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class="vector-toc-link" href="#Pedotransfer_function"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Pedotransfer function</span> </div> </a> <ul id="toc-Pedotransfer_function-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Determination_by_experimental_approach" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Determination_by_experimental_approach"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Determination by experimental approach</span> </div> </a> <button aria-controls="toc-Determination_by_experimental_approach-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Determination by experimental approach subsection</span> </button> <ul id="toc-Determination_by_experimental_approach-sublist" class="vector-toc-list"> <li 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id="toc-In-situ_(field)_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#In-situ_(field)_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>In-situ (field) methods</span> </div> </a> <ul id="toc-In-situ_(field)_methods-sublist" class="vector-toc-list"> <li id="toc-Pumping_Test" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Pumping_Test"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.1</span> <span>Pumping Test</span> </div> </a> <ul id="toc-Pumping_Test-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Augerhole_method" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Augerhole_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2.2</span> <span>Augerhole method</span> </div> </a> <ul id="toc-Augerhole_method-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Related_magnitudes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Related_magnitudes"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Related magnitudes</span> </div> </a> <button aria-controls="toc-Related_magnitudes-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Related magnitudes subsection</span> </button> <ul id="toc-Related_magnitudes-sublist" class="vector-toc-list"> <li id="toc-Transmissivity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Transmissivity"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Transmissivity</span> </div> </a> <ul id="toc-Transmissivity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Resistance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Resistance"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Resistance</span> </div> </a> <ul id="toc-Resistance-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Anisotropy" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Anisotropy"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Anisotropy</span> </div> </a> <ul id="toc-Anisotropy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relative_properties" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relative_properties"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Relative properties</span> </div> </a> <ul id="toc-Relative_properties-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ranges_of_values_for_natural_materials" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ranges_of_values_for_natural_materials"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Ranges of values for natural materials</span> </div> </a> <ul id="toc-Ranges_of_values_for_natural_materials-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" 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Available in 17 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-17" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">17 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%88%D8%B5%D9%8A%D9%84_%D9%87%D9%8A%D8%AF%D8%B1%D9%88%D9%84%D9%8A%D9%83%D9%8A" title="توصيل هيدروليكي – Arabic" lang="ar" hreflang="ar" data-title="توصيل هيدروليكي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Conductivitat_hidr%C3%A0ulica" title="Conductivitat hidràulica – Catalan" lang="ca" hreflang="ca" data-title="Conductivitat hidràulica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hydraulick%C3%A1_vodivost" title="Hydraulická vodivost – Czech" lang="cs" hreflang="cs" data-title="Hydraulická vodivost" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hydraulisk_konduktivitet" title="Hydraulisk konduktivitet – Danish" lang="da" hreflang="da" data-title="Hydraulisk konduktivitet" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de badge-Q70894304 mw-list-item" title=""><a href="https://de.wikipedia.org/wiki/Hydraulische_Leitf%C3%A4higkeit" title="Hydraulische Leitfähigkeit – German" lang="de" hreflang="de" data-title="Hydraulische Leitfähigkeit" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Veejuhtivus" title="Veejuhtivus – Estonian" lang="et" hreflang="et" data-title="Veejuhtivus" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Conductividad_hidr%C3%A1ulica" title="Conductividad hidráulica – Spanish" lang="es" hreflang="es" data-title="Conductividad hidráulica" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D8%AF%D8%A7%DB%8C%D8%AA_%D9%87%DB%8C%D8%AF%D8%B1%D9%88%D9%84%DB%8C%DA%A9" title="هدایت هیدرولیک – Persian" lang="fa" hreflang="fa" data-title="هدایت هیدرولیک" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Conductivit%C3%A9_hydraulique" title="Conductivité hydraulique – French" lang="fr" hreflang="fr" data-title="Conductivité hydraulique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%88%AC%EC%88%98%EA%B3%84%EC%88%98" title="투수계수 – Korean" lang="ko" hreflang="ko" data-title="투수계수" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%95%D7%9C%D7%99%D7%9B%D7%95%D7%AA_%D7%94%D7%99%D7%93%D7%A8%D7%90%D7%95%D7%9C%D7%99%D7%AA" title="מוליכות הידראולית – Hebrew" lang="he" hreflang="he" data-title="מוליכות הידראולית" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Filtracijos_koeficientas" title="Filtracijos koeficientas – Lithuanian" lang="lt" hreflang="lt" data-title="Filtracijos koeficientas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Doorlatendheid" title="Doorlatendheid – Dutch" lang="nl" hreflang="nl" data-title="Doorlatendheid" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Wsp%C3%B3%C5%82czynnik_filtracji" title="Współczynnik filtracji – Polish" lang="pl" hreflang="pl" data-title="Współczynnik filtracji" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%93%D0%B8%D0%B4%D1%80%D0%B0%D0%B2%D0%BB%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D0%BF%D1%80%D0%BE%D0%B2%D0%BE%D0%B4%D0%B8%D0%BC%D0%BE%D1%81%D1%82%D1%8C" title="Гидравлическая проводимость – Russian" lang="ru" hreflang="ru" data-title="Гидравлическая проводимость" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Vedenjohtavuus" title="Vedenjohtavuus – Finnish" lang="fi" hreflang="fi" data-title="Vedenjohtavuus" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Markens_vattengenomsl%C3%A4pplighet" title="Markens vattengenomsläpplighet – Swedish" lang="sv" hreflang="sv" data-title="Markens 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Ability of water to flow through a porous material</div> <p>In <a href="/wiki/Science" title="Science">science</a> and <a href="/wiki/Engineering" title="Engineering">engineering</a>, <b>hydraulic conductivity</b> (<span class="texhtml mvar" style="font-style:italic;">K</span>, in <a href="/wiki/SI_unit" class="mw-redirect" title="SI unit">SI units</a> of <a href="/wiki/Meter" class="mw-redirect" title="Meter">meters</a> per second), is a property of <a href="/wiki/Porous_material" class="mw-redirect" title="Porous material">porous materials</a>, <a href="/wiki/Soil" title="Soil">soils</a> and <a href="/wiki/Rock_(geology)" title="Rock (geology)">rocks</a>, that describes the ease with which a <a href="/wiki/Fluid" title="Fluid">fluid</a> (usually water) can move through the <a href="/wiki/Porosity" title="Porosity">pore space</a>, or fracture network.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It depends on the <a href="/wiki/Intrinsic_permeability" class="mw-redirect" title="Intrinsic permeability">intrinsic permeability</a> (<span class="texhtml mvar" style="font-style:italic;">k</span>, unit: m<sup>2</sup>) of the material, the degree of <a href="/wiki/Water_content" title="Water content">saturation</a>, and on the <a href="/wiki/Density" title="Density">density</a> and <a href="/wiki/Viscosity" title="Viscosity">viscosity</a> of the fluid. Saturated hydraulic conductivity, <span class="texhtml"><i>K</i><sub>sat</sub></span>, describes water movement through saturated media. By definition, hydraulic conductivity is the ratio of volume flux to <a href="/wiki/Hydraulic_head#Hydraulic_gradient" title="Hydraulic head">hydraulic gradient</a> yielding a quantitative measure of a saturated soil's ability to transmit water when subjected to a hydraulic gradient. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Methods_of_determination">Methods of determination</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=1" title="Edit section: Methods of determination"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:HydrCondTable.GIF" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/HydrCondTable.GIF/450px-HydrCondTable.GIF" decoding="async" width="450" height="268" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fc/HydrCondTable.GIF/675px-HydrCondTable.GIF 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fc/HydrCondTable.GIF/900px-HydrCondTable.GIF 2x" data-file-width="944" data-file-height="562" /></a><figcaption>Overview of determination methods</figcaption></figure> <p>There are two broad approaches for determining hydraulic conductivity: </p> <ul><li>In the <i>empirical</i> approach the hydraulic conductivity is correlated to soil properties like <a href="/wiki/Porosity" title="Porosity">pore-size</a> and <a href="/w/index.php?title=Particle-size_(grain-size)&action=edit&redlink=1" class="new" title="Particle-size (grain-size) (page does not exist)">particle-size (grain-size)</a> distributions, and <a href="/wiki/Soil_texture" title="Soil texture">soil texture</a>.</li> <li>In the <i>experimental</i> approach the hydraulic conductivity is determined from hydraulic experiments that are interpreted using <a href="/wiki/Darcy%27s_law" title="Darcy's law">Darcy's law</a>.