Soil & Tillage Research 138 (2014) 9–16

Evaluating model-based relationship of cone index, soil water contentand bulk density using dual-sensor penetrometer data

J. Lin a, Y. Sun b,*, P. Schulze Lammers c

a School of Technology, Beijing Forestry University, 100083 Beijing, Chinab College of Information and Electrical Engineering, China Agricultural University, 100083 Beijing, Chinac Department of agricultural engineering, University of Bonn, 53115 Bonn, Germany

A R T I C L E I N F O

Article history:

Received 25 January 2013

Received in revised form 17 December 2013

Accepted 21 December 2013

Keywords:

Soil strength

Model

Soil cone index

Soil water content

Soil bulk density

A B S T R A C T

The relationship among cone index (CI), soil water content (u) and bulk density (Db) plays a critical role in

assessing soil physical conditions. To predict Db as functions of the measurements of CI and u, a variety of

semi-empirical CI-models have been established historically, however a study for validating these

models has not been found. In this study four CI-models, one considered the penetration depth as

variable but others did not, were evaluated under laboratory condition. The methodology was to use our

own developed dual-sensor vertical penetrometer (DSVP) to simultaneously measure CI and volumetric

soil water content (uv), and then to compare the bulk density (Db) core-measured to that model-

predicted by the DSVP data. Two types of soil samples (silt-loam and clay) were tested. Because a

previous study speculated that penetration depth could confound the CI measured, two depth-

dependent factors were incorporated into each CI-model for validating this speculation. Our study found

that two of the four models tested fit the experimental data with acceptable R2 (>0.70) and RMSE

(<0.093 g cm�3). In contrast, the experimental results confirmed that CI in Model-1 had a peak value

adapting a wide range of u. More ever, the results indicated that the DSVP combined with Model-1 or

Model-2 can be used as a tool to predict Db when CI and u are simultaneously measured.

� 2014 Elsevier B.V. All rights reserved.

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1. Introduction

Soil compaction is a major concern for agricultural fieldmanagement because it can either positively or negatively affectsplant growth and crop yield (Chen and Weil, 2011). Moderatecompaction may speed up the rate of seed germination and reducewater loss, whereas excessive compaction results in higher soilstrength and does not provide adequate pores and spaces for root’selongation (Tolon-Becerra et al., 2011; Modolo et al., 2011).

Soil compaction is commonly assessed through soil bulkdensity (Db, g cm�3), which can be determined by diverse methods.One method is cylinder core sampling. With known volume of thecylinder, Db can be determined in laboratory. However, there aresome shortcomings of this method. First, the sampling workload istoo heavy to obtain a large quantity of core samples at differentdepths in the field. Second, it is time-consuming because the coresamples should be oven-dried for 24 h at 105 8C for calculating Db.Finally, the soil condition could be disturbed during the samplingprocess. Another available tool is gamma-ray tomography, but the

* Corresponding author. Tel.: +86 10 62737416/+86 10 82380725;

fax: +86 10 62736741.

E-mail address: pal@cau.edu.cn (Y. Sun).

0167-1987/$ – see front matter � 2014 Elsevier B.V. All rights reserved.

http://dx.doi.org/10.1016/j.still.2013.12.004

potential risk of radiation exposure restricted its application(Hernanz et al., 2000; Borges and Pires, 2012). In contrast,penetrometer has been widely accepted as a practical instrumentfor assessing soil strength (Vaz et al., 2011). To make thepenetration results comparable under different field conditions,the American Society of Agricultural and Biological EngineersASABE Standards (S313.3, 2009a) recommended two types ofpenetrometers with a standard test procedure ASABE StandardsEP542 (2009b). The standards also defined the cone index (CI, MPa)as penetration resistance (PR) divided by cone cross-sectional area.

