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Prediction of Tillage Implement Draught using Cone Penetrometer Data
J. Agric. Engng Res. (1999) 73, 65}76 Article No. jaer.1998.0394, available online at http://www.idealibrary.com on
Prediction of Tillage Implement Draught using Cone Penetrometer Data J. M. A. Desbiolles; R. J. Godwin; J. Kilgour; B. S. Blackmore On-Farm Machinery Division, Agricultural Machinery Research and Design Centre, University of South Australia, The Levels Campus, Mawson Lakes SA 5095, Australia; e-mail: [email protected] Agricultural and Biosystems Engineering Department, School of Agriculture Food and Environment, Cran"eld University, Silsoe, Bedford MK45 4DT, UK (Received 22 September 1997; accepted in revised form 6 November 1998)
A novel approach to the prediction of tillage implement draught has previously been reported which involves a simple reference tine (standard tine) in relation to which tillage implements are rated in a reference soil in terms of their draught requirements. This prediction methodology makes use of the standard tine draught measured in situ to predict the draught required by any indexed tillage implement operating under the same soil condition. The standard tine draught in the reference soil is also described as the product of a soil strength factor S and a geometrical factor G . Results of an investigation conducted to assess the usefulness of cone penetrometer data Q when included in this prediction methodology are reported in this study. Speci"c cone penetration energy P signi"cantly correlated with the soil strength factor S in two sandy-loam C (r"0)93) and two clay (r"0)75) soils. Their relationship was quanti"ed in a dimensionless parameter F, ratio of P over S, which was found to depend upon working depth, soil type and soil moisture content. Multiple C regression equations for F with soil moisture content and working depth were de"ned empirically for clay and sandy soil categories. Using these equations, the draught of the standard tine operating in three separate soil conditions was predicted over a working depth range (0)1}0)4 m) within a 15)5% error. The draughts of four multi-tool tillage implements operating at a typical working depth in three soil conditions were predicted using the measured standard tine draught data with a 17% error on an average. Using the standard tine draught values predicted from the cone penetrometer data, the average prediction error increased to 26%. The performance of the prediction models using the cone penetrometer data re#ected a compromise between the improved practicality of the in situ data collection and the reduced prediction accuracy. Its usefulness, however, should be assessed in the light of the signi"cant di$culties associated with using the current analytical methods for in situ predictions (requiring fundamental soil mechanical characteristics) and for complex tool shapes. 1999 Silsoe Research Institute
where the soil strength factor S is modelled in a zero soil surface surcharge and adhesionless soil (i.e. reference soil condition). This soil strength factor is a function of fundamental soil properties as described in the Godwin and Spoor analytical model2
1. Introduction A new approach to the prediction of implement draught (i.e. horizontal pulling force) in tillage studies was reported by Desbiolles et al.1 The methodology involved is based on the Godwin and Spoor 2 analytical model and describes the draught D of a simple narrow Q tine at a 453 rake angle (i.e. referred hereafter as standard tine) operating at a low speed, above its critical depth and in a reference soil condition, as the product of two factors, namely S and G , related to soil strength and tool Q geometry, respectively: D "S;G (1) Q Q 0021-8634/99/050065#12 $30.00/0
S"(cdN #cdN ) (sin d#cos d) (2) A A where N and N are dimensionless N-factors dependent A A on the soil internal friction angle , d is the tine working depth, c the soil bulk unit weight, c the soil cohesion and d the soil}tool interface friction angle. The geometrical factor G is theoretically de"ned1 as a linear function of Q the standard tine width w and working depth d: G "0)707w#1)225d Q 65
(3)
1999 Silsoe Research Institute
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J . M. A. D ES B IOL L ES E ¹ A ¸.
Notation A c C G C N d d G D D D D
P
?
e E F F N G I m A n
cone surface area, m soil cohesion, kN/m soil cone index, kPa Mallows statistics tine or tool working depth, m imaginary tine working depth, m draught, in "eld soil conditions (measured or predicted), kN draught in laboratory soil conditions (measured or predicted), kN equivalent draught reduction due to tool interactions within an implement, kN Draught requirement of tool accessories in a multi tool implement, kN error factor expressed over a working depth range, % deviation of sample mean from population mean, % ratio, S/P C penetration force, N geometrical factor, m tool index soil moisture content dry basis, % number of single tillage tools in a multi-tool implement
n N ,N A A P P C r R R ? s S t < w X z d c
Subscripts s standard tine t single tillage tool w multi tool tillage implement i imaginary tine
The expression for G is valid for any standard Q tine working above its critical depth. The soil strength factor S (in the reference soil condition) can be estimated empirically at a given depth d by using any standard tine of width w as a measuring device, from the knowledge of its draught D . Q D Q S" (4) 0)707w#1)225d The prediction methodology was developed and validated1 for single tillage tools operating at a low velocity (e.g. 2 km/h) to re#ect the quasi-static conditions dictated by the analytical model.2 It consists of two stages, namely (1) to establish in a reference soil condition some comparative relationships (i.e. tool index I) linking the draught of the standard tine D to that of each tillage Q tool D and (2) to measure the draught of the standard R tine D in the "eld. The tool draught D in that "eld Q R condition is predicted from Eqn (5): where