</li></ul> <p>The experimental approach is broadly classified into: </p> <ul><li><a href="/wiki/Laboratory" title="Laboratory">Laboratory</a> tests using soil samples subjected to hydraulic <a href="/wiki/Experiment" title="Experiment">experiments</a></li> <li><i>Field tests</i> (on site, in situ) that are differentiated into: <ul><li>small-scale field tests, using observations of the water level in cavities in the soil</li> <li>large-scale field tests, like <a href="/wiki/Pumping_test" class="mw-redirect" title="Pumping test">pumping tests</a> in <a href="/wiki/Water_well" class="mw-redirect" title="Water well">wells</a> or by observing the functioning of existing horizontal <a href="/wiki/Drainage" title="Drainage">drainage</a> systems.</li></ul></li></ul> <p>The small-scale field tests are further subdivided into: </p> <ul><li><a href="/wiki/Infiltration_(hydrology)" title="Infiltration (hydrology)">infiltration</a> tests in cavities <i>above</i> the <a href="/wiki/Water_table" title="Water table">water table</a></li> <li><a href="/wiki/Slug_test" title="Slug test">slug tests</a> in cavities <i>below</i> the <a href="/wiki/Water_table" title="Water table">water table</a></li></ul> <p>The methods of determining hydraulic conductivity and other hydraulic properties are investigated by numerous researchers and include additional empirical approaches.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Estimation_by_empirical_approach">Estimation by empirical approach</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=2" title="Edit section: Estimation by empirical approach"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Estimation_from_grain_size">Estimation from grain size</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=3" title="Edit section: Estimation from grain size"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Allen_Hazen" title="Allen Hazen">Allen Hazen</a> derived an <a href="/wiki/Empirical_method" class="mw-redirect" title="Empirical method">empirical</a> formula for approximating hydraulic conductivity from grain-size analyses: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K=C(D_{10})^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo>=</mo> <mi>C</mi> <mo stretchy="false">(</mo> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K=C(D_{10})^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88845185737a256ca627416b7b18cc5cd6362f6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.595ex; height:3.176ex;" alt="{\displaystyle K=C(D_{10})^{2}}"></span></dd></dl> <p>where </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4fc55753007cd3c18576f7933f6f089196732029" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.766ex; height:2.176ex;" alt="{\displaystyle C}"></span> 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.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="Source referenced (A.F. Salarashayeri & M. Siosemarde) but never given (October 2022)">citation needed</span></a></i>]</sup></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle D_{10}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{10}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b774d198cec2a4cdc5badbee5b181064ed2ff416" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.8ex; height:2.509ex;" alt="{\displaystyle D_{10}}"></span> is the <a href="/wiki/Diameter" title="Diameter">diameter</a> of the 10 <a href="/wiki/Percentile" title="Percentile">percentile</a> grain size of the material.</dd></dl> <div class="mw-heading mw-heading3"><h3 id="Pedotransfer_function">Pedotransfer function</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=4" title="Edit section: Pedotransfer function"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Pedotransfer_function" title="Pedotransfer function">pedotransfer function</a> (PTF) is a specialized empirical estimation method, used primarily in the <a href="/wiki/Soil_science" title="Soil science">soil sciences</a>, but increasingly used in hydrogeology.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> 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 <a href="/wiki/Particle_size" title="Particle size">particle size</a>, and <a href="/wiki/Bulk_density" title="Bulk density">bulk density</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Determination_by_experimental_approach">Determination by experimental approach</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=5" title="Edit section: Determination by experimental approach"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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. </p> <div class="mw-heading mw-heading3"><h3 id="Laboratory_methods">Laboratory methods</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=6" title="Edit section: Laboratory methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Constant-head_method">Constant-head method</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=7" title="Edit section: Constant-head method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a rel="nofollow" class="external text" href="http://www.geotechdata.info/geotest/constant-head-permeability-test">constant-head method</a> 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 <span class="texhtml">Δ<i>V</i></span> of water measured in a time <span class="texhtml">Δ<i>t</i></span>, over a specimen of length <span class="texhtml mvar" style="font-style:italic;">L</span> and cross-sectional area <span class="texhtml mvar" style="font-style:italic;">A</span>, as well as the head <span class="texhtml mvar" style="font-style:italic;">h</span>, the hydraulic conductivity (<span class="texhtml mvar" style="font-style:italic;">K</span>) can be derived by simply rearranging <a href="/wiki/Darcy%27s_law" title="Darcy's law">Darcy's law</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K={\frac {\Delta V}{\Delta t}}{\frac {L}{Ah}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>L</mi> <mrow> <mi>A</mi> <mi>h</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K={\frac {\Delta V}{\Delta t}}{\frac {L}{Ah}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/508111071f41f53c17aa4fc6197bcd343959ce11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:13.642ex; height:5.509ex;" alt="{\displaystyle K={\frac {\Delta V}{\Delta t}}{\frac {L}{Ah}}}"></span></dd></dl> <p><i>Proof: </i> Darcy's law states that the volumetric flow depends on the <a href="/wiki/Pressure_gradient" title="Pressure gradient">pressure differential</a> <span class="texhtml">Δ<i>P</i></span> between the two sides of the sample, the <a href="/wiki/Permeability_(earth_sciences)" class="mw-redirect" title="Permeability (earth sciences)">permeability</a> <span class="texhtml mvar" style="font-style:italic;">k</span> and the <a href="/wiki/Dynamic_viscosity" class="mw-redirect" title="Dynamic viscosity">dynamic viscosity</a> <span class="texhtml mvar" style="font-style:italic;">μ</span> as: <sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\Delta V}{\Delta t}}=-{\frac {kA}{\mu L}}\Delta P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <mi>A</mi> </mrow> <mrow> <mi>μ</mi> <mi>L</mi> </mrow> </mfrac> </mrow> <mi mathvariant="normal">Δ</mi> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\Delta V}{\Delta t}}=-{\frac {kA}{\mu L}}\Delta P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d5e68d7b2e5e43df56d3844bf979ccef44af87e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.968ex; height:5.843ex;" alt="{\displaystyle {\frac {\Delta V}{\Delta t}}=-{\frac {kA}{\mu L}}\Delta P}"></span></dd></dl> <p>In a constant head experiment, the head (difference between two heights) defines an excess water mass, <span class="texhtml mvar" style="font-style:italic;">ρAh</span>, where <span class="texhtml mvar" style="font-style:italic;">ρ</span> is the density of water. This mass weighs down on the side it is on, creating a pressure differential of <span class="texhtml">Δ<i>P</i> = <i>ρgh</i></span>, where <span class="texhtml mvar" style="font-style:italic;">g</span> is the gravitational acceleration. Plugging this directly into the above gives </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\Delta V}{\Delta t}}=-{\frac {k\rho gA}{\mu L}}h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <mi>ρ</mi> <mi>g</mi> <mi>A</mi> </mrow> <mrow> <mi>μ</mi> <mi>L</mi> </mrow> </mfrac> </mrow> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\Delta V}{\Delta t}}=-{\frac {k\rho gA}{\mu L}}h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4c6901557ccc2f3f2ad67365712f9c7e9061cec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:16.913ex; height:6.009ex;" alt="{\displaystyle {\frac {\Delta V}{\Delta t}}=-{\frac {k\rho gA}{\mu L}}h}"></span></dd></dl> <p>If the hydraulic conductivity is defined to be related to the hydraulic permeability as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K={\frac {k\rho g}{\mu }},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>k</mi> <mi>ρ</mi> <mi>g</mi> </mrow> <mi>μ</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K={\frac {k\rho g}{\mu }},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f485834c45182f68f36a109358128d8d0dd4cccc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:10.177ex; height:5.843ex;" alt="{\displaystyle K={\frac {k\rho g}{\mu }},}"></span></dd></dl> <p>this gives the result. </p> <div class="mw-heading mw-heading4"><h4 id="Falling-head_method">Falling-head method</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=8" title="Edit section: Falling-head method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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. .