Soil and Environmental Analysis: Physical Methods - Chapter 4 pot

Slichter 1899 argued that the flow of water in soil described by Darcy’s law is analogous to the flow of electricity and heat inconductors, and so generally Darcy’s law may be written in v

The physical law describing water movement through saturated porous materials

in general and soils in particular was proposed by Darcy (1856) in his work cerned with the water supplies for the town of Dijon He established the law fromthe results of experiments with water flowing down columns of sands in an ex-perimental arrangement shown schematically inFig 1 Darcy found that the vol-

con-ume of water Q flowing per unit time was directly proportional to the sectional area A of the column and to the difference Dh in hydraulic head causing

cross-the flow as measured by cross-the level of water in manometers, and inversely

propor-tional to the length L of the column Thus

KA Dh

L where the proportionality constant K is now known as the hydraulic conductivity

of the porous material The dimensions of K are those of a velocity, LT⫺1 Typical

values of K for soils of different textures are given inTable 1 Conversion factorsrelating various units are given inTable 2 Since the hydraulic conductivity of asoil is inversely proportional to the viscous drag of the water flowing between thesoil particles, its value increases as the viscosity of water decreases with increas-ing temperature, by about 3% per⬚C

The hydraulic head is the sum of the soil water pressure head (the pressurepotential discussed inChap 2expressed in units of energy per unit weight) andthe elevation from a given datum level It is measured directly by the level of water

in the manometers above a datum in Darcy’s experiment and is the water potential

expressed as the work done per unit weight of water in transferring it from areference source at the datum level The potential may also be defined as the workdone per unit volume of water, in which case the potential difference causing theflow would bergDh, where r is the density of water and g is the acceleration due

to gravity; Darcy’s law using potentials defined in this way would give K in units

with dimensions M⫺1L3T Here we will adopt the usual convention of defining

the potential as the work done per unit weight, that is as a head of water, so that K

is simply expressed in units of a velocity This is very convenient when computingwater flows in soils, but it has the disadvantage that the value of the hydraulic

conductivity of a porous material depends on g This means that the hydraulic

conductivity of a given porous material depends on altitude and is smaller at thetop of a mountain than at sea level, but this is of little importance in most practicalproblems concerned with groundwater movement

Equation 1 describes the flow of water in porous materials at low velocitieswhen viscous forces opposing the flow are much greater than the inertial forces

Fig 1 Darcy’s experimental arrangement

The ratio of the inertial forces to the viscous forces is represented by the Reynoldsnumber (Muskat, 1937; Childs, 1969) which may be defined as

vdr

h

where v is the mean flow velocity, d a characteristic length (for example, the mean

pore diameter),r the density of water as before, and h the viscosity of water.When Re exceeds a value of about 1.0, Darcy’s law no longer describes the flow

of water through porous materials Under field conditions this is unlikely to occurexcept in some situations of flow in gravels and in structural fissures and wormholes

Darcy’s work was concerned with one-dimensional flow However, flows insoil are most often two- or three-dimensional, so Eq 1 has to be extended to takeinto account multidimensional flow Slichter (1899) argued that the flow of water

in soil described by Darcy’s law is analogous to the flow of electricity and heat inconductors, and so generally Darcy’s law may be written in vectorial notation as

Table 1 Hydraulic Conductivity Values of Saturated Soils

Soil

Hydraulic conductivity(mm d⫺ 1)

* Example: To convert x cm min⫺ 1 to meters per day, find 1 in the

cm min ⫺ 1 column Numbers on the same horizontal row are values

in other units equivalent to 1 cm min ⫺ 1 , so that 1 cm min ⫺ 1 ⬅

14.4 m d ⫺ 1and x cm min⫺ 1⬅ 14.4x m d⫺ 1

where v is the flow velocity and h is the hydraulic potential of the soil water

expressed as the hydraulic head as in Eq 1, with the flow normal to the tials If the water is considered to be incompressible and the soil does not shrink

