a simplified method for estimating soil compaction

A simpli®ed method for estimating soil compaction

M.F. O'Sullivan*, J.K. Henshall, J.W. Dickson

Environmental Division, SAC, Bush Estate, Penicuik, Midlothian, EH26 0PH, UK

Received 22 December 1997; accepted 14 October 1998

Abstract

We describe a simpli®ed model that allows users to explore some of the main aspects of soil compaction. It is intended for use

by non-experts, such as students, and is written as an easy-to-use spreadsheet. It estimates soil bulk density under the centre-

line of a wheel track from readily available tyre details. The model uses an analytical method to estimate the propagation of

stress in the soil. It contains compactibility data for contrasting soils and it accounts for both rebound and recompression

realistically. We present examples that show the potential of the model in selecting tyres and wheel systems to minimise

compaction. # 1999 Elsevier Science B.V. All rights reserved.

Keywords: Traf®c; Model; Bulk density; Contact area; Education

1. Introduction

Compaction of soil by agricultural machines can

have adverse effects on crop production and the

environment. Excessive compaction leads to degrada-

tion of the soil resource, increased pollution of water

and air and increased requirement for inputs to main-

tain crop growth. Compaction problems can be found

in most parts of the world but they are particularly

severe where highly mechanised agriculture is prac-

tised on land subject to high rainfall (Soane and Van

Ouwerkerk, 1994).

A large number of soil and wheel variables in¯u-

ence compaction and their interaction is complex. We

can state general principles for minimising compac-

tion damage, e.g. minimise loads and maximise tyre±

soil contact area, but quantitative predictions for

individual cases are not easy. This makes it dif®cult

to give farmers speci®c advice on, for example, tyre

sizes for minimising compaction. In this situation,

mathematical modelling is an inexpensive way of

making reasonably con®dent predictions about

unknown situations, without resorting to expensive

®eld work. A model in this sense is a collection of

equations that interact with one another or an extended

hypothesis (Addiscott, 1993). One particular bene®t of

such a model is that it allows students to explore the

effects of the factors that in¯uence compaction and

promotes effective, heuristic learning.

In this paper, we present information about a sim-

pli®ed soil compaction model that is intended for use

by non-experts, such as students of agriculture and

environmental science or suitably trained agricultural

consultants. Our main objective was to produce a

simple procedure that students could use to explore

some of the factors that control soil compaction.

Soil & Tillage Research 49 (1999) 325±335

*Corresponding author. Tel.: +44-131-535-3046; fax: +44-131-

535-3056; e-mail: [email protected]

0167-1987/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved.

P I I : S 0 1 6 7 - 1 9 8 7 ( 9 8 ) 0 0 1 8 7 - 1

2. Structure of the model

The model aims to estimate the dry bulk density

under the centre-line of a wheel track and consists of

three main components. Firstly, the forces applied by

the vehicle at the soil surface are modelled. This

involves predicting the contact area between the wheel

and the soil and then distributing the load over that

area in some appropriate manner. The model then uses

an analytical method to estimate how the stresses

propagate through the soil. In the third component,

appropriate soil parameter values are selected to

describe the effect of stress on soil volume change.

There are more sophisticated models that use tech-

niques such as the ®nite element method to simulate

soil deformations in detail (Kirby, 1989; Chi et al.,

1993). However, such models are dif®cult to use

because they demand advanced expertise in comput-

ing and soil mechanics. Students are used to working

with PC-based spreadsheets, so we implemented the

model as an Excel spreadsheet, with the core of the

model written as a macro in Visual Basic. Users do not

need any knowledge of macros to run the model. The

inputs required are in the customary metric units found

in tyre manufacturers' data books, i.e. bar, ton and

mm. The model converts these to SI units.