<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> If the head drops from <span class="texhtml mvar" style="font-style:italic;">h<sub>i</sub></span> to <span class="texhtml mvar" style="font-style:italic;">h<sub>f</sub></span> in a time <span class="texhtml">Δ<i>t</i></span>, then the hydraulic conductivity is equal to </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K={\frac {L}{\Delta t}}\ln {\frac {h_{f}}{h_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>L</mi> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mi>ln</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K={\frac {L}{\Delta t}}\ln {\frac {h_{f}}{h_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb60fe3813a82a404007c8aa22dbd19f67139016" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.801ex; height:6.176ex;" alt="{\displaystyle K={\frac {L}{\Delta t}}\ln {\frac {h_{f}}{h_{i}}}}"></span></dd></dl> <p><i>Proof: </i> As above, Darcy's law reads </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\Delta V}{\Delta t}}=-K{\frac {A}{L}}h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>V</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <mi>L</mi> </mfrac> </mrow> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\Delta V}{\Delta t}}=-K{\frac {A}{L}}h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5cb56b3e25581434d7d8bb4291a981d56ba2c7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:15.45ex; height:5.509ex;" alt="{\displaystyle {\frac {\Delta V}{\Delta t}}=-K{\frac {A}{L}}h}"></span></dd></dl> <p>The decrease in volume is related to the falling head by <span class="texhtml">Δ<i>V</i> = Δ<i>hA</i></span>. Plugging this relationship into the above, and taking the limit as <span class="texhtml">Δ<i>t</i> → 0</span>, the differential equation </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {dh}{dt}}=-{\frac {K}{L}}h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>h</mi> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>K</mi> <mi>L</mi> </mfrac> </mrow> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {dh}{dt}}=-{\frac {K}{L}}h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8251d5a8ced3d2c79851144cf2d8712c739cdbb3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.539ex; height:5.509ex;" alt="{\displaystyle {\frac {dh}{dt}}=-{\frac {K}{L}}h}"></span></dd></dl> <p>has the solution </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h(t)=h_{i}e^{-{\frac {K}{L}}(t-t_{i})}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>K</mi> <mi>L</mi> </mfrac> </mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>−</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h(t)=h_{i}e^{-{\frac {K}{L}}(t-t_{i})}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b20aef2e708b649bb48bda2b92522ca826fbb442" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.858ex; height:4.009ex;" alt="{\displaystyle h(t)=h_{i}e^{-{\frac {K}{L}}(t-t_{i})}.}"></span></dd></dl> <p>Plugging in <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h(t_{f})=h_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> <mo stretchy="false">(</mo> <msub> <mi>t</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h(t_{f})=h_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ada720cb7629a0b93cf0456ac91e4f90e2823610" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.698ex; height:3.009ex;" alt="{\displaystyle h(t_{f})=h_{f}}"></span> and rearranging gives the result. </p> <div class="mw-heading mw-heading3"><h3 id="In-situ_(field)_methods"><span id="In-situ_.28field.29_methods"></span>In-situ (field) methods</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=9" title="Edit section: In-situ (field) methods"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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. </p> <div class="mw-heading mw-heading4"><h4 id="Pumping_Test">Pumping Test</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=10" title="Edit section: Pumping Test"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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. </p> <div class="mw-heading mw-heading4"><h4 id="Augerhole_method">Augerhole method</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=11" title="Edit section: Augerhole method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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 <a href="/wiki/Slug_test" title="Slug test">slug test</a>, can be used for determining the hydraulic conductivity below the water table.<br /> The method was developed by Hooghoudt (1934)<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> in The Netherlands and introduced in the US by Van Bavel en Kirkham (1948).<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><br /> The method uses the following steps: </p> <ol><li>an augerhole is perforated into the soil to below the water table</li> <li>water is bailed out from the augerhole</li> <li>the rate of rise of the water level in the hole is recorded</li> <li>the <span class="texhtml mvar" style="font-style:italic;">K</span>-value is calculated from the data as:<sup id="cite_ref-Oost_8-0" class="reference"><a href="#cite_note-Oost-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></li></ol> <ol><li><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K=F{\frac {H_{o}-H_{t}}{t}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>K</mi> <mo>=</mo> <mi>F</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mrow> <mi>t</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K=F{\frac {H_{o}-H_{t}}{t}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cf358b64ba75f1ff4039e4ec0d4a8d48e10f5b1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.3ex; height:5.176ex;" alt="{\displaystyle K=F{\frac {H_{o}-H_{t}}{t}}}"></span></dd></dl></li></ol> <p>where: </p> <ul><li><span class="texhtml mvar" style="font-style:italic;">K</span> is the horizontal saturated hydraulic conductivity (m/day)</li> <li><span class="texhtml mvar" style="font-style:italic;">H</span> is the depth of the water level in the hole relative to the water table in the soil (cm): <ul><li><span class="texhtml"><i>H<sub>t</sub></i> = <i>H</i></span> at time <span class="texhtml mvar" style="font-style:italic;">t</span></li> <li><span class="texhtml"><i>H<sub>o</sub></i> = <i>H</i></span> at time <span class="texhtml"><i>t</i> = 0</span></li></ul></li> <li><span class="texhtml mvar" style="font-style:italic;">t</span> is the time (in seconds) since the first measurement of <span class="texhtml mvar" style="font-style:italic;">H</span> as <span class="texhtml mvar" style="font-style:italic;">H<sub>o</sub></span></li> <li><span class="texhtml mvar" style="font-style:italic;">F</span> is a factor depending on the geometry of the hole: <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F={\frac {4000r}{h'}}\left(20+{\frac {D}{r}}\right)\left(2-{\frac {h'}{D}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4000</mn> <mi>r</mi> </mrow> <msup> <mi>h</mi> <mo>′</mo> </msup> </mfrac> </mrow> <mrow> <mo>(</mo> <mrow> <mn>20</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>D</mi> <mi>r</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mn>2</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>h</mi> <mo>′</mo> </msup> <mi>D</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F={\frac {4000r}{h'}}\left(20+{\frac {D}{r}}\right)\left(2-{\frac {h'}{D}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a2376352f845f4e6f40dfe8073ee4e9122928d7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:33.779ex; height:6.176ex;" alt="{\displaystyle F={\frac {4000r}{h'}}\left(20+{\frac {D}{r}}\right)\left(2-{\frac {h'}{D}}\right)}"></span></dd></dl></li></ul> <p>where: </p> <ul><li><span class="texhtml mvar" style="font-style:italic;">r</span> is the radius of the cylindrical hole (cm)</li> <li><span class="texhtml mvar" style="font-style:italic;">h'</span> is the average depth of the water level in the hole relative to the water table in the soil (cm), found as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h'={\tfrac {H_{o}+H_{t}}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>h</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>o</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h'={\tfrac {H_{o}+H_{t}}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6520ad4f7c051fe214f30e1a44ceff1422ef3f06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:11.426ex; height:3.843ex;" alt="{\displaystyle h'={\tfrac {H_{o}+H_{t}}{2}}}"></span></li> <li><span class="texhtml mvar" style="font-style:italic;">D</span> is the depth of the bottom of the hole relative to the water table in the soil (cm).</li></ul> <figure typeof="mw:File/Thumb"><a href="/wiki/File:PANAZ1.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/PANAZ1.JPG/200px-PANAZ1.JPG" decoding="async" width="200" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/PANAZ1.JPG/300px-PANAZ1.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/PANAZ1.JPG/400px-PANAZ1.JPG 2x" data-file-width="640" data-file-height="480" /></a><figcaption>Cumulative frequency distribution (<a href="/wiki/Lognormal" class="mw-redirect" title="Lognormal">lognormal</a>) of hydraulic conductivity (X-data)</figcaption></figure> <p>The picture shows a large variation of <span class="texhtml mvar" style="font-style:italic;">K</span>-values measured with the augerhole method in an area of 100 ha.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> The ratio between the highest and lowest values is 25. The cumulative frequency distribution is <a href="/wiki/Lognormal" class="mw-redirect" title="Lognormal">lognormal</a> and was made with the <a href="/wiki/Cumulative_frequency_analysis" title="Cumulative frequency analysis">CumFreq</a> program. </p> <div class="mw-heading mw-heading2"><h2 id="Related_magnitudes">Related magnitudes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=12" title="Edit section: Related magnitudes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Transmissivity">Transmissivity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=13" title="Edit section: Transmissivity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The transmissivity is a measure of how much water can be transmitted horizontally, such as to a pumping well.<br /> </p> <dl><dd><small><i>Transmissivity</i> should not be confused with the similar word <a href="/wiki/Transmittance" title="Transmittance">transmittance</a> used in <a href="/wiki/Optics" title="Optics">optics</a>, meaning the fraction of incident light that passes through a sample.