equipoten-or swell, the equation of continuity is

so that h is described by Laplace’s equation

2

Thus it is only a matter of solving Eq 5 for the hydraulic head h with the given

boundary conditions in order to obtain a complete solution to a given flow

prob-lem in saturated soil in one, two, or three dimensions With h known throughout the flow region from Eq 5, flows can be found from Eq 3 if K is known Con-

versely, if flows and hydraulic heads are measured in the flow region, the hydraulicconductivity can be deduced Measurement techniques for the determination ofhydraulic conductivities of porous materials in general, including soils, make use

of solutions of Laplace’s equation with the prescribed boundary conditions posed by the particular method

im-The concept of hydraulic conductivity is derived from experiments on form porous materials Methods of measuring hydraulic conductivity assume im-plicitly that the flow in the soil region concerned is given by Darcy’s law with thehead distribution described by Laplace’s equation (Eq 5); that is, among otherfactors they presuppose that the soil is uniform As discussed in Sec II, soils can

uni-be far from uniform uni-because of heterogeneities at various scales, and ments need to be made on some representative volume of the whole flow region.Thus although values of ‘‘hydraulic conductivity’’ for a soil in a given region canalways be obtained using any method, such values will be of little relevance in thecontext of predicting flows if the volume of soil sampled by the method is unre-presentative of the soil region as a whole

measure-In the above discussion it has been tacitly assumed that the hydraulic ductivity of the soil is the same in all directions However, anisotropy in soil prop-erties can occur because of structural development and laminations, giving differ-ent hydraulic conductivity values in different directions Darcy’s law then has to

con-be expressed in tensor form (Childs, 1969) In anisotropic soils the streamlines offlow are orthogonal to the equipotential surfaces only when the flow is in thedirection of one of the three principal directions The theory of flow in anisotropicsoils (Muskat, 1937; Maasland, 1957; Childs, 1969) shows that Laplace’s equationcan still be used to obtain solutions to flow problems if a transformation incorpo-rating the components of hydraulic conductivity in the principal directions is ap-plied to the spatial coordinates If the soil is anisotropic, the two- and three-dimensional flows usually used in hydraulic conductivity measurement techniques

in the field require analysis using this theory to obtain values of the hydraulicconductivity in the principal directions.

II FUNDAMENTAL CONSIDERATIONS

OF FLOW THROUGH SOILS

A Soil Considered as a Continuum

The movement of water through soils takes place in the tortuous channels tween the soil particles with velocities varying from point to point and described

be-by the Stokes–Navier equations (Childs, 1969) Darcy’s law does not considerthis microscopic flow pattern between the particles but instead assumes the watermovement to take place in a continuum with a uniform flow averaged over space

It therefore describes the flow of water macroscopically in volumes of soil muchlarger than the size of the pores It can thus only be used to describe the macro-

scopic flow of water through soil regions of volume greater than some tative elementary volume that encompasses many soil particles.

represen-The concept of representative elementary volume of a porous material ismost easily illustrated by considering the measurement of the water content of

a sample of unstructured ‘‘uniform’’ saturated soil, starting with a very small ume and then increasing the sample size For volumes smaller than the size of thesoil particles the sample volume would include only solid matter if located whollywithin a soil particle, giving zero soil water content, but would contain only water

vol-if located wholly in a pore, giving a soil water content of one All values betweenzero and one are possible when the sample is located partly within a soil particleand partly within the pore As the volume is increased with the sample having tocontain both pore volume and solid particle, the lower limit of measured watercontent increases while the upper limit decreases, as shown inFig 2a When thesize of sample is sufficiently large, repeated measurements on random samples ofthe soil give the same value of soil water content The smallest sample volumethat produces a consistent value is the representative elementary volume Mea-surements of hydraulic conductivity and other soil properties need to be made onvolumes larger than this volume While additive soil properties, such as the watercontent, can be obtained by averaging a large number of measurements made onsmaller volumes within the representative elementary volume, the hydraulic con-ductivity cannot be obtained in this way because of the interdependent complexpattern of flows in between soil particles that this property embraces

Figure 2a illustrates the variability of a soil physical property that exists inall porous materials at a small enough scale because of their particulate nature.Variability can also be present in soils at larger scales For example, in aggregatedand structured soils where a distribution of macropores between the aggregates or

peds is superimposed on the interparticle micropore space, the soil water contentwould vary with sample size as shown in Fig 2b; only when the sample sizeencompasses a representative sample of macropore space do we have a represen-tative volume This volume will be characteristic of the soil’s structure that deter-mines the hydraulic conductivity of the bulk soil.

