|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| '''Hydraulic conductivity''', symbolically represented as <math>K</math>, is a property of vascular plants, soils and rocks, that describes the ease with which a fluid (usually water) can move through pore spaces or fractures. It depends on the [[intrinsic permeability]] of the material and on the degree of [[Saturation (chemistry)|saturation]], and on the [[density]] and [[viscosity]] of the fluid. Saturated hydraulic conductivity, ''K<sub>sat</sub>'', describes water movement through saturated media.
| | Nothing to write about myself really.<br>I enjoy of finally being a part of this site.<br>I just wish I am useful in some way .<br><br>Feel free to surf to my web page: [http://city-wiz.com/node/170915 fifa 15 Coin generator] |
| | |
| Typical ranges of hydraulic conductivity for different soils can be found on [http://www.geotechdata.info/parameter/permeability.html Geotechdata.info database].
| |
| | |
| ==Methods of determination==
| |
| [[File:HydrCondTable.GIF|thumb|450px|Overview of determination methods]]
| |
| There are two broad categories of determining hydraulic conductivity:
| |
| *''Empirical'' approach by which the hydraulic conductivity is correlated to soil properties like [[Porosity|pore size]] and [[particle size (grain size)]] distributions, and [[soil texture]]
| |
| *''Experimental'' approach by which the hydraulic conductivity is determined from hydraulic experiments using [[Darcy's law]]
| |
| | |
| The experimental approach is broadly classified into:
| |
| *[[Laboratory]] tests using soil samples subjected to hydraulic [[experiment]]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 test]]s in [[Water well|wells]] or by observing the functioning of existing horizontal [[drainage]] systems.
| |
| The small scale field tests are further subdivided into:
| |
| *[[Infiltration (hydrology)|infiltration]] tests in cavities ''above'' the [[water table]]
| |
| *[[slug test]]s in cavities ''below'' the [[water table]]
| |
| | |
| ==Estimation by empirical approach==
| |
| | |
| ===Estimation from grain size===
| |
| [[Allen Hazen]] derived an [[Empirical method|empirical]] formula for approximating hydraulic conductivity from grain size analyses:
| |
| :<math>K = C (D_{10})^2</math>
| |
| where
| |
| :<math>C</math> Hazen's empirical coefficient, which takes a value between 0.4 and 10.0 (depending on literatures), with an average value of 1.0. NB This should have units. 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.
| |
| :<math>D_{10}</math> 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 science]]s, however has increasing use in hydrogeology.<ref>{{cite journal |author=Wösten, J.H.M., Pachepsky, Y.A., and Rawls, W.J. |title=Pedotransfer functions: bridging the gap between available basic soil data and missing soil hydraulic characteristics |year=2001 |volume=251 |issue=3-4 |pages=123–150 |doi=10.1016/S0022-1694(01)00464-4 |journal=[[Journal of Hydrology]] |bibcode = 2001JHyd..251..123W }}</ref> 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 [http://www.geotechdata.info/geotest/constant-head-permeability-test.html 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 quantity (volume) of water flowing through the soil specimen is measured over a period of time. By knowing the quantity <math>Q</math> of water measured, length <math>L</math> of specimen, cross-sectional area <math>A</math> of the specimen, time <math>t</math> required for the quantity of water <math>Q</math> to be discharged, and head <math>h</math>, the hydraulic conductivity can be calculated:
| |
| | |
| :<math>\frac{Q}{t} = Av\,</math>
| |
| where <math>v</math> is the flow velocity. Using [[Darcy's Law]]:
| |
| :<math>v = Ki\,</math>
| |
| and expressing the hydraulic gradient <math>i</math> as:
| |
| :<math>i = \frac{h}{L}</math>
| |
| where <math>h</math> is the difference of hydraulic head over distance <math>L</math>, yields:
| |
| :<math>\frac{Q}{t} = \frac{AKh}{L}</math>
| |
| Solving for <math>K</math> gives:
| |
| :<math>K = \frac{QL}{Aht}</math>
| |
| | |
| ====Falling-head method====
| |