<i></i></small></dd></dl> <p>An <a href="/wiki/Aquifer" title="Aquifer">aquifer</a> may consist of <span class="texhtml mvar" style="font-style:italic;">n</span> soil layers. The transmissivity <span class="texhtml mvar" style="font-style:italic;">T<sub>i</sub></span> of a horizontal flow for the <span class="texhtml mvar" style="font-style:italic;">i</span>th soil layer with a <i>saturated</i> thickness <span class="texhtml mvar" style="font-style:italic;">d<sub>i</sub></span> and horizontal hydraulic conductivity <span class="texhtml mvar" style="font-style:italic;">K<sub>i</sub></span> is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{i}=K_{i}d_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{i}=K_{i}d_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dfbcc9a00745b35f12e2904b70e180b8a341b09" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.037ex; height:2.509ex;" alt="{\displaystyle T_{i}=K_{i}d_{i}}"></span></dd></dl> <p>Transmissivity is directly proportional to horizontal hydraulic conductivity <span class="texhtml mvar" style="font-style:italic;">K<sub>i</sub></span> and thickness <span class="texhtml mvar" style="font-style:italic;">d<sub>i</sub></span>. Expressing <span class="texhtml mvar" style="font-style:italic;">K<sub>i</sub></span> in m/day and <span class="texhtml mvar" style="font-style:italic;">d<sub>i</sub></span> in m, the transmissivity <span class="texhtml mvar" style="font-style:italic;">T<sub>i</sub></span> is found in units m<sup>2</sup>/day.<br /> The total transmissivity <span class="texhtml mvar" style="font-style:italic;">T<sub>t</sub></span> of the aquifer is the sum of every layer's transmissivity:<sup id="cite_ref-Oost_8-1" class="reference"><a href="#cite_note-Oost-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T_{t}=\sum T_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mo>∑</mo> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T_{t}=\sum T_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/458284a92e61cd68fc5943d1628e8f0160d193aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:11.181ex; height:3.843ex;" alt="{\displaystyle T_{t}=\sum T_{i}}"></span></dd></dl> <p>The <i>apparent</i> horizontal hydraulic conductivity <span class="texhtml mvar" style="font-style:italic;">K<sub>A</sub></span> of the aquifer is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{A}={\frac {T_{t}}{D_{t}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{A}={\frac {T_{t}}{D_{t}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28324add99db96ec2b4832c0a106617618329511" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:10.123ex; height:5.676ex;" alt="{\displaystyle K_{A}={\frac {T_{t}}{D_{t}}}}"></span></dd></dl> <p>where <span class="texhtml mvar" style="font-style:italic;">D<sub>t</sub></span>, the total thickness of the aquifer, is the sum of each layer's individual thickness: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle D_{t}=\sum d_{i}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mo>∑</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle D_{t}=\sum d_{i}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb7f7b9df55f337d21b7ea515057e015cb402217" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.345ex; height:2.843ex;" alt="{\textstyle D_{t}=\sum d_{i}.}"></span> </p><p>The transmissivity of an aquifer can be determined from <a href="/wiki/Pumping_test" class="mw-redirect" title="Pumping test">pumping tests</a>.<sup id="cite_ref-Boon_10-0" class="reference"><a href="#cite_note-Boon-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p><i>Influence of the water table</i><br /> When a soil layer is above the <a href="/wiki/Water_table" title="Water table">water table</a>, 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 (<span class="texhtml mvar" style="font-style:italic;">D<sub>t</sub></span>) 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. </p> <div class="mw-heading mw-heading3"><h3 id="Resistance">Resistance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=14" title="Edit section: Resistance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <i>resistance</i> to vertical flow (<span class="texhtml mvar" style="font-style:italic;">R<sub>i</sub></span>) of the <span class="texhtml mvar" style="font-style:italic;">i</span>th soil layer with a <i>saturated</i> thickness <span class="texhtml mvar" style="font-style:italic;">d<sub>i</sub></span> and vertical hydraulic conductivity <span class="texhtml mvar" style="font-style:italic;">K<sub>v<sub>i</sub></sub></span> is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{i}={\frac {d_{i}}{K_{v_{i}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{i}={\frac {d_{i}}{K_{v_{i}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da34766526ffed66a818fcdf6d5b08ffe6956bca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:10.126ex; height:6.009ex;" alt="{\displaystyle R_{i}={\frac {d_{i}}{K_{v_{i}}}}}"></span></dd></dl> <p>Expressing <span class="texhtml mvar" style="font-style:italic;">K<sub>v<sub>i</sub></sub></span> in m/day and <span class="texhtml mvar" style="font-style:italic;">d<sub>i</sub></span> in m, the resistance (<span class="texhtml mvar" style="font-style:italic;">R<sub>i</sub></span>) is expressed in days.<br /> The total resistance (<span class="texhtml mvar" style="font-style:italic;">R<sub>t</sub></span>) of the aquifer is the sum of each layer's resistance:<sup id="cite_ref-Oost_8-2" class="reference"><a href="#cite_note-Oost-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{t}=\sum R_{i}=\sum {\frac {d_{i}}{K_{v_{i}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mo>∑</mo> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{t}=\sum R_{i}=\sum {\frac {d_{i}}{K_{v_{i}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d2d90756f85c00b131200eca19603478816dc41e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:23.298ex; height:6.009ex;" alt="{\displaystyle R_{t}=\sum R_{i}=\sum {\frac {d_{i}}{K_{v_{i}}}}}"></span></dd></dl> <p><br /> The <i>apparent</i> vertical hydraulic conductivity (<span class="texhtml mvar" style="font-style:italic;">K<sub>v<sub>A</sub></sub></span>) of the aquifer is: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{v_{A}}={\frac {D_{t}}{R_{t}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{v_{A}}={\frac {D_{t}}{R_{t}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3e906d3035df09a7f75e6d2299674d7ada2b8508" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:10.852ex; height:5.676ex;" alt="{\displaystyle K_{v_{A}}={\frac {D_{t}}{R_{t}}}}"></span></dd></dl> <p>where <span class="texhtml mvar" style="font-style:italic;">D<sub>t</sub></span> is the total thickness of the aquifer: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle D_{t}=\sum d_{i}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>t</mi> </mrow> </msub> <mo>=</mo> <mo>∑</mo> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle D_{t}=\sum d_{i}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb7f7b9df55f337d21b7ea515057e015cb402217" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.345ex; height:2.843ex;" alt="{\textstyle D_{t}=\sum d_{i}.}"></span> </p><p>The resistance plays a role in <a href="/wiki/Aquifer" title="Aquifer">aquifers</a> 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. </p> <div class="mw-heading mw-heading2"><h2 id="Anisotropy">Anisotropy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=15" title="Edit section: Anisotropy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>When the horizontal and vertical hydraulic conductivity (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle K_{h_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle K_{h_{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/232e26cad2902ba6170e8ef66c6742d4733e3e08" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.777ex; height:2.843ex;" alt="{\textstyle K_{h_{i}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle K_{v_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle K_{v_{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abd51f456fc1250e1efc73d974372a51d7d90078" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.628ex; height:2.843ex;" alt="{\textstyle K_{v_{i}}}"></span>) of the <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle i{\mbox{-th}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>-th</mtext> </mstyle> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle i{\mbox{-th}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58ef71770e5ab3f832a513aaff1b45dc9c310827" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.774ex; height:2.176ex;" alt="{\textstyle i{\mbox{-th}}}"></span> soil layer differ considerably, the layer is said to be <a href="/wiki/Anisotropy" title="Anisotropy">anisotropic</a> with respect to hydraulic conductivity.<br /> When the <i>apparent</i> horizontal and vertical hydraulic conductivity (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle K_{h_{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle K_{h_{A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dd63f227cfd43e79384bf1fa56a546af9f1bb5b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.317ex; height:2.843ex;" alt="{\textstyle K_{h_{A}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle K_{v_{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle K_{v_{A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3b028f818c3cd5d8e39ccbe1ca9ca8a8a98d657" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.168ex; height:2.843ex;" alt="{\textstyle K_{v_{A}}}"></span>) differ considerably, the <a href="/wiki/Aquifer" title="Aquifer">aquifer</a> is said to be <a href="/wiki/Anisotropy" title="Anisotropy">anisotropic</a> with respect to hydraulic conductivity.<br /> An aquifer is called <i>semi-confined</i> when a saturated layer with a relatively small horizontal hydraulic conductivity (the semi-confining layer or <a href="/wiki/Aquitard" class="mw-redirect" title="Aquitard">aquitard</a>) 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 <a href="/wiki/Pumping_test" class="mw-redirect" title="Pumping test">pumping tests</a>.