Soil & Tillage Research 125 (2012) 14–22

The effects of compaction and soil drying on penetrometer resistance

W. Gao a, C.W. Watts b, T. Ren a, W.R. Whalley b,*a Department of Soil and Water Sciences, China Agricultural Univ., Beijing 100193, Chinab Rothamsted Research, West Common, Harpenden, St. Albans AL5 2JQ, UK

A R T I C L E I N F O

Keywords:

Soil drying

Soil structure

Pedotransfer functions

A B S T R A C T

Penetrometer resistance is widely used as a measure of the mechanical impedance that roots experience

in either drying or compacted soil. However, there are relatively few models to predict penetrometer

resistance that can be applied without detailed knowledge of soil texture, organic matter content, soil

water status, density or other soil variables. Few models allow the effects of management on

penetrometer resistance to be predicted in a simple way. It would be useful if it were possible to predict

the effects of structure, compaction, and soil drying on penetrometer resistance. We designed a

laboratory experiment to explore how compaction and subsequent soil drying affected the penetrometer

resistance of three soils: a loamy sand and two silty clay soils with very different organic carbon

contents. By assuming that penetrometer resistance is proportional to the small strain shear modulus, G,

we were able to develop an empirical model to explain the effects of compaction and soil drying on

penetrometer resistance. The parameters of the model were determined by fitting it to experimental

data collected in the laboratory. The model was tested on field data using sensed matric potential data

and measured soil density data. Model predictions were compared with those obtained with an earlier

model. Both approaches explained approximately 60% of the variance in the measured penetrometer

data. The future application of this approach is discussed.

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1. Introduction

Lower root elongation is almost always associated with lowershoot growth and hence yields (Whalley et al., 2008). While themechanistic explanation for the effects of high soil strength onlower yields is not fully understood (Dodd et al., 2010), there is awidely reported association between strong soil and lower yields(Masle and Passioura, 1987; Lipiec and Hatano, 2003; Whalleyet al., 2006, 2008). Interpreting the effects of abiotic stresses onboth root and shoot elongation can be complicated because they(water stress and soil strength in particular) are highly correlatedand it can be unclear which stress (or stress combination) islimiting growth (Whitmore and Whalley, 2009; Bengough et al.,2011). Penetrometer resistance is widely used as a measure of themechanical impedance that roots experience in either drying orcompacted soils (Whalley et al., 2007). The resistance of a standardpenetrometer tends to be higher than that experienced by roots,mainly due to the effects of soil to metal friction that is higher thanroot to soil friction (Bengough et al., 1997; Whalley et al., 2005).However, penetrometer resistance is closely correlated with bothroot and crop growth.

* Corresponding author. Tel.: +44 01582 763133; fax: +44 01582 760 981.

E-mail address: Richard.whalley@rothamsted.ac.uk (W.R. Whalley).

0167-1987/$ – see front matter � 2012 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.still.2012.07.006

It would be useful to have a simple model to relate soil physicalconditions and the effects of soil management to penetrometerresistance. The soil factors that affect penetrometer resistance areknown, for example: bulk density, soil water status, soil depth andcompaction episodes (Aggarwal et al., 2006; Whalley et al., 2007;Whitmore et al., 2011). It is also the case that many approaches topredict soil penetrometer resistance from a number of soilcharacteristics including particles size distribution, organic mattercontent, bulk density, and water content have been published.Recent examples have been described by To and Kay (2005), Stockand Downes (2008), and Vaz et al. (2011) and these are oftenreferred to as pedotransfer functions (PTF). While they are useful ina descriptive sense and can give direct predictions of the effect ofsoil drying on penetrometer resistance, their usefulness fordeveloping a soil management strategy is limited. An interestingapproach is described by Dexter et al. (2007), who used the slope ofthe water release characteristic at the point of inflexion to predictpenetrometer resistance. The advancement made by Dexter et al.(2007) was to relate a soil property that can be manipulated by asoil management strategy to penetrometer resistance. Theapproach of Dexter et al. (2007) is more sophisticated than theconventional PTF because more subtle aspects of soil structure canbe considered. Another important limitation of the conventionalPTF approach is that they require too many soil variables to bemeasured and many of these (e.g. particle size distributions) vary