Many previous studies noted that CI is not only stronglydependent on Db, but also on soil water content and texturalcompositions (Busscher, 1990; Sojka et al., 2001; Vaz andHopmans, 2001; Dexter et al., 2007; Santos et al., 2012; Quraishiand Mouazen, 2013a). For modeling the relationship among CI, Db,soil water content (u) and soil textures, Ayers and Perumpral(1982), Upadhyaya (1982) and Busscher (1990) presented differentCI-models drawn from laboratory conditions. Thereafter, Hernanzet al. (2000) incorporated penetration depth as an independentvariable into the Busscher model. For the soil samples tested, Ayersand Perumpral (1982) artificially made five ratios of Zircon sandto clay (0.1, 0.25, 0.5, 0.75 and 1.0 in sand percent) at three levels ofDb and eight levels of gravimetric soil water content (ug, g g�1).The experiment of Upadhyaya (1982) was only concerned with

J. Lin et al. / Soil & Tillage Research 138 (2014) 9–1610

silt-loam soil at multiple levels of ug. Busscher (1990) tested seventypes of soils but detailed information of textural compositionswas absent. Both Ayers and Perumpral (1982) and Upadhyaya(1982) used the ASABE standard cone penetrometer, whereasBusscher (1990) used a flat-tipped cone (diameter: 5 mm). Thesesingle-sensor penetrometers only measured the CI and wereunable to account for the affecting factors on CI.

Over the past decades, with the intention for simultaneousmeasurements of penetration resistance (PR) and volumetric soilwater content (uv), various soil water content sensors have beencombined with the conventional penetrometers. One of thesemethods was Time Domain Reflectometry (TDR) sensor (Topp et al.,1996; Young et al., 2001; Vaz and Hopmans, 2001). An alternativemethod was to integrate near infrared spectroscopy sensors into thepenetration rod (Newman and Hummel, 1999; Hummel et al., 2004;Quraishi and Mouazen, 2013b). Apart from these, capacitancesensors were embedded into a penetration rod (Singh et al., 1997) ora penetration cone (Sun et al., 2004). Although uv and CI have beensimultaneously measured using the developed dual-sensor verticalpenetrometers (DSVPs), to our knowledge no study has beenreported for validating the developed CI-models by this advancedtechnique. Certainly, if a mathematical model was accepted as thebest fit to the relationship of CI, u and Db, it would definitely benefitwide applications of the DSVPs. Thus, the aim of our study was tovalidate four of the existing CI-models using own innovative DSVP.For this, two soil types (silt-loam and clay soils) were tested underthe laboratory condition.

Dual-sen sorinstrument

Control box

Soil sample ithe cylinde r

Experiment f

(a)

O

W

(b)

Fig. 1. The experimental system of the dual-sensing vertical penetrometer (a), electric lay

met the ASABE standard (c).

2. Materials and methods

2.1. A general description of the concerned models

Model-1 presented by Ayers and Perumpral (1982) was

CI ¼ A1DbA2

A3 þ ðug � A4Þ2(1)

where Db is bulk density in g cm�3, CI is cone index in MPa, ug isgravimetric soil water content in g g�1, A1–A4 are positivecoefficients (dimensionless) and need to be determined withrespect to specific soil types. For separating the effect of ug on CI,the following equation is used

@CI

@ug¼ �B1DA2

b

2ðug � A4Þ

ðA3 þ ðug � A4Þ2Þ2

(2)

Furthermore, a maximum of CI in Eq. (1) can be found by

@CI

@ug

����ug¼A4

¼ 0 (3)

since

@2CI

@u2g

����� ug ¼ A4¼ �2

A1

B23

DA2

b < 0 (4)

n

rame

Coaxial line

Fri nge field

SC

ave detector

AF

ab

a b

Zo

Wave detector

(c)

out of soil water content sensor (b) and the dimension of the combined cone, which

J. Lin et al. / Soil & Tillage Research 138 (2014) 9–16 11

Clearly, the peak shows a non-monotonic relationship betweenCI and ug.

Model-2 (Upadhyaya, 1982) was present as

CI ¼ B1DB2

b e�B3ug (5)

where B1–B3 are dimensionless coefficients depending on themeasured soil types as well. Different from Model-1, CI in Model-2decreases exponentially as ug increases.