2.1. Contact area estimation

The model was intended to demonstrate the in¯u-

ence of vehicle characteristics on compaction. In

practice, the characteristics that could be changed

include tyre size, in¯ation pressure and load. It is

important, therefore, to include the effects of changes

in these parameters on contact area in the model. It is

also desirable that the model should demand only

information that would be readily available to the

potential users. Grecenko (1995) reviewed equations

that aim to estimate contact area but all of them have

some limitations. They may require parameter values

that are not readily available; their application may be

restricted to a narrow range of tyres or ground con-

ditions; or they may not estimate the effects of an

important parameter, such as tyre width. These limita-

tions necessitated development of a new empirical

model.

Two equations were derived, one to estimate the

contact area on a rigid surface and the other for soft

soil. The independent variables chosen were the tyre

width and diameter, load and in¯ation pressure. The

equations for both surfaces were of the form:

A � s1bd � s2L� s3L=pi (1)

where L is the tyre load (kN), b is the tyre section

width (m), d is the tyre overall diameter (m), pi is the

in¯ation pressure (kPa) and s1, s2, and s3 are empirical

parameters.

The parameters for a rigid surface was derived from

our unpublished data, with additional data from Plack-

ett (1984) and Blackwell (1979). The data for soft soil

were collected in compaction experiments conducted

over a number of years. These experiments were

conducted on soil that had been intensively loosened

to a surface bulk density of 1.0 Mg mÿ3 or less. The

soils were mainly sandy loams and sandy clay loams

and the water content was always well below ®eld

capacity. These equations apply to cross ply tyres only

because these tyres predominated over radials in the

available data. The values of the parameters s1, s2 and

s3 for both surfaces are given in Table 1.

Radial tyres de¯ect in a different way to cross ply

tyres to produce a larger area of contact with the soil.

However, we had only a limited number of compar-

isons of contact areas of radial and cross ply tyres of

the same size. These results indicated that the contact

area of a radial tyre is between 20% and 50% greater

than that of the equivalent cross ply. Accordingly, the

model uses the same equations for both cross ply and

radial tyres but the estimated contact area is increased

by a conservative value of 20% for radials.

The validity of Eq. (1) was checked by comparing

results with independent data. Areas calculated for a

rigid surface were compared with estimates made

using equations published by Steiner and SoÈhne

(1979). Their equations were not used in the model

as they did not include tyre width as an independent

variable, their results were based on a small range of

Table 1

Constants of Eq. (1) for estimating contact area from tyre width,

diameter, inflation pressure and load for rigid and soft surfaces

Constant Rigid Soft

s1 0.041 0.310

s2 0 0.00263

s3 0.613 0.239

326 M.F. O'Sullivan et al. / Soil & Tillage Research 49 (1999) 325±335

tyre sizes and, in particular, their work did not include

very wide tyres. Results were compared for one of the

tyre sizes that Steiner and SoÈhne (1979) used in

developing their model. This was a typical tractor

drive tyre and the results of both methods agree

reasonably well, as shown in Fig. 1, which also

includes the contact area estimated by the equation

of McKyes (1985)

A � bd

�(2)

where � is a constant that takes the value 4 for a rigid

surface and 2 for soft soil.

Results for soft soil were compared with the method

of Schwanghart (1991), who proposed a simple,

mechanistic model for estimating contact area on soft

soil. In addition to tyre dimensions, this model

requires the empirical Bekker sinkage constants for

the soil and a spring constant for the tyre. The spring

constant depends on tyre size, construction and in¯a-

tion pressure, but the absence of readily available data

for tyre spring constants made this model unsuitable

for our purposes. The contact areas estimated by

Eq. (1) for a 16.9/14±34 tyre are compared in

Fig. 2 with the predictions of Schwanghart's (Schwan-

ghart (1991)) model, using his values for the tyre

spring constants. The values of the Bekker sinkage

constants used were typical of a soft soil but they were

chosen to maximise agreement between methods over

a range of loads and in¯ation pressures. Fig. 2 shows

that Eq. (1) reproduces the same general behaviour as

Schwanghart's (Schwanghart (1991)) model and that

good agreement is possible.