W. Gao et al. / Soil & Tillage Research 125 (2012) 14–22 15

around fields and are not easily determined. Progress has beenmade at reducing the number of variables required by PTF modelsof penetrometer resistance, mainly by defining soil water status asthe product, Sc, where S is the degree of saturation and c is thematric potential (Whalley et al., 2007). For a wide range of loosesoils penetrometer resistance was simply found to be proportionalto Sc (Whalley et al., 2005). In recent work, Gao et al. (2012)developed an empirical model for penetrometer resistance, whichwas based on the compression characteristic of soil. For relativelymoist and hence compressible soils, they were able to predict thepenetrometer resistance of five soils compressed to differentdegrees and drained to high matric potentials (i.e. very moist soils).The advantage of this model was that it used only three parametersand was independent of soil type within the range of soils studied.An application of this model would be to relate the mechanicalimpedance to seedling growth to ground pressures due totrafficking. It would be useful if it were also possible to predictthe effects of soil drying on the increase in penetrometer resistanceas a function of soil structure and previous compaction episodes.Ultimately, this would allow us to predict how compaction and soilmanagement affect yield.

In this paper our objective is to explore the effects of appliedstress, density, matric potential, and soil structure (as summarizedby the air entry potential) on penetrometer resistance. We developa model for penetrometer resistance with relatively few fittedparameters. This model is based on the simple idea thatpenetrometer resistance is proportional to the shear modulus.The model was tested using penetrometer measurements from thefield, sensed matric potential data, and measured soil density data.Model predictions were also compared with those obtained withan earlier empirical model of Whalley et al. (2007). The utility ofthe model developed is that it can be used to explore the effect ofrelatively complex interactions between applied pressure, voidratio, air entry potential and matric potential on penetrometerresistance.

2. Materials and methods

2.1. Lab experiments

2.1.1. Soil samples

Three soils with contrasting physical and mechanical propertieswere used in our experiments (Table 1). They were collected fromthe top 20 cm of two Rothamsted Research experimental fields:Highfield (Harpenden) and Butt Close (Woburn). The soil textureswere silty clay loam that had grassland and fallow soil manage-ment (Watts and Dexter, 1997) and loamy sand that was from anarable site (Whalley et al., 2008). The soils will be referred to as:arable loamy sand (ALS), Fallow, silt clay loam (FZCL), and Grassland,

Table 1The properties of soil used in the experiments.

Property Rothamsted

Soil abbreviation FZCL

Land use Fallow

Location Highfield Rothamsted

Latitude 51.804208N

Longitude 0.361408W

Soil type FAOa Chromic Luvisol

Sand (g kg�1 dry soil) 178

Silt (g kg�1 dry soil) 525

Clay (g kg�1 dry soil) 297

Texture, SSEWb classa Silt clay loam

Particle density (g cm�3) 2.614

Organic matter (g kg�1 dry soil) 20

a Avery (1980).b Soil Survey of England and Wales.

silt clay loam (GZCL). Soil samples were gently broken up by handunder field moist conditions before being air dried and sievedthrough a 2-mm sieve.

2.1.2. Consolidation behaviour

We determined the water content um at which these soils weremost compressible with the method described by Gregory et al.(2010). The air-dried soil samples were slowly wetted to a range ofwater contents. The moist soils were stored in plastic bags at 4 8Cfor 48 h before being packed into plastic tubes (64 mm in diameter,50 mm height) using a pneumatic soil press fitted with a 60-mmdiameter piston. The press was set to give soil an axial stress of200 kPa. There were three replications for each soil and watercontent. During the compaction process, there was no visible waterdrainage from the soil cores. The wetted soil samples were packedinto the tubes in layers approximately 10-mm deep. The soil coreswere weighed before the samples were oven-dried at 105 8C for24 h for the determination of dry bulk density and water content.