<sup id="cite_ref-Boon_10-1" class="reference"><a href="#cite_note-Boon-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup><br /> When calculating flow to <a href="/wiki/Drainage" title="Drainage">drains</a><sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> or to a <a href="/wiki/Water_well" class="mw-redirect" title="Water well">well</a> field<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> in an aquifer with the aim to <a href="/wiki/Watertable_control" title="Watertable control">control the water table</a>, the anisotropy is to be taken into account, otherwise the result may be erroneous. </p> <div class="mw-heading mw-heading2"><h2 id="Relative_properties">Relative properties</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=16" title="Edit section: Relative properties"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Because of their high porosity and permeability, <a href="/wiki/Sand" title="Sand">sand</a> and <a href="/wiki/Gravel" title="Gravel">gravel</a> <a href="/wiki/Aquifer" title="Aquifer">aquifers</a> have higher hydraulic conductivity than <a href="/wiki/Clay" title="Clay">clay</a> or unfractured <a href="/wiki/Granite" title="Granite">granite</a> aquifers. Sand or gravel aquifers would thus be easier to extract water from (e.g., using a pumping <a href="/wiki/Water_well" class="mw-redirect" title="Water well">well</a>) because of their high transmissivity, compared to clay or unfractured bedrock aquifers. </p><p>Hydraulic conductivity has units with dimensions of length per time (e.g., m/s, ft/day and (<a href="/wiki/Gallon" title="Gallon">gal</a>/day)/ft<sup>2</sup> ); 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 <i>K</i> values. </p><p>Hydraulic conductivity (<i>K</i>) is one of the most complex and important of the properties of aquifers in hydrogeology as the values found in nature: </p> <ul><li>range over many <a href="/wiki/Orders_of_magnitude" class="mw-redirect" title="Orders of magnitude">orders of magnitude</a> (the distribution is often considered to be <a href="/wiki/Lognormal_distribution" class="mw-redirect" title="Lognormal distribution">lognormal</a>),</li> <li>vary a large amount through space (sometimes considered to be <a href="/wiki/Random" class="mw-redirect" title="Random">randomly</a> spatially distributed, or <a href="/wiki/Stochastic" title="Stochastic">stochastic</a> in nature),</li> <li>are directional (in general <i>K</i> is a symmetric second-rank <a href="/wiki/Tensor" title="Tensor">tensor</a>; e.g., vertical <i>K</i> values can be several orders of magnitude smaller than horizontal <i>K</i> values),</li> <li>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),</li> <li>must be determined indirectly through field <a href="/wiki/Pumping_test" class="mw-redirect" title="Pumping test">pumping tests</a>, laboratory column flow tests or inverse computer simulation, (sometimes also from <a href="/wiki/Particle_size" title="Particle size">grain size</a> analyses), and</li> <li>are very dependent (in a <a href="/wiki/Nonlinearity" class="mw-redirect" title="Nonlinearity">non-linear</a> way) on the water content, which makes solving the <a href="/wiki/Vadose_zone" title="Vadose zone">unsaturated flow</a> equation difficult. In fact, the variably saturated <i>K</i> for a single material varies over a wider range than the saturated <i>K</i> values for all types of materials (see chart below for an illustrative range of the latter).</li></ul> <div class="mw-heading mw-heading2"><h2 id="Ranges_of_values_for_natural_materials">Ranges of values for natural materials</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=17" title="Edit section: Ranges of values for natural materials"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>Table of saturated hydraulic conductivity (<i>K</i>) values found in nature</b> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Groundwater_Freeze_and_Cherry_1979_Table_2-2.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Groundwater_Freeze_and_Cherry_1979_Table_2-2.png/220px-Groundwater_Freeze_and_Cherry_1979_Table_2-2.png" decoding="async" width="220" height="241" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Groundwater_Freeze_and_Cherry_1979_Table_2-2.png/330px-Groundwater_Freeze_and_Cherry_1979_Table_2-2.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/Groundwater_Freeze_and_Cherry_1979_Table_2-2.png/440px-Groundwater_Freeze_and_Cherry_1979_Table_2-2.png 2x" data-file-width="663" data-file-height="727" /></a><figcaption>a table showing ranges of values of hydraulic conductivity and permeability for various geological materials</figcaption></figure> <p>Values are for typical fresh <a href="/wiki/Groundwater" title="Groundwater">groundwater</a> conditions — using standard values of <a href="/wiki/Viscosity" title="Viscosity">viscosity</a> and <a href="/wiki/Specific_gravity" class="mw-redirect" title="Specific gravity">specific gravity</a> for water at 20 °C and 1 atm. See the similar table derived from the same source for <a href="/wiki/Permeability_(fluid)" class="mw-redirect" title="Permeability (fluid)">intrinsic permeability</a> values.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <table border="1" width="600"> <tbody><tr> <td bgcolor="#FAEBD7"><i>K</i> (cm/<a href="/wiki/Second" title="Second">s</a>) </td> <td>10² </td> <td>10<sup>1</sup> </td> <td>10<sup>0</sup>=1 </td> <td>10<sup>−1</sup> </td> <td>10<sup>−2</sup> </td> <td>10<sup>−3</sup> </td> <td>10<sup>−4</sup> </td> <td>10<sup>−5</sup> </td> <td>10<sup>−6</sup> </td> <td>10<sup>−7</sup> </td> <td>10<sup>−8</sup> </td> <td>10<sup>−9</sup> </td> <td>10<sup>−10</sup> </td></tr> <tr> <td bgcolor="#FAEBD7"><i>K</i> (ft/<a href="/wiki/Day" title="Day">day</a>) </td> <td>10<sup>5</sup> </td> <td>10,000 </td> <td>1,000 </td> <td>100 </td> <td>10 </td> <td>1 </td> <td>0.1 </td> <td>0.01 </td> <td>0.001 </td> <td>0.0001 </td> <td>10<sup>−5</sup> </td> <td>10<sup>−6</sup> </td> <td>10<sup>−7</sup> </td></tr> <tr> <td bgcolor="#FAEBD7">Relative Permeability </td> <td colspan="4" align="center">Pervious </td> <td colspan="4" align="center">Semi-Pervious </td> <td colspan="5" align="center">Impervious </td></tr> <tr> <td bgcolor="#FAEBD7"><a href="/wiki/Aquifer" title="Aquifer">Aquifer</a> </td> <td colspan="5" align="center">Good </td> <td colspan="4" align="center">Poor </td> <td colspan="4" align="center">None </td></tr> <tr> <td bgcolor="#FAEBD7">Unconsolidated <a href="/wiki/Sand" title="Sand">Sand</a> & <a href="/wiki/Gravel" title="Gravel">Gravel</a> </td> <td colspan="2" align="center">Well Sorted Gravel </td> <td colspan="3" align="center">Well Sorted Sand or Sand & Gravel </td> <td colspan="4" align="center">Very Fine Sand, Silt, <a href="/wiki/Loess" title="Loess">Loess</a>, <a href="/wiki/Loam" title="Loam">Loam</a> </td> <td colspan="4"> </td></tr> <tr> <td bgcolor="#FAEBD7">Unconsolidated Clay & Organic </td> <td colspan="4"> </td> <td colspan="2" align="center"><a href="/wiki/Peat" title="Peat">Peat</a> </td> <td colspan="3" align="center">Layered <a href="/wiki/Clay" title="Clay">Clay</a> </td> <td colspan="4" align="center">Fat / Unweathered Clay </td></tr> <tr> <td bgcolor="#FAEBD7">Consolidated Rocks </td> <td colspan="4" align="center">Highly Fractured Rocks </td> <td colspan="3" align="center"><a href="/wiki/Petroleum_geology" title="Petroleum geology">Oil Reservoir</a> Rocks </td> <td colspan="2" align="center">Fresh <a href="/wiki/Sandstone" title="Sandstone">Sandstone</a> </td> <td colspan="2" align="center">Fresh <a href="/wiki/Limestone" title="Limestone">Limestone</a>, <a href="/wiki/Dolomite_(rock)" title="Dolomite (rock)">Dolomite</a> </td> <td colspan="2" align="center">Fresh <a href="/wiki/Granite" title="Granite">Granite</a> </td></tr></tbody></table> <p>Source: modified from Bear, 1972 </p> <table class="wikitable"> <caption>Hydraulic conductivity at Liquid Limit for several Clays<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </caption> <tbody><tr> <th>Soil Type</th> <th>Liquid Limit, LL (%)</th> <th>Void Ratio at Liquid Limit, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e_{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e_{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87147bac67ca61f8effb067e244f2ed34c56aa35" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.435ex; height:2.009ex;" alt="{\displaystyle e_{L}}"></span> (%)</th> <th>Hydraulic conductivity, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 10^{-7}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>7</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{-7}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60f7bc29238b21553311d8359274b4782ecb3f73" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.658ex; height:2.676ex;" alt="{\displaystyle 10^{-7}}"></span> cm/s </th></tr> <tr> <th>Bentonite </th> <td>330</td> <td>9.24</td> <td>1,28 </td></tr> <tr> <th>Bentonite <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6ef363cd19902d1a7a71fb1c8b21e8ede52406" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle +}"></span> sand </th> <td>215</td> <td>5,91</td> <td>2,65 </td></tr> <tr> <th>Natural marine soil </th> <td>106</td> <td>2,798</td> <td>2,56 </td></tr> <tr> <th>Air-dried marine soil </th> <td>84</td> <td>2,234</td> <td>2,42 </td></tr> <tr> <th>Open-dried marine soil </th> <td>60</td> <td>1,644</td> <td>2,63 </td></tr> <tr> <th>Brown soil </th> <td>62</td> <td>1,674</td> <td>2,83 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=18" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Aquifer_test" title="Aquifer test">Aquifer test</a></li> <li><a href="/wiki/Hydraulic_analogy" title="Hydraulic analogy">Hydraulic analogy</a></li> <li><a href="/wiki/Pedotransfer_function" title="Pedotransfer function">Pedotransfer function</a> – for estimating hydraulic conductivities given soil properties</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=19" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"> <a rel="nofollow" class="external free" href="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">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</a>. Hydraulic conductivity definition </span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFSahuSaha2016" class="citation journal cs1">Sahu, Sudarsan; Saha, Dipankar (2016). <a rel="nofollow" class="external text" href="https://doi.org/10.2113/gseegeosci.22.4.319">"Empirical Methods and Estimation of Hydraulic Conductivity of Fluvial Aquifers"</a>. <i>Environmental & Engineering Geoscience</i>. <b>22</b> (4): <span class="nowrap">319–</span>340. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2016EEGeo..22..319S">2016EEGeo..22..319S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2113%2Fgseegeosci.22.4.319">10.2113/gseegeosci.22.4.319</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Environmental+%26+Engineering+Geoscience&rft.atitle=Empirical+Methods+and+Estimation+of+Hydraulic+Conductivity+of+Fluvial+Aquifers&rft.volume=22&rft.issue=4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E319-%3C%2Fspan%3E340&rft.date=2016&rft_id=info%3Adoi%2F10.2113%2Fgseegeosci.22.4.319&rft_id=info%3Abibcode%2F2016EEGeo..22..319S&rft.aulast=Sahu&rft.aufirst=Sudarsan&rft.au=Saha%2C+Dipankar&rft_id=https%3A%2F%2Fdoi.org%2F10.2113%2Fgseegeosci.22.4.319&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHydraulic+conductivity" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWösten,_J.H.M.,_Pachepsky,_Y.A.,_and_Rawls,_W.J.2001" class="citation journal cs1">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". <i><a href="/wiki/Journal_of_Hydrology" title="Journal of Hydrology">Journal of Hydrology</a></i>. <b>251</b> (<span class="nowrap">3–</span>4): <span class="nowrap">123–</span>150. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2001JHyd..251..123W">2001JHyd..251..123W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1016%2FS0022-1694%2801%2900464-4">10.1016/S0022-1694(01)00464-4</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+Hydrology&rft.atitle=Pedotransfer+functions%3A+bridging+the+gap+between+available+basic+soil+data+and+missing+soil+hydraulic+characteristics&rft.volume=251&rft.issue=%3Cspan+class%3D%22nowrap%22%3E3%E2%80%93%3C%2Fspan%3E4&rft.pages=%3Cspan+class%3D%22nowrap%22%3E123-%3C%2Fspan%3E150&rft.date=2001&rft_id=info%3Adoi%2F10.1016%2FS0022-1694%2801%2900464-4&rft_id=info%3Abibcode%2F2001JHyd..251..123W&rft.au=W%C3%B6sten%2C+J.H.M.%2C+Pachepsky%2C+Y.A.%2C+and+Rawls%2C+W.J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHydraulic+conductivity" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_journal" title="Template:Cite journal">cite journal</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://imechanica.org/files/JCIS-2019-Tailoring%20porous%20media%20for%20controllable%20capillary%20flow_0.pdf">Controlling capillary flow</a> an application of Darcy's law </span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">Liu, Cheng "Soils and Foundations." Upper Saddle River, New Jersey: Prentice Hall, 2001 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-13-025517-3" title="Special:BookSources/0-13-025517-3">0-13-025517-3</a></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">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.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">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.</span> </li> <li id="cite_note-Oost-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Oost_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Oost_8-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Oost_8-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">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. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/90-70754-33-9" title="Special:BookSources/90-70754-33-9">90-70754-33-9</a>. Free download from: <a rel="nofollow" class="external autonumber" href="http://www.waterlog.info/articles.htm">[1]</a>, under nr. 6, or directly as PDF : <a rel="nofollow" class="external autonumber" href="http://www.waterlog.info/pdf/chap12.pdf">[2]</a></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">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 : <a rel="nofollow" class="external autonumber" href="http://www.waterlog.info/articles.htm">[3]</a>, under nr. 2, or directly as PDF : <a rel="nofollow" class="external autonumber" href="http://www.waterlog.info/pdf/analysis.pdf">[4]</a></span> </li> <li id="cite_note-Boon-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-Boon_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Boon_10-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">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. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/90-70754-54-1" title="Special:BookSources/90-70754-54-1">90-70754-54-1</a> On line : <a rel="nofollow" class="external autonumber" href="http://content.alterra.wur.nl/Internet/webdocs/ilri-publicaties/publicaties/Pub57/Pub57.pdf">[5]</a></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">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: <a rel="nofollow" class="external autonumber" href="http://www.waterlog.info/pdf/enerart.pdf">[6]</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090219221547/http://www.waterlog.info/pdf/enerart.pdf">Archived</a> 2009-02-19 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> . 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. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7923-3651-8" title="Special:BookSources/978-0-7923-3651-8">978-0-7923-3651-8</a>. On line: <a rel="nofollow" class="external autonumber" href="http://www.waterlog.info/pdf/enerbal.pdf">[7]</a>. The corresponding free EnDrain program can be downloaded from: <a rel="nofollow" class="external autonumber" href="http://www.waterlog.info/endrain.htm">[8]</a></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">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: <a rel="nofollow" class="external autonumber" href="http://www.waterlog.info/pdf/wellspac.pdf">[9]</a>. The corresponding free WellDrain program can be downloaded from : <a rel="nofollow" class="external autonumber" href="http://www.waterlog.info/weldrain.htm">[10]</a></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBear,_J.1972" class="citation book cs1">Bear, J. (1972). <i>Dynamics of Fluids in Porous Media</i>. <a href="/wiki/Dover_Publications" title="Dover Publications">Dover Publications</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-486-65675-6" title="Special:BookSources/0-486-65675-6"><bdi>0-486-65675-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dynamics+of+Fluids+in+Porous+Media&rft.pub=Dover+Publications&rft.date=1972&rft.isbn=0-486-65675-6&rft.au=Bear%2C+J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AHydraulic+conductivity" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Table 4.4 James K. Mitchell, Kenichi Soga, Fundamentals of SoilBehavior, third ed., John Wiley & Sons Inc., Hoboken, NJ, 2005, 577 pp., ISBN 0-471-46302-7.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text">Nagaraj, T. S., Pandian, N. S., and Narasimha Raju, P. S. R. 1991. An approach for prediction of compressibility and permeability behaviour of sand-bentonite mixes, Indian Geotechnical Journal, Vol. 21, No. 3, pp. 271–282</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Hydraulic_conductivity&action=edit&section=20" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.fxsolver.com/solve/share/jZLNM1J9bHMGTCqIglfgmQ==/">Hydraulic conductivity calculator</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist 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class="mw-selflink selflink">hydraulic conductivity</a></li> <li><a href="/wiki/Specific_storage" title="Specific storage">storativity</a></li> <li><a href="/wiki/Permeability_(earth_sciences)" class="mw-redirect" title="Permeability (earth sciences)">permeability</a></li> <li><a href="/wiki/Porosity" title="Porosity">porosity</a></li> <li><a href="/wiki/Water_content" title="Water content">water content</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Geotechnical_engineering316" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Geotechnical_engineering" title="Template:Geotechnical engineering"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Geotechnical_engineering" title="Template talk:Geotechnical engineering"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Geotechnical_engineering" title="Special:EditPage/Template:Geotechnical engineering"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Geotechnical_engineering316" style="font-size:114%;margin:0 4em"><a href="/wiki/Geotechnical_engineering" title="Geotechnical engineering">Geotechnical engineering</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/Offshore_geotechnical_engineering" title="Offshore geotechnical engineering">Offshore geotechnical engineering</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Geotechnical_investigation" title="Geotechnical investigation">Investigation</a> <br />and<br />instrumentation</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Field (<i>in situ</i>)</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"><div class="div-col" style="column-width: 33em;"> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Core_sample.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Core_sample.svg/20px-Core_sample.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Core_sample.svg/30px-Core_sample.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Core_sample.svg/40px-Core_sample.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Core_drill" title="Core drill">Core drill</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Cone_penetration_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Cone_penetration_test.svg/20px-Cone_penetration_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Cone_penetration_test.svg/30px-Cone_penetration_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Cone_penetration_test.svg/40px-Cone_penetration_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Cone_penetration_test" title="Cone penetration test">Cone penetration test</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Geo-electrical_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Geo-electrical_sounding.svg/20px-Geo-electrical_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Geo-electrical_sounding.svg/30px-Geo-electrical_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/Geo-electrical_sounding.svg/40px-Geo-electrical_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Geo-electrical_sounding&action=edit&redlink=1" class="new" title="Geo-electrical sounding (page does not exist)">Geo-electrical sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:In_situ_permeameter_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/In_situ_permeameter_test.svg/20px-In_situ_permeameter_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7b/In_situ_permeameter_test.svg/30px-In_situ_permeameter_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7b/In_situ_permeameter_test.svg/40px-In_situ_permeameter_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Permeability_(Earth_sciences)" class="mw-redirect" title="Permeability (Earth sciences)">Permeability test</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Load_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Load_test.svg/20px-Load_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Load_test.svg/30px-Load_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Load_test.svg/40px-Load_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Load_test" class="mw-redirect" title="Load test">Load test</a> <ul><li><a href="/wiki/Static_load_testing" title="Static load testing">Static</a></li> <li><a href="/wiki/Dynamic_load_testing" title="Dynamic load testing">Dynamic</a></li> <li><a href="/wiki/Statnamic_load_test" title="Statnamic load test">Statnamic</a></li></ul></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Pore_pressure_measurement.