It is only in materials that show behavior similar to that depicted in Fig 2athat continuum physics, such as that implied by Darcy’s law, can be appliedmacroscopically without difficulty to soil water flow problems In materials such

as that illustrated in Fig 2b, boundary conditions at the surfaces of the aggregatesand fissures affect the flow patterns throughout the soil region However, for satu-rated conditions, so long as sufficiently large volumes are considered, continuumphysics can still be applied to water flows at this larger scale using an appropriatevalue of hydraulic conductivity measured on the bulk soil

B Heterogeneity

Because of the complex geometry of the pore system of soils, there is an inherentheterogeneity at pore size dimensions that is not observed when measurementsare made on volumes containing a large number of pores Soil heterogeneity usu-ally implies variations of soil properties between soil volumes containing such

a large number of pores Such heterogeneity occurs at many scales in the ing progression:

follow-Particle→ aggregate → pedal/fissure → field → regional

Fig 2 Measurement of soil water content (a) of a saturated ‘‘uniform’’ soil and (b) of

a saturated soil with superimposed macrostructure (r.e.v ⫽ representative elementaryvolume)

The objective in making measurements of hydraulic conductivity is to enablequantitative predictions of soil water flows under given conditions In a soil show-ing heterogeneity at various scales, different values of hydraulic conductivity ap-ply at different spatial scales and need to be obtained by appropriate measurementtechniques For example, the calculation of water movement to roots requiresmeasurements at the scale of the soil aggregates, whereas the calculation of theflow to land drains in the same soil requires measurements at a much larger scalethat takes into account the flow through fissures For hydrological purposes mea-surements need to be made at an even larger scale in order to consider flows at thefield or regional scale.

The discussion so far has considered soil heterogeneity as stochastic so thatmeasurements of physical properties can be made on a sample larger than somerepresentative elementary volume However, changes in soil occur often abruptly

or as a trend, that is, in a deterministic manner One particularly important aspect

of soil variability occurs with the variation of the soil with depth This has a found effect on field soil water regimes There is often a gradual change of soilproperties with depth that makes it impossible to define a representative elemen-tary volume as previously described In such cases it is assumed that Eq 1 definesthe hydraulic conductivity; hence with vertical flow in soils with a hydraulic con-

pro-ductivity K(z) varying with the height z, we have

v

dh/dz

where v is the vertical flow velocity; that is, we assume the soil to be a continuum

with properties varying with depth

C Equivalent Hydraulic Conductivity

As noted in Sec I, the measurement of the flow that occurs with imposed ary conditions in a uniform soil allows the determination of the hydraulic conduc-tivity For a nonuniform soil the measurement gives an equivalent hydraulic con-ductivity value for the flow region with the given imposed boundary conditions;that is, a value of hydraulic conductivity that would give the measured flow underthe same conditions if the soil were uniform

bound-If the hydraulic conductivity varies spatially so that K ⫽ K(x, y, z), the metic and harmonic mean values Kaand Khof a unit cube of soil are given by

It can be shown that (Youngs, 1983a)

where Keis the equivalent hydraulic conductivity that would actually be measured

in any given direction Since

where Kgis the geometric mean value, this result is in keeping with the fact thatthe geometric mean is often taken as the equivalent hydraulic conductivity valuefor groundwater flow computations For an isotropic soil it can be argued (Youngs,1983a) that