The rigid surface parameters are used if the soil bulk

density is 1.8 Mg mÿ3 or greater and the soft soil

parameters if the soil bulk density is 1.0 Mg mÿ3 or

less. For intermediate densities the program inter-

polates linearly between the rigid surface and soft

soil values.

Since the smallest tyre used in the development of

Eq. (1) was a 7.50±16, the estimated contact areas for

very small tyres are unreliable. Estimated areas can

exceed the product of width and diameter, which is

physically impossible. Small tyres are sometimes

®tted to trailers, where they may carry large loads,

and so it is important to be able to model their effects.

In cases where the area estimated by Eq. (1) is greater

than a set fraction (f) of the product of width and

diameter, the model uses Eq. (2). The value of f is set

to 0.7 for soft soil and 0.35 for a rigid surface and an

averaging procedure is used to smooth the transition

between the two equations.

Fig. 1. Contact areas of 16.9±38 (X) and 16.9R38 (R) tyres on a rigid surface, as estimated by Eq. (1) (1), the equations of Steiner and SoÈhne

(1979) (SS) and McKyes (1985) (M). The tyres were compared at their maximum (P) and minimum (p) inflation pressures, with the maximum

recommended load (L) and half the maximum recommended load (l) at each pressure.

M.F. O'Sullivan et al. / Soil & Tillage Research 49 (1999) 325±335 327

2.2. Stress distribution and propagation

The distribution of stress over the contact area and

the propagation of vertical stress down through the soil

are essentially the same as in the model of Smith

(1985), who based his model on the work of SoÈhne

(1953). The load is assumed to act on a circle with an

area equal to the tyre±soil contact area. This assump-

tion may be unrealistic but a circular contact patch

maximises the vertical stress in the soil, compared to

an ellipse or rectangle, and so the assumption is

conservative. The distribution of stress with the radius

of the contact patch is described by a parabola of 16th,

fourth or second-order for hard, ®rm or soft soil,

respectively. Stress transmission through the soil is

based on the Boussinesq equation, which describes the

propagation of stresses under a point load acting on a

homogeneous, isotropic, semi-in®nite, ideal elastic

medium. This method was ®rst applied to agricultural

soils by SoÈhne (1953), with the addition of empirical

concentration factors to account for non-ideal beha-

viour. The radial stress, �r, at distance, r, under a point

load, Q, is

�r � �Q cos�ÿ2 �

2�r2(3)

where � is the angle between the radius and the vertical

and � is a concentration factor. The concentration

factor takes the values 3, 4, 5 or 6 for ideal (very

hard), hard, ®rm or soft soils, respectively. For a

circular contact patch, this equation can be integrated

with the parabolas describing the distribution of con-

tact stress to estimate the vertical stress under the

centre line. The resulting equations were presented by

Smith (1985).

There are many limitations to this method and the

main ones were summarised by Olsen (1994). The

most fundamental limitation is that the derivation of

Eq. (3) assumes Poisson's ratio is 0.5, which implies

no volume change. The analysis also assumes small

strains, whereas large, permanent deformations can

occur in topsoil during the passage of a wheel. There-

fore, the method is not strictly applicable to loose

topsoils. The model attempts to overcome this pro-

blem by applying the load in a number of increments.

A further limitation is that the equations were devel-

oped for an ideal elastic medium that is homogeneous,

isotropic and semi-in®nite. Real soils are not ideal

elastic media and their properties vary both laterally

and with depth. One consequence of this idealisation is

that stress is underestimated where a loose topsoil

overlays a dense subsoil, which leads to the under-

estimation of compaction by heavy vehicles on

layered soils.

Fig. 2. Contact areas of a 16.9/14±34 tyre on soft soil, as estimated by Eq. (1) (*, ^) and the model of Schwanghart (1991) (*, }) at

inflation pressures of 60 kPa (*, *) and 200 kPa (^, }).