2.1.3. Soil water release characteristic curve and penetrometer

resistance measurement

The complete experimental regime is summarized in Fig. 1. Air-dry soil samples were wetted to the water contents um, where thesoil was most compressible. The soil samples were thencompressed with an axial pressure of 30, 200, and 1000 kPa,respectively. These axial pressures were selected to represent low,moderate, and high axial pressures covering the range that mightbe experienced in the field (e.g. Kim et al., 2010). The cylindricalplastic tubes (64 mm in diameter, and 50 mm height) were packedin layers approximately 10 mm deep. The final height of soil in thecores was typically 46 mm. In the case of the soil compacted withan axial stress of 1000 kPa there was some water drainage from thesoil during compaction.

The compressed soil samples were then equilibrated on atension table at 0 kPa. Water retention characteristics weredetermined by equilibrating the saturated cores to a range ofwater potentials; �1, �3, �5, �7, �10, and �30 kPa with a tensiontable and �100, �300, and �500 kPa, with a pressure plateapparatus. At each water potential, the new weight and height ofsoil cores were recorded. The measurements at �1, �3, �5, and�7 kPa were used solely to determine the shape of the waterrelease characteristic at high matric potentials and not used insubsequent measurements. The penetrometer resistance wasmeasured on all the other samples. The method of measuringsoil penetrometer resistance, Q, was described by Gao et al. (2012).Briefly, a small cone penetrometer with a cone-base diameter of2 mm and 608 cone angle was driven into the soil at a rate of20 mm/min using a universal test frame (Davenport–Nene TestFrame DN10, Wigston, UK). The force required to push the cone

Woburn

GZCL ALS

Grass Arable

Highfield Rothamsted Butt Close, Woburn

51.804028N 52.012208N0.361828W 0.596658WChromic Luvisol Cambic Arenosols

179 876

487 55

333 70

Silt clay loam Loamy sand

2.464 2.660

54 10

Fig. 1. The steps of the measuring soil water release curve and penetrometer

resistance.

W. Gao et al. / Soil & Tillage Research 125 (2012) 14–2216

into the soil was measured using an electronic balance andrecorded at 1 Hz. The penetrometer was pushed 30 mm into thesoil and three replicate measurements were made in each soil core.Following these measurements, the soil samples were oven-driedfor 24 h at 105 8C, to determine soil dry bulk density and watercontent. In total 45 samples were measured for each soil: 3(compression pressure levels) � 5 (water potentials) � 3 (replica-tions).

2.2. Field experiments

We used an existing field experiment, on the Woburn site (seeTable 1), that was designed to investigate the effect of irrigationand nitrogen fertilizer on yields of 12 different wheat varieties. Thefield experiment was a split–split-plot design in 3 blocks. Irrigationwas applied to main plots and the nitrogen treatment to subplots.Varieties were randomly assigned to sub-subplots of the nitrogensubplots. In total there were 48 treatment combinations, 2 levels ofirrigation by 2 levels of nitrogen by 12 varieties, giving 144 plots. Inthis work we only reported data from a single high-yielding UKwheat variety (Robigus).

Soil penetrometer resistance was measured on the 12 plotsgrowing Robigus with a Bush recording penetrometer (Findlay,Irvine Ltd., Bog Road, Penicuik, Midlothian, UK) fitted with a9.45 mm diameter (base area 7 � 10�5 m), 308 cone. Fivepenetrations were made per plot on five dates of 2010 duringthe growing season: 12/04, 26/04, 07/05, 25/05, and 04/06.

To measure soil water content one access tube per plot wasinstalled to accommodate a dielectric soil moisture sensor (ProfileProbe, Delta-T Devices, Burwell, Cambridge, UK).Water contentmeasurements were made at depths of 0.1, 0.2, 0.3, 0.4, 0.6, and1.0 m at approximately weekly intervals (see Whalley et al., 2004).Matric potential was also measured with buried porous matrixsensors at a depth of 20 cm as described by Whalley et al. (2009)and these were logged at hourly intervals. Bulk density at a depthof 20 cm was determined by taking soil cores.

Only soil penetrometer resistance and soil drying data are ofconcern in this paper and no other measurements are discussed.

