5 HYDRAULIC CONDUCTIVITY 5.1 DEFINITION The hydraulic conductivity of a soil is a measure of the soil's ability to transmit water when submitted to a hydraulic gradient. Hydraulic conductivity is defined by Darcy's law, which, for one-dimensional vertical flow, can be written as follows: where U is Darcy's velocity (or the average velocity of the soil fluid through a geometric cross-sectional area within the soil), h is the hydraulic head, andz is the vertical distance in the soil. The coefficient of roortionality, K, in !"uation #.$ is called the hydraulic conductivity. The term coefficient of ermeability is also sometimes used as a synonym for hydraulic conductivity. %n the basis of !"uation #.$, the hydraulic conductivity is defined as the ratio of Darcy's velocity to the alied hydraulic gradient. The dimension of K is the same as that for velocity, that is, length er unit of time (&T-$). Hydraulic conductivity is one of the hydraulic roerties of the soil' the other involves the soil's fluid retention characteristics. These roerties determine the behavior of the soil fluid within the soil system under secified conditions. (ore secifically, the hydraulic conductivity determines the ability of the soil fluid to flow through the soil matri) system under a secified hydraulic gradient' the soil fluid retention characteristics determine the ability of the soil system to retain the soil fluid under a secified ressure condition. The hydraulic conductivity deends on the soil grain si*e, the structure of the soil matri), the tye of soil fluid, and the relative amount of soil fluid (saturation) resent in the soil matri). The imortant roerties relevant to the solid matri) of the soil include ore si*e distribution, ore shae, tortuosity, secific surface, and orosity. &n relation to the soil fluid, the imortant roerties include fluid density, , and fluid viscosity, . +or a subsurface system saturated with the soil fluid, the hydraulic conductivity, K, can be e)ressed as follows (,ear $-./): where k, the intrinsic ermeability of the soil, deends only on roerties of the solid matri), and g/, called the fluidity of the li"uid, reresents the roerties of the ercolating fluid. The hydraulic conductivity, K, is e)ressed in terms of length er unit of time (lT-$), the intrinsic ermeability, k, is e)ressed in l/, and the fluidity, g0, in l-$T-$. ,y using!"uation #./, Darcy's law can be rewritten e)licitly in terms of its coefficient of roortionality (hydraulic conductivity K): 1hen the fluid roerties of density and viscosity are 2nown, !"uation #.3 can be used to e)erimentally determine the value ofthe intrinsic ermeability, k, and the hydraulic conductivity, K, as will be shown in 4ection #./. The values of saturated hydraulic conductivity in soils vary within a wide range of several orders of magnitude, deending on the soil material. Table #.$ lists the range of e)ected values of K for various unconsolidated and consolidated soil materials. The e)ected reresentative values of K for soil materials of different te)tures are resented in Table #./. 5 more detailed list of e)ected reresentative values of K based on the grain si*e distribution, degree of sorting, and silt content of several soil materials is resented in Tables #.3 and #.6. 4ection /.$./ discusses soil te)tures. ,ecause of the satial variability usually found in the geological formation of soils, saturated hydraulic conductivity values also show variations throughout the sace domain TABLE 5.1 Range of Saturated Hdrau!"#Condu#t"$"t of Var"ou% So"! &ater"a!%4aturated Hydraulic 7onductivity, K (m0yr)4oil Tye8nconsolidated deosits9ravel7lean sand4ilty sand4ilt, loess9lacial till8nweathered marine clay$ : $;6 - $ : $;.$ : $;/ - $ : $;#$ : $;$ - $ : $;6$ : $;-/ - $ : $;/$ : $;-# - $ : $;$$ : $;-# - $ : $;-/ermeable basalt?arst limestone$ : $;-@ - $ : $;-/$ : $;-. - $ : $;-3 $ : $;-3 - $ : $;$$ : $;-/ - $ : $;$$ : $;-$ - $ : $;3 $ : $;$ - $ : $;#$ : $;$ - $ : $;#4ource: 5dated from +ree*e and 7herry ($-.-).within a subsurface geological formation. 4uch a geological formation is said to be heterogeneous. &f the roerties of the geologic formation are invariable in sace, the formation is homogeneous. 