number of required replications in CI data samples dimensionless N-factors probability level speci"c cone penetration energy parameter, kJ/m or kN/m coe$cient of linear correlation, % coe$cient of multiple correlation, % adjusted coe$cient of determination of the regression, % standard error of the regression, regression units soil strength factor, kN/m statistical Student's t value statistical coe$cient of variation, % standard tine width, m tine inner spacing on an implement, m statistical z value soil}tool interface friction angle, deg soil bulk unit weight, kN/m soil internal friction angle, deg
D "I;D R Q
(5)
D I" R D Q
(6)
This method was shown to provide predictions typically within 15% of the measured draught for a range of single tillage tines operating under four soil conditions.1 However, constraints associated with such methodology are: (1) the need for speci"c "eld equipment to acquire the standard tine draught data (i.e. force measurement equipment, standard tine and hitch frame, tractive machinery) and (2) the invasive aspects of carrying out the measurements in the intended "eld conditions with regard to the soil conditions and growing crops. The practicality of implementing this methodology could, therefore, be enhanced if the soil strength data in the "eld was obtained by using a quick, simple and non-destructive alternative method. Investigations were carried out to determine the suitability of the cone penetrometer in this context, this device being widely used as a practical tool to provide estimates of soil strength.3,4 The soil strength estimate in kPa, often referred to as cone index C , is a composite soil parameter, strongly in#uenced by G soil type, soil structural state and soil water content.5+8 The cone penetration resistance has often been used to predict the draught requirement of, principally, plough implements,9+11 where either C values at median working G depth or average C value over the working depth zone, G
P R ED I CT I O N O F TI LLA G E I M PL E ME N T D RA U G H T
have been used as in situ soil strength data. The approach followed here is di!erent as correlations were sought between the cone penetration resistance data and the soil strength factor S as measured by the standard tine [Eqn (4)] rather than with its draught itself. A general relationship between the parameter C and the factor S was G anticipated (see Fig. 1) since various aspects of soil}soil and soil}metal failure are known to in#uence both the C parameter3 and the soil strength factor S, as implied by G the soil mechanical properties d, c, c and in the theoretical model of Eqn (2). Additionally, the draught of 453 rake angle tines (and therefore the soil strength factor S) and the cone penetration resistance have been shown to display comparable trends8,12 with soil moisture content in frictional-cohesive soils. A fundamental di!erence, however, was also expected as S represents a bulk strength value which is in#uenced by the state of the soil over the whole depth pro"le (from the soil surface down to the working depth), as opposed to the C parameter comparG ing as a point estimate of soil strength at a given depth. As a result, a cone penetration energy criterion P C was de"ned, involving all the cone penetrometer readings within the soil pro"le and was expected to be conceptually similar to the soil strength factor S (see Fig. 1). The P parameter is given by the area enclosed under the C curve of the C versus depth relationship down to the G depth of work (Fig. 1) and is obtained from simple mathematical integration of the &&best "t'' C regression G equation with respect to working depth d [Eqn (7)]: B
P " C ) dd G C M
(7)
The units of P represent an energy per unit crossC sectional area of the cone (i.e. kPa;m,kJ/m) which
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characterize a speci"c cone penetration energy. These units are equivalent to the fundamental units of S (i.e. force/length). As a practical alternative in the "eld, P can C easily be approximated from the product of the average C value over a depth pro"le multiplied by the value of G the working depth d. The objectives of the study reported below were as follows: (i) to investigate the correlations between S and P for C a range of soil types, soil water contents, and across a typical working depth range, and to quantify some empirical relationships linking S to P ; C (ii) to assess the merit of relying upon the cone penetrometer to estimate the soil strength factor S, and ultimately to predict the in situ draught of the standard tine D , by validating these Q empirical relationships in a separate range of "eld conditions; (iii) to predict the draught of four primary tillage implements operating at a low speed and a typical working depth, using the standard tine prediction methodology [e.g. Eqn (5)] with the standard tine draught D either measured or predicted from cone Q penetrometer data. The results corresponding to each objective are reported in Sections 2, 3 and 4 respectively. 2. Correlations between soil strength factor and cone penetration energy 2.1. Materials and methods Cone penetrometer resistance data was acquired at four di!erent sites (two sandy-loam, soils A and C, and two clay soils, soils B and D) on six separate occasions
Fig. 1. Conceptual relationship between the soil strength factor S and the cone penetration energy P C
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Table 1 Field conditions (a) referred to in the correlation analyses and (b) for the veri5cation of the models Mechanical analysis Soil reference
Texture
Sand,%
Silt,%
Clay,%
Soil moisture content in 0)1}0)2 m layer, % dry basis
(a) Soil conditions for correlation analyses Soil A Sandy-loam Soil B Clay Soil C Sandy-loam Soil D Clay
69 25 67 13
15 26 18 21
16 49 15 66
13)7}20)5* 23)0}29)0* 14)6}17)8* 30)2}43)3*
(b) Soil conditions for model veri,cations Soil E Sandy-loam Soil F Clay Soil G Sandy-loam
69 15 59
15 25 25
16 60 16
13)8R 34.6R 13)8R
* Soil moisture range encountered over trial period (six experiments/soil type). R Soil moisture at time of trial (1 experiment/ soil type).
