Soil and Environmental Analysis: Physical Methods - Chapter 6 pptx

Infiltration of water into soil can occur asa result of there being a pond of free water on the soil surface, so that the soilcontrols the amount infiltrated, or water can be supplied to t

Infiltration, because it is both a key soil process and an important logical mechanism, has been twice studied: once by soil physicists and again byhydrologists Historically, their approaches have been quite different In the for-mer case, infiltration was the prime focus of detailed study of small-scale soilprocesses, and in the latter, infiltration was just one mechanism in a complicatedcascade of processes operating across the scale of a catchment Latterly, access topowerful computers has meant that hydrologists have been able to incorporate thesoil physicists’ detailed mechanistic descriptions of infiltration into their hydro-logical models of watershed functioning This has increased the need to measurethe parameters that control infiltration.

hydro-239

To the memory of John Philip (1927–1999), for without his endeavors this would have been a very short chapter.

In this chapter, I first describe the development of one-dimensional pondedinfiltration theory, discussing both analytical and quasi-analytical solutions Inpassing, I mention empirical descriptions of infiltration before discussing the keydevelopment of a simple algebraic expression for infiltration that employs physi-cally based parameters Emphasis is placed on theoretical approaches, for theycan predict infiltration through having parameters capable of field measurement.The preeminent roles of the physical state of the soil surface and the nature of theupper boundary condition are stressed Infiltration of water into soil can occur as

a result of there being a pond of free water on the soil surface, so that the soilcontrols the amount infiltrated, or water can be supplied to the surface at a givenrate, say by rainfall, so the soil only controls the profile of wetting, not the amountinfiltrated

Next, I show how measurement of infiltration can be used, in an inversesense, to determine the soil’s hydraulic properties In this way, it is possible topredict infiltration into the soil, and general prediction of water movement throughsoil can also be made using these measured properties Hydraulic interpretation ofthe theoretical parameters in the governing equations is outlined, as is the impact

of infiltration on solute transport through soil A list is presented of the variousdevices that have been developed to measure, in the field, the soil’s capillary andconductive properties that control infiltration An outline of their respective merits

is presented, as is a comparative ranking of utility Finally, I conclude with a sentation of some illustrative results and identify some issues that still remainproblematic

pre-Elsewhere in this book, there are complementary chapters on measurement

of the soil’s saturated conductivity (Chap 4) and the unsaturated hydraulic ductivity function (Chap 5) Here the emphasis is on devices capable of in situobservation of infiltration, and the measurement in the field of those saturated andunsaturated properties that control the time course, and quantity, of infiltration

A One-Dimensional Ponded Infiltration

Significant theoretical description of water flow through a porous medium began

in 1856 with Henry Darcy’s observations of saturated flow through a filter bed ofsand in Dijon, France (Philip, 1995) Darcy found that the rate of flow of water,

J (m s⫺1), through his saturated column of sand of length L (m), was proportional

to the difference in the hydrostatic head, H (m), between the upper water surface

and the outlet:

DH

in which Darcy called K ‘‘un coefficient de´pendent du degre´ de perme´abilite´ du sable.’’ We now call this the saturated hydraulic conductivity Ks(m s⫺1) (Chap 4).

In 1907, Edgar Buckingham of the USDA Bureau of Soils established the retical basis of unsaturated soil water flow He noted that the capillary conduc-tance of water through soil, now known as the unsaturated hydraulic conductivity,was a function of the soil’s water content,u (m3m⫺3), or the capillary pressure

theo-head of water in the soil, h (m) The characteristic relationship between h andu(Chap 3) was also noted by Buckingham (1907), so that he could write K⫽ K(h),

or if so desired, K ⫽ K(u) The total head of water at any point in the soil, H, is the sum of the gravitational head due to its depth z below some datum, conve-

niently here taken as the soil surface, and the capillary pressure head of water in

the soil, h: H ⫽ h ⫺ z Here, h is a negative quantity in unsaturated soil, due to

the capillary attractiveness of water for the many nooks and crannies of the soilpore system Thus locally in the soil, Buckingham found that the flow of watercould be described by

which identifies the roles played by capillarity, the first term on the right handside, and gravity, the second term These two forces combine to move waterthrough unsaturated soil (Chap 5) In deference to the discoverers of the satu-rated form, Eq 1, and the unsaturated form, Eq 2, the equation describing waterflow at any point in the soil is generally referred to as the Darcy –Buckinghamequation