3 2

The measurement of hydraulic conductivity by any method gives an lent value for the particular flow pattern produced in a uniform soil by the bound-ary conditions used in the measurement The value will be different for differentboundary conditions if the soil varies spatially For example, strata of less per-meable soil at right angles to the direction of flow, that is strata coinciding ap-proximately with the equipotentials, reduce the value significantly, whilst morepermeable strata have little effect When, however, such strata are in the direction

equiva-of flow, the reverse is the case The dependence equiva-of the equivalent hydraulic ductivity value on the boundary conditions of the flow region has been furtherdemonstrated in calculations of flow through an earth bank with a complex spatialvariation of hydraulic conductivity (Youngs, 1986)

con-Hydraulic conductivities obtained by methods employing any boundaryconditions will give correct predictions when used in computations of ground-water flows in uniform soils However, the accuracy of predictions in a non-uniform soil will be dependent on the relevance of the measured equivalenthydraulic conductivity If the measurement imposes boundary conditions that pro-duce flow patterns very different from those of the flows to be calculated, then thepredictions will lack accuracy For accurate predictions the pattern of flow in themeasurement must approximate as near as possible to that of the problem, sincelocal variations of hydraulic conductivity can distort flows profoundly

Thus the measurement of hydraulic conductivity is not a simple matter whenthe soil is nonuniform Methods used to make measurement in such soils must beconditioned by the purpose for which they are made Otherwise values obtainedare of little relevance Unless otherwise stated, the methods described in this chap-ter, as in other reviews of methods (Reeve and Luthin, 1957; Childs, 1969; Bou-wer and Jackson, 1974; Kessler and Oosterbaan, 1974; Amoozegar and Warrick,1986), assume that the soil is uniform and isotropic; that is, it is assumed that themeasurements are on flow regions made up of several representative elementaryvolumes with no preferential direction

III LABORATORY MEASUREMENTS

A General Principles

Many laboratory measurements of hydraulic conductivity on saturated samples ofsoils essentially repeat Darcy’s original experiments described in Sec I The prin-ciples that apply for soil samples taken from the field are the same as those for thesands used by Darcy The soil is removed from the field, hopefully undisturbed,

so as to form a column on which measurements can be made, with the sides closed by impermeable walls With the column of soil standing on a permeablebase, the soil is saturated and the surface ponded so that water percolates throughthe soil The soil water pressure head in the soil is measured at positions down thecolumn, and the rate of flow of water through the soil is measured The hydraulicconductivity is the rate of flow per unit cross-sectional area per unit hydraulic headgradient An arrangement used for measuring hydraulic conductivity is known as

en-a permeen-ameter While gren-avity is the usuen-al driving force for flow in permeen-ameters,

use can be made of centrifugal forces to increase the hydraulic head gradientswhen measuring the hydraulic conductivity of saturated low permeability soils(Nimmo and Mellow, 1991)

In addition to methods that involve measurements on a completely saturatedmaterial, there are other methods that involve wetting up an unsaturated samplefrom a surface maintained saturated at zero soil water pressure These methodsutilize infiltration theory (described inChap 6) in order to obtain the hydraulicconductivity of the saturated soil from measurements on the rate of uptake ofwater by the soil

B Collection and Preparation of Soil Samples

For loosely bound soil materials such as sands and sieved soils that are often used

in various tests, care has to be taken to obtain uniform packing of columns onwhich measurements are to be made If the material is not packed uniformly asthe column is filled, separation of different-sized particles can occur, resulting in

a column with spatially variable hydraulic conductivity; even columns of coarsesand can pack to give a two-fold variation of hydraulic conductivity down thecolumn (Youngs and Marei, 1987) In filling columns it is useful to attach a shortextension length to the top of the column and fill above the top, pouring continu-ously but slowly while tamping to obtain a uniform density The material in thetop extension is then removed, leaving the bottom part for the measurement Forgranulated materials with particles passing through a 2 mm sieve, the representa-tive elementary volume is small enough to allow columns of small diameter,

100 mm or less, to be used

The taking of field soil samples requires great care so as to obtain samples

as near representative of the field soil as possible The size of sample required

cannot easily be inferred from visual inspection because fine cracks in soils, thatcontribute largely to the hydraulic conductivity of a soil, may not be noticed Inpoorly structured soils small samples of cross-sectional area 0.01 m2or less can

be representative for such purposes as groundwater-flow calculations In highlystructured soils the size of a sample that is representative for a measurement willdepend on the purpose for which the measurement is required Small samples ofthe size of those suitable for poorly structured soils might suffice for some pur-poses, for example for studies on water movement in the soil matrix betweencracks in a fissured soil, but for groundwater-movement predictions generally amuch larger sample that includes the highly conducting cracks and fissures is re-quired Cylindrical samples 0.4 m in diameter and 0.6 m high have been used(Leeds-Harrison and Shipway, 1985; Leeds-Harrison et al., 1986) For specialpurposes larger ‘‘undisturbed’’ samples can be obtained as for lysimeter studies(Belford, 1979; Youngs, 1983a), typically 0.8 m in diameter