providing a range of soil textures and moisture contents (i.e. 24 soil conditions) summarized in Table 1(a). Under these same soil conditions, the draught requirement of a 70 mm wide standard tine was measured over a comparable range of depths. The cone penetration data was collected with a handheld electronic penetrometer following the general procedure outlined13 in the ASAE Standard S 313)2. A 303 apex angle, 12)83 mm diameter cone was used, whose base was set as the depth reference. The penetration resistance readings were recorded at regular depth intervals (every 30 mm for tillage tines, 20 mm for shallower working plough tools) over a working depth range matching that of the standard tine. The force output readings were transformed into pressure units of kPa using appropriate conversion factors to quantify the soil cone index values. The very "rst reading of each data set was systematically discarded as unrepresentative of stress conditions close to the soil surface, and the next following reading was then assumed to be representative of the soil condition up to the soil surface. Care was taken to ensure that any potential drag resistance from the cone shaft was minimized in moist sticky soil conditions (soil D) by ensuring any soil build-up was removed from the penetrometer rod at the start of each sampling. At least 50 sets of cone penetration readings were acquired at random locations within each experimental plot, which satis"ed the minimum replication requirement (n "47) as determined by the following formula, after Neville and Kennedy,14 assuming the cone penetrometer data to be independent15 and normally distributed:16
n "
(8)
where the expected coe$cient of variation < of the mean cone penetration at a given depth (i.e. standard deviation over mean ratio in %) was taken as 35%, later con"rmed by subsequent readings; the admissible level of deviation E of the sample mean from the unknown population mean, also expressed on a percentage basis, was set at 10%; and the limit value t of the Student's t distribution from the assumption of normality, was chosen at a given risk level (i.e. t"z"1)96 at the 5% level for large samples). The coe$cients of variation (i.e. ratios of standard deviation over mean) of the mean cone penetrometer readings varied between 20 and 40%, with the lowest variation observed in the plastic clay soil D, and the highest in the dry, compact soil B. The cone penetration resistance data acquired in the more compact soil conditions (soils A, B and C) typically depicted a maximum at approximately 0)25 m depth (clay soil B, e.g. Fig. 2) or deeper, at 0)35 m depth (sandy loam soils A and C). In the wetter clay soil D, the cone penetrometer values tended to continually increase with sampling depth. Regression analyses were applied to the cone penetration data sets with the aim of establishing the characteristic C versus depth relationships in each soil type and G condition. The regression equations (polynomial functions of depth) based upon the least-squares method were selected from their goodness of "t17 such that they best represented the experimental data sets. This was achieved with the lowest error mean square values (i.e. higher values of the adjusted coe$cient of determination of the regression R and adequate Mallows C statistic17) which ? N also provided closest to normally distributed residuals. Simple mathematical integration of the C equations G
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P R ED I CT I O N O F TI LLA G E I M PL E ME N T D RA U G H T
according to Eqn (7) was then carried out to de"ne the corresponding cone penetration energy P equations over C the depth range. The trend of the P curves is dependent C upon that of their respective C curves, and overall exG hibit some linearity in their relationship with depth (e.g. Fig. 2). Details of the methodology and materials used to acquire draught data D for a 70 mm wide standard tine Q were reported by Desbiolles et al.1 Also reported were the corresponding 24 regression equations and their respective R coe$cients ranging from 64 to 98%. The values of ? the in situ soil strength factor S were then computed over the depth range using Eqn (4), assuming that its validity could be extended to "eld soil conditions (the validity of this assumption was to be tested in the accuracy achieved by the prediction methodology). The general &®ression equation approach'' adopted in the study had the practical advantage of allowing P and S values to be easily C determined at any required depths for use in the prediction methodology. In each of the 24 soil conditions, sampling for soil moisture content was also organised at "ve random locations within each plot, and was restricted to the
0)1}0)2 m depth layer, representing a highly #uctuating layer under both rainfall input and drying sun-rays. Moisture contents were determined using the oven dry technique at 1053C for 48 h and were expressed on a percentage dry basis.
2.2. Correlation analysis Figure 2 gives an example of the data collected in the clay soil B, at 24)6% moisture content (dry basis), showing the relationships obtained for C , P and D , S. The G C Q correlation coe$cients between S and C or S and G P parameters are summarised in Table 2. The most C reliable correlation was found between S and P as anC ticipated, with highly signi"cant positive coe$cients of 0)929 and 0)752 in the sandy-loam (soils A and C) and clay (soils B and D) soil categories, respectively. The level of correlation in soil B and in soil D was lessened when pooling the data sets of these two soils together, possibly as a consequence of the high in#uence of soil moisture upon both soil strength factor S and cone penetration resistance C , being a likely source of discrepancies. In G order to quantify the correlation between S and P , a C ratio F was de"ned as given by Eqn (9) S F" P C
Fig. 2. Sample standard tine and cone penetrometer xeld data (soil B, 24)6% moisture content)
(9)
The values of the F ratios were computed at 50 mm depth intervals over the 0)05}0)45 m depth range using "tted values of S and P obtained from their respective C regression equations under the 24 soil conditions. The F ratio plots are shown as line curves in Fig. 3 and Fig. 4 for two soil categories, namely predominantly frictional (sandy soils A and C) and predominantly cohesive (clay soils B and D) soils, respectively. The empirical F ratio relationships are strongly in#uenced by working depth (i.e. exponential decay relationship), particularly in the shallow range. This depth e!ect was anticipated since the slopes of the S and P curves di!ered signi"cantly, as is C exampli"ed in Fig. 2. Additionally, some e!ect of soil moisture content can clearly be observed among the family of curves in the clay soil category (Fig. 4), with a trend for greater F ratio values observed at higher moisture contents. This highlights the fact that the standard tine draught sensitivity to soil moisture content is di!erent from that of the cone penetration resistance. Overall, the e!ect of soil moisture content is less obvious in the sandy-loam class (Fig. 3) and at the deeper depths in both soil categories. The more pronounced interaction with soil moisture content in the clay soil category is not surprising since the in#uence of soil moisture on soil strength is typically greatest in cohesive soils which, as
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Table 2 Correlation coe7cients r between soil strength factor S and cone penetrometer variables Ci or Pe Correlation coezcient Pooled results Paired data set
Soil A
Soil B
Soil C
Soil D
Soils A, C
Soils B, D
(C , S) (P , S) C n
0)816 0)934 47
0)167* 0)888 47
0)483 0)947 45
0)717 0)904 47
0)736 0)929 92
0)112* 0)752 94
Soils A, B, C, D 0)365 0)787 186
Note: All coe$cients of linear correlation r are signi"cant at the 1% level (*not signi"cant at the 5% level). n is sample size of paired data set (C , S) or (P , S) from which r was determined. S, C and P data (n values) were obtained over a range of soil C C moisture content and working depths in each of the four soil conditions (A, B, C, D).