Model-3 (Busscher, 1990) was proposed as

CI ¼ C1DC2

b ugC3 ug > 0 (6)

Similar to the coefficients of Model-1 and Model-2, C1–C3 aredimensionless and associated with the soil types measured.

Model-4 (Hernanz et al., 2000) was regarded as a modifiedversion of Model-3 considering the effect of penetration depth on CI

CI ¼ C1DC2

b ugC3 dC4 (7)

where d is the penetration depth in mm, C4 is also dependent onsoil types.

According to their explanation, assuming that both Db and ug

remain constant in Eq. (7), CI increases as d increases because thevalue of the load supported by the soil increases as well.

2.2. Dual-sensing instrument

The used DSVP (Fig. 1a) was invented through a collaborativeresearch between the Research Center for Precision Agriculture,China Agricultural University and the Department of AgriculturalEngineering, the University of Bonn, Germany (Sun et al., 2004).This apparatus consisted of a permanent magnet DC-motor(M63 � 60/I, Kahlig Antriebstechnik GmbH, Germany), a depthtransducer, a control box, and a rack and rigging parts. The nominalvoltage and maximal output-power of the DC-motor was 12 V and99 W, respectively. The depth transducer (10-turn, 10 kV, apotentiometer with �0.25% linearity) was mounted with the sameaxis of the DC-motor. As the penetration rod moved down and up, thepotentiometer was rotated in phase by a rack and pinion adjustmentso that the output of the depth transducer linearly varied with0.1 V cm�1. The maximum vertical movement was 500 mm. To meetthe ASABE Standards (S313.3, 2009a), the penetration velocity wascontrolled at 30 mm s�1.

As shown in Fig. 1b, for the simultaneous measurements of CI anduv, the tip of the rod and a metallic ring that neighbors the tip acted asthe two electrodes of a fringe-capacitance sensor, which incorpo-rates soil as part of the dielectric components. Due to the fact that therelative dielectric constant of free water (�80) is significantlygreater than that of most soil matrices (3–5), and of air (�1),uv can beindirectly determined by estimating the dielectric constants of wetsoil. The measurement principle was to determine the electricalimpedance (Zp) of the fringe-capacitance (see Fig. 1c) as

Z p ¼Zo

Ua � UbUb (8)

where Ua and Ub are output of wave detectors in V corresponding topoint a and b, respectively. Zo is an additional wired resistance. Forthe measurement frequency, several studies (Thomas, 1966; Bellet al., 1987; Campbell, 1990; Mohamed et al., 1997) concluded thatexcitation frequency should be above 30 MHz so that theuncertainties caused by soil conductivity and faulty contact couldbe largely minimized. Apart from these, Singh et al. (1997) foundthat other polarization effects occurred at a frequency of15.86 MHz, but the measurement at a frequency of 47.45 MHzwas relatively independent of the salt contents tested. Also, Gaskinand Miller (1996) demonstrated that the influence of soilconductivity could be sufficiently reduced if the frequency is

above 100 MHz. Following these studies, our sensor ran at100 MHz. The fundamental principle of frequency domain (FD)method can be found in the literatures (Gaskin and Miller, 1996;Sun et al., 2004).

The force-sensor with an associated amplifier (HBM-C9B/500N,Hottinger-Baldwin-Messtechnik, Germany) mounted at the upperend of penetration shaft was a strain-gauge load cell (0–1000 N).The dimensions of the penetration cone and rod (Fig. 1b)approximated to the recommendation by the ASABE Standards(S313.3, 2009a).

2.3. Modifications of Model-1 and Model-2

Since the reading of the dielectric sensor of the dual-sensorinstrument is of uv rather than ug, Model-1 had to be modified as

CI ¼ A1DbA2

A3 þ uv=Db � A4ð Þ2(9)

and Model-2 modified as

CI ¼ B1DB2

b e�B3uv=Db (10)

However, for both modified models Db could not be expressedas an explicit function of CI and uv such that Db = f(CI, uv). Due tothis, the online computations of Eqs. (9) and (10) tended to berelatively complicated.