2.3. A prediction of penetrometer resistance based on the small strain

shear modulus

In this work we used relatively dry soils that were likely to failelastically and we explore the hypothesis that Q is proportional to

an elastic modulus. The small strain shear modulus, G, is given by

G ¼ V2S r (1)

where VS is the velocity of a shear wave and r is the dry bulkdensity of soil. Whalley et al. (2012) have shown that in bothvariably compacted and saturated soils the velocity of a shear waveis given by

VS ¼ 2:368ð7:085 � eÞ2

1 þ es0:746

s � cccae

� ��0:55 !0:356

(2)

where e is the void ratio, ss is the net stress, c is the matricpotential, and cae is the matric potential at air entry. We will testthe function

Q ¼ kG (3)

where k is an adjustable parameter. G, could in principle, becalculated with Eqs. (1) and (2). It is necessary to know the air entrypotential to evaluate Eq. (2), but this may be estimated from thematric potential at the point of inflexion on the water releasecharacteristic (cinf). According to Dexter and Bird (2001)

cinf ¼1

a1

m

� �1=n

(4)

where a, m and n are Van Genuchten (1980) model parameters.An alternative to predicting, G, is to write Eq. (3) out in full as

Q ¼ r A�ðF � eÞ2

1 þ es p

s � cccae

� �b ! f

0@

1A

2

(5)

and fit it to our data. Here F, A*, p, f and b are empirical, adjustableparameters. A* is a lumped parameter (i.e. it includes both A (2.368in Eq. (2) see Whalley et al., 2012) and k). In our work Eq. (5) can befitted in two ways. Firstly, we may assume that ss is the axialcompression stress at the start of the experiment (i.e. 30, 200or1000 kPa, see Fig. 1). In this case the parameterized version ofEq. (5) provides an empirical model, which relates compaction ofwet soil to the increase in penetrometer resistance that occurs withsoil drying. Secondly, we may interpret the value of ss in its strictmeaning of the applied stress at soil surface when the penetrome-ter resistance is being measured. In this case ss = 0, and our datadoes not allow p to be estimated.

2.4. Statistical analysis

All the statistical analysis reported were performed usingGenstat v141. Models were fitted using the least-squares method.Comparisons between treatment means were made with analysisof variance.

3. Results

3.1. Consolidation data

Fig. 2 shows the relationship between dry bulk density andwater content for each soil following the application of 200 kPauniaxial pressure. Soil type significantly affected the maximumbulk density (P < 0.001). The soil with the greater soil organicmatter content had the lowest bulk density. The water contents atwhich bulk density reached maximum (um) were 0.17, 0.24, and0.35 g g�1, for soils ALS, FZCL and GZCL, respectively.

The dry bulk densities of the three soils after compaction withaxial stresses of either 30, 200 or 1000 kPa are given in Table 2. There-saturation process increased the volume of soil (Bullock et al.,1985), especially for FZCL and GZCL. As a result, the values of bulk

Water content (g g-1 )

0.00 0.10 0.20 0.30 0.40

So

il d

ry b

ulk

den

sit

y (

g c

m-3

)

1.10

1.20

1.30

1.40

1.50

1.60

1.70

1.80

ALS

FZCL

GZCL

Fig. 2. Consolidation of three soils under a constant 200 kPa compression pressure

as a function of water content. The curves were fitted using with a third-order

polynomial function. The bars indicate the S.E.

Table 2Dry bulk densities of three soils with the initial soil water content 0.17, 0.24 and

0.35 g g�1, respectively, after 30, 200 and 1000 kPa compression.

Soil Compression pressure (kPa)

30 200 1000

Bulk density (g cm�3)

ALS 1.50 (�0.02a) 1.58 (�0.02) 1.67 (�0.01)

FZCL 1.24 (�0.01) 1.53 (�0.01) 1.80 (�0.01)

GZCL 0.95 (�0.01) 1.16 (�0.01) 1.29 (�0.02)

a Standard error, n = 15.

W. Gao et al. / Soil & Tillage Research 125 (2012) 14–22 17

density following equilibration at 0 kPa were somewhat smallerthan the maximum bulk densities reported in Fig. 2. The bulkdensities of ALS, FZCL, and GZCL range from 1.50 to 1.67 g cm�3, 1.24to 1.80 g cm�3, and 0.95 to 1.29 g cm�3, respectively.