a result, exhibit a wide range of soil failures18 and of physical states (i.e. cemented, friable, plastic or liquid). The above observations translated in correlation coef"cients r"0)59 and r"0)31 between the F ratio and the soil moisture content data in the clay and sandy soil categories, respectively, and r"0)53 and r"0)68 be-
tween the F ratio and the exponential of working depth d in the clay and sandy soil categories, respectively. Multiple regression analyses carried out separately for the clay (soils B and D) and sandy (soils A and C) categories de"ned the following empirical relationships between the F ratio values, soil moisture content m on A
Fig. 3. Ewects of soil moisture content and working depth on F ratio relationships (sandy soil category, soils A and C): , 13}15%; , 15}17%; , 17}19%; , 19}21%
Fig. 4. Ewects of soil moisture content and working depth on F ratio relationships (clay soil category, soils B and D): , 20}25%; , 25}30%; , 30}35%; , 40}45%
P R ED I CT I O N O F TI LLA G E I M PL E ME N T D RA U G H T
% dry basis, and working depth d in metres: F "!0)2764#0)0573 ln(m )#0)1543e\B AJ?W A (R"59)1%, s"0)0051)
(10)
F "!0)054#0)00153m #0)0694e\B Q?LBW A (R"62)8%, s"0)0129)
(11)
where R is the coe$cient of multiple correlation and s is the standard error. These relationships are valid over the experimental depth range (i.e. 0)05}0)45 m) and soil moisture content range expressed on a dry basis (13}21% and 23}43% in the sandy and clay soil categories, respectively). The coe$cients of determination of the regression equations are moderate, possibly as a result of the limited set of soil moisture data, which was acquired within the 0)1}0)2 m depth layer only. A more extensive set of soil moisture content data acquired by layer within the whole soil pro"le could possibly have generated more accurate relationships. All regression coe$cients are highly signi"cant (probability P"0)001), with the exponential depth parameter contributing 49% of the regression sums of squares in the clay soil category, and 84% in the sandy soil category. The F ratio relationships [Eqns (10) and (11)] can be used to estimate the soil strength factor S in a "eld soil condition by applying Eqn (9), from the knowledge of (i) the cone penetration resistance pro"le down to the working depth d of the standard tine, upon which to estimate the speci"c cone penetration energy P at depth d apC plying Eqn (7) and (ii) the soil moisture content (dry basis) within the 0)1}0)2 m depth layer, to compute the empirical F ratio estimate at the working depth d in the relevant soil category. The standard tine draught D can Q then be estimated from cone penetrometer data from D "F;P ;G (12) Q C Q which, combined with Eqn (5), now provides an alternative estimate of the tillage tool draught D : R D "I;F;P ;G (13) R C Q 3. Field validation of ratio of soil strength to speci5c cone penetration energy 3.1. Experimental method Three additional "eld conditions were considered, namely two friable sandy loam (soils E and G) and a compact clay (soil F), whose textures and moisture contents are also given in Table 1(b). Sampling for soil moisture content was carried out using the method detailed in Section 2.1. The standard tine draught data was acquired at a low velocity (1)5}2 km/h) in a replicated
71
and randomized manner at several depths within the 0)1}0)4 m depth range, using an instrumented four wheel drive tractor and a three point hitched frame onto which a 70 mm wide standard tine was "tted. Gauge wheels provided depth settings at 25 mm intervals. The actual depth of work of each run was measured at four locations and the mean value calculated and matched to the corresponding standard tine draught reading. The force measurements were conducted using an extended octagonal ring transducer, previously described by Godwin,19 sampling the transducer output signals at a frequency of 100 Hz. Multiple regression analyses (polynomial functions of depth) were conducted on each data set, in a similar fashion to that reported in Section 2.1, to establish the characteristic standard tine draught versus depth relationships under the three soil conditions (see Fig. 5). Fitted draught values at selected depths were then referred to as the measured standard tine draught data. Cone penetration resistance data were also acquired in a similar manner to that outlined in Section 2.1, and led to the formulation of speci"c cone penetration energy P equaC tions for the three soil conditions (soils E to G) by applying Eqn (7). The standard tine draught D operating Q at a depth d was predicted following the model of Eqn (12), and the predicted relationships are shown in Fig. 5.
