A method for prediction of soil penetration resistance

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Soil & Tillage Research 93 (2007) 412–419

A method for prediction of soil penetration resistance

A.R. Dexter *, E.A. Czyz, O.P. Gate

Institute of Soil Science and Plant Cultivation (IUNG-PIB), ul. Czartoryskich 8, 24-100 Pulawy, Poland

Received 2 January 2006; received in revised form 24 April 2006; accepted 27 May 2006

Abstract

A new equation for predicting penetration resistance of soil is presented. The equation contains two main additive terms: the first

is a measure of the degree of compactness of the soil and the second gives the contribution of pore water to the soil strength. It is

proposed that these terms are applicable to soils of different texture, at different bulk densities and at different water contents. The

equation is calibrated and tested using values of penetrometer resistance measured in the field at a range of locations in Poland.

Predictions from the equation are compared with predictions from two other published equations. It is shown that the performance

of the proposed equation is superior to the other two, at least for the Polish data set used in this work. On the basis of the assumption

that the proposed equation is correct, predictions of penetrometer resistance are made using pedotransfer functions to illustrate

typical effects of soil texture, bulk density and water content.

# 2006 Elsevier B.V. All rights reserved.

Keywords: Effective stress; Pedotransfer functions; Penetrometer resistance; S-theory

1. Introduction

Penetration resistance of soil is usually measured

with a penetrometer. Penetrometer resistance is widely

measured because it provides an easy and rapid method

of assessing soil strength. The theory of penetrometers

is presented in several publications (e.g. Bengough

et al., 2001). In these publications it may be seen that the

resistance to penetration is governed by several more

basic properties including soil shear strength, soil

compressibility and soil/metal friction. Unfortunately,

each of these factors is difficult to measure or predict,

and so approaches using these factors do not facilitate

the use of penetrometers.

The penetration resistance is itself of little value.

However, it correlates with several other properties that

are themselves of direct practical importance. For

example, the draught force (and hence the energy

* Corresponding author.

E-mail address: [email protected] (A.R. Dexter).

0167-1987/$ – see front matter # 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.still.2006.05.011

requirements) of tillage implements (e.g. Dawidowski

et al., 1988), vehicle trafficability (e.g. Dexter and

Zoebisch, 2002) and the growth (or elongation rate) of

plant roots (e.g. Taylor and Ratliff, 1969) in the soil.

These practical aspects are extremely difficult and time

consuming to measure and to study directly. Therefore,

penetration resistance is often used as a surrogate

measurement.

There is a need to be able to predict penetrometer

resistance from basic soil properties such as the soil

composition, bulk density and water content. It is

generally found that for any one soil, it is quite easy to

produce an empirical equation that accounts for

differences in bulk density and water content. However,

the predictions are often not so good when different

soils are being compared.

A typical equation used for prediction of penet-

rometer resistance, Q, is that used by da Silva and Kay

(1997):

Q ¼ aubDc (1a)

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A.R. Dexter et al. / Soil & Tillage Research 93 (2007) 412–419 413

which may also be written in terms of natural logarithms

as

ln Q ¼ ln aþ b ln qþ c ln D (1b)

where, D is the bulk density of the soil, u is some

measure of the soil water content and a, b and c are

adjustable parameters. Eqs. (1) can work quite well for

any one soil. When a range of soils is considered, then

additional pedotransfer functions (PTFs) are often used

with the form

a ¼ A1 þ A2 ðclayÞ þ A3ðOMÞ þ � � �b ¼ B1 þ B2 ðclayÞ þ B3ðOMÞ þ � � �c ¼ C1 þ C2 ðclayÞ þ C3ðOMÞ þ � � �

(2)

where, clay is the soil clay content, OM the organic

matter content, and the coefficients Ai, Bi and Ci are

determined by experiment and regression. This

approach typically uses at least nine different coeffi-

cients.

However, it cannot really be expected that an

equation such as Eq. (2) based on D and u could be

very successful. Common experience shows that bulk

density is not a good measure of the ‘‘degree of

compactness’’ of soil. For example, a bulk density of

1.4 Mg m�3 is a high value for a clay but is a low

value for a sand. Similarly a water content of a clay

that feels ‘‘dry’’ may be sufficient to make a sand feel

‘‘wet’’. Therefore, bulk density and water content do

not seem to form a very sound basis for a prediction

equation.

