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Hydraulic conductivity, symbolically represented as (unit: m/s), is a property of porous materials,
soil Soil, also commonly referred to as earth or dirt Dirt is an unclean matter, especially when in contact with a person's clothes, skin, or possessions. In such cases, they are said to become dirty. Common types of dirt include: * Debri ...
s and rocks, that describes the ease with which a fluid (usually water) can move through the
pore space Porosity or void fraction is a measure of the void (i.e. "empty") spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure ...
, or fractures network. It depends on the intrinsic permeability (, unit: m) of the material, the degree of
saturation Saturation, saturated, unsaturation or unsaturated may refer to: Chemistry * Saturation, a property of organic compounds referring to carbon-carbon bonds **Saturated and unsaturated compounds ** Degree of unsaturation **Saturated fat or fatty aci ...
, and on the
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
and
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
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 categories of determining hydraulic conductivity: *''Empirical'' approach by which the hydraulic conductivity is correlated to soil properties like
pore size Pore may refer to: Biology Animal biology and microbiology * Sweat pore, an anatomical structure of the skin of humans (and other mammals) used for secretion of sweat * Hair follicle, an anatomical structure of the skin of humans (and other m ...
and
particle size (grain size) Grain size (or particle size) is the diameter of individual grains of sediment, or the lithified particles in clastic rocks. The term may also be applied to other granular materials. This is different from the crystallite size, which re ...
distributions, and
soil texture Soil texture is a classification instrument used both in the field and laboratory to determine soil classes based on their physical texture. Soil texture can be determined using qualitative methods such as texture by feel, and quantitative methods ...
*''Experimental'' approach by which the hydraulic conductivity is determined from hydraulic experiments using
Darcy's law Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of ...
The experimental approach is broadly classified into: *
Laboratory A laboratory (; ; colloquially lab) is a facility that provides controlled conditions in which scientific or technological research, experiments, and measurement may be performed. Laboratory services are provided in a variety of settings: physic ...
tests using soil samples subjected to hydraulic
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome oc ...
s *''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 pump tests in wells or by observing the functioning of existing horizontal
drainage Drainage is the natural or artificial removal of a surface's water and sub-surface water from an area with excess of water. The internal drainage of most agricultural soils is good enough to prevent severe waterlogging (anaerobic condition ...
systems. The small scale field tests are further subdivided into: * infiltration tests in cavities ''above'' the
water table The water table is the upper surface of the zone of saturation. The zone of saturation is where the pores and fractures of the ground are saturated with water. It can also be simply explained as the depth below which the ground is saturated. T ...
* slug tests in cavities ''below'' the
water table The water table is the upper surface of the zone of saturation. The zone of saturation is where the pores and fractures of the ground are saturated with water. It can also be simply explained as the depth below which the ground is saturated. T ...
The methods of determination of hydraulic conductivity and other related issues are investigated by several researchers.


Estimation by empirical approach


Estimation from grain size

Allen Hazen derived an empirical formula for approximating hydraulic conductivity from grain size analyses: :K = C (D_)^2 where :C Hazen's empirical coefficient, which takes a value between 0.0 and 1.5 (depending on literatures), with an average value of 1.0. A.F. Salarashayeri & M. Siosemarde give C as usually taken between 1.0 and 1.5, with D in mm and K in cm/s. :D_ is the
diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid fo ...
of the 10
percentile In statistics, a ''k''-th percentile (percentile score or centile) is a score ''below which'' a given percentage ''k'' of scores in its frequency distribution falls (exclusive definition) or a score ''at or below which'' a given percentage fal ...
grain size of the material


Pedotransfer function

A pedotransfer function (PTF) is a specialized empirical estimation method, used primarily in the
soil science Soil science is the study of soil as a natural resource on the surface of the Earth including soil formation, classification and mapping; physical, chemical, biological, and fertility properties of soils; and these properties in relation to th ...
s, however has increasing use 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 Particle size is a notion introduced for comparing dimensions of solid particles ('' flecks''), liquid particles ('' droplets''), or gaseous particles ('' bubbles''). The notion of particle size applies to particles in colloids, in ecology, in ...
, 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