| The [http://www.geotechdata.info/geotest/falling-head-permeability-test falling-head method] is totally different than the constant head methods in its initial setup; however, the advantage to the falling-head method is that it can be used for both fine-grained and coarse-grained soils. The soil sample is first saturated under a specific head condition. The water is then allowed to flow through the soil without maintaining a constant pressure head.<ref>Liu, Cheng "Soils and Foundations." Upper Saddle River, New Jersey: Prentice Hall, 2001 ISBN 0-13-025517-3</ref>
| |
| | |
| :<math>K = \frac{2.3aL}{At}\log\left(\frac{h_1}{h_2}\right)</math>
| |
| | |
| ===In-situ (field) methods===
| |
| | |
| ====Augerhole method====
| |
| There are also in-situ methods for measuring the hydraulic conductivity in the field.<br>
| |
| When the water table is shallow, the augerhole method, a [[slug test]], can be used for determining the hydraulic conductivity below the water table. <br>
| |
| The method was developed by Hooghoudt (1934) <ref>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.</ref> in The Netherlands and introduced in the US by Van Bavel en Kirkham (1948).<ref>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.</ref> <br />
| |
| 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:<ref name="Oost">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. ISBN 90-70754-33-9. Free download from: [http://www.waterlog.info/articles.htm] , under nr. 6, or directly as PDF : [http://www.waterlog.info/pdf/chap12.pdf]</ref>
| |
| | |
| :K = F (Ho-Ht) <big>/</big> t
| |
| [[File:PANAZ1.JPG|thumb|200px|Cumulative frequency distribution (lognormal) of hydraulic conductivity (X-data)]]
| |
| | |
| 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), Ht = H at time t, Ho = H at time t = 0, t = time (in seconds) since the first measurement of H as Ho, and F is a factor depending on the geometry of the hole:
| |
| | |
| :F = 4000<math>r</math> <big>/</big> <math>h'</math>(20+D/<math>r</math>)(2−<math>h'</math>/D)
| |
| | |
| where: <math>r</math> = radius of the cylindrical hole (cm), <math>h'</math> is the average depth of the water level in the hole relative to the water table in the soil (cm), found as <math>h'</math>=(Ho+Ht)/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.<ref>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 : [http://www.waterlog.info/articles.htm] , under nr. 2, or directly as PDF : [http://www.waterlog.info/pdf/analysis.pdf]</ref> The ratio between the highest and lowest values is 25. The cumulative frequency distribution is [[lognormal]] and was made with the [[cumulative frequency analysis|CumFreq]] program.
| |
| | |
| ==Related magnitudes==
| |
| | |
| ===Transmissivity===
| |
| The transmissivity is a measure of how much water can be transmitted horizontally, such as to a pumping well. <br />
| |
| :<small>''Transmissivity'' should not be confused with the similar word [[transmittance]] used in [[optics]], meaning the fraction of incident light that passes through a sample.''</small>
| |
| An [[aquifer]] may consist of <math>n</math> soil layers. The transmissivity for horizontal flow <math>T_i</math> of the <math>i-th</math> soil layer with a ''saturated'' thickness <math>d_i</math> and horizontal hydraulic conductivity <math>K_i</math> is:
| |
| :<math>T_i = K_i d_i</math>
| |
| Transmissivity is directly proportional to horizontal hydraulic conductivity <math>K_i</math> and thickness <math>d_i</math>. Expressing <math>K_i</math> in m/day and <math>d_i</math> in m, the transmissivity <math>T_i</math> is found in units m<sup>2</sup>/day.<br/>
| |
| The total transmissivity <math>T_t</math> of the aquifer is:<ref name="Oost" />
| |
| :<math>T_t = \sum T_i</math> where <math>\sum</math> signifies the summation over all layers <math>i = 1, 2, 3, \cdots, n</math>.
| |
| | |
| The ''apparent'' horizontal hydraulic conductivity <math>K_A</math> of the aquifer is:
| |
| :<math>K_A = T_t / D_t</math>
| |
| where <math>D_t</math>, the total thickness of the aquifer, is <math>D_t = \sum d_i</math>, with <math>i = 1, 2, 3, \cdots, n</math>.