Canarache (1990a, 1990b) produced a method and a

computer program called PENETR for predicting Q.

This uses more complex relationships for the effects of

water content, clay content, bulk density, etc.

Another prediction equation has been proposed

recently by To and Kay (2005). This takes the form

Q ¼ ahb � ch (3)

Here, h is the pore water suction which is numerically

equal to the modulus of C (the matric water potential)

and the terms a, b and c (which do not have the same

values as those given in Eqs. (1) and (2)) are determined

as PTFs using equations of similar type to those shown

in Eq. (2), in this case having a total of up to 13

coefficients. The values of h were adjusted in the

laboratory. To and Kay (2005) obtained a value of

r2 = 0.47 when Eq. (3) was applied to undisturbed

samples of Canadian soils of all textures. However,

the value of r2 could be increased if the equation was

applied only to soils having a limited range of texture.

Practical application of Eq. (3) requires either measure-

ment of water potential (e.g. using tensiometers) or the

prediction of water potential using measurements of soil

water content in combination with a water-retention

curve that has been measured on the same soil at the

same density.

It should be noted that Canarache (1990a, 1990b)

and To and Kay (2005) did their measurements in the

laboratory on soil samples collected from the field. With

this approach, the values of penetration resistance, bulk

density and water content were all measured on the

same samples that were contained in steel cylinders.

This approach is not possible with measurements of

penetration resistance made in the field.

Dexter (2004a, 2004b, 2004c) defined a quantity S as

the slope, du/d (ln h), of the water retention curve at its

inflection point. He noted that values of S appeared to

have the same physical meaning in soils of all textures.

For example, it was observed that growth of plant roots

ceased at around S = 0.02, probably because of

mechanical impedance as can be measured with a

penetrometer. This led to the idea that S may be related

to penetrometer resistance and this is the subject of this

paper.

In this paper, we propose and test the equation

Q ¼ aþ b

�1

S

�þ cs0 (4)

where S is from Dexter (2004a, 2004b, 2004c) and s0 isthe effective stress. S was identified as an index of soil

physical quality and 1/S is a measure of the degree of

compactness of soil. It should be noted that this is

different from the measure of degree of compactness

used by Hakansson (1990). However, the term ‘‘degree

of compactness’’ is also used here because it conveys

exactly the meaning of (1/S).

The effective stress term, s0, gives the contribution of

the pore water to soil strength. This term has two

components: a pore water pressure term and a term due

to the surface tension in water menisci between the soil

mineral particles (Towner and Childs, 1972). Vepraskas

(1984) showed that the water menisci term could be

ignored for degrees of saturation, x > 0.4. The resulting

simplified equation was used successfully by Mullins

and Panayiotopoulos (1984) and by Whalley et al.

(2005), and will also be used here.

Because the evidence suggests that values of S and s0

have the same physical meanings in all soils, it seemed

possible that Eq. (4) may be applicable to widely

different soils with only its three coefficients a, b and c.

It should be noted that the effects of clay and organic

matter contents (and other factors) are already included

A.R. Dexter et al. / Soil & Tillage Research 93 (2007) 412–419414

in Eq. (4) through the two terms S and s0. The purposes

of this paper were to test Eq. (4) and to compare its

performance with that of the Canarache (1990a, 1990b)

and the To and Kay (2005) models.

2. Materials and methods

2.1. Soils

The measurements were made and samples were

collected from agricultural fields in different locations

in Poland. The positions of the locations were measured

by GPS for reference purposes and will enable the same

positions to be studied again in future, if required. The

samples represented soils with several genetic origins

including: glacial till, loess and alluvium. Penetration

resistance was measured and soil samples were

collected at depths of 10, 20, 30, 40 and 50 cm as

much as possible. In some cases, the soil was too dry

and strong below the normal depth of tillage (around

25 cm) for penetrations and sample collection to be

carried out. In these cases, only the plough layer was

measured and sampled.

A total of 85 different soil layers are represented.

Samples of these soils were all measured, collected,

stored and analysed by the same people and in the same

way. They, therefore, comprise a rather reliable data set

having consistent measurement errors.

The particle size distributions of the soils were

determined by sieving and sedimentation and the organic

matter contents were measured by wet oxidation.

