In science and engineering, hydraulic conductivity (, in SI units of meters per second) is a property of porous materials, soils and rocks, that describes the ease with which a fluid (usually water) can move through the pore space, or fracture network. https://www.preene.com/blog/2014/07/what-is-hydraulic-conductivity#:~:text=DEFINITIONS%20OF%20HYDRAULIC%20CONDUCTIVITY&text=In%20theoretical%20terms%2C%20hydraulic%20conductivity,the%20material%20is%20less%20permeable. Hydraulic conductivity definition It depends on the intrinsic permeability (, unit: m) of the material, the degree of saturation, and on the density and viscosity of the fluid. Saturated hydraulic conductivity, , describes water movement through saturated media. By definition, hydraulic conductivity is the ratio of volume flux to hydraulic gradient yielding a quantitative measure of a saturated soil's ability to transmit water when subjected to a hydraulic gradient.
Methods of determination
There are two broad approaches for determining hydraulic conductivity: In the empirical approach the hydraulic conductivity is correlated to soil properties like pore-size and grain-size distributions, and soil texture. In the experimental approach the hydraulic conductivity is determined from hydraulic experiments that are interpreted using Darcy's law.
The experimental approach is broadly classified into: Laboratory tests using soil samples subjected to hydraulic experiments Field tests (on site, in situ) that are differentiated into: small-scale field tests, using observations of the water level in cavities in the soil large-scale field tests, like pumping tests in wells or by observing the functioning of existing horizontal drainage systems. The small-scale field tests are further subdivided into: infiltration tests in cavities above the water table slug tests in cavities below the water table
The methods of determining hydraulic conductivity and other hydraulic properties are investigated by numerous researchers and include additional empirical approaches.
Estimation by empirical approach Estimation from grain size Allen Hazen derived an empirical formula for approximating hydraulic conductivity from grain-size analyses:
where Hazen's empirical coefficient, which takes a value between 0.0 and 1.5 (depending on literature), with an average value of 1.0. A.F. Salarashayeri & M. Siosemarde indicate C is usually between 1.0 and 1.5, with D in mm and K in cm/s. is the diameter of the 10 percentile grain size of the material.
Pedotransfer function A pedotransfer function (PTF) is a specialized empirical estimation method, used primarily in the soil sciences, but increasingly used in hydrogeology. There are many different PTF methods, however, they all attempt to determine soil properties, such as hydraulic conductivity, given several measured soil properties, such as soil particle size, and bulk density.
Determination by experimental approach There are relatively simple and inexpensive laboratory tests that may be run to determine the hydraulic conductivity of a soil: constant-head method and falling-head method.
Laboratory methods Constant-head method The constant-head method is typically used on granular soil. This procedure allows water to move through the soil under a steady state head condition while the volume of water flowing through the soil specimen is measured over a period of time. By knowing the volume of water measured in a time , over a specimen of length and cross-sectional area , as well as the head , the hydraulic conductivity () can be derived by simply rearranging Darcy's law:
Proof: Darcy's law states that the volumetric flow depends on the pressure differential between the two sides of the sample, the permeability and the dynamic viscosity as: Controlling capillary flow an application of Darcy's law
In a constant head experiment, the head (difference between two heights) defines an excess water mass, , where is the density of water. This mass weighs down on the side it is on, creating a pressure differential of , where is the gravitational acceleration. Plugging this directly into the above gives
If the hydraulic conductivity is defined to be related to the hydraulic permeability as
this gives the result.
Falling-head method In the falling-head method, the soil sample is first saturated under a specific head condition. The water is then allowed to flow through the soil without adding any water, so the pressure head declines as water passes through the specimen. The advantage to the falling-head method is that it can be used for both fine-grained and coarse-grained soils. .Liu, Cheng "Soils and Foundations." Upper Saddle River, New Jersey: Prentice Hall, 2001 If the head drops from to in a time , then the hydraulic conductivity is equal to
Proof: As above, Darcy's law reads
The decrease in volume is related to the falling head by . Plugging this relationship into the above, and taking the limit as , the differential equation
has the solution
Plugging in and rearranging gives the result.
In-situ (field) methods In compare to laboratory method, field methods gives the most reliable information about the permeability of soil with minimum disturbances. In laboratory methods, the degree of disturbances affect the reliability of value of permeability of the soil.
Pumping Test Pumping test is the most reliable method to calculate the coefficient of permeability of a soil. This test is further classified into Pumping in test and pumping out test.