Th
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 \Delta V of water measured in a time \Delta t, over a specimen of length L and cross-sectional area A, as well as the head h, the hydraulic conductivity, K, can be derived by simply rearranging
Darcy's law Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of ...
: :K = \frac\frac ''Proof: '' Darcy's law states that the volumetric flow depends on the pressure differential, \Delta P, between the two sides of the sample, the permeability, k, and the
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
, \mu, as: :\frac=-\frac\Delta P In a constant head experiment, the head (difference between two heights) defines an excess water mass, \rho A h, where \rho is the density of water. This mass weighs down on the side it is on, creating a pressure differential of \Delta P = \rho g h, where g is the gravitational acceleration. Plugging this directly into the above gives :\frac=-\frach If the hydraulic conductivity is defined to be related to the hydraulic permeability as :K = \frac, 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. . If the head drops from h_i to h_f in a time \Delta t, then the hydraulic conductivity is equal to :K = \frac\ln\frac ''Proof: '' As above, Darcy's law reads :\frac=-K\frac h The decrease in volume is related to the falling head by \Delta V = \Delta h A. Plugging this relationship into the above, and taking the limit as \Delta t\rightarrow 0, the differential equation :\frac = -\frach has the solution :h(t) = h_ie^. Plugging in h(t_f)=h_f 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) in The Netherlands and introduced in the US by Van Bavel en Kirkham (1948).
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 K-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

/ref> :K=F \left( H_o-H_t \right)/t where: K= horizontal saturated hydraulic conductivity (m/day), H= depth of the waterlevel in the hole relative to the water table in the soil (cm), H_t=H at time t, H_o=H at time t=0, t= time (in seconds) since the first measurement of H as H_o, and F is a factor depending on the geometry of the hole: :F=4000r/h'(20+D/r)(2-h'/D) where: r= radius of the cylindrical hole (cm), h' is the average depth of the water level in the hole relative to the water table in the soil (cm), found as h'=(H_o+H_t)/2, and D 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 K-values measured with the augerhole method in an area of 100 ha. The ratio between the highest and lowest values is 25. The cumulative frequency distribution is lognormal and was made with the CumFreq program.


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 Transmittance of the surface of a material is its effectiveness in transmitting radiant energy. It is the fraction of incident electromagnetic power that is transmitted through a sample, in contrast to the transmission coefficient, which is t ...
used in
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...
, meaning the fraction of incident light that passes through a sample.''
An
aquifer An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials ( gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characteris ...
may consist of n soil layers. The transmissivity T_i of a horizontal flow for the i\mbox soil layer with a ''saturated'' thickness d_i and horizontal hydraulic conductivity K_i is: :T_i = K_i d_i Transmissivity is directly proportional to horizontal hydraulic conductivity K_i and thickness d_i. Expressing K_i in m/day and d_i in m, the transmissivity T_i is found in units m2/day.
The total transmissivity T_t of the aquifer is: :T_t = \sum T_i where \sum signifies the summation over all layers i = 1, 2, 3, \dots, n. The ''apparent'' horizontal hydraulic conductivity K_A of the aquifer is: :K_A = T_t / D_t where D_t, the total thickness of the aquifer, is D_t = \sum d_i, with i = 1, 2, 3, \dots, n. 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

/ref> ''Influence of the water table''
When a soil layer is above the
water table The water table is the upper surface of the zone of saturation. The zone of saturation is where the pores and fractures of the ground are saturated with water. It can also be simply explained as the depth below which the ground is saturated. T ...
, 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 (D_t) 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 (R_i) of the i\mbox soil layer with a ''saturated'' thickness d_i and vertical hydraulic conductivity K_ is: : R_i=d_i/K_ Expressing K_ in m/day and d_i in m, the resistance (R_i) is expressed in days.
The total resistance (R_t) of the aquifer is: :R_t=\sum R_i=\sum d_i/K_ where \sum signifies the summation over all layers: i=1,2,3,...,n.
The ''apparent'' vertical hydraulic conductivity (K_) of the aquifer is: :K_=D_t/R_t where D_t is the total thickness of the aquifer: D_t=\sum d_i, with i=1,2,3,...,n. The resistance plays a role in
aquifer An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials ( gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characteris ...
s 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 (K_ and K_) of the i\mbox soil layer differ considerably, the layer is said to be anisotropy, anisotropic with respect to hydraulic conductivity.
When the ''apparent'' horizontal and vertical hydraulic conductivity (K_ and K_) differ considerably, the
aquifer An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials ( gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characteris ...
is said to be anisotropy, 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.
When calculating flow to drains or to a
well A well is an excavation or structure created in the ground by digging, driving, or drilling to access liquid resources, usually water. The oldest and most common kind of well is a water well, to access groundwater in underground aquifers. The ...
field in an aquifer with the aim to control the water table, the anisotropy is to be taken into account, otherwise the result may be erroneous.