The samples were not collected in the period

immediately following tillage in the spring when the

spatial variability of soil physical properties is high,

but mostly in late June, July or early August which is

just before or just after harvest. At the time of sample

collection, the soil had settled to a quasi-equilibrium

state. The crops in the fields were mostly barley or

wheat. Although visible wheel tracks were avoided,

it is possible that earlier wheel tracks, that were no

longer visible, may have contributed to spatial hetero-

geneity.

Sample collection for measurement of particle size

distribution, bulk density, water content, and water

retention characteristics were made from an area of

approximately 1 m2 in each field. Penetrometer

penetrations were made in an area of about 2 m radius

from the centre of the sample collection area. Therefore,

all samples and all measurements were made as nearly

as practically possible from a single point in each field.

This was in an attempt to reduce the effects of spatial

variability to a minimum.

2.2. Penetrometer resistance

A model CP20 cone penetrometer (Agridry RIMIK

Pty. Ltd., Toowoomba, Australia) was used in the field

at all locations. This measures the mean vertical stress

required for penetration of a steel cone of 12.8 mm

diameter and 308 total included angle. The maximum

value of stress that can be recorded is Q = 5000 kPa.

The penetrometer records electronically the value of Q

at intervals of 2.5 cm. The data were subsequently

down-loaded to a computer for analysis. We used every

fourth value to give the values of Q at 10, 20, 30, 40 and

50 cm depth.

Ten replicate penetrations were done for each

location. In some cases, penetration into the sub-soil

was not possible because of the high soil strength.

However, these ‘‘missing data’’ were not ignored but

were taken into account. To do this, the value 9999 was

written into the data file where data were ‘‘missing’’.

Then we did not use mean values of Q but median

values. Therefore, if 1, 2, 3 or 4 of the 10 replicate data

were ‘‘missing’’ then the median value was unaffected

and was used to represent the soil strength. If five or

more values were ‘‘missing’’, then the remaining values

were not used. For normally distributed values, the

median and the mean are similar.

2.3. Soil bulk density and water content

Bulk density was measured on soil samples collected

in 100 cm3 stainless steel cylinders of approximately

5 cm height. Each cylinder was then closed at both ends

with metal caps and was then placed in a polythene bag

that was closed tightly. This ensured that the samples

would remain at their field water content. Usually, four

replicate samples were taken from each layer although

in a few cases there were more (e.g. 8). These were dried

at 105 8C for 48 h in an oven. The dry mass of the soil

divided by the cylinder volume gave the bulk density, D

(g cm�3 = Mg m�3). The gravimetric water content, u(kg kg�1) was calculated as the mass of water in the soil

sample divided by the mass of the dry soil.

2.4. Water retention characteristics

Soil water retention was measured as follows.

Samples were collected in 100 cm3 stainless steel

cylinders of approximately 5 cm height. Each cylinder

was then closed at both ends with metal caps and was

then placed in a polythene bag that was closed tightly.

This ensured that the samples would remain at their

field water content. The importance of preventing


samples from drying has been shown by Baumgartl

(2003). He showed that drying a soil to water contents

drier than it has experienced before can cause

irreversible shrinkage with corresponding changes to

the pore size distribution and the water retention

characteristic. Samples were not collected from every

10 cm depth layer, but usually only from three depth

layers: the middle of the plough layer (e.g. 10–15 cm

depth), the compaction pan (e.g. at 30 cm depth), and

from the sub-soil (at 40 or 50 cm depth). All samples

were from well-defined soil layers.

The water retention characteristic for each layer

was measured at 11 different pore water suctions:

h = 10, 20, 40, 80, 250, 500, 1000, 2000, 4000, 8000

and 15,000 hPa. Sample height was approximately

5 cm for the first four suctions, 2.5 cm at 250 hPa and

1 cm for the higher suctions. The 2.5 cm samples were

prepared by removing the top half of the soil from

cylinders with a spoon. The 1 cm samples were

prepared by crumbling the soil into small aggregates.

These aggregates were still very large compared with

the size-scale of the soil features being investigated at

those suctions. The use of aggregates ensures that

there are many points of contact between the soil and

the ceramic pressure plates. Larger samples were used

at the lower suctions in order to have samples that

were large compared with the sizes of the structural

features being investigated (i.e. ‘‘representative

samples’’). Smaller samples (i.e. samples of lower

height) were used at the higher suctions in order to

reduce the time for equilibration of the soil water.