For Model-3 (Eq. (6)) and Model-4 (Eq. (7)), the variable u allowsbeing either uv or ug because of

CI ¼ C1DC2

b uC3g ¼ C1DC2

b

uv

Db

� �C3

¼ C1DCbu

C3v ; and C ¼ C2 � C3

or

CI ¼ C1DC2

b uC3g dC4 ¼ C1DC2

b

uv

Db

� �C3

dC4 ¼ C1DCbu

C3v dC4 ; and C

¼ C2 � C3

That is, Model-3 and Model-4 adapt to the volumetricmeasurement of the dual-sensor without any modification.Moreover, for Model-3 and Model-4 Db allows to be rearrangedas an explicit function of CI and uv such that

Db ¼CI

C1uC3v

!1=C2

(11)

and

Db ¼CI

C1uC3v dC4

! 1=C2ð Þ

(12)

Thus, using Model-3 or Model-4 for the on-line computation ofDb is relatively simple and fast.

2.4. Soil samples preparation

Two types of agricultural soil (silt-loam and clay) were used.Table 1 lists their textural compositions. These soils were oven-dried for 24 h at 105 8C and passed through a 2 mm sieve. Aftersieving, they were remoistened with 5 levels of ug ranging from dryto saturation and then uniformly packed into small cylinders(inner radius = 100 mm, height = 165 mm) with Db = 1.4 g cm�3 forthe fringe-capacitance sensor calibration (five replicates weremade at each level of ug), and packed into large cylinders (innerradius = 200 mm, height = 600 mm) for penetration measure-ments. The packing procedure of the soil samples for penetration

Table 1Textural compositions of the two types of soil samples tested.

Soil type Clay (g g�1)

<0.002 mm

Silt (g g�1)

0.02–0.002 mm

Sand (g g�1)

2–0.02 mm

Clay 0.73 0.13 0.14

Silt-loam 0.16 0.67 0.17

R² = 0.9719

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0 0.1 0.2 0.3 0. 4 0.5 0.6

Mea

sure

d Vo

lum

etric

Wat

er C

onte

nt(c

m3

cm-3

)

Outpu t of Water Sen sor (V)

clay

silt-loa m

Fig. 2. Calibration results of the fringe capacitance sensor from the clay and the silt-

loam samples.

J. Lin et al. / Soil & Tillage Research 138 (2014) 9–1612

measurement followed the Proctor compaction tests described byAyers and Perumpral (1982). To control the desired densities, asteel cylindrical mold (diameter = 140 mm, height = 20 mm)welded with a metal rod (diameter = 25 mm, length = 700 mm)acted as a drop hammer (10 kg). By dropping the hammer at aconstant height (300 mm) and controlling the numbers of blow perlayer, the soil columns with the desired densities were made. Fourpenetration tests were replicated at each level of ug combined withthree levels of Db (1.0, 1.2, and 1.4 g cm�3) for both soil types. Thedata were averaged along a depth increment of 5 mm. After eachpenetration, five core samples were collected with a depth intervalof 100 mm.

3. Results and discussion

3.1. Calibration of the fringe-capacitance sensor

Fig. 2 shows that the calibration results of the fringe-capacitance sensor fit a quadratic equation with R2 = 0.97 eventhough the textural compositions of the two groups of soil (silt-loam and clay) were different. The wettest sample of the silt-loamwas uv = 0.36 cm3 cm�3 (nearly saturated). Because of the difficultyin preparing the heavy clay soil samples with high water content,the wettest sample of the clay soil was with higher moisture(uv = 0.44 cm3 cm�3) but still unsaturated. The quadratic relation-ships between the outputs of the finger-capacitance sensors and uv

were previously reported by Sun et al. (2004, 2006, 2009) withrespect to sandy-loam and silt-loam samples (R2 > 0.95). Thesimilar calibration results could be attributed to for the similargeometry of the cone combined with the two-ring electrodes.