L A Richards (1931) combined the mass-balance expression that the poral change in the water content of the soil at any point is due to the local fluxdivergence,

tem-⳵u ⫽ ⫺ ⳵J

(3)

冉 冊 冉 冊⳵t z ⳵z t

with the Darcy–Buckingham description of the water flux J, to arrive at the

gen-eral equation of soil water flow,

where t (s) is time Unfortunately, this formula, known as Richards’ equation,

does not have a common dependent variable, foru appears on the left and h on

the right The British physicist E C Childs ‘‘decided to try some other sis that water movement is decided by the moisture concentration gradient [and] that water moves according to diffusion equations’’ (Childs, 1936) Childsand Collis-George (1948) noted that the diffusion coefficient for water in soil

hypothe-could be written as K(u) dh/du From this, in 1952 the American soil physicist

Arnold Klute wrote Richards’ equation in the diffusion form of

冉 冊

This description shows soil water flow to be dependent on both the soil water

diffusivity function D(u), and the hydraulic conductivity function K(u), but this

nonlinear partial differential equation is of the Fokker –Planck form, which is toriously difficult to solve Klute (1952) developed a similarity solution to thegravity-free form of Eq 5, subject to ponding of free water at one end of a soilcolumn

no-Five years later, the Australian John Philip developed a power-series tion to the full form of Eq (5), subject to the ponding of water at the surface of

solu-a verticsolu-al column of soil, initisolu-ally solu-at some low wsolu-ater contentun(Philip, 1957a)

This general solution predicts the rate of water entry through the soil surface, i (t)

(m s⫺1), following ponding on the surface The surface water content is tained at its saturated value, us The cumulative amount of water infiltrated is

main-I (m), being the integral of the rate of infiltration since ponding was established.

As well, I can be found from the changing water content profile in the soil,

where the sorptivity S (m s⫺1/2) and the coefficients A, A3, A4, can be

itera-tively calculated from the diffusivity and conductivity functions, D(u) and K(u) The form of Eq 7 indicates that I increases with time, but at an ever-decreasing rate In other words, the rate of infiltration i ⫽ dI/dt is high initially, due to the

capillary pull of the dry soil But with time the rate declines to an asymptote.Special analytical solutions can be found for cases where certain assump-tions are made about the soil’s hydraulic properties When the soil water diffusiv-

ity can be considered to be a constant, and K varies linearly withu, an analyticalsolution is possible This is because Eq 5 becomes linearized (Philip, 1969) and

so there is an analytical solution for infiltration into a soil whose hydraulic erties can be considered only weakly dependent onu At the other end of the scale

prop-of possible behavior, Philip (1969) presented an analytical solution for a soilwhose diffusivity could be considered a Dirac d-function, in which D is zero,

except at us where it goes to infinity For the analytical solution, this so-called

delta-soil, or Green and Ampt soil, also needs to have K ⫽ Ksatus, and K⫽ 0 forall otheru

Philip and Knight (1974) showed that the Dirac d-function solution duces a rectangular profile of wetting (shown later inFig 4) It was this geometricform of wetting that was used as the physical basis for Green and Ampt’s (1911)functional model of infiltration If a rectangular profile of wetting is assumed, then

pro-behind the wetting front located at depth zf,u(z)⫽ us, for 0⬍ z ⬍ zf; and beyondthe wetting front,u(z)⫽ un, z ⬎ zf If the soil has a shallow free-water pond at

the surface, and if it is considered that there is a wetting front potential head, hf,

at zf, then the Darcy–Buckingham law (Eq 2) predicts the rate of water ing through the surface as

quasi-analyti-Knight (1974) using a flux– concentration relationship, F( Ѳ), that hides much of

the nonlinearity in the soil’s hydraulic properties of D and K Here Ѳ is the

nor-malized water content

Considering these mathematical solutions to the flow equation for

infiltra-tion I, subject to ponding, Childs (1967) commented that ‘‘further investigainfiltra-tions

to throw yet more light on the basic principles of the flow of water tend to bematters of crossing t’s and dotting i’s serious difficulties remain in the path ofpractical application of theory [being] held back by the inadequate develop-ment of methods of assessment of the relevant parameters.’’