3.2. Water retention characteristic curves

The water retention characteristic curves of the soils are shownin Fig. 3. We fitted the van Genuchten function (Van Genuchten,1980) to our data and the parameters are listed in Table 3. Analysisof variance (ANOVA) indicated that the gravimetric water contentfor the most compressed soil was smaller than the water contentfor the low compression treatments at a higher matric potential ofapproximately 1 kPa (P < 0.001). This is consistent with the resultsreported by Gregory et al. (2010). The saturated water content inGZCL was higher than in FZCL (P < 0.001).

3.3. The relationship between penetrometer resistance, compaction

and water potential

Fig. 4 shows penetrometer resistance, Q, plotted against matricpotential, c, and the initial axial compression pressure. Analysis ofvariance showed that penetrometer resistance was affectedsignificantly by initial compression pressure (P < 0.001) andmatric potential (P < 0.001). For ALS and FZCL, we found Log10(Q)linearly related to Log10(c). For GZCL, Log10(Q) increased at matricpotentials smaller than �100 kPa, but was insensitive at highermatric potentials. At a given c, soil Q was significantly greater inhighly compressed soils compared to loose soils (30 kPa compres-sion pressure) (P < 0.001).

For the loamy sand (ALS) the relationships between Log10(Q)and Log10(c) for the three different levels of consolidation wereparallel to each other (P < 0.001, from grouped regressionanalysis). There were no simple relationships between the appliedtreatments (soil type, compression, and matric potential) andLog10(Q) (see Fig. 4).

3.4. A model for penetrometer resistance

We fitted Eq. (5) to measured data and the values of the fittedparameters are given in Table 4. When fitting this equation itbecame clear that it was over parameterized to the extent that itwas difficult to estimate stable values of A* and F. This was becauseif A* increased, F decreased to compensate. Thus we set A* = 1.

However, this meant that adjustments in F, had to compensate forthe differences in void ratio as well as providing a scaling factor. Tomake the fitting process possible, with A* = 1, we found it wasnecessary to use kN m�3 as density units in Eq. (5). Given that theequation is dimensionally inconsistent due to the exponent p and f,this seemed unimportant.

We made two different assumptions about the value of netstress. First we assumed that ss was the compaction stress (seeFig. 1). In this case the model is entirely empirical; however, ourexperimental regime (Fig. 1) represents the effects of consolidationof wet soil and the subsequent effects of drying. The fitted values ofQ are plotted against the measured data in Fig. 5a. The fitted curveexplained 85.1% of the variance in our experimental data. SecondEq. (5) was fitted assuming ss = 0 kPa (Fig. 5b). This is a realisticdescription of the soil at the point where the penetrometerresistance is measured. The fit to the data is somewhat poorer andexplained 77.3% of the variance in the experimental data. With thisapproach the value of p cannot be determined from ourmeasurements. Interestingly, the values of the parameters thatare common for both fitting approaches are similar (see Table 4).Importantly for the soils we tested we were able to use the sameset of adjustable parameters for all three soils.

3.5. Prediction of penetrometer resistance measured in the field

Fig. 6 shows predictions of the penetrometer resistance, Q, forthe field soil made with two different methods plotted against themeasured data. In addition to Eq. (5) we used the model describedby Whalley et al. (2007) and written as

Log10 Q ¼ 0:35ð�0:009ÞLog10ðcSÞ þ 0:93ð�0:0572Þr

þ 1:2623ð�0:0832Þ (6)

where S is the degree of saturation. When Eq. (5) was used topredict penetrometer resistance, we assumed an overburdenpressure (ss) of 4 kPa due to the weight of the seedbed and an air-entry potential of �12 kPa. The agreement between predictionsand measurements of Q in the field were similar with both Eqs. (5)and (6) and they explained approximately 60% of the variance inthe field data.

4. Discussion

4.1. Penetrometer resistance, matric potential and consolidation

Our data confirm the widely reported increases in penetrome-ter resistance associated with soil drying and compaction (e.g., Toand Kay, 2005). The effect of higher organic matter content inlowering soil penetrometer resistance can be seen on the silty loamsoil (compare FZCL and GZCL in Fig. 4b and c). Higher soil organicmatter contents made Q less sensitive to soil drying (see Fig. 4f).From Fig. 4 it was clear that there is not a simple relationshipbetween the applied pressure, soil drying and Q.