3.2. Comparison of model-predicted and core-measured Db

Tables 2 and 3 summarized the coefficients determined by theleast-square of RMSE for each CI-model. In general, both R2 (�0.76)

Table 2The coefficients of each CI-model, which were experimentally determined from the cla

Model-1 (Eq. (9)) Model-2 (Eq. (10))

Coefficient Value Coefficient Value

A1 353.10 B1 1852.30

A2 8.81 B2 3.02

A3 15.26 B3 0.82

A4 9.38

R2 0.76 R2 0.72

RMSE (g cm�3) 0.068 RMSE (g cm�3) 0.093

Table 3The coefficients of each CI-model, which were experimentally determined from the sil

Model-1 (Eq. (9)) Model-2 (Eq. (10))

Coefficient Value Coefficient Value

A1 459.56 B1 547.40

A2 8.74 B2 6.76

A3 15.38 B3 0.56

A4 3.79

R2 0.77 R2 0.70

RMSE (g cm�3) 0.057 RMSE (g cm�3) 0.056

and RMSE (�0.068 g cm�3) of Model-1 were better than those ofthe other models for each soil type. For Model-2, the R2 (�0.70) andthe RMSE (�0.093 g cm�3) were also good. Fig. 3a shows that thelevels of R2 for all models were distinctly different but there waslittle difference of R2 between the two soil types for each CI-model.In contrast, Fig. 3b shows that the RMSEs of the clay samples(�0.111 g cm�3) were apparently higher than those of the silt-loam (�0.080 g cm�3) for all models. This might be due to the factthat the clay samples could not be prepared such uniformly as thesilt-loam samples.

In addition, either Fig. 4 or Fig. 5 exhibits a group of scatter-plotsto compare the Db predicted by each CI-model and that core-measured for each soil type. These scatter-plots confirmed that themodified Model-1 and Model-2 (Eqs. (9) and (10)) betterapproximated the experimental data between them Model-1provides the best fit to the experimental data.

3.3. Evaluating the influence of water content

Among these models tested, only Model-1 showed a peak valueof CI in relation to ug, whereas the others assumed a negative

y samples.

Model-3 (Eq. (6)) Model-4 (Eq. (7))

Coefficient Value Coefficient Value

C1 132.40 C1 156.30

C2 0.11 C2 0.98

C3 �1.12 C3 �0.02

C4 0.76

R2 0.60 R2 0.62

RMSE (g cm�3) 0.111 RMSE (g cm�3) 0.109

t-loam samples.

Model-3 (Eq. (6)) Model-4 (Eq. (7))

Coefficient Value Coefficient Value

C1 135.70 C1 125.90

C2 0.23 C2 0.17

C3 �1.35 C3 �0.04

C4 0.49

R2 0.61 R2 0.62

RMSE (g cm�3) 0.080 RMSE (g cm�3) 0.080

Fig. 3. Accuracy comparisons of R2 (a) and RMSE (b) for the four CI-models with

respect to the clay and silt-loam samples.

Fig. 4. Accuracy comparisons of R2 and RMSE between the data of the mode

J. Lin et al. / Soil & Tillage Research 138 (2014) 9–16 13

influence of ug on CI. To separate the effect of Db on CI in Model-1,Eq. (1) is rearranged as

h ¼ CI

DbA2¼ A1

A3 þ ðug � A4Þ2(13)

so that h is a simple function of ug as expressed in Eq. (13). Fig. 6shows the test results calculated by the ratio of the CI to the Db

core-measured. As expected, the peak value (hmax) appearedaround ug = A4 for each soil type. The hmax = 241.49 for the silt-loamsample occurred at ug = 3.60%, which was close to the calculated A4

(3.79) in Table 3. Likewise, hmax = 345.26 for the clay sample (73%of clay content) took place at ug = 11.30%, which slightly deviatedto that (ug = 9.38%) in Table 2. Also, the peaks of our experimentwere in line with the observations of Ayers and Perumpral (1982),who found a peak for 25% of clay content at ug = 3.0% and anotherpeak at ug = 9.0% for 75% of clay content. Indeed, the peaks existedand shifted with clay contents, but all occurred at low levels of u.Therefore, only Model-1 can be adopted for simulation with arelatively dry soil conditions.