3.2. Prediction of standard tine draught An error factor e was arbitrarily de"ned to assess the performance of the cone penetrometer based predictions of the standard tine draught. The error factor e is characterized over a depth range and is computed as the area contained between the curves of the predicted and measured draught}depth relationships, expressed as a proportion (percentage) of the corresponding area contained under the curve of the measured draught}depth relationship. The factor e is estimated on an area basis and is therefore not sensitive to the e!ect of positive and negative prediction errors at speci"c depths and, being de"ned over a depth range, is a direct measure of the di!erence between the predicted and measured curves being easily quanti"ed with the available regression equations. The standard tine draught D was predicted with Q a 15)5% error over the 0)1}0)4 m depth range in the two sandy-loam soils (soils E and G), representing a 0)6}0)8 kN average prediction error. The standard tine draught was predicted with a 13)4% overall error over the same depth range in the clay soil F, corresponding to a 1)6 kN prediction error on average. A tendency to under-predict consistently at the deeper depths was noted. These data suggest that the correlations established between S and
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J . M. A. D ES B IOL L ES E ¹ A ¸.
by rede"ning the F ratio relationships based upon a more extensive soil moisture content data set, sampled by depth layer over the working depth pro"le.
4. Draught predictions for tillage implements 4.1. Multi-tool tillage implement prediction models Multi-tool tillage implements were considered as an association of n single tillage tools. The implement draught D can thus be approximated as n times the U draught D of a single tool, subsequently corrected to R account for (1) the tool interactions within the implement frame, depending upon working depth and tool spacing, and (2) the e!ects of any additional attachment or accessories "tted. In a model for tool interaction, reported by Godwin et al.,20 the interaction between two adjacent tines is modelled from the overlap between the assumed areas of disturbance, and results in a decrease in the draughts of the two tines. This force reduction is assumed to equate to the draught D of an imaginary tine produG cing the corresponding soil disturbance in the interacting zone (Fig. 6). In particular, the model is characterized by the following assumptions: 1. The soil failure boundaries slope sideways at 453 (see Fig. 6). 2. The imaginary tine has negligible width, thus creating side crescent failures only, and is inclined at the rake angle of the main tines.
Fig. 5. Measured and predicted standard tine draught in three soil conditions: , predicted, , xtted; , measured data
P have the potential to become a useful empirical link C between in-"eld soil strength data, as measured by the standard tine, and cone penetrometer data, in the form of speci"c cone penetration energy. These correlations can be used to enhance the practicality of the empirical draught prediction methodology for tillage implements operating in "eld conditions, as described in Section 1. Possible improvements in the predictions may be obtained
Fig. 6. Tool interaction model for multi-tine implements (adapted from Godwin et al.20)
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3. The working depth d of the imaginary tine is given by G the intersection point of the 453 theoretical failure boundaries (see Fig. 6), which is a function of the tine inner spacing X and of the tine working depth d: X d "d! G 2
(14)
In this study, the imaginary tines were assumed to be at 453 rake angle and treated as imaginary standard tines (w"0) whose draught D was modelled by applying the G concept of Eqn (1): D "S;G G G
(15)
where, from Eqn (3), G "1)225;d (16) G G and S is the soil strength factor at the depth d , and is G obtained from the standard tine draught data. The total draught reduction D due to tool interaction on an impleP ment comprising n equally spaced tines working at a depth d, is thus given by D "(n!1);D (17) P G The implement draught D is thus estimated by U D "n;D !D #D (18) U R P ? where D is the additional draught due to "tted accessor? ies or attachments, either measured or estimated from relevant literature data. In the model of Eqn (18), D can R either be estimated from Eqn (5) (i.e. standard tine or ST method) or from Eqn (13) (i.e. cone penetrometer or CP method).
4.2. Field experiment methodology Four primary tillage implements were considered, namely: (i) a chisel implement ("ve curved blade tines); (ii) a high lift winged subsoiler (single shank); (iii) an one way
disc plough (three furrows); and (iv) a reversible mouldboard plough (three furrows). The implement draught measurements were carried out in a random and replicated manner and at a low velocity (1)5}2 km/h) in soils E to G as part of a separate investigation,21 but were conducted simultaneously while acquiring the standard tine draught and cone penetrometer data, reported in Section 3. The implement draught was measured with two tractors using a shear pin dynamometer mounted on the drawbar of the leading tractor towing the implement mounted on the second tractor. Force values were obtained by subtracting the rolling resistance of the second tractor with the implement raised, from the overall force of the tractor with the implement working at the required depth. The working depths were measured at several locations along each run, their mean calculated and matched to the corresponding draught. The transducer output signals were sampled at a frequency of 100 Hz. Details of the draught readings and working depth data were reported by Kirisci21 and the mean draught values with their standard deviations are reproduced in Table 3. The chisel and subsoiler implements consisted of single tillage units for which the tool index relationships I had already been established and reported by Desbiolles et al.1 The inner tine spacing X on the chisel implement was 0)32 m. The mouldboard plough comprised three bodies of a similar type (semi-helical) and at a similar furrow spacing (0)356 m) to that previously investigated by the authors.1 Added accessories included (1) mouldboard extensions, (2) skimmers and (3) coulters on share, each one with a particular pulling requirement. However, the overall draught of the combination of mouldboard body and coulter was expected to be less than that of a (less e$cient) mouldboard body by itself, as is supported in the existing literature.22,23 For simplicity, the di!erence in draught requirement was assumed to be compensated by the pull requirement of accessories (1), (2), and of a rear gauge wheel. The tool index values I of
Table 3 Mean measured draught (standard deviation) of four tillage implements operating at typical working depths, adapted after Kirisci21 Draught, kN Tillage implement Chisel implement Subsoiler tine Disc plough Mouldboard plough
Soil E sandy-loam 33)3 15)7 12)9 14)1
(1)6) (1)4) (1)3) (1)4)
Soil F clay 40)0 22)8 18)7 33)1
(2)4) (1)3) (1)9) (1)8)
Working depth, m Soil G sandy-loam 8)7 12)4 9)5 12)6
(0)9) (1)9) (2)4) (1)8)
Soil E sandy-loam
Soil F clay
Soil G sandy-loam
0)31 0)40 0)17 0)20
0)17 0)33 0)14 0)19
0)17 0)42 0)15 0)23
74
J . M. A. D ES B IOL L ES E ¹ A ¸.