These analytical or quasi-analytical solutions are seldom used to predictinfiltration directly from the soil’s hydraulic properties The theory and its de-velopment are presented here, for they identify the underpinning physics of infil-tration Nowadays, however, the current power of computers, coupled with theburgeoning growth of numerical recipes for solving nonlinear partial differen-tial equations, has meant that brute-force numerical solutions to Eq 5 for infil-

tration are easily obtained, provided that the functional properties of D and K

are known Thus given a knowledge of the soil’s hydraulic properties, it is areasonably straightforward exercise to predict infiltration, either analytically ornumerically

Infiltration measurements hold the key to obtaining in situ characterization

of these soil properties It is possible to use Eq 7 or the like in an inverse sense,

to use infiltration observations to infer the soil’s hydraulic character The time

course of water entry into soil, I(t), depends, as Eq 7 shows, on coefficients that relate to the hydraulic properties of D(u) and K(u) Infiltration can quite easily be measured in the field Hence, I will proceed to show how this measurement of I

can be used to extract in situ information about the soil’s capillary and conductiveproperties

1 Empirical Descriptions

Before passing to the discussion of the developments that have led to the use ofmeasurements to predict one-dimensional infiltration behavior, I sidetrack a little

to review some of the empirical descriptions of the shape of i(t) This digression

is simply to complete our historical record of the study of infiltration, for suchempirical equations have little merit nowadays The Kostiakov –Lewis equation,

I ⫽ at b(Swartzendruber, 1993), has descriptive merit through its simplicity, yetcomparison with Eq 7 indicates the inadequacy of this power-law form, for in

reality b needs to be a function of time The hydrologist Horton (1940) posed that the decline in the infiltration rate could be described using i ⫽ i⬁⫹

pro-(io⫺ i⬁) exp(⫺bt), where the subscripts o and ⬁ refer to the initial and final rates

If description is all that is sought, then the three-term expression will performbetter due to its greater fitting ‘‘flexibility.’’ In neither case do the fitted parameters

have physical meaning, so care needs to be exercised in their extrapolation beyondthe fitted range.

2 Physically Based Descriptions

However, the two-term algebraic equation of Philip (1957b) is different from otherempirical descriptions It rationally incorporates physical notions Simply by trun-cating the power series of Eq 7, Philip (1957a) arrived at the expression for theinfiltration rate of

1 ⫺1/2

2

which will be applicable at short and intermediate times However at longer times,

we know for ponded infiltration that

→

t ⬁

The means by which these two expressions can best be joined has worried some

soil physicists, with A/Kshaving been found to be bracketed between 1 ⫺ 2/pand 2/3, but probably lying nearer the lower limit (Philip, 1988) However, asPhilip (1987) noted, relative to practical incertitudes, a two-term algebraic expres-sion often suffices, with both terms having physical meaning, plus correct short-and long-time behavior, viz

1 ⫺1/2

2

The coefficient of the square-root-of-time term, the sorptivity S, integrates the

capillary attractiveness of the soil Mathematically, as we will see later, this can

be linked to the soil water diffusivity function D(u) The role of capillarity

de-clines with the square root of time The second term, which is time independent,

is the saturated conductivity Ks, which is the maximum value of the conductivity

function K(h) that occurs when the soil is saturated, h⫽ 0 If the soil is initially

saturated (S⫽ 0), or if infiltration has been going on for a long time, then gravity

will alone be drawing water into the soil at the steady rate of Ks Eq 15 is aptlynamed Philip’s equation

