Methods for predicting the optimum and the range of soil watercontents for tillage based on the water retention curve

A.R. Dextera,*, N.R.A. Birdb

aInstitute of Soil Science and Plant Cultivation (IUNG), ul. Czartoryskich 8, 24-100 Pulawy, PolandbSilsoe Research Institute, Wrest Park, Silsoe, Bedford MK45 4HS, UK

Received 1 February 2000; received in revised form 28 July 2000; accepted 11 August 2000

Abstract

Information is needed on the range of soil water contents for tillage. The objective of the work was to develop methods for

the prediction of the soil water contents at which tillage may be done satisfactorily. Three water contents are considered: the

lower (dry) limit, the optimum water content, and the upper (wet) limit. This paper makes a synthesis of published results from

tillage and soil physics experiments and also includes some new experimental results. The effects of tillage are considered in

relation to some `̀ ®xed points'' including the lower plastic limit, ®eld capacity and a new ®xed point `̀ the in¯ection point''.

These considerations lead to methods for prediction of the lower (dry) tillage limit, the optimum water content, and the upper

(wet) tillage limit in terms of the parameters of the van Genuchten equation for soil water retention. Predictions can be made

in terms of soil composition through the use of pedotransfer functions for the parameters of the van Genuchten equation. The

new methods will enable the effects of soil degradation and climate change on tillage work days to be estimated. The results

are potentially mappable using geographic information systems. # 2001 Elsevier Science B.V. All rights reserved.

Keywords: Tillage; Soil water; Water retention curves; Compaction; Pedotransfer functions; GIS; van Genuchten equation

1. Introduction

The optimum water content for tillage (OPT) can be

de®ned as `̀ the water content at which tillage produces

the greatest proportion of small aggregates''. If soil is

tilled when it is wetter than this optimum water

content, then large clods can be produced and soil

structural damage can occur. If the soil is drier than the

optimum water content, then tillage requires excessive

energy and can also produce large clods.

Some experiments have been reported in which

tillage has been done in the ®eld when the soil has

been at different water contents, and the resulting

aggregate size distributions have been obtained by

sieving (for example). An optimum water content was

identi®ed by Bhushan and Ghildyal (1972) on a

lateritic sandy loam. They found that more small

aggregates were produced when tillage was done at

0.77yPL than when it was done at either 0.60yPL or

0.99yPL. Here, yPL is the lower plastic (or lower

Atterberg) limit of the soil and is the gravimetric

water content at which the consistency of freshly

moulded soil changes from plastic to brittle. Similarly,

Ojeniyi and Dexter (1979) found maximum produc-

tion of small aggregates when tillage of a sandy loam

was done at 0.9yPL. This soil contained 0.17 kg kgÿ1

Soil & Tillage Research 57 (2001) 203±212

* Corresponding author. Tel.: �48-81-886-3421/4960;

fax: �48-81-886-4547.

E-mail addresses: tonyd@iung.pulawy.pl (A.R. Dexter),

nigel.bird@bbsrc.ac.uk (N.R.A. Bird).

0167-1987/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 7 - 1 9 8 7 ( 0 0 ) 0 0 1 5 4 - 9

clay and was a Chromic Luvisol under the FAO soil

classi®cation system. Their results were incorporated

into a model for the prediction of soil structures

produced by tillage (Dexter, 1979). A similar relation-

ship between the OPT and the plastic limit was found

by Arndt (1964) for soil at Katherine in the Northern

Territory of Australia. Allmaras et al. (1969) found

that the surface roughness (which is related to the

presence of clods) of tilled soil was minimum when

tillage was done at yPL.

Research into soil friability, which can be de®ned as

`̀ the tendency of a mass of soil to crumble under the

action of an applied force'' has also shown that

friability of soil is maximum at a water content close

to yPL (Utomo and Dexter, 1981).

For several soils therefore, it has been found that the

optimum water content occurs in the vicinity of

yOPT � 0:9yPL. However, this has the limitations that

yPL is a property of moulded soil, and not of undis-

turbed soil in the ®eld, and also that many sandy soils

are not plastic and do not have a plastic limit. How-

ever, tillage of sandy soils can also cause damage to

the structure.