Soil samples can be collected in large-diameter PVC or glass fiber cylinders

A steel cutting edge is first attached to one end and the sample taken by jackingthe cylinder into the soil hydraulically While samples are usually taken vertically,horizontal samples can also be taken As the sampling cylinder is forced into thesoil, the surrounding soil is removed to lessen resistance to passage When therequired sample is contained in the cylinder, the surrounding soil is dug away to

a greater depth to allow a cutting plate to be jacked underneath, separating thesample from the soil beneath The sample is then removed to the laboratory, cov-ered by plastic sheeting in order to retain moisture In the laboratory the upper andlower faces are carefully prepared by removing any smeared or damaged surfacesbefore saturating the samples for the hydraulic conductivity measurements by in-filtrating water through the base to minimize air entrapment

While taking and removing the sample, soil disturbance or shrinkage mayoccur, notably with the soil coming detached from the side of the sampling cylin-der A seal can be made by pouring liquid bentonite down the edge The wetting

of the sample will swell the soil and make the seal watertight

An alternative method of preparing a sample for hydraulic conductivitymeasurements has been devised by Bouma (1977) A cylindrical column of soil issculptured in situ so that the column is left in the middle of a trench Plaster ofParis is then poured over it to seal the sides The column can then either be cutfrom the base and removed to the laboratory for measurements of hydraulic con-ductivity, both in saturated and unsaturated conditions, or alternatively left in placefor measurements to be made in the field A cube of soil is sometimes cut (Boumaand Dekker, 1981) so that flow measurements can be made in different directionsafter the removal of the plaster from the appropriate faces, allowing the compo-nents of hydraulic conductivity in the different directions to be obtained in aniso-tropic soils In a modification of the method (Bouma et al., 1982) a cube of soil is

carved around a tile drain so that measurements of hydraulic conductivity can bemade in this sensitive region in drained lands.

C Constant Head Permeameter

The constant head permeameter uses exactly the same arrangement as Darcy used

in 1856 as illustrated inFig 1 The soil column is supported on a permeable basesuch as a wire gauze or filter, or sometimes a sand table Water flows through thecolumn from a constant head of water on the soil surface and is collected formeasurement from an outlet chamber attached to the base Slichter (1899) rec-ommended that soil water pressures be measured within the soil column since henoted that ‘‘there appears sudden reduction in pressure as the liquid enters thesoil.’’ The error arising from not accounting for this reduction is considered to be

of no great importance today because of the recognition of the true degree ofaccuracy that can be expected for hydraulic conductivity values due to inhomo-geneities in most soils The hydraulic conductivity is given from the measure-ments by

QL

A Dh

where Q is the flow rate, L the length of the column, A its cross-sectional area,

andDh the head difference causing the flow In Eq 12, as with all formulae for K

in this chapter, the units of K are the same as the units used for length and time

for the quantities on the right hand side of the equation The measurements madeusing a constant head permeameter are interpreted as hydraulic conductivity val-ues assuming the soil to be uniform; that is, equivalent hydraulic conductivityvalues are inferred from measurements of the hydraulic conductance between thelevels at which the measurements of head are made

Errors often occur because of preferential boundary wall flow between thesoil and the sides of the permeameter This can be reduced by separately collectingand measuring the throughput from the central area of the sample (McNeal andRoland, 1964)

