Hydraulic conductivityFrom Wikipedia, the free encyclopedia

Hydraulic conductivity, symbolically represented as , is a property of vascular plants, soilsand rocks, that describes the ease with which a fluid (usually water) can move through porespaces or fractures. It depends on the intrinsic permeability of the material, the degree ofsaturation, and on the density and viscosity of the fluid. Saturated hydraulic conductivity, Ksat,describes water movement through saturated media.

Typical ranges of hydraulic conductivity for different soils can be found on Geotechdata.infodatabase (http://www.geotechdata.info/parameter/permeability.html).

Contents

1 Methods of determination

2 Estimation by empirical approach

2.1 Estimation from grain size

2.2 Pedotransfer function

3 Determination by experimental approach

3.1 Laboratory methods

3.1.1 Constant-head method

3.1.2 Falling-head method

3.2 In-situ (field) methods

3.2.1 Augerhole method

4 Related magnitudes

4.1 Transmissivity

4.2 Resistance

5 Anisotropy

6 Relative properties

7 Ranges of values for natural materials

8 Saturated Hydraulic Conductivity by Soil Texture

9 See also

10 References

11 External links

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 and particle size (grain size) distributions, and soil texture

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Overview of determination methods

Experimental approach by

which the hydraulic conductivity

is determined from hydraulic

experiments using Darcy's law

The experimental approach isbroadly 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 pump 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

Estimation by empirical approach

Estimation from grain size

Allen Hazen derived an empirical formula for approximating hydraulic conductivity from grainsize analyses:

where

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.

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 inthe soil sciences, however has increasing use in hydrogeology.[1] There are many different PTFmethods, 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.

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Determination by experimental approach

There are relatively simple and inexpensive laboratory tests that may be run to determine thehydraulic conductivity of a soil: constant-head method and falling-head method.

Laboratory methods

Constant-head method

The constant-head method (http://www.geotechdata.info/geotest/constant-head-permeability-test.html) is typically used on granular soil. This procedure allows water to move through thesoil under a steady state head condition while the quantity (volume) of water flowing throughthe soil specimen is measured over a period of time. By knowing the quantity of watermeasured, length of specimen, cross-sectional area of the specimen, time required for thequantity of water to be discharged, and head , the hydraulic conductivity can be calculated:

where is the flow velocity. Using Darcy's Law:

and expressing the hydraulic gradient as:

where is the difference of hydraulic head over distance , yields:

Solving for gives:

Falling-head method

The falling-head method (http://www.geotechdata.info/geotest/falling-head-permeability-test) istotally different from the constant head methods in its initial setup; however, the advantage tothe falling-head method is that it can be used for both fine-grained and coarse-grained soils. Thesoil sample is first saturated under a specific head condition. The water is then allowed to flowthrough the soil without maintaining a constant pressure head.[2]

In-situ (field) methods

Augerhole method

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Cumulative frequencydistribution (lognormal) ofhydraulic conductivity(X-data)

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 determiningthe hydraulic conductivity below the water table.The method was developed by Hooghoudt (1934) [3] in The Netherlands and introduced in theUS by Van Bavel en Kirkham (1948).[4]

The method uses the following steps:

an augerhole is perforated into the soil to below the water table1.

water is bailed out from the augerhole2.

the rate of rise of the water level in the hole is recorded3.

the K-value is calculated from the data as:[5]4.

K = F (Ho-Ht) / t

where: K = horizontal saturated hydraulic conductivity (m/day), H= depth of the waterlevel in the hole relative to the water table inthe soil (cm), Ht = H at time t, Ho = H at time t = 0, t = time (inseconds) since the first measurement of H as Ho, and F is a factordepending on the geometry of the hole:

F = 4000 / (20+D/ )(2− /D)

where: = radius of the cylindrical hole (cm), is the averagedepth of the water level in the hole relative to the water table in thesoil (cm), found as =(Ho+Ht)/2, and D is the depth of the bottomof the hole relative to the water table in the soil (cm).

The picture shows a large variation of K-values measured with theaugerhole method in an area of 100 ha.[6] 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 apumping 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 for horizontal flow of the soillayer 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:[5]

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where signifies the summation over all layers .

The apparent horizontal hydraulic conductivity of the aquifer is:

where , the total thickness of the aquifer, is , with .

The transmissivity of an aquifer can be determined from pumping tests.[7]

Influence of the water tableWhen a soil layer is above the water table, it is not saturated and does not contribute to thetransmissivity. When the soil layer is entirely below the water table, its saturated thicknesscorresponds 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 orfrom 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 smalltransmissivity, so that changes of the total transmissivity (Dt) resulting from changes in the levelof the water table are negligibly small.When pumping water from an unconfined aquifer, where the water table is inside a soil layerwith a significant transmissivity, the water table may be drawn down whereby the transmissivityreduces and the flow of water to the well diminishes.

Resistance

The resistance to vertical flow (Ri) of the soil layer with a saturated thickness andvertical hydraulic conductivity Kvi is:

Ri = / Kvi

Expressing Kvi in m/day and in m, the resistance (Ri) is expressed in days.