Increasing cloddiness when soil is tilled at water

contents greater than yPL has been reported by several

researchers including Patterson et al. (1980), Adem

et al. (1984), and Tisdall and Adem (1986).

The upper (wet) tillage limit, yUTL, of soils is not at

a constant water potential. Dexter (1988) made a

synthesis of the results of Heinonen and Pohjanheimo

(1962), Koenigs (1976), Boekel (1979), and Buiten-

dijk (1985), and showed that the upper tillage limit

(UTL) occurs at more negative matric water potentials

with increasing clay content of the soil. However, the

results from these authors could not be used to produce

a regression equation for the matric water potential at

the UTL because not all the papers gave the soil

compositions.

This effect of clay content is consistent with the

®nding of Dexter (1990) that the matric water poten-

tial (CPL) of six freshly moulded soils with clay

contents ranging from 0.185 to 0.668 kg kgÿ1 at the

lower plastic limit (yPL) is also more negative with

increasing clay content

CPL � 5:8ÿ 64�clay� �kPa� (1)

The data of Terzaghi et al. (1988) for 13 Uruguayan

soils with clay (clay) contents ranging from 0.18 to

0.41 kg kgÿ1 and with organic matter (OM) contents

ranging from 0.019 to 0.073 kg kgÿ1 were used to give

yUTL � 0:0775� 34�clay� � 191�OM� �kg kgÿ1�(2)

which is very similar to the relation found by Koenigs

(1976) for 20 Dutch soils

yUTL � 34�clay� � 155�OM� �kg kgÿ1� (3)

Tillage at water contents greater than yPL may also

destabilize and damage the soil structure. The appli-

cation of energy to soil wetter than yPL has been found

to increase the content of readily dispersible clay,

whereas the application of energy to soil drier than

yPL had no effect on the content of readily dispersible

clay (Watts et al., 1996). This is important because

clay dispersibility is indicative of soil instability.

The relationship between the lower plastic limit

(yPL) and the ®eld capacity (yFC) has been considered

by Boekel (1959, 1965). Here, ®eld capacity is de®ned

as the water content to which a ®eld will drain within a

few days after heavy rain or irrigation. yFC has been

found experimentally to correspond to a matric water

potential of about ÿ100 hPa. When soil is tilled when

it is wetter than yPL, it will deform plastically with

consequent destruction of the structure. It has been

noted that when yFC=yPL < 1, the soil will drain to a

water content at which no excessive structural damage

will occur on tillage. On the other hand, if

yFC=yPL > 1, then the soil will never drain to a water

content which is ideal for tillage. Unfortunately, most

clay soils drain extremely slowly, and in the ®eld are

usually wetter than yPL unless they are dried by water

extraction by plant roots.

Increasing cloddiness when soil is tilled at water

contents below the optimum has been reported by

Lyles and Woodruff (1962), Allmaras et al. (1969),

Bhushan and Ghildyal (1972), Ojeniyi and Dexter

(1979) and Watts and Dexter (1994). However, the

lower (dry) tillage limit, yLTL, is not as well de®ned as

the UTL. There is no water content at which the tillage

response changes suddenly. This point is considered

later in the paper.

The ®nding of Adem et al. (1984) and Tisdall and

Adem (1986) that tillage produced larger aggregates

with increasing water content (but below yPL) was for

the rather special case of soil which was initially ®nely

204 A.R. Dexter, N.R.A. Bird / Soil & Tillage Research 57 (2001) 203±212

divided in the form of micro-aggregates. Tillage of

such soil cannot produce further aggregate breakdown

and can only push micro-aggregates together to form

larger aggregates. This case is not discussed further in

this paper.

Very little work has been reported on the range of

water contents for tillage. Hoogmoed (1985) pointed

out that the range is usually narrow for soils with high

clay content and becomes wider for soils with lower

clay contents. Soil degradation usually reduces the

range and therefore the opportunities for tillage.