The concentration factors depend on soil water

content, soil structure and load characteristics (Black-

well and Soane, 1981; Horn, 1988; Gupta and Raper,

1994), and so selection of an appropriate factor is

problematic. Within the model, different concentra-

tion factors are chosen for very hard, hard, ®rm or soft

soil, based on soil bulk density (Smith, 1985).

These limitations mean that the model is more

suited to comparing the compaction caused by differ-

ent vehicles than for predicting the actual bulk density

in a particular ®eld (Smith, 1987). Despite the theo-

retical and practical objections to this stress propaga-

tion model, it can produce satisfactory results

(Blackwell and Soane, 1981; Gupta and Larson,

1982; Smith, 1985; Gupta and Raper, 1994; Olsen,

1994).

2.2.1. Estimating intermediate and minor principal

stresses

Eq. (3) is used to estimate the vertical stress under

the centre line of a wheel. However, compaction is

also in¯uenced by the con®ning stresses. It is more

appropriate, therefore, to characterise increases in

stress below a wheel in terms of the mean normal

stress, p. This also makes the model consistent with

the conventions of critical state soil mechanics, which

will facilitate further development. The mean normal

stress is de®ned as

p � �1 � �2 � �3

3(4)

where �1, �2 and �3 are mutually perpendicular major,

intermediate and minor principal stresses, respec-

tively. In the case of the centre line under a static

load, �1 is vertical, �2 is longitudinal, parallel to the

long axis of the loaded area, and �3 is transverse,

parallel to the short axis of the loaded area. The

direction of the principal stress rotates as a wheel

rolls over (Way et al., 1994; Bakker et al., 1995) but

such effects are ignored in this simple, static model.

Under the centre line of a contact patch, the major

principal stress is taken as the vertical stress, estimated

by Eq. (3). The values of the other two stresses will

depend on the size and shape of the contact patch and

the amount of wheelslip, in addition to the factors that

affect �1. The complete state of stress in the soil due to

both vertical and horizontal loads can be modelled

numerically for any shape of contact patch, using an

extension of Eq. (3) (Van Den Akker and Van Wijk,

1987; Johnson and Burt, 1990). Additional data on soil

stiffness or shear modulus and an estimate of wheel

slip would be required for the estimation of compac-

tion by such a model. The resulting model would be

more complicated and less usable by non-specialists.

Furthermore, despite its complexity, it would be sub-

ject to the fundamental objections already mentioned.

With the aim of maintaining simplicity, it was

decided to model the intermediate and minor principal

stresses empirically. Results from one of the more

sophisticated models (Johnson and Burt, 1990) were

examined to assess the effects of the main factors that

in¯uence the stress ratios, �1/�2 and �1/�3. This

investigation showed that �2 and �3 decrease more

rapidly with depth than �1. Although all three com-

ponents increase with applied load, the ratios �1/�2

and �1/�3, were independent of load. The major

principal stress predominates when the contact area

is small and when the soil is soft. Stresses were

estimated for a range of representative conditions,

using the Johnson and Burt (1990) model. Regression

equations were ®tted to these outputs to estimate both

stress ratios as a function of depth, contact area and

soil hardness. The form of both equations was

ln�1

�n

� c1zÿ c2A� c3� (5)

where z is the depth in metres, A is the contact area

(m2), � is the concentration factor (Eq. (3)) and �n

represents �2 or �3. The values of the constants c1, c2

and c3 for both stress ratios are in Table 2. The use of

this equation allows us to keep the model simple

enough for its intended purpose, while remaining

reasonably realistic.