3.4. Dependency of each model on penetration depth

Of these CI-models, only Model-4 considered the penetrationdepth (d) as an independent factor affecting CI. The major reasonwas that CI could accrete with the penetration depth because ofthe passive earth pressure at rest even if Db remained constant(Hernanz et al., 2000). From Tables 2 and 3, it is notable that R2 ofModel-4 was higher than that of Model-3 for both soil types.However, the values of C3 in Model-4 (i.e., the u-relatedcoefficient) were much reduced for the clay samples(C3 = �0.02) and the silt loam samples (C3 = �0.04). This meansthat the influence of soil water content on CI would be largely

l-predicted Db and those of the core-measured Db for the clay samples.

Fig. 5. Comparisons of R2 and RMSE between the data of the model-predicted Db and those of the core-measured Db for the silt-loam samples.

J. Lin et al. / Soil & Tillage Research 138 (2014) 9–1614

under estimated once the penetration depth as an independentfactor was combined. For this, we checked the previous resultsof Hernanz et al. (2000) again and found that their results(�0.08 < C3 < �0.07) were quite close to those in Tables 2 and 3.Using the similar strategy suggested by Hernanz et al. (2000)to modify Model-3 as Model-4, here we incorporatedtwo impact factors (dAi, eAid) of the penetration depth into

Table 4Comparison of the coefficients between Model-1 (Eq. (9)) without depth-dependent fa

Model coefficient Clay

Model-1 (Eq. (9)) Modified model

Eq. (14) E

A1 353.10 353.10 3

A2 8.81 8.81 8

A3 15.26 15.26 1

A4 9.38 9.38 9

A5 0.00 0

R2 0.76 0.76 0

RMSE (g cm�3) 0.068 0.068 0

Table 5Comparison of the coefficients between Model-2 (Eq. (10)) without depth-dependent f

Model coefficient Clay

Model-2 (Eq. (10)) Modified model

Eq. (16)

B1 1852.30 1843.60

B2 3.02 2.89

B3 0.82 0.72

B4 0.12

R2 0.72 0.73

RMSE (g cm�3) 0.093 0.085

Model-1 and Model-2, respectively, as follows,

CI ¼ A1DbA2 dA5

A3 þ uv=Db � A4ð Þ2(14)

CI ¼ A1DbA2 eA5d

A3 þ uv=Db � A4ð Þ2(15)

ctor and Model-1 with depth-dependent factors (Eqs. (14) and (15)).

Silt-loam

Model-1 (Eq. (9)) Modified model

q. (15) Eq. (14) Eq. (15)

52.90 459.60 459.10 459.30

.81 8.74 8.73 8.74

5.24 15.38 15.36 15.36

.34 3.79 3.79 3.78

.04 0.01 0.03

.76 0.77 0.77 0.77

.067 0.057 0.059 0.054

actor and Model-2 with depth-dependent factors (Eqs. (16) and (17)).

Silt-loam

Model-2 (Eq. (9)) Modified model

Eq. (17) Eq. (16) Eq. (17)

1906.10 547.40 506.10 519.30

2.75 6.76 6.99 6.43

0.77 0.56 0.49 0.40

0.10 0.06 0.11

0.73 0.70 0.70 0.71

0.088 0.056 0.054 0.054

Table 6Comparison of the coefficients among Model-3 (Eq. (6)) without depth-dependent factor and Model-3 with depth-dependent factor (Eq. (18)) and Model-4 (Eq. (7)).