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Pore_pressure_measurement.svg/20px-Pore_pressure_measurement.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Pore_pressure_measurement.svg/30px-Pore_pressure_measurement.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Pore_pressure_measurement.svg/40px-Pore_pressure_measurement.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> Pore pressure measurement <ul><li><a href="/wiki/Piezometer" class="mw-redirect" title="Piezometer">Piezometer</a></li> <li><a href="/wiki/Well#Classification" title="Well">Well</a></li></ul></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Ram_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Ram_sounding.svg/20px-Ram_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Ram_sounding.svg/30px-Ram_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5d/Ram_sounding.svg/40px-Ram_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Ram_sounding&action=edit&redlink=1" class="new" title="Ram sounding (page does not exist)">Ram sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Rock_control_drilling.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Rock_control_drilling.svg/20px-Rock_control_drilling.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Rock_control_drilling.svg/30px-Rock_control_drilling.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/Rock_control_drilling.svg/40px-Rock_control_drilling.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Rock_control_drilling&action=edit&redlink=1" class="new" title="Rock control drilling (page does not exist)">Rock control drilling</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Rotary_pressure_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Rotary_pressure_sounding.svg/20px-Rotary_pressure_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Rotary_pressure_sounding.svg/30px-Rotary_pressure_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Rotary_pressure_sounding.svg/40px-Rotary_pressure_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Rotary-pressure_sounding" title="Rotary-pressure sounding">Rotary-pressure sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Rotary_weight_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Rotary_weight_sounding.svg/20px-Rotary_weight_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Rotary_weight_sounding.svg/30px-Rotary_weight_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Rotary_weight_sounding.svg/40px-Rotary_weight_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Rotary_weight_sounding&action=edit&redlink=1" class="new" title="Rotary weight sounding (page does not exist)">Rotary weight sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Sample_series.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Sample_series.svg/20px-Sample_series.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/05/Sample_series.svg/30px-Sample_series.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/05/Sample_series.svg/40px-Sample_series.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Soil_test#Soil_testing" title="Soil test">Sample series</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Screw_plate_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Screw_plate_test.svg/20px-Screw_plate_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/75/Screw_plate_test.svg/30px-Screw_plate_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/75/Screw_plate_test.svg/40px-Screw_plate_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Screw_plate_test&action=edit&redlink=1" class="new" title="Screw plate test (page does not exist)">Screw plate test</a></li></ul> <ul><li><a href="/wiki/Deformation_monitoring" title="Deformation monitoring">Deformation monitoring</a> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Inclinometer.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Inclinometer.svg/20px-Inclinometer.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Inclinometer.svg/30px-Inclinometer.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Inclinometer.svg/40px-Inclinometer.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Inclinometer" title="Inclinometer">Inclinometer</a></li> <li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Settlement_recordings.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Settlement_recordings.svg/20px-Settlement_recordings.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Settlement_recordings.svg/30px-Settlement_recordings.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Settlement_recordings.svg/40px-Settlement_recordings.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Soil_consolidation" title="Soil consolidation">Settlement recordings</a></li></ul></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Shear_vane_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Shear_vane_test.svg/20px-Shear_vane_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Shear_vane_test.svg/30px-Shear_vane_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Shear_vane_test.svg/40px-Shear_vane_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Shear_vane_test" title="Shear vane test">Shear vane test</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Simple_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Simple_sounding.svg/20px-Simple_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Simple_sounding.svg/30px-Simple_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d4/Simple_sounding.svg/40px-Simple_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/w/index.php?title=Simple_sounding&action=edit&redlink=1" class="new" title="Simple sounding (page does not exist)">Simple sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Standard_penetration_test.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Standard_penetration_test.svg/20px-Standard_penetration_test.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Standard_penetration_test.svg/30px-Standard_penetration_test.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0d/Standard_penetration_test.svg/40px-Standard_penetration_test.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Standard_penetration_test" title="Standard penetration test">Standard penetration test</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Total_sounding.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Total_sounding.svg/20px-Total_sounding.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Total_sounding.svg/30px-Total_sounding.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/60/Total_sounding.svg/40px-Total_sounding.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Total_sounding" title="Total sounding">Total sounding</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Trial_pit.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Trial_pit.svg/20px-Trial_pit.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/71/Trial_pit.svg/30px-Trial_pit.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/71/Trial_pit.svg/40px-Trial_pit.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Trial_pit" title="Trial pit">Trial pit</a></li></ul> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Visible_rock.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Visible_rock.svg/20px-Visible_rock.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/14/Visible_rock.svg/30px-Visible_rock.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/14/Visible_rock.svg/40px-Visible_rock.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> <a href="/wiki/Bedrock" title="Bedrock">Visible bedrock</a></li></ul> <ul><li><a href="/wiki/Nuclear_densometer" class="mw-redirect" title="Nuclear densometer">Nuclear densometer test</a></li></ul> <ul><li><a href="/wiki/Exploration_geophysics" title="Exploration geophysics">Exploration geophysics</a></li></ul> <ul><li><a href="/wiki/Crosshole_sonic_logging" title="Crosshole sonic logging">Crosshole sonic logging</a></li></ul> <ul><li><a href="/wiki/Pile_integrity_test" title="Pile integrity test">Pile integrity test</a></li></ul> <ul><li><a href="/wiki/Wave_equation_analysis" title="Wave equation analysis">Wave equation analysis</a></li></ul></div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;"><a href="/wiki/Soil_test" title="Soil test">Laboratory <br />testing</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <li><a href="/wiki/Soil_classification" title="Soil classification">Soil classification</a></li> <li><a href="/wiki/Atterberg_limits" title="Atterberg limits">Atterberg limits</a></li> <li><a href="/wiki/California_bearing_ratio" title="California bearing ratio">California bearing ratio</a></li> <li><a href="/wiki/Direct_shear_test" title="Direct shear test">Direct shear test</a></li> <li><a href="/wiki/Hydrometer" title="Hydrometer">Hydrometer</a></li> <li><a href="/wiki/Proctor_compaction_test" title="Proctor compaction test">Proctor compaction test</a></li> <li><a href="/wiki/R-value_(soils)" title="R-value (soils)">R-value</a></li> <li><a href="/wiki/Sieve_analysis" title="Sieve analysis">Sieve analysis</a></li> <li><a href="/wiki/Triaxial_shear_test" title="Triaxial shear test">Triaxial shear test</a></li> <li><a href="/wiki/Oedometer_test" title="Oedometer test">Oedometer test</a></li> <li><a