To understand Eq 15 is to understand the basics of infiltration

B Multidimensional Ponded Infiltration

However, a one-dimensional geometric description is not always appropriate Forexample, infiltration into soil might be from a buried and leaking pipe, or it might

be from a finite surface puddle of water In these cases, the physics previously

described above must now be referenced to the geometry of the source The spective roles of capillarity and gravity in establishing the rate of multidimen-

re-sional infiltration, vo(t) (m s⫺1), through a surface of radius of curvature ro(m),

are now more complex Following Philip (1966), let m be the number of spatial

dimensions required for geometric description of the flow The geometry depicted

in Fig 1 might be a transverse section through a cylindrical channel This would

be a 2-D source with m⫽ 2 Or it could be a diametric cut through a spherical

pond that would be represent a 3-D geometry So here m⫽ 3 The more curved

the wetted perimeter of the source, the smaller is ro, and the greater is the role of

the soil’s capillarity relative to gravity In the limit as ro→ ⬁, the geometry

be-comes one-dimensional (m ⫽ 1), and the source spreads right across the soil’ssurface

As already noted, if the soil is considered to have a constant diffusivity D, and a linear K(u), then ananalytical solution can be found for one-dimensional

infiltration because the governing equation is linearized This also applies to

multidimensional infiltration, if the flow description of Eq 5, which has m⫽ 1,

is written in a form appropriate to a flow geometry with either m ⫽ 2 or m ⫽ 3

(Philip, 1966) Philip’s (1966) linearized multidimensional infiltration results areillustrative and are presented in Fig 2 There, the infiltration rate through the

wetted perimeter, vo, is normalized with respect to the saturated conductivity Ks,

and the time is normalized by a nondimensional time, tgrav⫽ (S/Ks)2 To allow

Fig 1. An idealized multidimensional infiltration source, in which water infiltrates into

the soil through a wetter perimeter of radius of curvature ro Capillarity and gravity bine to draw water into the dry soil

com-easy comparison, the radius of curvature is also normalized, and given as Ro⫽

ro[Ks(us⫺ un)2/pS2]

For the one-dimensional case in Fig 2 (m⫽ 1), the infiltration rate can beseen to fall, as the effects of capillarity fade with the square, and higher, roots of

time (Eq 7) At around t/ptgrav, the infiltration rate is virtually the asymptote of

vo ⫽ Ks Such behavior is predicted by Eq 15 Two cases are given for

two-dimensional flow from cylindrical channels, m⫽ 2 For the tightly curved channel

(Ro⫽ 0.05), the effect of the source geometry on capillarity is clearly seen, and

the infiltration rate is nearly two times Ksat dimensionless time 10 For the

less-curved channel (Ro⫽ 0.25), the geometry-induced enhancement of capillary

ef-fects is correspondingly less In the three-dimensional case (m⫽ 3), for the curved

spherical pond with Ro⫽ 0.05, the effect of capillarity is so enhanced by the 3-Dsource geometry that the infiltration rate through the pond walls achieves a steady

flux of over 5Ksby unit time

Whereas infiltration in one dimension (m ⫽ 1) gradually approaches Ks, the

source geometry in 2-D and 3-D (m⫽ 2 and 3) ensures that the infiltration rate

finally arrives at a true steady-state value, v⬁ In Fig 2, the time taken to realise v⬁

Fig 2. The normalized temporal decline in the rate of infiltration through the ponded

surface into a one-dimensional soil profile (m⫽ 1), and from two cylindrical channels

(m ⫽ 2) of contrasting radii of curvature (ro), as well as from two spherical ponds (m⫽ 3)

of different radii To allow comparison of one-, two-, and three-dimensional flows, theinfiltration rate, time, and radii of source curvature have all been normalized (Redrawnfrom Philip, 1966.)

is more rapid in 3-D than it is for m⫽ 2 This achievement of a steady flow rate

in 3-D is, as we will see later, a major advantage for certain devices in the fieldmeasurement of infiltration