5 geological formation is said to be isotroic if at any oint in the medium, the values of the saturated hydraulic conductivity (K) are indeendent of the direction of measurement. 5gain, because of the usually stratified nature of uncon-solidated sedimentary soil materials, soils are usually anisotroic. 1ithin an anisotroic geological formation, the vertical comonent of the saturated hydraulic conductivity is usually smaller (one to two orders of magnitude) than the hori*ontal comonent. 5.' &EASURE&ENT &ETHODOLO(Y The saturated hydraulic conductivity of water in soil (or the intrinsic ermeability of the soil) can be measured by both field andlaboratory e)eriments. !ither way, the e)erimental measurement of K (or k) consists in determining the numerical value for the coefficient in Darcy's e"uation. The methodology used for the e)erimental determination of K (or k) in either laboratory or field e)eriments is based on the following rocedures (,ear $-./): $. 5ssume a flow attern (such as one-dimensional flow in a orous medium) that can be described analytically by Darcy's law, /. >erform an e)eriment reroducing the chosen flow attern and measure all measurable "uantities in !"uation #.6, including fluid density, dynamic viscosity, flow velocity, and the gradient of the hydraulic head' and 3. 7omute thecoefficient K (or k)by substituting themeasured "uantitiesinto !"uation #.6above. (any differentlaboratory or fielde)eriments can beused to determinethecoefficient K (or k).TABLE 5.) E%t"*ated Saturated Hdrau!"#Condu#t"$"t"e% for F"ne+(ra"ned &ater"a!%9rain-4i*e7lass4aturatedHydraulic 7onductivity,K ($;3 m0yr)7lay A;.;;;$4ilt, clayey ;.$ - ;.64ilt, slightly sandy;.#4ilt, moderatelysandy;.B - ;.-4ilt, very sandy$.; -$./4andy silt $./4ilty sand $.64ource: !>5 ($-B@).5n e)tensive discussion on the resective measurement methodologies for laboratory and field e)eriments is resented in ?lute and Dir2sen ($-B@) and 5moo*egar and 1arric2 ($-B@), resectively. +or +84 sites, the standard methods used for determining saturated hydraulic conductivity in soil materials are those reared by the 5merican 4ociety for Testing and (aterials (54T( $--/a-o), the 8.4. !nvironmental >rotection 5gency (!>5 $-B@), the 8.4. Deartment of the 5rmy (D%5 $-.;), and the 8.4. Deartment of the &nterior (D%& $--;a,b). ,rief descritions of these ertinent standard methods are resented in Table #.#. =aboratory tests are carried out on small samles of soil materials collected during core-drilling rograms. ,ecause of the small si*es of the soil samles handled in the laboratory, the results of these tests are considered a oint reresentation of the soil roerties. &f the soil samles used in the laboratory test are truly undisturbed samles, the measured value of K (or k) should bea true reresentation of the in-situ saturated hydraulic conductivity at that articular samling oint. =aboratory methods may be used to evaluate the vertical and hori*ontal hydraulic conductivity in soil samles. +or instance, in undisturbed samles of either cohesive or cohesionless soils, the values of K obtained through laboratory tests corresond to thedirection in which the samle was ta2en, that is, generally vertical. The conductivity of disturbed (remolded) samles of cohesionless soils obtained in the laboratory can be used to aro)imate the actual value of K in the undisturbed (natural) soil inthe hori*ontal direction (D%5 $-.;). +or fine-grained soils, the undisturbed cohesive samle can be oriented accordingly, to obtain the hydraulic conductivity in either the vertical or hori*ontal direction. &n contrast to laboratory methods for measuring conductivity in soil samles, field methods, in general, involve a large region ofthe soil. 7onse"uently, the results obtained from field methods should reflect the influences of both the vertical and hori*ontal directions and should reresent an average value ofK. This situation is esecially imortant in highly TABLE 5., E%t"*ated Saturated Hdrau!"# Condu#t"$"t"e% for Sand% and (ra$e!% A##ord"ng to Degree of Sort"ng and S"!t Contenta4aturated Hydraulic 7onductivity, K ($;3m0yr)Degree of 4orting 4ilt 7ontent9rain-4i*e 7lass or oor (oderate 1ell 4light (oderate HighCery fine sand $ / 3 3 / $Cery fine to fine sand3 3 -b3 / $Cery fine to medium sand6 # - 6 3 /Cery fine to coarse sand# - - 6 3 3Cery fine to very coarse sand. - - @ 6 3Cery fine sand to fine gravelB - - . @ 6Cery fine sand to medium $$ - - - . #gravelCery fine sand to coarse gravel$6 - - $/ $; .