Youngs (1982) has described an alternative technique to measure the draulic conductivity in saturated soil columns with piezometers that are usuallyused to measure the soil water pressure head down the column, acting as intercep-tor drains, as illustrated inFig 3 With only one of the piezometers at a height Z above the base acting as a drain and removing water at a rate QZ, and with no flow

hy-through the base, the hydraulic conductance CLZbetween the top of the column at

height L and the height Z is given by

Q Z

hL ⫺ h0

where hLis the measured head of the ponded water on the surface and h0is thatmeasured at the base of the column When the conductance profile is obtained bymaking measurements of flows from successive piezometers down the column,the hydraulic conductivity profile is given by

⫺1

d 1

where K(Z) is the hydraulic conductivity at height Z This technique therefore can

be used (Youngs, 1982) to obtain the variation of hydraulic conductivity withdepth on a soil monolith contained in a lysimeter

D Falling Head Permeameter

The falling head permeameter is similar to the constant head permeameter cept that, instead of maintaining a constant head of water on the surface of the soil

ex-Fig 3 Measurement of hydraulic conductivity profiles down soil monoliths using ceptor drains

inter-sample, no water is added after a head is applied initially to the soil surface, andthe changing level of the head is observed as the water percolates through thesample Such an arrangement is shown in Fig 4 Magnification of the rate of fall

of the standing head is achieved by containing it in a tube of smaller

cross-sectional area A⬘ than the cross-cross-sectional area A of the soil sample With the height

of the water level h0(measured from the level of water in a manometer measuring

the head at the base of the column) at time t0falling to h1at time t1, the hydraulicconductivity is given by

Fig 4 Falling head permeameter

A variation of the falling head permeameter is the oscillating permeameter(Childs and Poulovassilis, 1960) This utilizes the passage of water to and frothrough the soil sample contained in a limited volume of water, very little in ex-cess of that required to saturate the pore space Such a small quantity of waterquickly comes to chemical equilibrium with the soil without affecting greatly itschemical composition, therefore remaining in equilibrium throughout the test,however long its duration Water flows through the saturated soil sample contained

in a tube under a head of water at the base of the column sinusoidally varyingabout a mean position This and the head of water standing on the surface of thesoil sample are recorded with time, for example with pressure transducers After

a few cycles, the two heads oscillate out of phase and with different amplitudes If

the amplitude of the forcing head is H0and that on the surface of the soil sample

is h0, the phase angleb is given by

The hydraulic conductivity can thus be found from the phase angle obtained either

by direct measurement or from measurements of the amplitudes of the heads andthe use of Eq 16

F Infiltration Method

Infiltration theory shows that the infiltration rate from a ponded surface into a longvertical column of uniform porous material eventually approaches a constant rate,equal to the hydraulic conductivity of the saturated material The approximate

Green and Ampt (1911) theory of infiltration gives the infiltration rate di/dt when the wetting front has advanced to a depth Z as

by observing the position of the wetting front while measuring the infiltration rate

from a ponded surface However, the fact that a linear plot is found when plotting

di/dt against 1/Z should not be taken as proof that the column is uniform, since it

has been found (Childs, 1967; Childs and Bybordi, 1969; Youngs, 1983b) thatsuch a linear plot is obtained in certain situations when there is a decrease inhydraulic conductivity with depth The intercept in this case is less than if the soilwere uniform, and it can even become negative The method is therefore onlyreliable if the soil profile is known to be uniform within the wetted depth, and thismay be difficult to ascertain

G Varying Moment Permeameter

The varying moment permeameter (Youngs, 1968a), although originally used tomeasure the hydraulic conductivity of unsaturated soils, provides a quick method

of measuring the hydraulic conductivity of soil samples that are initially rated Water is infiltrated horizontally at a positive pressure head into columns ofthe unsaturated soil, and the rate of change of moment of the advancing waterprofile about the plane through which infiltration takes place is measured It can

unsatu-Fig 5 Plot of the rate of infiltration di/dt against the reciprocal of the depth of wetting front 1/Z Solid line: uniform soil; broken line: soil with hydraulic conductivity decreasing

with depth

be shown that this rate of change of the moment is equal to the integral of thehydraulic conductivity with respect to the soil water pressure along the column

multiplied by the cross-sectional area A of the column Thus

surface and that in the soil not yet reached by the advancing water front,

respec-tively, and K ⬘(p) is the hydraulic conductivity of the soil that is a function of the soil water pressure head p in unsaturated soils but equal to K for saturated soils.