Fig. 3. Soil water retention characteristic curves of the three soils investigated under three levels of compression pressure: 30, 200 and 1000 kPa. The curves were fitted using

the van Genuchten model (van Genuchten, 1980).

Table 3Parameters of the van Genuchten function used to predict water content (u) dynamics with soil water potential (c), as shown in Fig. 3. The restriction m = 1 � 1/n was applied

during the fitting process.

Soil s (kPa) van Genuchten function parameters R2 cinf ¼ 1a

1m

� �1=n

us ur a n

ALS 30 0.261 0.067 0.618 3.477 0.967 6

200 0.234 0.037 0.463 3.022 0.986 29

1000 0.197 0.000 0.333 3.065 0.965 259

FZCL 30 0.389 0.145 0.712 3.583 0.983 3

200 0.260 0.168 0.425 4.207 0.987 32

1000 0.196 0.155 0.323 7.045 0.988 145

GZCL 30 0.594 0.364 0.748 5.208 0.993 2

200 0.434 0.327 0.329 3.820 0.995 195

1000 0.373 0.327 0.398 6.807 0.992 37

s is the initial compression pressure; us is the saturation water content (g g�1); ur is the residue water content (g g�1); a and n are the fitted parameters; R2 is the coefficient of

determination and is an indicator of goodness-of-fit; Cinf is the matric potential at the point of inflexion and taken as the air entry value (kPa).

W. Gao et al. / Soil & Tillage Research 125 (2012) 14–2218

Fig. 4. Penetrometer resistance, Q, of soils plotted against the compression pressure before drainage, s, and the matric potential, c, to which the soils were dried. For each

combination of compression pressure and matric potential the three replicates are plotted.

W. Gao et al. / Soil & Tillage Research 125 (2012) 14–22 19

4.2. The assumptions of Eq. (5)

Our model is based on the simple idea that penetrometerresistance is proportional to the small strain shear modulus, G.

Intuitively, the shear modulus seems insufficient to describe thecomplex deformations experienced by the soil during penetrome-ter measurements where soil is compressed and deformed in waysthat may be more appropriate to the other elastic moduli (i.e. Bulk

Table 4Parameters of the Eq. (5) when fitted to our experimental data. Due to over-

parameterization in Eq. (5) A* was fixed at 1. Two sets of parameters are listed for

different assumptions about ss. The assumption that ss = 0 is the most realistic but p

cannot be determined.

Parameters Value

ss = axial compaction

pressure (see Fig. 1)

ss = 0

F 3.469 (�0.208) 3.73 (�0.113)

A* 1 1

f 0.1887 (�0.0231) 0.1622 (�0.0513)

p 0.399 (�0.128) NA

b �0.1489 (�0.0539) �0.202 (�0.0134)

W. Gao et al. / Soil & Tillage Research 125 (2012) 14–2220

modulus and Young’s modulus). However, provided that thePoisson ratio has a narrow range and does not vary greatly with soildrying or consolidation, the relationships between the differentelastic moduli are deterministic. In the use of G it is implicit thatfailure is dominated by elastic processes, and since we are

Fig. 5. The fitted values of penetrometer resistance, Q from Eq. (5) plotted against the m

stress during sample preparation (see panel a) which explained 85.1% of the variance i

explained 77.3% of the variance in the data.

interested in relatively dry soils, this is perhaps a reasonableassumption.

In our comparisons, penetrometers of different size have beenused. Our model (Eq. (5)) for penetrometer resistance wasdeveloped using data from a 2-mm diameter cone whereas thefield data were collected using a penetrometer with a 9.45-mmdiameter cone. The simpler model of Whalley et al. (2007) (Eq. (6))was parameterized using a penetrometer with a 4-mm diametercone. Hernanz et al. (2000) have shown that penetrometerresistance is not particularly sensitive to the diameter of thecone. Misra and Li (1996) concluded that when the diameter of thepenetrometer was greater than 2 mm, the effect of penetrometersize on penetrometer resistance could be ignored. Thus we ignoredthe effect of penetrometer size.