In this device-context, it is useful to consider in more detail the

three-dimensional flow from a shallow, circular pond of water of radius ro The history

of the study of this problem is given in Clothier et al (1995), so here we need onlyconcern ourselves with the seminal result of Wooding (1968) The New ZealanderRobin Wooding was concerned about the radius requirements for double-ring in-filtrometers (shown later inFig 5), and he found a complex-series solution for thesteady flow from a shallow, circular surface pond of free water However, he didnote that the steady flow could be approximated by a simple equation in whichcapillary effects were added to the gravitational flow in inverse proportion to thelength of the wetted perimeter of the pond,

4fs

pro

Here the sum effect of the soil’s capillarity is expressed in terms of the integrals

of the hydraulic properties of D and K, the so-called matric flux potential

This formulation allows Wooding’s equation (Eq 16) for the steady volumetric

infiltration from the circular pond, Q⬁⫽ pro v⬁(m3s⫺1), to be written as

C Boundary Conditions

Thus far, we have only considered the case where water is supplied by a surfacepond of free water, namely

u(0, t) ⫽ us h(0, t) ⫽ 0 z ⫽ 0, t ⱖ 0 (21)This is termed a constant-concentration boundary condition and known mathe-matically as a first-type or Dirichlet boundary condition This is appropriate tocases where water is ponded on the ponded on the soil surface The soil’s hydraulicproperties, and source geometry, determine the rate and temporal decline in infil-tration (Fig 2) The water content at the soil’s surface is always at its saturatedvalue,us.

However, often water arrives at the soil surface as a flux, as might occurduring rainfall, or irrigation In this case, the upper boundary condition is the

Should the flux of water always be less than Ks, then the water content atthe surface will always be less thanus The soil at the surface will remain unsatu-

rated, ho⬍ 0, and all the incident water will enter the soil, with I ⫽ vot.

However, if the rate of water falling on the soil surface exceeds Ks, then

eventually at some time tp, the time to incipient ponding, the soil at the surface

will saturate; ho⫽ 0; uo⫽ us, t ⱖ tp After this incipient ponding, runoff fromthe free water pond can occur, and not all the applied water need enter the soil:

I ⬍ vot, for t ⱖ tp For the case of a constant flux, Perroux et al (1981) found that

a good approximation for the time to ponding was

2

S

2v (vo o ⫺ K )s

So the greater the flux the quicker the soil surface ponds Conversely, the drier the

soil initially, the greater is the capillarity of the soil, the higher is S, and so the

longer can the soil maintain its acceptance of all the applied water

The presence or absence of a surface pond of free water is critical for tration behavior in the macropore-ridden soils of the field This is shown inFig 3

infil-Only free water (ho⬎ 0) can enter surface-vented macropores Thus during

non-ponding flux infiltration, vo⬍ Ks, or prior to the time to ponding, t ⬍ tp, the soil

surface remains unsaturated, ho⬍ 0, so that water does not enter macropores.Rather the water droplets are absorbed right where they land Hence the pattern ofinfiltration and soil wetting is quite uniform, as capillarity attempts to even out

local heterogeneities However, following incipient ponding, t ⬎ tp, a free-waterfilm develops on the soil surface This free water can enter surface-vented macro-

pores, creating preferential flow through the soil, and lead to local variability inthe pattern of soil wetting If the infiltration capacity of the soil, both by matrixabsorption and macropore flow, is exceeded, there is the possibility of local runoffonce the surface storage has been overwhelmed (Dixon and Peterson, 1971).

The magnitude of the flux vorelative to the soil’s Ksis critical in determininginfiltration behavior, and during flux infiltration it is critical to know whether the

time to ponding has been reached The value of tpcan be deduced from a

knowl-edge of the soil’s sorptivity S, and conductivity Ks, given vo (Eq 23) So it is

imperative that S and Ksbe measured for field soils

D Hydraulic Characteristics of Soil

There are three functional properties necessary to describe completely the

hydrau-lic character of the soil: the soil water diffusivity function D(u), the unsaturated hydraulic conductivity function K(h), and the soil water characteristic u(h) How- ever since D ⫽ K dh/du, only two are sufficient to parameterize Eq 5 Whereas it

is possible to measure these functions in the laboratory, albeit with some difficulty,

it is virtually impossible to do so in the field (Chaps 3and5)