It is not easy to take tillage machinery to ®elds with

different soil types on many different dates to obtain

graphs showing the resulting tilth as a function of

water content. Therefore, there is a need for simpler,

quicker tests and prediction methods which can enable

the optimum water content (yOPT) to be determined

readily.

The objective of the work reported here was to

develop methods for predicting not only the OPT, but

also the range of water contents for tillage. This is

done in terms of the soil composition and also from the

water retention characteristics of the soil as described

by the van Genuchten (1980) equation. The para-

meters of this equation have been determined and

published for enormous numbers of soils and have

been incorporated into digital soil maps using geo-

graphic information systems (GISs) (e.g., WoÈsten

et al., 1999).

2. The water retention curve and the in¯ectionpoint

A typical soil water retention curve is shown in

Fig. 1. This shows how, when a soil is dried from

saturation, the water content, y, decreases as the matric

water potential, C, becomes more negative. In Fig. 1,

values of C are shown as their modulus, h, for ease of

plotting. Water retention measurements were ®tted to

the van Genuchten (1980) equation

y � �ySAT ÿ yRES��1� �ah�n�ÿm � yRES (4)

Here ySAT and yRES are the water content at saturation

and the residual water content, respectively, a a scal-

ing factor for the water potential, and m and n the

parameters which govern the shape of the curve. The

van Genuchten equation was ®tted with the Mualem

(1976) restriction

m � 1ÿ 1

n(5)

As shown in Appendix A, the water content at the

point of in¯ection (where the curvature changes sign)

of the van Genuchten equation, when plotted as log(h)

against y, was determined from

yINFL � �ySAT ÿ yRES� 1� 1

m

� �ÿm

�yRES (6)

Although we used the Mualem restriction (Eq. (5)),

the derivations given in Appendix A and in Eq. (6) are

general for the van Genuchten equation, and may be

used with or without this restriction.

This in¯ection point is shown on the example of a

water retention curve given in Fig. 1. There are two

possible in¯ection points depending on whether y is

plotted against h or against log(h). The ®rst of these is

an important characteristic of the water retention

curve as it has been interpreted as the `̀ breakthrough''

matric potential at which air ®rst penetrates all the way

through the soil (White et al., 1972; Dullien, 1992).

The second corresponds to the matric potential at

which the air content of the soil is increasing the most

rapidly with increasing log(h). The second of these

Fig. 1. Example of a soil water retention curve. Here log10 h is

plotted against the gravimetric water content. The water `̀ suction'',

h, is the modulus of the matric water potential measured in hPa.

A.R. Dexter, N.R.A. Bird / Soil & Tillage Research 57 (2001) 203±212 205

occurs at smaller values of water content than the ®rst.

These two in¯ection points are close together for soils

with narrow distributions of pore sizes but the differ-

ence between them increases with increasing width of

the pore size distribution. We have used the in¯ection

point of curves of y plotted against log(h) as we

conjecture that this is a more appropriate measure

of air entry into granular materials exhibiting broad

distributions of pore sizes as is the case for the natural

soils considered in this paper.

The use of this in¯ection point has physical mean-

ing because soil crumbling or fragmentation is a

consequence of the existence of surfaces of weakness

within the soil. Such surfaces of weakness are asso-

ciated with pre-existing micro-cracks which tend to

become air-®lled (and therefore weak) at the water

potentials considered (e.g., Hallett et al., 1995).

3. Materials and methods

3.1. Soils

Results are presented for ®ve soils which are all

from the Rothamsted modern long-term experiment at

High®eld at IACR, Rothamsted in England. The

experiment was established in 1949 on land with a

previous history of permanent pasture. It was set up

to investigate a range of crop rotation practices and

is described in detail by Johnston (1972). Five

treatments were sampled to obtain a wide range of

contents of soil OM. The soil designations used

in this paper and corresponding treatments are as

follows:

� Soil 1. Permanent fallow (PF): this was an area kept

as a bare fallow and cultivated several times each

year to prevent weed growth.

� Soil 2. Permanent arable (plots 9/10): this was an

area ploughed for the first time in 1948 and sub-

sequently cropped every year with cereals.