Sample size is always a compromise between these

two conflicting requirements. Two different replicates

were measured at each suction, therefore, 22 samples

were used to generate each water retention curve. It

should be noted that ‘‘suctions’’ are used here because

they are necessary in the van Genuchten (1980)

equation (suction = �matric water potential, where

the matric water potential is negative in unsaturated

soils). However, the van Genuchten equation works

only with positive numbers.

The sets of (u, h) data were fitted to the van

Genuchten (1980) water retention equation:

u ¼ ðusat � uresÞ½1þ ðahÞn��m þ ures (5)

where, u (kg kg�1) is the gravimetric water content at a

suction h, usat and ures, are the saturated and residual

water contents, respectively, h (hPa) is the pore water

suction, a (hPa�1) is a reciprocal suction that is char-

acteristic for the soil, and m and n are dimensionless

variables that describe the shape of the curve.

However, m and n were not considered as

independent variables but were assumed to be related

by the Mualem (1976) constraint:

m ¼ 1� 1

n(6)

The non-linear Eq. (5) was fitted iteratively to the

experimental data for each soil using the Levenberg–

Marquardt method (Marquardt, 1963).

Because not every depth layer was characterized,

the van Genuchten parameters for 15 cm depth were

used with the penetration resistance at both 10 and

20 cm depth. Similarly, the parameters for 40 or 50 cm

depth were used to characterize both the 40 and 50 cm

depths.

2.5. S and effective stress

The value of S was calculated as described by Dexter

(2004a) from the parameters of the fitted van Genuchten

(1980) equation using

S ¼ �nðusat � uresÞ�

1þ 1

m

��ð1þmÞ(7)

The value of the effective stress was calculated from

s0 ¼ xh (8)

where x is the degree of saturation (=(u � ures)/

(umax � ures)) and h (hPa) is the prevailing pore water

suction calculated using the inverted form of Eq. (5):

hðxÞ ¼ 1

a½x�1=m � 1�1=n

(9)

3. Results and discussion

The soils used had clay contents in the range from 2

to 25% with an arithmetic mean of 9.9%. Organic

matter (OM) contents ranged from 0.03 to 2.4% with a

mean of 1.21%, and bulk density (D) values ranged

from 1.24 to 1.81 g cm�3 with a mean of 1.54 g cm�3.

The values of bulk density in any one soil had a mean

standard deviation of 0.044 g cm�3. The mean gravi-

metric water content of the soils was 0.15 kg kg�1.

In a few locations, the penetrometer was able to

penetrate to its full working depth with every replicate.

Tests on these data using the Shapiro-Wilk normality

test show that in the majority of cases, the values of

penetrometer resistance, Q, at a given depth were

normally distributed to a level of statistical significance

of P = 0.05. We took this as justification of the use of


median values for locations where there were missing

values.

Although 15 out of the total of 85 soil layers had

degrees of saturation less than 0.4, we decided to use

Eq. (8) in every case because of its simplicity and ease

of use.

Measured values of penetration resistance, Q, were

regressed against 1/S and s0. This resulted in the

equation

Q ¼ 328ð�319Þ

þ 37:39ð�6:05Þ

�1

S

�þ 1:615ð�0:399Þ

s0 kPa;

r2 ¼ 0:375; p< 0:001

(10)

The three coefficients in Eq. (10) were different from

zero at the p = 0.2, p < 0.001 and p < 0.001 levels of

significance, respectively. In principle, the equation

could have been fitted without the constant term

because it is not significantly different from zero.

However, it was decided to keep it in order to have

residual values that were normally distributed. Interest-

ingly, when an interaction term (s0/S), was included it

was found to be not statistically significant (T = �0.17),

and did not increase the value of r2.

The low value of r2 requires some comment and

explanation. It is at least in part due to the spatial

variation of soil properties in the field. As discussed

above, the penetration resistance, water content and

bulk density, and the water retention characteristics

were all made using different soil samples. The extent to

which these all used ‘‘representative soil’’ is unknown.

Similarly, the water retention characteristics were not

determined for every soil layer as described at the end of

Section 2.4.