Nonetheless, if we were to observe the time course of ponded infiltration in

the field, i(t), then by inverse procedures we should be able to use Eq 15 to infer values of the saturated sorptivity S, and the saturated conductivity Ks In the firstcase, we would then have obtained a measurement of something that integrates

Fig 3. Infiltration of an applied flux of water into soil Left: non-ponding infiltration

when vo⬍ Ks, or ponding infiltration vo⬎ Ksprior to the time to ponding tp Right: pattern

of infiltration after incipient ponding, t ⬎ tp, when the possibility of runoff exists, as doesthe entry of free water into macropores

the soil’s capillarity, and in the second case we would know the maximum value

of the K(h) function Because we know in one case an integral measure, and in the

other a functional maximum, if we were willing to make some assumptions about

functional forms, we could infer the D andK functions from measurements of just

S and Ks, and some observations ofusandun Thus observations of infiltration inthe field can be used to establish the hydraulic characteristics of field soil.Formally, the sorptivity can be written as a complicated integral of the soilwater diffusivity function

us(u ⫺ u ) D(u)n 2

u n F(Ѳ)

where F is the flux– concentration relation of the quasi-analytical solution of

Philip and Knight (1974) (see Sec II.A) Parlange (1975) independently foundsome useful and simple algebraic versions of Eq 24 Eq 24 is difficult to invert

in order that D(u) might be deduced from S However, if we revisit the Kirchhoff

transform of Eq 17, we have the integral of the diffusivity as

us

un

so that by inspection of Eqs 24 and 25, we would expect a relationship between

fsand S2 White and Sully (1987) wrote this as

If we look yet again at Eq 17, we see thatfsis also the integral of the K(h)

function If an exponential conductivity function (Eq 18) is assumed, then

So by monitoring infiltration to infer both Ksand S (Eq 15), and by measuringusandun, Eqs 26 and 28 give us functional descriptions of the soil’s D(u) and K(h).

These capillary and gravity properties allow us to infer some metric characteristics of the soil’s hydraulic functioning Philip (1958) defined amacroscopic, mean ‘‘capillary length’’ lc, which can be written over the range

wer (1964) Note that if the soil’s K(h) is exponential (Eq 18), then Eq 27 shows

us thatlc⫽ a⫺1 Using Eq 28 giveslcin terms of easily measurable quantities,

Eqs 30 and 31 it is possible to use properties measured during infiltration (S and

Ks;usandun) to deduce something dynamic about the magnitude of the pore sizeclass involved in drawing water into the soil Namely,

13.5(us ⫺ u )Kn s

S

E Solute Transport During Infiltration

Water is the vehicle for solutes in soil Here, for simplicity, we consider a soil

lying horizontally with water being absorbed in the x direction During infiltration,

water-borne chemicals are transported into the soil The entry of water into soil is

a hydrodynamic phenomenon: the wetting front rides into the soil on ‘‘top’’ of theantecedent water content,un(Fig 4) For the case of ad-function soil, that is, onepossessing Green and Ampt’s (1911) rectangular profile of wetting, Eq 6 givesthe penetration of the wetting front as

uim(van Genuchten and Wierenga, 1976) In this mobile-immobile case, the solutefront would be further ahead at

Eq 34

So in a fully mobile caseum⫽ us, which is initially dry,un⫽ 0, the wetting frontand the invading inert solute front will be coincident;ᑬ ⫽ 1 If the soil is notinitially dry, then the wetting front will be ahead of the invasion front of the solute,

ᑬ ⬎ 1 If not all the soil’s water is mobile, then the solute will preferentiallyinfiltrate the soil through just the mobile domain, and the solute front may becloser to the wetting front The simple notions contained in Fig 4and Eq 35provide a useful means to model chemical transport processes during infiltration.Later, I will discuss how values ofumandᑬ might be measured and interpreted

In this section, I now consider eight devices that have been developed to measureinfiltration in the field The relative merits of these devices and instruments arelisted inTable 1and discussed later