The total resistance (Rt) of the aquifer is:[5]

Rt = Σ Ri = Σ / Kvi

where Σ signifies the summation over all layers: = 1, 2, 3, . . .The apparent vertical hydraulic conductivity (KvA) of the aquifer is:

KvA = Dt / Rt

where Dt is the total thickness of the aquifer: Dt = Σ , with = 1, 2, 3, . . .

The resistance plays a role in aquifers where a sequence of layers occurs with varying horizontalpermeability so that horizontal flow is found mainly in the layers with high horizontalpermeability while the layers with low horizontal permeability transmit the water mainly in avertical sense.

Anisotropy

When the horizontal and vertical hydraulic conductivity (Khi and Kvi) of the soil layer

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differ considerably, the layer is said to be anisotropic with respect to hydraulic conductivity.When the apparent horizontal and vertical hydraulic conductivity (KhA and KvA) differconsiderably, 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 horizontalhydraulic conductivity (the semi-confining layer or aquitard) overlies a layer with a relativelyhigh horizontal hydraulic conductivity so that the flow of groundwater in the first layer is mainlyvertical and in the second layer mainly horizontal.The resistance of a semi-confining top layer of an aquifer can be determined from pumpingtests.[7]

When calculating flow to drains [8] or to a well field [9] in an aquifer with the aim to control thewater 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 aquifers have higher hydraulicconductivity than clay or unfractured granite aquifers. Sand or gravel aquifers would thus beeasier to extract water from (e.g., using a pumping 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(gal/day)/ft² ); transmissivity then has units with dimensions of length squared per time. Thefollowing table gives some typical ranges (illustrating the many orders of magnitude which arelikely) for K values.

Hydraulic conductivity (K) is one of the most complex and important of the properties ofaquifers in hydrogeology as the values found in nature:

range over many orders of magnitude (the distribution is often considered to be lognormal),

vary a large amount through space (sometimes considered to be randomly 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 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 conditions — using standard values of viscosity andspecific gravity for water at 20°C and 1 atm. See the similar table derived from the same sourcefor intrinsic permeability values.[10]

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K (cm/s) 10² 101 100=1 10−1 10−2 10−3 10−4 10−5 10−6 10−7 10−8 10−9 10−10

K (ft/day) 105 10,000 1,000 100 10 1 0.1 0.01 0.001 0.0001 10−5 10−6 10−7

RelativePermeability

Pervious Semi-Pervious Impervious

Aquifer Good Poor None

UnconsolidatedSand & Gravel

WellSortedGravel

Well Sorted Sandor Sand & Gravel

Very Fine Sand, Silt,Loess, Loam

UnconsolidatedClay & Organic

Peat Layered Clay Fat / Unweathered Clay

ConsolidatedRocks

Highly Fractured RocksOil Reservoir

RocksFresh

Sandstone

FreshLimestone,Dolomite

FreshGranite

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

Wösten, J.H.M., Pachepsky, Y.A., and Rawls, W.J. (2001). "Pedotransfer functions: bridging the gap

between available basic soil data and missing soil hydraulic characteristics". Journal of Hydrology

251 (3-4): 123–150. Bibcode:2001JHyd..251..123W (http://adsabs.harvard.edu

/abs/2001JHyd..251..123W). doi:10.1016/S0022-1694(01)00464-4 (https://dx.doi.org

/10.1016%2FS0022-1694%2801%2900464-4).

1.

Liu, Cheng "Soils and Foundations." Upper Saddle River, New Jersey: Prentice Hall, 2001 ISBN

0-13-025517-3

2.

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.

3.

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.

4.

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: [1] (http://www.waterlog.info/articles.htm) , under nr. 6, or directly as PDF : [2]

(http://www.waterlog.info/pdf/chap12.pdf)

5.

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 : [3] (http://www.waterlog.info/articles.htm) , under nr. 2, or directly as PDF : [4]

6.

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(http://www.waterlog.info/pdf/analysis.pdf)

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 : [5] (http://content.alterra.wur.nl/Internet/webdocs/ilri-publicaties

/publicaties/Pub57/Pub57.pdf)

7.

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 : [6] (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 :

[7] (http://www.waterlog.info/pdf/enerbal.pdf). The corresponding free EnDrain program can be

downloaded from: [8] (http://www.waterlog.info/endrain.htm)

8.

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: [9] (http://www.waterlog.info/pdf/wellspac.pdf) . The corresponding free WellDrain program

can be downloaded from : [10] (http://www.waterlog.info/weldrain.htm)

9.

Bear, J. (1972). Dynamics of Fluids in Porous Media. Dover Publications. ISBN 0-486-65675-6.10.

External links

Hydraulic conductivity calculator (http://www.fxsolver.com/solve/share

/jZLNM1J9bHMGTCqIglfgmQ==/)

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Categories: Hydrology Hydraulic engineering Soil mechanics Soil physics

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