+ine sand3 6 @ 6 3 /+ine to medium sand@ . - # 6 3+ine to coarse sand@ B - @ # 6+ine to very coarse sandB - - . # 6+ine sand to fine gravel$; - - B . #+ine sand to medium gravel$3 - - $; B @+ine sand to coarse gravel$@ - - $/ $; B(ediumsand. - $; . @ 6(ediumto coarsesandB $; - B @ #(ediumto very coarse sand- $/ - B . #(ediumsand to fine gravel$$ - - - B @(ediumsand to medium gravel$# - - $3 - .(ediumsand to coarse gravel$B - - $# $/ -7oarse sand- $/ $# $; B @7oarse to very coarse sand$; $# - $; B @7oarse sand to fine gravel$3 $@ - $/ $; B7oarse sand to medium gravel$@ - - $3 $; B7oarse sand to coarse gravel/; - - $# $$ $;Cery coarse sand$/ $@ /$ $3 $; BCery coarse tofine gravel$# /6 - $3 $/ $;Cery coarse tomedium gravel$- /# - $@ $6 $$Cery coarse sand to coarse gravel/3 - - $B $# $/+ine gravel$B /6 3; /# $@ $/+ine to medium gravel// 3. - // $- $#+ine to coarse gravel/. 3. - /@ /$ $@(ediumgravel/. /@ 6# /. // $B(ediumto coarsegravel33 #/ - 33 /. /$7oarse gravel3. #/ @. 3. 3/ /@a 5 ($-B@).TABLE 5.5 Standard La-orator and F"e!d &et.od% for &ea%ur"ng Saturated Hdrau!"# Condu#t"$"t/ 0/"n So"! &ater"a!%(ethodTye(ethod4ecification5lication 5 ($-B@)54T( ($--/m)?lute and Dir2son ($-B@)7onductivity test with samling tubes8ndisturbed samles of cohesionless soil that cannot be removed from the samling tube without e)cessive disturbance.The measured conductivity corresonds to thedirection in which the samle was ta2en (generally vertical)' may be erformed under constant-head or falling-head flow conditions,deending on the estimated conductivity of the samle.D%5 ($-.;)7onductivity test with ressure chamber7ohesive fine-grained soil samlesin the undisturbed, disturbed (remolded), or comacted state in a fully saturated condition.4hould be used only in soils that are originallyfully saturated' can be erformed under conditions of loading e)ected in the field' lea2age along the sides of the samle can be revented' usually erformed under falling-head flow conditions.D%5 ($-.;)!>5 ($-B@) 7onductivity test with bac2 ressure7ohesive fine-grained soil samlesin the undisturbed, disturbed (remolded), or comacted state that are not fully saturated.The additional ressure (bac2 ressure) alied to the ore fluid of the soil samle reduces the si*e of the gas bubbles in the ores, increasing the degree of water saturation' usually erformed under constant-head flow conditions.D%5 ($-.;)!>5 ($-B@)54T( ($--/m)TABLE 5.5 1Cont.2(ethod (ethodTye 4ecification5lication um-out test method develoed rimarily forgroundwater systems' the method consists of removing a slug of water instantaneously froma well and measuring the recovery of the water in the well' alicable to wells that fullyor artially enetrate the interval of interest in the unconfined a"uifer' the measured K rimarily reflects the value in the hori*ontal direction.!>5 ($-B@)4ingle-well (slug) test in moderately ermeable formations under confined conditions4aturated soil materials of moderately hydraulic conductivity in testing *ones under confined conditions, entirely oen to the well screen or oen borehole.>um-out test method develoed rimarily forgroundwater systems' the method consists of removing a slug of water instantaneously froma well and measuring the recovery of the water in the well' used in confined a"uifer (saturated *one of the soil under confined conditions)' the method assumes that the tested *one is uniform in all radial directions from the test well.!>5 ($-B@)4ingle-well (modified slug) test in e)tremely tight formations under confined conditions4aturated soil materials with low to e)tremely low conductivity suchas silts, clays, and shales.(+or K as low as $.; : $;-# m0yr).>um-out test method develoed rimarily forgroundwater systems' the test is conducted by suddenly ressuri*ing a ac2ed-off *one of thesoil in a ortion of a borehole or well within the confined *one and then monitoring the ressure decay afterwards' used in confined a"uifer (saturated *one of the soil under confined conditions).!>5 ($-B@)TABLE 5.5 1Cont.2(ethodTye(ethod4ecification5lication