1 Buffered Rings

The easiest way to observe ponded infiltration in the field is simply to watch therate that water disappears from a surface puddle However, as shown in Fig 1,two factors control infiltration from a pond, capillarity and gravity In order toeliminate the perimeter effects of capillarity, buffered rings have been used so thatthe flow in the inner ring is due only to gravity (Fig 5) By this arrangement, it is

hoped that the steady flux from the inner ring, v⬁, might be the saturated hydraulic

conductivity Ks, since capillary effects would be quenched by flow from the buffer

ring, vo* To determine what size the radius of the inner ring, r1, needs to be

relative to that of the buffer, r2, Bouwer (1961) and Youngs (1972) used an trical-analog approach, whereas Wooding (1968) provided a simple expressionbased on the properties of the soil (Eq 16) The ASTM standard double-ring in-filtrometer has radii of 150 and 300 mm (Lukens, 1981), although the correct ratio

elec-will be soil dependent, and related to the relative sizes of the conductivity K and the sorptivity S (Eq 16) The flows voand vo* can be measured using a Mariottesupply system that maintains a constant head within the rings (Constantz, 1983)

Or more simply, a nail can be pushed into the soil, and a measuring cylinder used

to top-up the water level to it at regular intervals This approach may require a

large amount of water, especially if the soil is dry and has a high S, such that in the buffer ring vo* is large From the measured steady flux it is assumed that v⬁⫽

Ks The role of the buffer ring is to eliminate capillary effects, so this methodprovides only the saturated hydraulic conductivity and leaves unresolved any mea-sure of the soil’s capillarity

device was found as the sum of the first six columns, multiplied by the Information content A high Utility score indicates usefulness, with themaximum range possible being from 150 down to 6

Technicalskillsrequired

Sitedisturbance

Ease ofdataanalysis

Ease oftime–spacereplication

Informationcontent Utility score

2 Single Ring

If a single ring were forced into the soil to some depth, L, then that ring would

confine the flow to the vertical and thereby eliminate the multidimensional fusion created by capillarity Talsma (1969) developed a method whereby it ispossible to measure both the sorptivity and the conductivity A metal ring of a

con-diameter about 300 mm and length L of around 250 mm is pressed into the soil so

as to minimize the disturbance of the soil’s structure A free-board of about 50 mm

is left, and a graduated scale is laid diametrically across the ring, with one end onthe rim and the other on the soil surface The slope of the scale is measured Afixed volume of water is then carefully poured into the ring, and the early-timerate of infiltration is obtained from the descent of the water surface along thesloping scale At very short times, soon after infiltration commences and beforegravitational effects intercede, it is reasonable to assume that the integral form of

Eq 15 can be written as

1/2

→

t 0

so that the sorptivity can be found as the slope of I(公t) Because gravity’s impact

grows slowly, it can be difficult to select the length of period within which to fit

Eq 37 Smiles and Knight (1976) found that plotting (It⫺1/2) against公t allowed

a more robust means of extracting S from the cumulative infiltration data.

Fig 5. Infiltration into soil from two concentric rings pressed gently into the soil The

flow in the outer ring of radius r2, is vo*, and this is presumed to eliminate perimetric

capillary effects so that the steady flux in the inner ring v⬁can be considered Ks

After the initial wetting, typically after about 10 to 15 minutes, Talsma’smethod requires that the ring containing the soil be exhumed and placed on a fine-mesh metal grid A Mariotte device is then used to maintain a small head of water,

ho, on the surface of the soil Once water is dripping out the bottom, the steady

flow rate J can be measured, and Darcy’s law (Eq 1) used to find the saturated hydraulic conductivity Ks