By measuring dM/dt for different pressure heads p0of infiltrating water, the draulic conductivity of the saturated soil can be obtained using Eq 19 from the

hy-slope of the plot of dM/dt against p0

IV FIELD MEASUREMENTS BELOW A WATER TABLE

A General Principles

In situ measurements of hydraulic conductivity below the water table provide themost reliable values for use in estimating groundwater flows, especially when theysample large volumes of soil Techniques usually employ unlined or lined wellssunk below the water table and involve measurements of flow into or out of thewells when the water levels in them are perturbed from the equilibrium The hy-draulic conductivity values are calculated from the solution of the potential prob-lem for the flow region with the imposed boundary conditions If no analyticalsolution is available, recourse can be made to electric analogs or numerical meth-ods to obtain solutions The various well techniques for measuring the hydraulicconductivity of soils when the water table is near the soil surface are given par-ticular attention in books on land drainage (Reeve and Luthin, 1957; Bouwer andJackson, 1974) where values are required for design purposes Since all gave sat-isfactory results in a comparison of well methods in a hydraulic sand tank (Smilesand Youngs, 1965), it would appear that the choice of method depends largely onsite conditions, resources available, and individual preference However, in somemethods the flow is predominantly horizontal while in others it is vertical, so that

if the soil is suspected of being anisotropic, the method to be employed must takeinto consideration the direction of flow in the region under investigation

For satisfactory measurements, wells must be large enough to allow a resentative volume of soil to be sampled However, it is not easy to deduce thevolume of soil sampled in a given measurement Some indication of this volumemight be obtained from the volume traced out by 90% (say) of the streamtubes for

rep-a 90% (srep-ay) reduction in herep-ad It obviously increrep-ases with the size of well used Itwill also depend on other geometrical factors of the flow system; for example, thearea of the well walls through which water can flow, and the spacing of wells in

a multiwell system

Well radii of 50 mm or more are typically used The wells are best madewith post augers,* and special tools can be used to form the holes into an exactcylindrical shape Some difficulties may be encountered doing this (Childs et al.,1953) First, there is the common problem of making holes when the soil is stony;stones may have to be cut with chisels during the operation Secondly, there is theproblem of unstable soils slumping below the water table; permeable liners can beused to alleviate this problem And thirdly, in clay soils there is the problem ofsmearing of the sides of the walls of the wells, thus creating surfaces of low con-ductance that restrict flow; to lessen this effect the wells are first emptied to allowinflowing water to unblock the pores before measurements are made

While the use of wells gives a practical and convenient method of providing

an arrangement of groundwater flows that can be analyzed to give hydraulic ductivity values, any arrangement of sinks and/or sources that produce flows thatcan be analyzed may be used for the purpose For example, land drains, whichsample much larger regions of soil than can be sampled with wells, can be used

con-as permeameters (Hoffman and Schwab, 1964; Youngs, 1976)

B Auger-Hole Method

In the auger-hole method of determining the hydraulic conductivity of a soil, anunlined cylindrical hole is made below the water table (Fig 6) The position ofthe water table is found by allowing the water in the hole to return to its equilib-rium water level The water level in the hole is then lowered by removing water

by pumping or bailing, and its rate of rise is observed as it returns to equilibrium.Alternatively, the water level can be raised by adding water, and measurementsmade on the falling level This is useful when the equilibrium depth of water inthe hole is small The hydraulic conductivity is calculated from measurementstaken during the early stage of return before there is appreciable water table draw-down around the hole, using the formula

* A comprehensive range of augers are given in the catalogue of Eijkelkamp Agrisearch Equipment

bv, P.O Box 4, 6987 ZG Gesbeek, The Netherlands.

of different hydraulic conductivity below the bottom of the hole, and the depth y, all expressed as a fraction of the depth H of the water in the hole when in equilib- rium with the water table; thus we can write C ⫽ C(r/H, s/H, y/H).