Model coefficient Clay Silt-loam

Model-3 (Eq. (6)) Modified model Model-3 (Eq. (6)) Modified model

Eq. (7) Eq. (18) Eq. (7) Eq. (18)

C1 132.40 156.30 104.90 135.70 125.90 189.40

C2 0.11 0.98 0.73 0.23 0.17 0.20

C3 �1.12 �0.02 �0.10 �1.35 �0.04 �0.09

C4 0.76 0.24 0.49 0.32

R2 0.60 0.62 0.61 0.61 0.62 0.61

RMSE (g cm�3) 0.111 0.109 0.107 0.080 0.080 0.083

J. Lin et al. / Soil & Tillage Research 138 (2014) 9–16 15

CI ¼ B1DB2

b e�B3uv=Db dB4 (16)

CI ¼ B1DB2

b e�B3uv=DbþB4d (17)

Besides, eC4d was also incorporated into Model-3 as

CI ¼ C1DC2

b uC3v eC4d (18)

Tables 4–6 present the calculated coefficients referring to eachsoil type. As one of significant results, A5 in Eqs. (14) and (15) (i.e.,the depth-related coefficient) was approximated to zero for bothsoil types, evidencing that the effect of the penetration depth on CI

was ignorable. Moreover, Table 4 shows that the values of othercoefficients (A1–A4) of Eqs. (14) and (15) were only slightlychanged comparing to those of Eq. (8) in Tables 2 and 3. This alsodemonstrated that the influence of penetration depth for Model-1could be ignored. For Model-2, the R2 and the RMSE in Table 5confirmed that no significant improvement was made withintroducing the two depth-dependent factors. Unlike Model-1and Model-2, Table 6 shows that C3 of Model-3 (i.e., the u-relatedcoefficient) became rather smaller for both soil types after eC4d

being introduced, indicating that uv had very limited influence onCI. Certainly, this did not fit the soil mechanics.

In addition to above discussions, two recent publications (Sunet al., 2012; Cai et al., 2013) also concluded that the PRmeasurement was nearly independent of the penetration depthfor the ASABE Standard small cone for a board range of agriculturalsoils. Their conclusions were based on a novel experimentalmethod by penetrating a specific cylinder packed with soil sample.When the penetration shaft and cone went through the cylinder,the PR measurement equated the summation of the coneresistance and the friction resistance between the soil penetrated

Fig. 6. The relationship between h and CI measurements with respect to the clay

samples and the silt-loam samples, where h is the ratio of CI to Db defined in Eq. (13)

so that the influence of Db on CI could be separated for Model-1. In this figure each

curve had a peak or hmax referring to a specific ug.

and the shaft wall. Once the cone penetrated out of the hole on thebottom of the cylinder, the PR measurement only related to thefriction resistance. In this study, we embedded the fringe-capacitance sensor into the ASABE Standard small cone withoutchanging any of the geometry of the cone. Therefore, this model-evaluated study also showed the importance of the ASABEStandard small cone.

4. Conclusions

Using our developed DSVP, the four of existing CI-models havebeen evaluated for the two soil samples under the laboratoryconditions. Based on the experimental results achieved, threeconclusions can be drawn as follows:

(i) Either Model-1 or Model-2 had better accuracy for estimatingDb in contrast to Model-3 and Model-4. Especially, Model-1associated with the four coefficients can be adapted to a widerange of soil water content because the other three modelsignored the peak of CI, which occurred at low levels of soilwater content.

(ii) No improvement was made assuming that the penetrationdepth was an independent factor in each CI-model. However,this evidenced that the effect of the passive earth pressure atrest on the PR measurements was ignorable when the ASABEStandards small cone was used.

(iii) Our study also confirmed that the developed DSVP with a goodCI-model could greatly contribute to estimating Db onlinethrough the simultaneous measurements of soil water contentand bulk density in situ.

Acknowledgment

This paper was supported by the Fundamental Research Fundsfor the Central Universities (no. YX2011-5) and NSFC project (no.11202031). We also wish to thank the financial support of theInternational Cooperation Fund of the Ministry of Science andTechnology, China (2010DFA34670) for promoting this Sino-German Cooperation Group Research.

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