� Soil 3. Ley±arable rotation (plots 15/16): since

1948 this area has been maintained in a 3 year

grass/clover, 3 year cereal rotation; samples were

collected during the second year of the cereal

phase.

� Soil 4. Reseeded grass (plots 13/14): this area was

ploughed initially in 1948 and reseeded to grass

shortly after; since that date it has remained in

grass.

� Soil 5. Permanent grass (plots 23/24): this is an

unbroken continuation of the original permanent

pasture on the site.

The soil on this site belongs to the Batcombe series

(Claydon and Hollis, 1984), being a ®ne silty loam

over clay drift with silicious stones. This soil series is

approximately equivalent to Chromic Luvisols and

Andic Acrisols as de®ned in the FAO soil classi®ca-

tion system (Avery, 1980).

Samples of aggregates of 9±13 mm were collected

from the upper 100 mm layer of each plot with the

minimum possible disturbance. Subsamples were used

to determine the particle size distributions (British

Standard 1377, 1975) and the OM contents (Walkley

and Balck, 1934). The compositions of these soils are

given in Table 1. It can be seen that the principal

difference between the soils is in the OM content.

3.2. Water retention measurements

Batches of aggregates were wetted slowly from

below by capillarity to saturation. They were then

drained to water suctions, h, of 10, 20, 40, and 80 hPa

on a sand table apparatus, and to 250, 500, 1000, 2000,

4000, 8000, and 15 000 hPa on ceramic pressure plate

extractors. Two replicate samples were measured for

each soil at each suction. The water contents were then

measured gravimetrically by drying the samples at

1058C for 24 h. The mean water contents for every

value of suction were then ®tted to the van Genuchten

(1980) equation (parameter given in Table 2) using the

non-linear curve-®tting program RETC (van Genuch-

ten et al., 1991). It was found that the van Genuchten

Table 1

Compositions of the experimental soils (after Watts and Dexter,

1997)

Soil Sand

(kg kgÿ1)

Silt

(kg kgÿ1)

Clay

(kg kgÿ1)

Organic matter

(kg kgÿ1)

1 0.09 0.67 0.25 0.019

2 0.13 0.63 0.24 0.026

3 0.11 0.64 0.25 0.036

4 0.11 0.63 0.27 0.048

5 0.11 0.67 0.23 0.054

206 A.R. Dexter, N.R.A. Bird / Soil & Tillage Research 57 (2001) 203±212

equation with the Mualem restriction (Eq. (5)) ®tted

the experimental data very well.

3.3. Determination of `̀ ®xed points''

The lower plastic (or Atterberg) limit, yPL, was

determined as the gravimetric water content at which

a rolled thread of soil just begins to crack when it has a

diameter of 3 mm (British Standard 1377, 1975). Ten

replicate measurements were made for each soil.

The ®eld capacity, yFC, was estimated as the gravi-

metric water content at a suction of 100 hPa. The

values were calculated from the van Genuchten equa-

tion as ®tted to each soil.

The permanent wilting point of plants for each soil,

yPWP, was determined as the gravimetric water content

at a suction of 15 000 hPa. The values were calculated

from the van Genuchten equation as ®tted to each soil.

The in¯ection point, yINFL, was determined as a

gravimetric water content from the parameters of the

van Genuchten equation using Eq. (6).

4. Results and discussion

4.1. OPT

The optimum water content for tillage, yOPT, was

®rstly estimated as 0.9yPL. It can be seen from the data

in Table 3 that this is very close to the water content at

the in¯ection point, yINFL, of the water retention curve

as shown in Fig. 1. Therefore, it was decided to adopt

the relationship

yOPT � yINFL (7)

Values of yOPT for the High®eld soils are given in

Table 4.

4.2. Dry limit for tillage

The lower (dry) tillage limit, yLTL, is not a sharply

de®ned point as can be inferred from the references

given in Section 1, and therefore its de®nition is

somewhat arbitrary. Here, the arbitrary de®nition

which is used is `̀ the water content at which the

strength of the soil is twice the strength at the optimum

water content''.