the mouldboard body previously investigated and reported by the authors were referred to in the predictions. The disc plough comprised three disc units of similar characteristics to those of a single plough disc previously investigated and for which tool index relationships I had been established.1 The 20% wider furrow spacing on the plough implement (i.e. 0)305 m as opposed to 0)254 m) was accounted for by incorporating a multiplying factor of 1)2 (i.e. 0)305/0)254 ratio) into Eqn (18), assuming near-constant ploughing resistance per unit width. Disc plough accessories included (1) disc scrapers and (2) a side thrust wheel. The additional draught requirement due to disc scrapers, whose function is to increase the turning over ability of the disc plough, is mainly a function of operating speed and working depth, and that of the side thrust wheel is a function of the magnitude of the soil/disc force reaction (e.g. soil strength). To account for their e!ect, and where no information could be isolated in the literature available to the authors, the added draught value D was arbitrarily set at 10% of the overall ? implement draught. Draught predictions for the four implements were computed in line with the comments above based upon the measured standard tine and cone penetrometer methods, and the prediction errors were evaluated and expressed as a percentage proportion of the measured draught values.
4.3. Prediction of implement draught The overall prediction performance of the models is shown in Table 4. These prediction accuracies are to be assessed in light of the variability in the measured draught values, such as the coe$cients of variation (stan-
dard deviation/mean) of the mean measured draught shown in Table 3 and ranging from 5}26%. The standard tine (ST) models predicted the implement draught within 15}19% on average over the three soil conditions. As expected, the prediction error increased to within 11}41% range with the cone penetrometer (CP) models due to the additional link (F ratio) used in the prediction model. Overall, the standard tine and cone penetrometer models predicted within 17 and 26% of the measured draught, respectively, comparing favourably with the accuracy for in situ draught predictions reported in the literature.2,20,24 Table 4 shows in particular that the ST model predictions fell well within two standard deviations (i.e. 95% con"dence interval) of the mean measured draught values. The best overall performance (16)3 and 10)9% error for the standard tine and cone penetrometer models, respectively) was achieved with the disc plough. Improved predictions on average were obtained with the cone penetrometer models, which in the authors' opinion illustrates the potential case where the prediction errors (in both the predicted D and predicted D ) are compensaQ R tory rather than additive (e.g. in this case, a signi"cant compensation occurred in soil G). The standard tine model performance with the mouldboard plough implement was also satisfactory with a below 15% average prediction error (compared to a 25% error on average with the cone penetrometer models, mainly due to additive e!ects in prediction errors found in soil G). A similar situation was observed with the subsoiler tine (18)7 and 28)5% errors on an average for the standard tine and cone penetrometer models, respectively). The performance of the multi-tine chisel implement was least satisfactory (18)4 and 41)1% respective average errors). The larger prediction errors observed
Table 4 Prediction error of standard tine (ST) and cone penetrometer (CP) models for four tillage implements operating in three soil conditions Error, % Tillage implement
Chisel implement Subsoiler tine Disc plough Mouldboard plough Mean (all tools)
Soil E sandy-loam
Soil G sandy-loam
Mean sandy-loam
Soil F clay
Mean all soils
ST
CP
ST
CP
ST
CP
ST
CP
ST
CP
!17)9 !24)6 !10)2 18)7 17)9
!36)0 !49)7 !12)4 14)7 28)2
4)4 16)1 !36)6 17)9 18)8
46)2 !11)2 !6)0 44)1 26)9
11)2 20)4 23)4 18)3 18)3
41)1 30)5 9)2 29)4 27)6
!32)8 !15)4 2)0 !6)6 14)2
!41)2 !24)6 14)4 !16)2 24)1
18)4 18)7 16)3 14)4 16)9
41)1 28)5 10)9 25)0 26)4
Note: ST: Standard tine model [Eqn (5)], CP: Cone penetrometer model [Eqn (13)], all means are computed from absolute values.