| |
| | |
| The transmissivity of an aquifer can be determined from [[pumping test]]s.<ref name="Boon">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. ISBN 90-70754-54-1 On line : [http://content.alterra.wur.nl/Internet/webdocs/ilri-publicaties/publicaties/Pub57/Pub57.pdf]</ref>
| |
| | |
| ''Influence of the water table'' <br />
| |
| 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. <br >
| |
| 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 (Dt) resulting from changes in the level of the water table are negligibly small. <br />
| |
| 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<sub>i</sub>) of the <math>i-th</math> soil layer with a ''saturated'' thickness <math>d_i</math> and vertical hydraulic conductivity Kv<sub>i</sub> is:
| |
| : R<sub>i</sub> = <math>d_i</math> / Kv<sub>i</sub>
| |
| Expressing Kv<sub>i</sub> in m/day and <math>d_i</math> in m, the resistance (R<sub>i</sub>) is expressed in days. <br />
| |
| The total resistance (Rt) of the aquifer is:<ref name="Oost" />
| |
| :Rt = <big>Σ</big> R<sub>i</sub> = <big>Σ</big> <math>d_i</math> / Kv<sub>i</sub>
| |
| where <big>Σ</big> signifies the summation over all layers: <math>i </math>= 1, 2, 3, . . .<math> n</math> <br />
| |
| The ''apparent'' vertical hydraulic conductivity (Kv<sub>A</sub>) of the aquifer is:
| |
| :Kv<sub>A</sub> = Dt / Rt
| |
| where Dt is the total thickness of the aquifer: Dt = <big>Σ</big> <math>d_i</math>, with <math>i</math>= 1, 2, 3, . . .<math> n</math>
| |
| | |
| The resistance plays a role in [[aquifer]]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 (Kh<sub>i</sub> and Kv<sub>i</sub>) of the <math>i-th</math> soil layer differ considerably, the layer is said to be [[anisotropy|anisotropic]] with respect to hydraulic conductivity.<br />
| |
| When the ''apparent'' horizontal and vertical hydraulic conductivity (Kh<sub>A</sub> and Kv<sub>A</sub>) differ considerably, the [[aquifer]] is said to be [[anisotropy|anisotropic]] with respect to hydraulic conductivity.<br />
| |
| 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. <br>
| |
| The resistance of a semi-confining top layer of an aquifer can be determined from [[pumping test]]s.<ref name="Boon" /> <br />
| |
| When calculating flow to [[Drainage|drains]] <ref>The energy balance of groundwater flow applied to subsurface drainage in anisotropic soils by pipes or ditches with entrance resistance. International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands. On line : [http://www.waterlog.info/pdf/enerart.pdf] . Paper based on: R.J. Oosterbaan, J. Boonstra and K.V.G.K. Rao, 1996, “The energy balance of groundwater flow”. Published in V.P.Singh and B.Kumar (eds.), Subsurface-Water Hydrology, p. 153-160, Vol.2 of Proceedings of the International Conference on Hydrology and Water Resources, New Delhi, India, 1993. Kluwer Academic Publishers, Dordrecht, The Netherlands. ISBN 978-0-7923-3651-8 . On line : [http://www.waterlog.info/pdf/enerbal.pdf]. The corresponding free EnDrain program can be downloaded from: [http://www.waterlog.info/endrain.htm]</ref> or to a [[Water well|well]] field <ref>Subsurface drainage by (tube)wells, 9 pp. Explanation of equations used in the WellDrain model. International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands. On line: [http://www.waterlog.info/pdf/wellspac.pdf] . The corresponding free WellDrain program can be downloaded from : [http://www.waterlog.info/weldrain.htm]</ref> in an aquifer with the aim to [[Watertable control|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]] and [[gravel]] [[aquifer]]s have higher hydraulic conductivity than [[clay]] or unfractured [[granite]] aquifers. Sand or gravel aquifers would thus be easier to extract water from (e.g., using a pumping [[Water well|well]]) 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 ([[gallon|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]] (the distribution is often considered to be [[lognormal distribution|lognormal]]),
| |
| * vary a large amount through space (sometimes considered to be [[random]]ly spatially distributed, or [[stochastic]] in nature),
| |
| * are directional (in general ''K'' is a symmetric second-rank [[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 test]]s, laboratory column flow tests or inverse computer simulation, (sometimes also from [[Particle size|grain size]] analyses), and
| |
| * are very dependent (in a [[nonlinearity|non-linear]] way) on the water content, which makes solving the [[vadose zone|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]] conditions — using standard values of [[viscosity]] and [[specific gravity]] for water at 20°C and 1 atm.