These strengths, t, may be estimated in terms of the

effective stresses (see, e.g., Greacen, 1960; Mullins

and Panayiotopoulos, 1984). To a ®rst approximation,

we may write that

tOPT � kwOPThOPT (8)

tLTL � kwLTLhLTL � 2tOPT (9)

where the w values are the degrees of

saturation � y=ySAT. The coef®cient, k, is assumed

to be a constant, the value of which depends on the

type of strength measurement. In this paper, the

Table 2

Parameters of the van Genuchten equation obtained for the

experimental soils

Soil ySAT

(kg kgÿ1)

yRES

(kg kgÿ1)

m n a (hPaÿ1)

1 0.208 0 0.1137 1.128 0.0072

2 0.252 0.124 0.4215 1.729 0.0025

3 0.298 0 0.1346 1.156 0.0173

4 0.439 0 0.1180 1.134 0.1329

5 0.417 0 0.1398 1.163 0.0319

Table 3

Some hydraulic `̀ ®xed points'' for the experimental soils, where

yPL is the lower plastic limit, yFC the ®eld capacity, yPWP the

permanent wilting point of plants, and yINFL the water content at

the in¯ection point of the water retention curve

Soil yPL

(kg kgÿ1)

yFC

(kg kgÿ1)

yPWP

(kg kgÿ1)

yINFL

(kg kgÿ1)

1 0.182 0.196 0.114 0.161

2 0.230 0.248 0.133 0.201

3 0.254 0.258 0.126 0.224

4 0.340 0.309 0.159 0.338

5 0.344 0.334 0.153 0.311

Table 4

Predicted tillage limits for the soils considered, where yLTL is the

lower tillage limit, yOPT the optimum water content for tillage,

yUTL the upper tillage limit, and DyRANGE the width of the range of

water contents for tillage

Soil yLTL

(kg kgÿ1)

yOPT

(kg kgÿ1)

yUTL

(kg kgÿ1)

DyRANGE

(kg kgÿ1)

1 0.146 0.161 0.180 0.034

2 0.170 0.201 0.221 0.051

3 0.199 0.224 0.253 0.054

4 0.305 0.338 0.378 0.073

5 0.275 0.311 0.353 0.078

A.R. Dexter, N.R.A. Bird / Soil & Tillage Research 57 (2001) 203±212 207

interest is only in relative strength values, and so the

value of k need not be considered.

A computer program in the language BASIC was

written to determine numerically the value of the

water content at the lower tillage limit (LTL), yLTL,

in terms of the parameters of the van Genuchten

equation and of the criteria included in Eqs. (8) and

(9).

4.3. Wet limit for tillage

Further analysis of the data presented by Terzaghi

et al. (1988), shows that on average, for the 13

Uruguayan soils, yUTL � 1:04yPL. From this result

and from the other results presented in the review

of literature in Section 1, it seems clear that the upper

(wet) tillage limit, yUTL, can, for practical purposes, be

identi®ed with yPL

yUTL � yPL (10)

Comparison with the results given in Tables 2 and 3,

shows that this can reliably be estimated in terms of

the parameters of the water retention curve using the

equation

yUTL � yINFL � 0:4�ySAT ÿ yINFL� (11)

4.4. The range of water contents for tillage

The range of water contents, DyRANGE, over which

tillage may satisfactorily be done is de®ned as the

difference between UTL and LTL

DyRANGE � yUTL ÿ yLTL (12)

4.5. An example

The data obtained for the High®eld soil are shown

in the Tables 1±4. It can be seen that the compositions

of the soils are essentially the same except for the OM

contents. It can be seen in Table 2 that the OM content

has signi®cant effects on the parameters of the van

Genuchten equation for these samples. Results for the

OPT and for the UTL and LTL are shown in Fig. 2.

Regression lines show the trends of these values as

functions of soil OM content. It can also be seen

clearly that the range of water contents for tillage

decreases with decreasing soil OM content.

4.6. Use of these results with pedotransfer functions

Pedotransfer functions have been developed for the

prediction of the parameters of the van Genuchten

equation in terms of soil composition (contents of clay,

silt and OM) and in terms of soil state as expressed by

the dry bulk density (WoÈsten et al., 1999). These

pedotransfer functions are regression equations which

have been determined with data from 5521 soil sam-

ples. Although these pedotransfer functions cannot be

expected to give accurate predictions of the behaviour

of any single soil, they can be used to examine trends

of behaviour.