Relative properties

Because of their high porosity and permeability,
sand Sand is a granular material composed of finely divided mineral particles. Sand has various compositions but is defined by its grain size. Sand grains are smaller than gravel and coarser than silt. Sand can also refer to a textural class o ...
and gravel
aquifer An aquifer is an underground layer of water-bearing, permeable rock, rock fractures, or unconsolidated materials ( gravel, sand, or silt). Groundwater from aquifers can be extracted using a water well. Aquifers vary greatly in their characteris ...
s have higher hydraulic conductivity than
clay Clay is a type of fine-grained natural soil material containing clay minerals (hydrous aluminium phyllosilicates, e.g. kaolin, Al2 Si2 O5( OH)4). Clays develop plasticity when wet, due to a molecular film of water surrounding the clay par ...
or unfractured
granite Granite () is a coarse-grained ( phaneritic) intrusive igneous rock composed mostly of quartz, alkali feldspar, and plagioclase. It forms from magma with a high content of silica and alkali metal oxides that slowly cools and solidifies under ...
aquifers. Sand or gravel aquifers would thus be easier to extract water from (e.g., using a pumping
well A well is an excavation or structure created in the ground by digging, driving, or drilling to access liquid resources, usually water. The oldest and most common kind of well is a water well, to access groundwater in underground aquifers. The ...
) because of their high transmissivity, compared to clay or unfractured bedrock aquifers. Hydraulic conductivity has units with dimensions of length per time (e.g., m/s, ft/day and ( gal/day)/ft² ); transmissivity then has units with dimensions of length squared per time. The following table gives some typical ranges (illustrating the many orders of magnitude which are likely) for ''K'' values. Hydraulic conductivity (''K'') is one of the most complex and important of the properties of aquifers in hydrogeology as the values found in nature: * range over many
orders of magnitude An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic dis ...
(the distribution is often considered to be lognormal), * vary a large amount through space (sometimes considered to be
random In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual ra ...
ly spatially distributed, or stochastic in nature), * are directional (in general ''K'' is a symmetric second-rank
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
; e.g., vertical ''K'' values can be several orders of magnitude smaller than horizontal ''K'' values), * are scale dependent (testing a m³ of aquifer will generally produce different results than a similar test on only a cm³ sample of the same aquifer), * must be determined indirectly through field pumping tests, laboratory column flow tests or inverse computer simulation, (sometimes also from grain size analyses), and * are very dependent (in a non-linear way) on the water content, which makes solving the unsaturated flow equation difficult. In fact, the variably saturated ''K'' for a single material varies over a wider range than the saturated ''K'' values for all types of materials (see chart below for an illustrative range of the latter).


Ranges of values for natural materials

Table of saturated hydraulic conductivity (''K'') values found in nature Values are for typical fresh
groundwater Groundwater is the water present beneath Earth's surface in rock and soil pore spaces and in the fractures of rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit of rock or an unconsolidated ...
conditions — using standard values of
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...
and
specific gravity Relative density, or specific gravity, is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest ...
for water at 20 °C and 1 atm. See the similar table derived from the same source for intrinsic permeability values. Source: modified from Bear, 1972


See also

*
Aquifer test An aquifer test (or a pumping test) is conducted to evaluate an aquifer by "stimulating" the aquifer through constant pumping, and observing the aquifer's "response" ( drawdown) in observation wells. Aquifer testing is a common tool that hydroge ...
*
Hydraulic analogy The electronic–hydraulic analogy (derisively referred to as the drain-pipe theory by Oliver Lodge) is the most widely used analogy for "electron fluid" in a metal conductor. Since electric current is invisible and the processes in play in ...
* Pedotransfer function – for estimating hydraulic conductivities given soil properties


References


External links


Hydraulic conductivity calculator
{{DEFAULTSORT:Hydraulic Conductivity Hydrology Hydraulic engineering Soil mechanics Soil physics