| |
| See the similar table derived from the same source for [[permeability (fluid)|intrinsic permeability]] values.<ref>{{cite book |author=Bear, J. |year=1972 |title=Dynamics of Fluids in Porous Media |publisher=[[Dover Publications]] |isbn=0-486-65675-6}}</ref>
| |
| | |
| {| border="1" width="600"
| |
| | bgcolor="#FAEBD7" | ''K'' (cm/[[second|s]])
| |
| | 10²
| |
| | 10<sup>1</sup>
| |
| | 10<sup>0</sup>=1
| |
| | 10<sup>−1</sup>
| |
| | 10<sup>−2</sup>
| |
| | 10<sup>−3</sup>
| |
| | 10<sup>−4</sup>
| |
| | 10<sup>−5</sup>
| |
| | 10<sup>−6</sup>
| |
| | 10<sup>−7</sup>
| |
| | 10<sup>−8</sup>
| |
| | 10<sup>−9</sup>
| |
| | 10<sup>−10</sup>
| |
| |-
| |
| | bgcolor="#FAEBD7" | ''K'' (ft/[[day]])
| |
| | 10<sup>5</sup>
| |
| | 10,000
| |
| | 1,000
| |
| | 100
| |
| | 10
| |
| | 1
| |
| | 0.1
| |
| | 0.01
| |
| | 0.001
| |
| | 0.0001
| |
| | 10<sup>−5</sup>
| |
| | 10<sup>−6</sup>
| |
| | 10<sup>−7</sup>
| |
| |-
| |
| | bgcolor="#FAEBD7" | Relative Permeability
| |
| | colspan="4" align="center" | Pervious
| |
| | colspan="4" align="center" | Semi-Pervious
| |
| | colspan="5" align="center" | Impervious
| |
| |-
| |
| | bgcolor="#FAEBD7" | [[Aquifer]]
| |
| | colspan="5" align="center" | Good
| |
| | colspan="4" align="center" | Poor
| |
| | colspan="4" align="center" | None
| |
| |-
| |
| | bgcolor="#FAEBD7" | Unconsolidated [[Sand]] & [[Gravel]]
| |
| | colspan="2" align="center" | Well Sorted Gravel
| |
| | colspan="3" align="center" | Well Sorted Sand or Sand & Gravel
| |
| | colspan="4" align="center" | Very Fine Sand, Silt, [[Loess]], [[Loam]]
| |
| | colspan="4" |
| |
| |-
| |
| | bgcolor="#FAEBD7" | Unconsolidated Clay & Organic
| |
| | colspan="4" |
| |
| | colspan="2" align="center" | [[Peat]]
| |
| | colspan="3" align="center" | Layered [[Clay]]
| |
| | colspan="4" align="center" | Fat / Unweathered Clay
| |
| |-
| |
| | bgcolor="#FAEBD7" | Consolidated Rocks
| |
| | colspan="4" align="center" | Highly Fractured Rocks
| |
| | colspan="3" align="center" | [[Petroleum geology|Oil Reservoir]] Rocks
| |
| | colspan="2" align="center" | Fresh [[Sandstone]]
| |
| | colspan="2" align="center" | Fresh [[Limestone]], [[Dolomite]]
| |
| | colspan="2" align="center" | Fresh [[Granite]]
| |
| |}
| |
| Source: modified from Bear, 1972
| |
| | |
| ==Saturated Hydraulic Conductivity by Soil Texture==
| |
| | |
| ==See also==
| |
| *[[Aquifer test]]
| |
| *[[Pedotransfer function]]–for estimating hydraulic conductivities given soil properties
| |
| | |
| ==References==
| |
| <references/>
| |
| | |
| {{Aquiferproperties}}
| |
| {{Geotechnical engineering|state=collapsed}}
| |
| | |
| {{DEFAULTSORT:Hydraulic Conductivity}}
| |
| [[Category:Hydrology]]
| |
| [[Category:Hydraulic engineering]]
| |
| [[Category:Soil mechanics]]
| |
| [[Category:Soil physics]]
| |