Care should be taken with the values of soil density

which are used. These should be the values for the soil

which it is desired to fragment. This could be either the

density of the `̀ total soil'' (e.g., the arable layer) or

could be the density of clods. The values of these may

be expected to be different.

Pedotransfer functions allowed the investigation of

the effects of clay content on the tillage limits. The

following assumptions were made: that for each clay

content, the contents of silt and sand are equal, that the

OM was constant at 0.03 kg kgÿ1, and that the bulk

Fig. 2. Predicted values of the UTL, the OPT, and the LTL for the

High®eld soil as functions of soil OM content. These are shown as

UTL, OPT, and LTL, rather than as yUTL, yOPT, and yLTL for greater

clarity. The regression lines show how the range of water contents

for tillage becomes smaller with decreasing OM content.

208 A.R. Dexter, N.R.A. Bird / Soil & Tillage Research 57 (2001) 203±212

density was constant at 1.5 Mg mÿ3. The results are

shown in Fig. 3. It can be seen that it is predicted that

yLTL, yOPT, and yUTL all increase with increasing clay

content. Interestingly, it can be seen that the range of

water content for tillage, DyRANGE, decreases with

increasing clay content as observed by Hoogmoed

(1985).

The effects of soil bulk density on yLTL, yOPT, and

yUTL were determined with the assumptions of a

constant clay content of 0.25 kg kgÿ1 and a constant

OM content of 0.03 kg kgÿ1. The results are shown in

Fig. 4. It can be seen that the predicted values of yLTL,

yOPT, and yUTL all decrease with increasing bulk

density. It is also interesting to note that the range

of water contents for tillage also decreases with

increasing bulk density. This is consistent with the

observation that compacted or otherwise structurally

degraded soils are in a condition suitable for tillage on

fewer days than non-compacted or non-degraded soils.

The use of the pedotransfer functions shows that

changes in soil OM content alone have no signi®cant

effect on yLTL, yOPT or yUTL. Therefore, we may

conclude that the effects of OM shown in Fig. 2 are

indirect effects. What we are seeing is the combined

effect of OM on soil density and the effect of density

on yLTL, yOPT, and yUTL. This illustrates the important

point that we must be very careful when we are using

variables which are correlated, otherwise erroneous

conclusions may be reached.

5. Summary and conclusions

It is clear that properties of disturbed (e.g.,

moulded) soil are not appropriate for the prediction

of the behaviour of undisturbed soil in the ®eld. The

water retention curve represents the state of undis-

turbed soil and therefore provides a better basis for the

prediction of other water-related properties of undis-

turbed soil.

Methods for predicting the lower (dry) limit, the

optimum water content, and the upper (wet) limit for

tillage have been developed and presented. These are

presented in terms only of the physical properties of

undisturbed soil. These limits may be slightly different

for different tillage implements as observed by

Bhushan and Ghildyal (1972). This is because the

transition from brittle to plastic ¯ow of soil depends

Fig. 3. Values of the UTL, the OPT, and the LTL as functions of

soil clay content. These values were calculated using pedotransfer

functions. The distance between the UTL and LTL curves shows

how the range of water contents for tillage decreases with

increasing soil clay content.

Fig. 4. Values of the UTL, the OPT, and the LTL as functions of

soil bulk density. These values were calculated using pedotransfer

functions. The distance between the UTL and LTL curves shows

how the range of water contents for tillage decreases with

increasing soil compaction.

A.R. Dexter, N.R.A. Bird / Soil & Tillage Research 57 (2001) 203±212 209

upon the combinations of stresses applied by the

implement and acting in the soil. These interactions

have been discussed by Spoor and Godwin (1979) and

Stafford (1982). In spite of this limitation, the ®ndings

presented and discussed in this paper relate to typical

tillage operations in the (uncon®ned) arable layer of

the soil.