P R ED I CT I O N O F TI LLA G E I M PL E ME N T D RA U G H T
with this multi-tine implement may be explained by potentially signi"cant #uctuations in working depth due to the lack of gauge wheels on that implement (i.e. sensitivity to tractor pitch and roll) which may have rendered the working depth estimates less accurate. No e!ect of soil type on the prediction performance was detected. The overall performance of the standard tine based models for predicting the in situ draught of multi-tool tillage implements is encouraging, characterised with similar prediction error levels to those reported for single tools.1 Conversely, whilst the cone penetrometer is attractive for its practicality and rapidity in acquiring in situ soil strength data for input into the models, the study has shown that its use typically comes at the cost of prediction accuracy. This was expected due to the additional F ratio parameter input into the models. However, the authors believe that more accurate F ratio relationships could be de"ned based upon a more extensive set of soil moisture data sampled by layers within the soil pro"le. The usefulness of the cone penetrometer models should be assessed in light of the signi"cant di$culties associated in applying the current analytical methods to in situ force predictions (relying upon fundamental soil mechanical properties c, c, , d and c ) for complex tool shapes. ? 5. Conclusions (1) The investigation has produced a novel approach for using cone penetrometer data to predict the in situ draught of tillage implements, by highlighting signi"cant correlations between speci"c cone penetration energy and an in situ soil strength parameter as measured by a standard time. (2) The draught requirement of a 70 mm wide standard tine was predicted successfully from cone penetrometer data in three soil conditions within 15% error over the 0)1}0)4 m working depth range. These prediction results compare very favourably with the accuracy for draught measurements reported in the literature and with the typical variability observed within this study. (3) The investigations also showed that an existing prediction methodology, previously developed and validated for single tillage tools, could predict within 17% on average the draught of four di!erent multitool tillage implements, from the knowledge of the standard tine draught measured in situ. (4) When using the standard tine draught values estimated from cone penetrometer data, the tillage implement draught could be predicted within 26% on average. This performance level is still useful as the cone penetrometer method provides quicker results in a practical manner.
75
Acknowledgements This research work was partly funded by the Ministry of Agriculture, Fisheries and Food, UK, and by Silsoe College of Cran"eld University. The authors are especially grateful to the technical sta! of the College for their helpful participation.
References 1
Desbiolles J M A; Godwin R J; Kilgour J; Blackmore B S A novel approach to the prediction of tillage tool draught using a standard tine. Journal of Agricultural Engineering Research, 1997, 66, 295}309 2 Godwin R J; Spoor G Soil failure with narrow tines. Journal of Agricultural Engineering Research, 1977, 22(4), 213}228 3 Koolen A J; Kuipers H Agricultural Soil Mechanics. Berlin: Springer, 1983 4 Campbell D J; O:Sullivan M F The cone penetrometer in relation to tra$cability, compaction and tillage. In: Soil Analysis: Physical Methods. (Smith K A; Mullins C E, eds). New York: Marcel Dekker Inc., 1991 5 Freitag D R Penetration tests for soil measurements. Transactions of the American Society of Agricultural Engineers, 1968, 11(4), 751}753 6 Elbanna E B; Witney B D Cone penetration resistance as a function of the clay ratio, soil moisture content and speci"c weight. Journal of Terramachanics, 1987, 24(1), 41}56 7 Wells L G; Treesuwan O The response of various soil strength indices to changing water content and bulk density. Transactions of the American Society of Agricultural Engineers, 1978, 21(4), 854}861 8 Ayers P D; Perumpral J V Moisture and density e!ect on cone index. Transactions of the American Society of Agricultural Engineers, 1982, 25(5), 1169}1172 9 Gee Clough D; McAllister M; Pearson G; Evenden D W The empirical prediction of tractor-implement "eld performance. Journal of Terramechanics, 1978, 15(2), 81}94 10 Oskoui K E; Rackham D H; Witney B D The determination of plough draught * Part II: the measurement and prediction of plough draught for 2 mouldboard shapes in 3 soil series. Journal of Terramechanics, 1982, 19(3), 153}164 11 Dawidovski J B; Worona M; Hencel A The determination of plough draught from soil penetration resistance. Proceedings of the 11th International Soil Tillage Research Organisation Conference: Tillage and Crop Production. Edinburgh, Scotland, Vol. 2 (Section 4), 11}15 July 1988, 457}462 12 Campbell D J; Sta4ord J V; Blackwell P S. The plastic limit as determined by the drop cone-test in relation to the mechanical behaviour of soil. Journal of Soil Science, 1980, 31(1), 11}24 13 A.S.A.E. Standard S313.2: Soil cone penetrometer. ASAE: Standards, Engineering practices and data 1990, 37th Edn. St Josepth, MI, USA: American Society of Agricultural Engineers, 1990 14 Neville A M; Kennedy J B Basic statistical methods for Engineers and Scientists. Scranton, PA: International Textbook Company, 1977
76 15
16
17
18
19
20
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O:Sullivan M F; Dickson J W; Campbell D J Interpretation and presentation of cone resistance data in tillage and tra$c studies. Journal of Soil Science, 1987, 38(1), 137}148 Kogure K; Chira Y; Yamagushi H Basic study of the probabilistic approach to the prediction of soil tra$cability * statistical characterisitics of cone index. Journal of Terramechanics, 1985, 22(3), 147}156 Draper N R; Smith H Applied Regression Analysis, 2nd edn. New York: Wiley, 1981 Rajaram G; Gee-Clough D Force-distance behaviour of tine implements. Journal of Agricultural Engineering Research, 1988, 41(3), 81}98 Godwin R J An extended octagonal ring transducer for use in tillage studies. Journal of Agricultural Engineering Research, 1975, 20(5), 347}352 Godwin R J; Spoor G; Soomro M S The e!ect of tine arrangement on soil forces and disturbance. Journal of Agricultural Engineering Research, 1984, 30(1), 47}56