class="mw-selflink-fragment" href="#Experimental_approach">Hydraulic conductivity tests</a></li> <li><a href="/wiki/Water_content#Measurement" title="Water content">Water content tests</a></li> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Soil" title="Soil">Soil</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Types</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Clay" title="Clay">Clay</a></li> <li><a href="/wiki/Silt" title="Silt">Silt</a></li> <li><a href="/wiki/Sand" title="Sand">Sand</a></li> <li><a href="/wiki/Gravel" title="Gravel">Gravel</a></li> <li><a href="/wiki/Peat" title="Peat">Peat</a></li> <li><a href="/wiki/Loam" title="Loam">Loam</a></li> <li><a href="/wiki/Loess" title="Loess">Loess</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Properties</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Hydraulic conductivity</a></li> <li><a href="/wiki/Water_content" title="Water content">Water content</a></li> <li><a href="/wiki/Void_ratio" title="Void ratio">Void ratio</a></li> <li><a href="/wiki/Bulk_density" title="Bulk density">Bulk density</a></li> <li><a href="/wiki/Thixotropy" title="Thixotropy">Thixotropy</a></li> <li><a href="/wiki/Reynolds%27_dilatancy" class="mw-redirect" title="Reynolds' dilatancy">Reynolds' dilatancy</a></li> <li><a href="/wiki/Angle_of_repose" title="Angle of repose">Angle of repose</a></li> <li><a href="/wiki/Friction#Angle_of_friction" title="Friction">Friction angle</a></li> <li><a href="/wiki/Cohesion_(geology)" title="Cohesion (geology)">Cohesion</a></li> <li><a href="/wiki/Porosity" title="Porosity">Porosity</a></li> <li><a href="/wiki/Permeability_(earth_sciences)" class="mw-redirect" title="Permeability (earth sciences)">Permeability</a></li> <li><a href="/wiki/Specific_storage" title="Specific storage">Specific storage</a></li> <li><a href="/wiki/Shear_strength_(soil)" title="Shear strength (soil)">Shear strength</a></li> <li><a href="/wiki/Soil_liquefaction" title="Soil liquefaction">Sensitivity</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Structures <br />(<a href="/wiki/Soil-structure_interaction" title="Soil-structure interaction">Interaction</a>)</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Natural features</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Topography" title="Topography">Topography</a></li> <li><a href="/wiki/Vegetation" title="Vegetation">Vegetation</a></li> <li><a href="/wiki/Terrain" title="Terrain">Terrain</a></li> <li><a href="/wiki/Topsoil" title="Topsoil">Topsoil</a></li> <li><a href="/wiki/Water_table" title="Water table">Water table</a></li> <li><a href="/wiki/Bedrock" title="Bedrock">Bedrock</a></li> <li><a href="/wiki/Subgrade" title="Subgrade">Subgrade</a></li> <li><a href="/wiki/Subsoil" title="Subsoil">Subsoil</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;"><a href="/wiki/Earthworks_(engineering)" title="Earthworks (engineering)">Earthworks</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li>Shoring structures <ul><li><a href="/wiki/Retaining_wall" title="Retaining wall">Retaining walls</a></li> <li><a href="/wiki/Gabion" title="Gabion">Gabion</a></li> <li><a href="/wiki/Ground_freezing" title="Ground freezing">Ground freezing</a></li> <li><a href="/wiki/Mechanically_stabilized_earth" title="Mechanically stabilized earth">Mechanically stabilized earth</a></li> <li><a href="/wiki/Pressure_grouting" title="Pressure grouting">Pressure grouting</a></li> <li><a href="/wiki/Slurry_wall" title="Slurry wall">Slurry wall</a></li> <li><a href="/wiki/Soil_nailing" title="Soil nailing">Soil nailing</a></li> <li><a href="/wiki/Tieback_(geotechnical)" title="Tieback (geotechnical)">Tieback</a></li></ul></li> <li><a href="/wiki/Land_development" title="Land development">Land development</a></li> <li><a href="/wiki/Landfill" title="Landfill">Landfill</a></li> <li><a href="/wiki/Digging" title="Digging">Excavation</a></li> <li><a href="/wiki/Trench" title="Trench">Trench</a></li> <li><a href="/wiki/Embankment_(earthworks)" title="Embankment (earthworks)">Embankment</a></li> <li><a href="/wiki/Cut_(earthworks)" title="Cut (earthworks)">Cut</a></li> <li><a href="/wiki/Causeway" title="Causeway">Causeway</a></li> <li><a href="/wiki/Terrace_(earthworks)" title="Terrace (earthworks)">Terracing</a></li> <li><a href="/wiki/Tunnel#Cut-and-cover" title="Tunnel">Cut-and-cover</a></li> <li><a href="/wiki/Cut_and_fill" title="Cut and fill">Cut and fill</a></li> <li><a href="/wiki/Fill_dirt" title="Fill dirt">Fill dirt</a></li> <li><a href="/wiki/Grading_(engineering)" class="mw-redirect" title="Grading (engineering)">Grading</a></li> <li><a href="/wiki/Land_reclamation" title="Land reclamation">Land reclamation</a></li> <li><a href="/wiki/Track_bed" title="Track bed">Track bed</a></li> <li><a href="/wiki/Erosion_control" title="Erosion control">Erosion control</a></li> <li><a href="/wiki/Earth_structure" title="Earth structure">Earth structure</a></li> <li><a href="/wiki/Expanded_clay_aggregate" title="Expanded clay aggregate">Expanded clay aggregate</a></li> <li><a href="/wiki/Crushed_stone" title="Crushed stone">Crushed stone</a></li> <li><a href="/wiki/Geosynthetics" title="Geosynthetics">Geosynthetics</a> <ul><li><a href="/wiki/Geotextile" title="Geotextile">Geotextile</a></li> <li><a href="/wiki/Geomembrane" title="Geomembrane">Geomembrane</a></li> <li><a href="/wiki/Geosynthetic_clay_liner" title="Geosynthetic clay liner">Geosynthetic clay liner</a></li> <li><a href="/wiki/Cellular_confinement" title="Cellular confinement">Cellular confinement</a></li></ul></li> <li><a href="/wiki/Infiltration_(hydrology)" title="Infiltration (hydrology)">Infiltration</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;"><a href="/wiki/Foundation_(engineering)" title="Foundation (engineering)">Foundations</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Shallow_foundation" title="Shallow foundation">Shallow</a></li> <li><a href="/wiki/Deep_foundation" class="mw-redirect" title="Deep foundation">Deep</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Soil_mechanics" title="Soil mechanics">Mechanics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Forces</th><td class="navbox-list-with-group navbox-list navbox-even" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Effective_stress" title="Effective stress">Effective stress</a></li> <li><a href="/wiki/Pore_water_pressure" title="Pore water pressure">Pore water pressure</a></li> <li><a href="/wiki/Lateral_earth_pressure" title="Lateral earth pressure">Lateral earth pressure</a></li> <li><a href="/wiki/Overburden_pressure" title="Overburden pressure">Overburden pressure</a></li> <li><a href="/wiki/Preconsolidation_pressure" title="Preconsolidation pressure">Preconsolidation pressure</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:10.0em;font-weight: normal;">Phenomena/<br />problems</th><td class="navbox-list-with-group navbox-list navbox-odd" style="padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Permafrost" title="Permafrost">Permafrost</a></li> <li><a href="/wiki/Frost_heaving" title="Frost heaving">Frost heaving</a></li> <li><a href="/wiki/Consolidation_(soil)" class="mw-redirect" title="Consolidation (soil)">Consolidation</a></li> <li><a href="/wiki/Soil_compaction" title="Soil compaction">Compaction</a></li> <li><a href="/wiki/Earthquake" title="Earthquake">Earthquake</a> <ul><li><a href="/wiki/Response_spectrum" title="Response spectrum">Response spectrum</a></li> <li><a href="/wiki/Seismic_hazard" title="Seismic hazard">Seismic hazard</a></li> <li><a href="/wiki/S_wave" title="S wave">Shear wave</a></li></ul></li> <li><a href="/wiki/Landslide" title="Landslide">Landslide</a> analysis <ul><li><a href="/wiki/Slope_stability_analysis" title="Slope stability analysis">Stability analysis</a></li> <li><a href="/wiki/Landslide_mitigation" title="Landslide mitigation">Mitigation</a></li> <li><a href="/wiki/Landslide_classification" title="Landslide classification">Classification</a></li> <li><a href="/wiki/Sliding_criterion_(geotechnical_engineering)" title="Sliding criterion (geotechnical engineering)">Sliding criterion</a></li> <li><a href="/wiki/Road#Slab_stabilization" title="Road">Slab stabilisation</a></li></ul></li> <li><a href="/wiki/Bearing_capacity" title="Bearing capacity">Bearing capacity</a> * <a href="/wiki/Stress_distribution_in_soil" title="Stress distribution in soil">Stress distribution in soil</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Software" title="Software">Numerical analysis <br />software</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/SEEP2D" title="SEEP2D">SEEP2D</a></li> <li><a href="/w/index.php?title=STABL&action=edit&redlink=1" class="new" title="STABL (page does not exist)">STABL</a></li> <li><a href="/wiki/SVFlux" title="SVFlux">SVFlux</a></li> <li><a href="/wiki/SVSlope" title="SVSlope">SVSlope</a></li> <li><a href="/wiki/UTEXAS" title="UTEXAS">UTEXAS</a></li> <li><a href="/wiki/Plaxis" title="Plaxis">Plaxis</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Geoprofessions" title="Geoprofessions">Related fields</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Geology" title="Geology">Geology</a></li> <li><a href="/wiki/Geochemistry" title="Geochemistry">Geochemistry</a></li> <li><a href="/wiki/Petrology" title="Petrology">Petrology</a></li> <li><a href="/wiki/Earthquake_engineering" title="Earthquake engineering">Earthquake engineering</a></li> <li><a href="/wiki/Geomorphology" title="Geomorphology">Geomorphology</a></li> <li><a href="/wiki/Soil_science" title="Soil science">Soil science</a></li> <li><a href="/wiki/Hydrology" title="Hydrology">Hydrology</a></li> <li><a href="/wiki/Hydrogeology" title="Hydrogeology">Hydrogeology</a></li> <li><a href="/wiki/Biogeography" title="Biogeography">Biogeography</a></li> <li><a href="/wiki/Earth_materials" title="Earth materials">Earth materials</a></li> <li><a href="/wiki/Archaeology" title="Archaeology">Archaeology</a></li> <li><a href="/wiki/Agricultural_science" title="Agricultural science">Agricultural science</a> <ul><li><a href="/wiki/Agrology" class="mw-redirect" title="Agrology">Agrology</a></li></ul></li></ul> </div></td></tr></tbody></table></div>    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