage materials is mostly determined by the grain size of the soil's finest particles.

### Geological studies and research

The genesis of the sample, whether igneous, sedimentary, or metamorphic, is the primary determinant of this geological permeability. Environmental research topics such as coastal erosion forecasts employ geological permeability measures to analyze the state of samples under long-term environmental circumstances. It is also used a lot in the field of oil exploration, hydrogeology, and petroleum geology.

## Permeability of liner soils in hydraulic conductivity

The liner soils present in the landfill systems should have very little hydraulic conductivity to prevent the entry of leachates and other toxins from the landfill into the underlying soil. The soil is just beneath the geomembrane and acts as a second barrier to keep leachate from escaping the landfill and entering the environment. This layer also helps to keep landfill gas from escaping. Before initiating landfill construction, the native soils underlying the dump are prepared in such a way that it remains impermeable to the leachate.

## Context and Applications

This topic of hydraulic conductivity has significance in the Geoenvironmental and hydrogeological fields of study and is taught in the following disciplines.

- Bachelors of Technology (Civil Engineering)
- Masters of Technology (Geotechnical Engineering)
- Masters of Technology (Geotechnical Engineering)
- Masters of Technology (Hydrology and Water Resources Engineering)

## Practice Problem

Q 1. The ratio of the velocity to hydraulic gradient is defined as which of the following hydraulic properties?

- Hydraulic conductivity
- Porosity
- Pedotransfer
- None of the above

Answer: Option a

Explanation: Hydraulic conductivity by Darcy's law is defined as the ratio of velocity to the hydraulic gradient. It is a measure of the permeability of the porous media.

Q 2. Which of the following are the laboratory tests for determining the permeability of a certain soil sample?

- Constant head and falling-head tests
- Pumping in and pumping out tests
- Infiltration tests and slug tests
- Falling head tests and pumping in tests

Answer: Option a

Explanation: In constant head and falling head tests, the core samples are tested in the laboratory for the measurement of permeability, while pumping in and pumping out tests are field methods for determining permeability.

Q 3. What is the use of a permeameter?

- A device used for the measurement of permeability
- A device used for the measurement of soil texture of anisotropic soil
- A device used to measure open-access water table or groundwater
- None of the above

Answer: Option a

Explanation: A laboratory instrument for determining the hydraulic conductivity of rock and soil samples, as well as the soil permeability coefficient.

Q 4. Which are the following factors influencing hydraulic conductivity?

- Grain size
- Degree of saturation
- Void ratio
- All the above

Answer: Option d

Explanation: All of the above are factors influencing the hydraulic conductivity of the soil. Permeability varies with the square of the particle size. If the soil is less or partly saturated even on the application of water, the permeability and hydraulic conductivity of the soil are less. If the soil has lesser voids, the permeability will be less.

Q 5. Which of the following is the unit of transmissivity?

- m
^{3}/day/m - m/sec
- m
^{2}/sec - None of the above

Answer: Option a

Explanation: Transmissivity is the rate at which the groundwater can pass a unit width of an aquifer and is denoted by the unit m^{3}/day/m.

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