2.3. Estimation of compaction from stress

The compactness of the soil is expressed as its

speci®c volume (v), which is the ratio of the total

Table 2

Constants of Eq. (5) for estimating stress ratios from depth, contact

area and stress concentration factor

Constant �1/�2 �1/�3

c1 5.30 4.66

c2 2.08 2.06

c3 0.21 0.32


volume of the soil (i.e. voids and solids) to the volume

of solids alone. The use of speci®c volume maintains

consistency with critical state soil mechanics although

dry bulk density (�b) is probably more widely under-

stood. Accordingly, the model converts the ®nal spe-

ci®c volume to bulk density before output. The

relationship between these two variables is

v � �s

�b

(6)

where �s is the density of solids. The compactibility of

soil is assessed in terms of its virgin compression line

(VCL), which is the maximum speci®c volume a soil

can have at any given value of mean normal stress. In

other words, the VCL is the result of isotropic com-

pression with no distortion. The equation that is gen-

erally used as a good representation of the VCL within

the range of practical interest is

v � N ÿ �n ln �p� (7)

where �n is the compression index and N is the speci®c

volume at p � 1 kPa.

One of the main factors that affects compactibility

is the soil water content and it is intended that users of

the model should be able to investigate the effect of

this. Therefore, the model needs data on the para-

meters of the VCL, N and �n, and the effect of water

content on them. It uses data for two contrasting soil

types, a sandy loam and a clay loam, published by

O'Sullivan et al. (1994). The intercept of the VCL, N,

is modelled as a quadratic function of soil water

content:

N � Aÿ B�wÿ C�2 (8)

where w is the gravimetric water content and A, B and

C are constants for a given soil type. The VCL tends to

pivot about a point in v±ln (p) space as the water

content changes. Accordingly the slope, �n, is esti-

mated from N and the co-ordinates of the pivot point,

vp and pp

�n � N ÿ vp

pp

(9)

The co-ordinates of the pivot point also vary with soil

type (O'Sullivan et al., 1994). Petersen (1993) found

that the VCL does not pivot about a point, in which

case an independent equation would be needed to

estimate �n. Values of the constants A, B, C, vp and

pp in Eqs. (8) and (9) for the two soils are shown in

Table 3.

When the soil is unloaded, it rebounds along a

straight line in v±ln (p) space. The slope of this

rebound line, �, also varies with water content, similar

to N and �n, but the values of � for these soils were

small (Kirby and O'Sullivan, 1997). The ratio of � to

the compression index, �n, was found to vary linearly

with water content for both soils. A single equation for

both soils accounted for 76% of the variance in �when

water content was expressed as a fraction of the cone

penetrometer plastic limit (PL) (Campbell, 1976). The

equation used was

�

�n

� 0:119ÿ 0:082w

PL(10)

Alternatively, � could be modelled as a quadratic

function of water content for each soil.

Recompression is generally assumed to occur along

the same line as rebound. However, this assumption

takes no account of the known tendency of soil to

compact slightly with repeated application of the same

load. Accurate modelling of the effects of repeated

loading is important because tandem wheels are often

used as a way of reducing compaction. O'Sullivan and

Robertson (1996) developed a simple but more rea-

listic model of rebound and recompression, which is

illustrated in Fig. 3. Recompression takes place along

the same straight line as rebound until a yield stress is

reached close to the VCL. Stresses greater than this

yield stress cause both non-recoverable and elastic

deformations. The slope of the steeper recompression

line, �, was found to be equal to the geometric mean of

�n and �, and the separation between the yield line and

the VCL, m, was 1.3, with units of ln (p).

Table 3

Constants of Eqs. (8) and (9) for estimating soil parameters from

water content and cone penetrometer plastic limits (PL)

Constant Sandy loam Clay loam

A 2.430 2.813

B 0.0055 0.0128

C 11.2 17.4

pp 6.918 5.996

vp 1.572 1.557

PL 17 26

The original data are in O'Sullivan et al. (1994).


Eqs. (8)±(10) give reasonably precise estimates of

speci®c volume. The residual mean square errors

between the estimated and original speci®c volumes

were 0.032 for the sandy loam and 0.076 for the clay

loam.

3. Implementation

The model is implemented as an Excel spreadsheet,

as mentioned in Section 1. On opening the spread-

sheet, the user is presented with a blank table contain-

ing a row for each tyre to be simulated and columns for

load, in¯ation pressure and tyre width and diameter.