This simple and inexpensive method allows measurement of both the soil’s

capillarity via S and the saturated conductivity of Ks However, extreme care has

to be taken to minimize the disturbance of the soil during insertion In rous soil this will be difficult, and furthermore any macropores that are continuousthrough the entire core will short-circuit the matrix and result in an erroneously

macropo-high value of Ks

3 Twin Rings

With the buffered-ring system, capillarity effects are hopefully eliminated Withthe single-ring technique, hopefully the effects due to capillarity are measuredbefore those of gravity intervene But in the twin-ring method of Scotter et al.(1982), two separate rings of different size are used to exploit the dependence ofcapillarity on the radius of curvature of the wetted source (Fig 1) The capillaryand gravitational influences on infiltration can be separated (Youngs, 1972) Tworings of different diameters are used, and these are simply pressed lightly into thesoil surface A constant head of water is maintained inside both rings, so that theunconfined steady 3-D flow (Figs 1 and2) can be measured: v1for the smaller

ring of radius r1, and v2for the larger ring of r2 The flux density of flow from thesmaller ring will be higher than that of the larger ring by an amount that will reflect

the soil’s capillarity, namely its sorptivity (Figs 1 and 2) Substituting r1and r2

into Eq 16 gives simultaneous equations that can be resolved to find the tivity as

conduc-v r1 1 ⫺ v r2 2

r1 ⫺ r2and the matric flux potential as

how the variance in S and Kscan be calculated

This twin-ring technique allows both the soil’s capillarity and its ity to be measured, and here the disturbance to the soil’s structure is minimal It isonly necessary to press the rings gently into the soil surface, and a mud caulkingcan be used to seal the ring to the surface The technique requires, however, thatthere be a significant difference in the fluxes between rings, and this is dependent

conductiv-upon the relative sizes of the soil’s capillarity and conductivity (Figs 1and2).

Scotter et al (1982) showed that these effects are equal when a ring of radius re⫽4fs/pKsis used Larger rings are required to obtain an estimate of the Ksof finer-textured soils, and small rings are required to obtain a good estimate of thefsof

coarse-textured soils Scotter et al (1982) thought rings of r⫽ 0.025 and 0.5 mwould be suitable for a wide range of soils If the difference in the radii is not large

enough, or if there are too few replicates to obtain a reliable estimate of the v ’s,{erroneous values will result (Cook and Broeren, 1994)

B Wells and Auger Holes

1 Glover’s Solution

It has long been known that water flow from a small surface well soon attains a

steady rate, Q (m3s⫺1), and that in some way this flux is related to the soil’s

hydraulic character, the depth of water in the hole, H, and its radius, a (Fig 6).

If capillarity is ignored, and if it can be considered that the surrounding soil is

wet and draining at the rate of Ks, then it is the pressure head H that generates the flow Q Glover (1953) found that the soil’s hydraulic conductivity could thus be

have commonly been used Talsma and Hallam (1980) used this method to sure the hydraulic conductivity for various soils in some forested catchments TheMariotte device can be simple, and the technique is quite rapid Measurements areeasy to replicate spatially Especial care must, however, be taken when creatingthe hole to ensure that no smearing or sealing of the walls occurs The surface

mea-condition of the walls in the well is critical, for it exerts great control on Q Any

smearing will throttle discharge from the well

Philip (1985) showed that the neglect of capillarity can result in Eq 40

providing an estimate of Ksthat might be an order of magnitude too high, cially in fine-textured soils wherefsis large Capillarity establishes the size of the

espe-saturated bulb around the well and controls in part the flow Q Its role in the

infiltration process needs to be considered

2 Improved Theory and New Devices

Independently, and via different means, Stephens (1979) and Reynolds et al.(1985) developed new theory of the role of the soil’s capillarity in establishing the

steady flow Q from a well Reynolds et al (1985) proposed that two simultaneous measurements be made using different ponded heights H1and H2so that an ap-proach similar to Eqs 38 and 39 might be used However, the difficulty in obtain-

ing a sufficiently large range in H1⫺ H2weakens the utility of this method.The approach of Stephens et al (1987) was to use the shape of the soil watercharacteristicu(h) to correct Q for capillarity This correction came from results

obtained using a numerical solution to the auger-hole problem

Alternatively, Elrick et al (1989) simply estimated a value ofa (Eq 18)from an assessment of the soil’s texture and structure For compacted, structure-less media they considereda to be about 1 m⫺1, for fine-textured soils 4 m⫺1, andstructured loams 12 m⫺1 For coarse-textured or macroporous soils they thought

a could be taken as 36 m⫺1 Givena, the solution of Reynolds and Elrick (1987)

gives the value of Ksfrom Q as