Augerhole method There are also in-situ methods for measuring the hydraulic conductivity in the field. When the water table is shallow, the augerhole method, a slug test, can be used for determining the hydraulic conductivity below the water table. The method was developed by Hooghoudt (1934)S.B.Hooghoudt, 1934, in Dutch. Bijdrage tot de kennis van enige natuurkundige grootheden van de grond. Verslagen Landbouwkundig Onderzoek No. 40 B, p. 215-345. in The Netherlands and introduced in the US by Van Bavel en Kirkham (1948).C.H.M. van Bavel and D. Kirkham, 1948. Field measurement of soil permeability using auger holes. Soil. Sci. Soc. Am. Proc 13:90-96. The method uses the following steps: an augerhole is perforated into the soil to below the water table water is bailed out from the augerhole the rate of rise of the water level in the hole is recorded the -value is calculated from the data as:Determination of the Saturated Hydraulic Conductivity. Chapter 12 in: H.P.Ritzema (ed., 1994) Drainage Principles and Applications, ILRI Publication 16, p.435-476. International Institute for Land Reclamation and Improvement, Wageningen (ILRI), The Netherlands. . Free download from: , under nr. 6, or directly as PDF :
where: is the horizontal saturated hydraulic conductivity (m/day) is the depth of the water level in the hole relative to the water table in the soil (cm): at time at time is the time (in seconds) since the first measurement of as is a factor depending on the geometry of the hole:
where: is the radius of the cylindrical hole (cm) is the average depth of the water level in the hole relative to the water table in the soil (cm), found as is the depth of the bottom of the hole relative to the water table in the soil (cm).
The picture shows a large variation of -values measured with the augerhole method in an area of 100 ha.Drainage research in farmers' fields: analysis of data. Contribution to the project “Liquid Gold” of the International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands. Free download from : , under nr. 2, or directly as PDF : The ratio between the highest and lowest values is 25. The cumulative frequency distribution is lognormal
Related magnitudes Transmissivity The transmissivity is a measure of how much water can be transmitted horizontally, such as to a pumping well. Transmissivity should not be confused with the similar word transmittance used in optics, meaning the fraction of incident light that passes through a sample. An aquifer may consist of soil layers. The transmissivity of a horizontal flow for the th soil layer with a saturated thickness and horizontal hydraulic conductivity is:
Transmissivity is directly proportional to horizontal hydraulic conductivity and thickness . Expressing in m/day and in m, the transmissivity is found in units m2/day. The total transmissivity of the aquifer is the sum of every layer's transmissivity:
The apparent horizontal hydraulic conductivity of the aquifer is:
where , the total thickness of the aquifer, is the sum of each layer's individual thickness:
The transmissivity of an aquifer can be determined from pumping tests.J.Boonstra and R.A.L.Kselik, SATEM 2002: Software for aquifer test evaluation, 2001. Publ. 57, International Institute for Land reclamation and Improvement (ILRI), Wageningen, The Netherlands. On line :
Influence of the water table When a soil layer is above the water table, it is not saturated and does not contribute to the transmissivity. When the soil layer is entirely below the water table, its saturated thickness corresponds to the thickness of the soil layer itself. When the water table is inside a soil layer, the saturated thickness corresponds to the distance of the water table to the bottom of the layer. As the water table may behave dynamically, this thickness may change from place to place or from time to time, so that the transmissivity may vary accordingly. In a semi-confined aquifer, the water table is found within a soil layer with a negligibly small transmissivity, so that changes of the total transmissivity () resulting from changes in the level of the water table are negligibly small. When pumping water from an unconfined aquifer, where the water table is inside a soil layer with a significant transmissivity, the water table may be drawn down whereby the transmissivity reduces and the flow of water to the well diminishes.
Resistance The resistance to vertical flow () of the th soil layer with a saturated thickness and vertical hydraulic conductivity is:
Expressing in m/day and in m, the resistance () is expressed in days. The total resistance () of the aquifer is the sum of each layer's resistance:
The apparent vertical hydraulic conductivity () of the aquifer is:
where is the total thickness of the aquifer:
The resistance plays a role in aquifers where a sequence of layers occurs with varying horizontal permeability so that horizontal flow is found mainly in the layers with high horizontal permeability while the layers with low horizontal permeability transmit the water mainly in a vertical sense.
Anisotropy When the horizontal and vertical hydraulic conductivity ( and ) of the soil layer differ considerably, the layer is said to be anisotropic with respect to hydraulic conductivity. When the apparent horizontal and vertical hydraulic conductivity ( and ) differ considerably, the aquifer is said to be anisotropic with respect to hydraulic conductivity. An aquifer is called semi-confined when a saturated layer with a relatively small horizontal hydraulic conductivity (the semi-confining layer or aquitard) overlies a layer with a relatively high horizontal hydraulic conductivity so that the flow of groundwater in the first layer is mainly vertical and in the second layer mainly horizontal. The resistance of a semi-confining top layer of an aquifer can be determined from pumping tests.