There are two additional columns where the estimated

contact area and mean contact pressure appear once

the tyre data are entered. The contact areas are esti-

mated by Eqs. (1) and (2). The user also has the

opportunity to select soil type, initial bulk density

and water content pro®les. This information is used to

calculate the parameters of the virgin compression and

rebound lines (N, �n and �) from Eqs. (8)±(10). The

program contains routines to ensure that the ranges of

the original data are not exceeded.

The Visual Basic macro that runs the model is

activated from this opening screen. The user can

choose to start with a clean sheet or to append results

to those of previous runs. The macro chooses a stress

concentration factor (Eq. (3)) at each depth from the

initial density and water content. For each wheel, the

stress is applied in four increments. For each incre-

ment of stress, the major principal stress is estimated

at each depth from the load and contact area. The

intermediate and minor principal stresses are esti-

mated by Eq. (5) and the mean normal stress is then

calculated (Eq. (4)). Speci®c volume is calculated

from this stress from the virgin compression and

recompression lines (Fig. 3). This process is repeated

for each wheel in the system. At the end of the run, the

soil is allowed to rebound and the ®nal speci®c volume

is converted to bulk density (Eq. (6)). Rut depth is

estimated from the density changes but is likely to be

underestimated as the model does not account for

lateral displacement of soil.

As the model runs, the stresses and resulting spe-

ci®c volumes for each wheel are stored in a separate

sheet. This sheet is useful for detailed studies of how

the model is working. Once the run is completed, the

user is presented with a results sheet that contains the

®nal bulk densities for the system, which are also

plotted as a graph of bulk density against depth. This

sheet also contains the input information for the

wheels simulated, the soil type and the initial condi-

tions. If the user had chosen to append the output to

Fig. 3. A model of rebound and recompression in terms of specific volume (v) and mean normal stress (p).


existing output, the ®nal results for all systems are

displayed.

4. Model validation

The model is intended primarily to illustrate the

general principles that govern compaction and was not

designed to agree closely with ®eld measurements. In

particular, the soil compaction parameters and, thus,

model output, are very sensitive to water content

(Eqs. (8)±(10)). Therefore, even small differences in

soil properties between the test site and the soils used

in the model will lead to discrepancies. However, a

comparison with measured data can illustrate some of

the advantages and limitations of the model. Accord-

ingly, model output was compared with some of the

data in Smith and Dickson (1990), who carried out

their work on soils that were similar to the ones

included in the model.

First, we investigated the effects of moderate loads

and in¯ation pressures, using data for a 16.9±34 tyre.

Smith and Dickson (1990) measured dry bulk density

before and after running this tyre at two loads and two

in¯ation pressures on deeply loosened soil. The model

was run using water contents representative of wet soil

and it ranked the treatments in the same order as the

data. The agreement between measurements and

model was also good and the results for the treatments

causing the least and the most compaction are illu-

strated in Fig. 4. We investigated the effects of water

content and found that the model always ranked the

treatments in the correct order unless the soil was very

wet, when even a small load caused severe compac-

tion.

The model was also run for a 6 tonne trailer that

Smith and Dickson (1990) investigated on conven-

tionally ploughed soil. This run also used water con-

tents representative of wet soil. The agreement

between the modelled and measured bulk densities

was not so good in this case, as shown in Fig. 5. At the

bottom of the plough layer, 0.2±0.3 m depth, the

model underestimated compaction and it overesti-

mated compaction in the top few centimetres.

The discrepancy near the surface was probably due

to soil loosening by the lugs of driving wheels, the

failure of the model to account for lateral movement of

soil and measurement errors (Smith, 1985). The

underestimation of compaction at the bottom of the

plough layer is probably due largely to the failure of

the assumptions of an in®nite, homogeneous medium

in Eq. (3). The underlying dense subsoil causes the

stress generated by a heavy load to concentrate in this

layer but Eq. (3) cannot account for this effect. There-

Fig. 4. Comparison of model output (*) with measured data (*) for a 16.9R34 tyre carrying 1.20 tonne at 50 kPa inflation pressure (left) and

2.47 tonne at 200 kPa inflation pressure (right) on deeply loosened soil.


fore, predictions for systems that involve heavy vehi-

cles running on loose soil over a dense layer will

underestimate the actual compaction in the ®eld.