Formulae for obtaining the factor C in Eq 20 have been given by Diserens

(1934), Hooghoudt (1936), Kirkham and van Bavel (1949), and Ernst (1950) An

exact mathematical solution in the form of an infinite series was obtained for C

by Boast and Kirkham (1971) Their results are presented inTable 3 Ernst’s mulae may be written:

Fig 6 Geometry of the auger-hole method

2 1 215 204 193 178 155 143 137 135 133 133 131 123 1060.75 227 216 208 195 172 160 154 152 152 151 148 140 1230.5 271 261 252 240 218 203 196 194 194 193 190 181 161

5 1 60.2 56.3 53.6 49.6 44.9 42.8 41.9 41.5 41.2 40.1 37.60.75 63.6 60.3 57.9 54.3 47.6 46.6 46.4 45.9 44.8 42.10.5 76.7 73.5 71.1 67.4 62.5 60.2 59.1 58.8 58.3 57.1 54.1

10 1 21.0 19.6 18.7 17.5 16.4 15.8 15.5 15.5 15.4 15.2 14.60.75 22.2 21.0 20.2 19.1 18.0 17.4 17.2 17.2 17.1 16.8 16.20.5 27.0 25.9 24.9 23.9 22.6 22.0 21.8 21.7 21.6 21.3 20.6

20 1 6.86 6.41 6.15 5.87 5.58 5.45 5.4 5.38 5.36 5.31 5.170.75 7.27 6.89 6.65 6.38 6.09 5.97 5.9 5.89 5.88 5.82 5.670.5 8.90 8.51 8.26 7.98 7.66 7.52 9.5 7.44 7.41 7.35 7.16

50 1 1.45 1.37 1.32 1.29 1.24 1.22 1.21 1.19 1.180.75 1.54 1.47 1.42 1.39 1.35 1.32 1.31 1.30 1.280.5 1.90 1.82 1.79 1.74 1.69 1.67 1.66 1.65 1.61

100 1 0.43 0.41 0.39 0.39 0.38 0.37 0.37 0.37 0.360.75 0.46 0.44 0.42 0.42 0.41 0.41 0.41 0.39 0.390.5 0.57 0.54 0.53 0.52 0.51 0.51 0.51 0.50 0.50

Source: After Boast and Kirkham (1971).

most purposes; however, Ploeg and van der Howe (1988) pointed out that valuesusing these formulae can differ from Boast and Kirkham’s values by as much as

25% Equations 21 and 22 give the hydraulic conductivity K in the same units as those for the rate of rise of the water level dy/dt, as are the values of C given in

Table 3; published presentations for the shape factor usually require dy/dt values

to have units cm s⫺1to give K in units m d⫺1, and this can give rise to confusion.Measurements are sometimes made using seepage into large holes below the watertable, a method sometimes referred to as the ‘‘pit-bailing’’ method Then shape

factors are required for r ⬎ H, a situation not encountered with the normal use of

auger holes These have been given by Boast and Langebartel (1984)

The flow into auger holes is primarily horizontal, so that in anisotropic soilsthe results obtained approximate to the horizontal component of the hydraulicconductivity Although the method has been developed, as have most other meth-ods, for use in uniform soils, it can be used in layered soils to estimate the hydrau-lic conductivity in the different layers (Hooghoudt, 1936; Ernst, 1950; Kessler andOosterbaan, 1974)

C Piezometer Method

A piezometer is an open-ended pipe driven into the soil that measures the

ground-water pressure below the ground-water table The piezometer method uses pipes or linedwells with diameters usually much larger than for those used for groundwaterpressure measurements, sunk below the water table, with or without a cavity atthe bottom, as illustrated in Fig 7 The cavity is usually cylindrical in shape,although other shapes, for example hemispherical, can be used As in the auger-hole method, after the water level in the well has come into equilibrium with thewater table, it is depressed by pumping or bailing and its rate of rise observed as

it returns to equilibrium The hydraulic conductivity is then given by

A(d/r, w/r, s/r).

Shape factors obtained with an electric analog were given by Frevert andKirkham (1948) More accurate values were presented by Smiles and Youngs(1965), and a comprehensive table of accurate values, reproduced inTable 4, wasgiven by Youngs (1968b) As shown by these values, so long as the cavity is not