4.3. Predicting field data and the use of models to aid soil management

The simple model of Whalley et al. (2007) and the morecomplex model developed in this work (Eq. (5)) gave predictions of

easured data. Here we also assumed that the net stress was equivalent to the axial

n the data. We also fitted Eq. (5) assuming a net stress of zero (see panel b) which

Fig. 6. A comparison of penetrometer resistance measured in the field with

predicted penetrometer resistance. Penetrometer resistance estimated with three

different approaches is plotted against penetrometer resistance measured in the

field for the loamy sand (ALS). For the field data penetrometer resistance, water

content and matric potential data were available at a depth of 20 cm. To use Eq. (5)

we assumed an over burden pressure of 4 kPa (i.e. ss) and an air entry potential of

�12 kPa.

W. Gao et al. / Soil & Tillage Research 125 (2012) 14–22 21

penetrometer resistance which were similar to the measuredvalues (Fig. 6). Eq. (6) can be used with relatively little informationsince only soil density, saturation, and matric potential need to beknown, although without modification the effect of depth cannotbe studied (see Whitmore et al., 2011). Although additionalinformation is needed to use Eq. (5) it may be a more usefulmanagement tool because it has some predictive capacity. It can beused to explore the effects of ground pressure and depth (ss), soilstructure (cae), soil drying (c), and soil density (r or e). WhenEq. (5) was fitted assuming ss = axial compaction pressure (on thewet soil), the effects of ground pressure during seedbed prepara-tion on the penetrometer resistance in the seedbed when it driescan be explored.

Fig. 7. Predictions of the effects of applied pressure (or overburden pressure) and

matric potential on penetrometer resistance. We used the compression

characteristic of ALS to relate net stress, ss, to void ratio and density.

In Fig. 7 we plotted penetrometer resistance calculated withEq. (5) against matric potential and applied pressure. We used thecompression characteristic for loamy sand (Whalley et al., 2011) tocalculated density and void ratio for various applied pressures. Thedata in Fig. 7 predict that any increase in net stress (e.g., groundpressure), during seedbed preparation for example, increasespenetrometer resistance and high values occur at relatively highmatric potentials. Eq. (5) provides an approach to investigate theeffect of relatively complex interactions between compactionpressure (or depth) and soil drying on penetrometer resistance.

It should be noted that Eq. (5) has only one more adjustableparameter than Eq. (6), since A* is set to 1 (see Table 4). For bothEqs. (5) and (6) the values of the adjustable parameters were notsensitive to the soil type. In future work it will be important to:

(i) Test Eq. (5) with field data from a wider range of soils.(ii) Extend the scope of Eq. (5) so that the effect of soil moisture at

the time of compaction can be taken into account.(iii) Determine the ameliorative effects of wet–dry cycles.

Point (ii) is readily dealt with by additional experimental workand by representing ss as an effective stress variable taking intoaccount matric potential at the time of compaction. Theameliorative effects of wet–dry cycles may be more problematic;however, it is likely that they can be included in our model byadjustment to both density and the air entry potential. To apply themodel we have developed in a more practical application, there issome scope of simplification because

ccae

� �b

(7)

be replaced by the degree of saturation, S (see Whalley et al., 2012).It is also the case that sensors to measure soil density are becomingmore common (e.g. Liu et al., 2008). A potential opportunity is tovalidate the basis for the development of Eq. (5) by comparingmeasured Q and G data.

5. Conclusion

We have confirmed the widely reported relationships betweenpenetrometer resistance, compaction and soil drying. A novelempirical model to explain penetrometer resistance was proposedthat allows the effects of applied pressure, density, air entrypotential and matric potential to be investigated. We discuss thepotential of this model for use as a soil management tool as well asthe limitations that need to be addressed. We also propose futureresearch priorities.

Acknowledgements

This work was supported by EPSRC grant EP/H040617/1 usingfacilities funded by the UK Biotechnology and Biological SciencesResearch Council (BBSRC). Weida Gao is supported by the ChineseScholarship Council. We thank Rodger White for help with thestatistical analysis.

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