However, the model can rank systems in order of

the compaction they are likely cause. Users of the

model are given a choice of initial conditions which

were chosen to minimise this problem of stress con-

centration.

5. Applications of the model

The model can be used in a number of ways with

students. One application is a tyre selection exercise,

which is also relevant in consultancy. An example of

this type of exercise is to minimise the compaction

caused by the rear axle of a tractor of 5 Mg unladen

mass, ®tted as standard with 16.9R38 rear tyres, by

®nding suitable alternative tyres in manufacturers'

data books. The alternative tyres should have roughly

the same overall diameter as the standard. Three

possible low pro®le tyres were identi®ed: 600/

65R38, 680/75R32 and 800/65R32. The ®rst of these

alternatives could be ®tted on the existing rims but the

other two would require the additional expense of new

rims and wheel centres. The model was used to

estimate the compaction that each tyre is likely to

cause and the results are shown in Fig. 6. The 600/

65R38 would cause slightly less compaction than the

standard tyre. Both the other alternative tyres would

reduce compaction by a greater amount but the dif-

ference between them is small. The most suitable tyre

would depend on the severity of the compaction

problem and the farmer's willingness to invest in

alternative tyres. The 600/65R38 would give some

bene®t and would be relatively cost-effective but the

680/75R32 would probably be the best buy if compac-

tion was causing severe problems. A more complete

assessment would require information on the eco-

nomic impacts of compaction and, in particular, the

effect of compaction on crop yield, which is outside

the scope of the present model. The rolling circum-

ference would also need to be considered in the case of

a four-wheel drive tractor as the ratio of the circum-

ferences of front and rear tyres are ®xed.

A second example illustrates the effects of tandem

and single axle trailers on the two soil types. In this

example, the effects of a tractor and trailer with an

8 tonne payload were modelled with both a single axle

and tandem axles on the trailer. The in¯ation pressure

in the trailer tyres was reduced appropriately for the

smaller load being carried by each tyre in the tandem

con®guration. The model was run for the two soil

types and the results are compared with the model

predictions for a typical, unladen 70 kW tractor

(Fig. 7). On both soil types, the use of tandem axles

caused less compaction but the differences between

Fig. 5. Comparison of initial conditions (�), model output (*) and measured data (*) for a heavily laden trailer on conventionally ploughed

soil.


trailers were larger on the clay loam than on the sandy

loam. Subsoil compaction is likely to be greater with

the single axle trailer.

The output from the model must be interpreted in

terms of the impact on farm pro®tability or the envir-

onment. This aspect is not addressed within the model

at present due to the dif®culties in quantifying such

effects in a universal manner. We have found it useful

to give a scale to the results by modelling a system that

is known to cause no problems and a system that is

Fig. 6. Dry bulk densities estimated by the compaction model for three alternative rear tyres, 600/65R38 (}), 680/75R32 (�) and 800/65R32

(&), compared with the 16.9R38 tyre (*) fitted as standard to a 5 Mg tractor running on a sandy loam.

Fig. 7. The estimated effects of a tandem (}) and a single axle (&) trailer, each carrying 8 tonne, compared with an unladen tractor (~) on a

clay loam (left) and a sandy loam (right).


likely to cause severe damage. Further interpretation

needs local knowledge and some expertise, so students

will need guidance about the likely effects of compac-

tion on the land they are concerned about.

Acknowledgements

This work was carried out with ®nancial support

from the Scottish Of®ce Agriculture, Environment and

Fisheries Department. A copy of the Excel spreadsheet

is available by e-mail from [email protected].

This is not a commercial product, so no support can be

given and no liability is accepted by SAC.

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a simplified method for estimating soil compaction

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