Table 1 provides some information about the

variability of key physical properties of soils of

different genetic origin used in the experiments. The

Table 1

Representative values of the coefficients of variation (COVs) found for

the measurements of bulk density, D, gravimetric water content, u, and

penetrometer resistance, Q

Genetic origin Plough layer Subsoil

D u Q D u Q

Alluvium 0.023 0.023 0.39 0.047 0.035 0.14

Loess 0.028 0.024 0.29 0.039 0.024 0.19

Glacial till 0.027 0.071 0.38 0.012 0.051 0.35

Separate values are given for the plough layer and for the subsoil

layers for soils of the three different genetic origins used in the

experiments. The values are for a single depth at a single point and

on a single measurement date. They do not include between-site

variation.

variabilities are expressed as mean values of the

coefficient of variation (standard deviation divided by

the mean). There were no statistically significant

correlations between the values of D and u even though

these were measured on the same samples. It can readily

be shown that the variations in D and u do not fully

account for the observed variations in Q. For example, if

the value of D is set 1 standard deviation higher and the

value of u is set 1 standard deviation lower than some

measured value (both of which would tend to increase

Q), then the predicted value of Q increases by only

about 6%. We, therefore, conclude that factors other

than D and u contribute to the values of Q measured in

the field.

The Pearson correlation coefficient between mea-

sured values of Q and those predicted using Eq. (10) is:

R ¼ 0:612; p< 0:001 (11)

This may be compared with that between measured

values of Q and those predicted using the Canarache

(1990a, 1990b) method for the same set of Polish soils:

R ¼ 0:532; p< 0:001 (12)

Although Eq. (11) shows a higher correlation

coefficient for Eq. (10), this is partly to be expected

because Eq. (10) was tested using the Polish soil data

used in its development. However, the Canarache

equations were developed using data for Romanian soils

having on average higher clay contents.

When we compared the measured values of Q with

those predicted using Eq. (3) using To and Kay’s

coefficients for loam for all the soils, we obtained only

R ¼ 0:274; p ¼ 0:21 (13)

When their coefficients for sand were used, R was

smaller.

We attribute the small value of R in Eq. (13) to the

fact that pore water suctions, h, were here estimated

from measured water contents in combination with the

inverted van Genuchten equation (Eq. (9)). This is in

contrast with the work of To and Kay (2005) who were

able to control the values of h in the laboratory. Another

factor is that To and Kay’s equations were developed

using Canadian soils, but were tested here on Polish

soils.

The fit of Eq. (10), as measured by r2, is low. We

believe that this is largely due to the spatial variation of

the soil physical properties in the field and because the

water content, bulk density and water retention

characteristics were measured on different soil samples.

Additionally, values of pore water suction, h, must be

estimated from measured soil water contents in


Table 2

Typical values of S for the 12 FAO/USDA soil texture classes together with the parameters used in their calculation

FAO/USDA texture class % Clay % Silt OM (%) D (Mg m�3) usat (kg kg�1) a (hPa�1) n S

cl 60 20 4.47 1.249 0.395 0.0217 1.103 0.0296

sa cl 42 7 3.61 1.334 0.335 0.0616 1.139 0.0317

si cl 47 47 3.85 1.309 0.362 0.0220 1.104 0.0273

cl l 34 34 3.22 1.376 0.324 0.0400 1.127 0.0285

si cl l 34 56 3.22 1.376 0.325 0.0226 1.129 0.0290

sa cl l 27 13 2.89 1.414 0.299 0.0727 1.169 0.0326

l 17 41 2.41 1.474 0.278 0.0314 1.208 0.0354

si l 14 66 2.26 1.492 0.269 0.0134 1.245 0.0385

si 5 87 1.83 1.552 0.243 0.0045 1.392 0.0485

sa l 10 28 2.07 1.518 0.258 0.0400 1.278 0.0405

1 sa 4 13 1.78 1.559 0.239 0.0534 1.406 0.0488

sa 3 3 1.73 1.566 0.226 0.0671 1.581 0.0594

Values of organic matter content (OM) and bulk density, r, were obtained as described in Dexter (2004a). The values of the parameters usat, a and n of

Eq. (5) were calculated using the values for clay, silt, OM and r in the pedotransfer functions of Wosten et al. (1999). Notes: sa = sand, si = silt,

l = loam, cl = clay.

Fig. 1. Predicted values of the index of soil physical quality, S, that

correspond with values of penetrometer resistance, Q, for two differ-

ent values of soil water suction, h.

combination with the inverted form of the van

Genuchten equation (Eq. (9)) the parameters of which

also have associated measurement errors and spatial

variability.