This research has investigated the relationship

between yOPT and the soil water retention curve. In

particular, the new ®xed point which has been devel-

oped is the `̀ in¯ection point'' for the water retention

curve plotted as y against log(h). This is the water

content, yINFL, of a draining soil at which air is

entering the most rapidly with increasing log(h).

We have discussed this point in relation to the air-

breakthrough point at which continuous air-®lled

pores ®rst extend throughout the entire soil volume.

Equations have been developed and presented for this

in¯ection point in terms of the parameters of the van

Genuchten equation for the soil water retention char-

acteristic. yOPT has now been identi®ed with yINFL.

This new method for predicting yOPT has physical

meaning because it explains soil break-up in terms of

zones of weakness in the soil which are identi®ed with

air-®lled pores.

It may appear unsatisfactory that measurements of

the plastic limit have been used to calibrate the new

methods, the purpose of which is to avoid the use of

the plastic limit. Certainly, the plastic limit is not

appropriate for soils which are either not plastic or

which are highly compacted. The soils from

Rothamsted, which were used to calibrate the new

methods, do not suffer from either of the above

problems. For these soils, under normal conditions,

we believe that the plastic limit method is satisfactory

for predicting the OPT and the UTL. Therefore, the

measurements of the plastic limit for these soils could

be used to calibrate the new methods.

Although the OPTand the UTL and LTL can now be

predicted with these new methods, it is not possible

with these methods to predict the quality of the soil

structures produced by tillage. This depends on the

friability of the soil as discussed by Utomo and Dexter

(1982), Watts and Dexter (1998), and Dexter and

Watts (2000).

The use of the new methods for the prediction of

the OPT and the UTL and LTL can be combined

with the use of pedotransfer functions for the predic-

tion of the parameters of the van Genuchten equation

for soil hydraulic properties. This is particularly

attractive because it results in predictions which are

internally self-consistent. If the results are combined

with soil water balance models, they can have a wide

range of potential applications which include the

following:

1. studies of the effects of soil degradation such as

compaction or loss of soil OM on the number of

available work days for tillage, and

2. studies of the effects of different climate change

scenarios on the number of available work days

for tillage.

The results may be readily incorporated into GISs to

produce maps of, e.g., the range of water contents for

tillage or the number of work days available for

tillage. The results obtained from the new methods

are compatible with all the principal ®ndings and

conclusions in the published literature. However, it

would be very valuable if these new methods could be

evaluated and `̀ ®ne-tuned'' through the use of future

tillage experiments in the ®eld.

Acknowledgements

Prof. D.S. Powlson and Dr. P.R. Poulton of IACR,

Rothamsted are thanked for giving permission for the

collection of soil samples from the High®eld experi-

ment. The work was funded in part by the European

Commission INCO-Copernicus project number

ERBIC15-CT98-0106.

Appendix A. Derivation of the in¯ection point ofthe van Genuchten water retention curve

The van Genuchten (1980) equation for water

retention is

y � �ySAT ÿ yRES��1� �ah�n�ÿm � yRES (A.1)

which may be plotted as curves of log(h) y against

log(h), as in Fig. 1. We may write

dyd ln�h� �

dydh

dh

d ln�h� (A.2)

210 A.R. Dexter, N.R.A. Bird / Soil & Tillage Research 57 (2001) 203±212

where ln(h) is the natural logarithm of h. Therefore,

dyd ln�h� � ÿmn�ySAT ÿ yRES�anhn�1� �ah�n�ÿmÿ1

(A.3)

At the in¯ection point

d2yd ln�h2�� ÿmn�ySAT ÿ yRES�anfnhnÿ1�1� �ah�n�ÿmÿ1

� hn�ÿmÿ 1�annhnÿ1�1� �ah�n�ÿmÿ2gh� 0 (A.4)

Therefore, the modulus of the water potential at the

in¯ection point is

h � 1

a1

m

� �1=n

(A.5)

Substituting back into Eq. (A.1) gives the water con-

tent at the in¯ection point as

yINFL � �ySAT ÿ yRES� 1� 1

m

� �ÿm

�yRES (A.6)

which is the required result.

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