One of the main assumptions that has been made is

that penetrometer resistance is directly proportional to

effective stress. No account has been taken of the fact

that soil shear strength increases with the product of the

effective stress and the coefficient of internal friction,

tan w, of the soil. Although a value of w of around 358 is

typical for agricultural soils, the actual range varies

from 0 to 458. The value of w tends to be larger with

increasing particle size and with increasing particle

angularity (Dexter and Tanner, 1972). It is also true that

neither friction between the penetrometer cone and the

soil nor possible cementation between soil particles is

accounted for in the approach used here.

The effects of soil/penetrometer friction could be

removed by the use of a rotating penetrometer, as used

by Whalley et al. (2005). Those authors found that

effective stress alone could be used to predict

penetrometer resistance in soils of low density, but

not in soils of high density. This is exactly what is

predicted by Eq. (10): at low densities, S is large and the

effective stress term dominates; however, at high

densities, S is small and effective stress alone is not

sufficient for prediction of Q.

4. Examples of some predictions

For the purposes of these predictions we use the data

for different soil textural classes presented in Table 2.

We also use the PTFs of Wosten et al. (1999) which give

the parameters of the van Genuchten water retention

equation in terms of soil composition and bulk density.

These are the same data that were used for illustrative

purposes in Dexter (2004a, 2004b, 2004c). This enables

derived results to be compared directly.

Fig. 1 shows the values of S that correspond to

different values of penetrometer resistance, Q, at two

values of water matric suction, h. Both values of h

correspond to ‘‘field capacity’’. However, h = 100 hPa

is the value used in most countries for the suction to

which saturated soil will drain, whereas, h = 330 hPa is

the value used in the USA. The values were calculated

by setting the value of h and then calculating the

corresponding values of u for the different soil texture

classes. Then the value of D was iterated until the value

of Q was 1000, 1250, 1500, etc. (kPa). The values in the

graph are the means for all the 12 FAO/USDA soil

texture classes shown in Table 2.


Fig. 2. Values of bulk density, D, for different values of soil clay

content that are predicted to give various values of penetration

resistance, Q, at a soil water suction of h = 100 hPa.

Fig. 3. Predictions of how penetrometer resistance, Q, varies with

gravimetric water content, u, for three soil texture classes.

By iteration, it is also possible to estimate the values

of soil bulk density for soils with different clay contents

(as given in Table 2) that will give various values of

penetrometer resistance, Q, when the soil is at field

capacity (defined as h = 100 hPa). The results are shown

in Fig. 2. These curves were fitted to the following

equations:

� F
or Q = 1500 kPa when h = 100 hPa:
D ¼ 1:107þ 0:774 exp

��clay

22:47

�; r2 ¼ 0:989

(14)

� F
D ¼ 1:203þ 0:785 exp

��clay

32:75

�; r2 ¼ 0:989

(15)

� F
D ¼ 1:282þ 0:777 exp

��clay

39:38

�; r2 ¼ 0:991

(16)

� F
D ¼ 1:348þ 0:762 exp

��clay

43:61

�; r2 ¼ 0:991

(17)

Predicted values of penetrometer resistance, Q, as a

function of gravimetric water content, u, are shown for

three soil texture classes in Fig. 3. This was calculated

using the representative soil properties as given in

Table 2. It should be noted that the effect of water

content occurs entirely through the effective stress.

As explained above, the results presented in

Figs. 1–3 are based on predictions using the

pedotransfer functions of Wosten et al. (1999). They,

therefore, represent predictions based on the average

properties of European soils of the given texture

classes. It must not be assumed that these predictions

are accurate for any particular soil. However, it may be

assumed that the trends and effects that they illustrate

are typical.

5. Conclusions

The equation (Eq. (10)) that has been proposed for

penetrometer resistance is the sum of two simple terms:

one represents the degree of compactness of the soil,

whereas, the other represents the effect of water. The

first term is the reciprocal of Dexter’s (2004) index of

soil physical quality. The second is the effective stress

due to pore water pressure.

We conjecture that this equation is applicable to all

soil types and texture classes without any change in

equation parameters. However, this needs to be tested in

future research.

The equation that is proposed (Eq. (10)) is both

logical and physically meaningful. Future research

should be aimed at testing this proposed equation in a

wider range of soil types. The equation could perhaps be

improved by taking account of friction.

Acknowledgement

Ms. O.P. Gate would like to thank the European

Commission Proland project (contract number QLK4-

CT-2002-30663) for the support that enabled this work

to be done.


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A method for prediction of soil penetration resistance