21
22
23
24
Kirisci V A "eld method for predicting the draught forces of tillage implements. PhD thesis. Silsoe College of Cran"eld University, Silsoe, Bedford, 1994 Girma G Measurement and prediction of forces on plough bodies*I: measurement of forces and soil dynamic parameters. Proceedings of the 11th International Congress on Agricultural Engineering. Dublin, Vol. III of IV (Agricultural Mechanisation) 4}8 September 1989: 1539}1545. Land and Water Use (Dodds; Grace, eds). Rotterdam: Balkema A A Publishers, 1989 Bernacki H; Haman J; Kanafojski Cz Agricultural machines, theory and construction. Translation TT 69-50019 for the United States Department of Agriculture and the Agricultural Research Service, Washington, DC. Warsaw, Poland: Scienti"c Publications Foreign Cooperation Center of the Central Institute for Scienti"c, Technical and Economic Information, 1972 McKyes E; Ali O S The cutting of soil by narrow blades. Journal of Terramechanics, 1977, 14(2), 43}58
Prediction of Tillage Implement Draught using Cone Penetrometer Data J. M. A. Desbiolles; R. J. Godwin; J. Kilgour; B. S. Blackmore On-Farm Machinery Division, Agricultural Machinery Research and Design Centre, University of South Australia, The Levels Campus, Mawson Lakes SA 5095, Australia; e-mail: [email protected] Agricultural and Biosystems Engineering Department, School of Agriculture Food and Environment, Cran"eld University, Silsoe, Bedford MK45 4DT, UK (Received 22 September 1997; accepted in revised form 6 November 1998)
A novel approach to the prediction of tillage implement draught has previously been reported which involves a simple reference tine (standard tine) in relation to which tillage implements are rated in a reference soil in terms of their draught requirements. This prediction methodology makes use of the standard tine draught measured in situ to predict the draught required by any indexed tillage implement operating under the same soil condition. The standard tine draught in the reference soil is also described as the product of a soil strength factor S and a geometrical factor G . Results of an investigation conducted to assess the usefulness of cone penetrometer data Q when included in this prediction methodology are reported in this study. Speci"c cone penetration energy P signi"cantly correlated with the soil strength factor S in two sandy-loam C (r"0)93) and two clay (r"0)75) soils. Their relationship was quanti"ed in a dimensionless parameter F, ratio of P over S, which was found to depend upon working depth, soil type and soil moisture content. Multiple C regression equations for F with soil moisture content and working depth were de"ned empirically for clay and sandy soil categories. Using these equations, the draught of the standard tine operating in three separate soil conditions was predicted over a working depth range (0)1}0)4 m) within a 15)5% error. The draughts of four multi-tool tillage implements operating at a typical working depth in three soil conditions were predicted using the measured standard tine draught data with a 17% error on an average. Using the standard tine draught values predicted from the cone penetrometer data, the average prediction error increased to 26%. The performance of the prediction models using the cone penetrometer data re#ected a compromise between the improved practicality of the in situ data collection and the reduced prediction accuracy. Its usefulness, however, should be assessed in the light of the signi"cant di$culties associated with using the current analytical methods for in situ predictions (requiring fundamental soil mechanical characteristics) and for complex tool shapes. 1999 Silsoe Research Institute
where the soil strength factor S is modelled in a zero soil surface surcharge and adhesionless soil (i.e. reference soil condition). This soil strength factor is a function of fundamental soil properties as described in the Godwin and Spoor analytical model2
1. Introduction A new approach to the prediction of implement draught (i.e. horizontal pulling force) in tillage studies was reported by Desbiolles et al.1 The methodology involved is based on the Godwin and Spoor 2 analytical model and describes the draught D of a simple narrow Q tine at a 453 rake angle (i.e. referred hereafter as standard tine) operating at a low speed, above its critical depth and in a reference soil condition, as the product of two factors, namely S and G , related to soil strength and tool Q geometry, respectively: D "S;G (1) Q Q 0021-8634/99/050065#12 $30.00/0
S"(cdN #cdN ) (sin d#cos d) (2) A A where N and N are dimensionless N-factors dependent A A on the soil internal friction angle , d is the tine working depth, c the soil bulk unit weight, c the soil cohesion and d the soil}tool interface friction angle. The geometrical factor G is theoretically de"ned1 as a linear function of Q the standard tine width w and working depth d: G "0)707w#1)225d Q 65
(3)
1999 Silsoe Research Institute
66
J . M. A. D ES B IOL L ES E ¹ A ¸.
Notation A c C G C N d d G D D D D
P
?
e E F F N G I m A n
cone surface area, m soil cohesion, kN/m soil cone index, kPa Mallows statistics tine or tool working depth, m imaginary tine working depth, m draught, in "eld soil conditions (measured or predicted), kN draught in laboratory soil conditions (measured or predicted), kN equivalent draught reduction due to tool interactions within an implement, kN Draught requirement of tool accessories in a multi tool implement, kN error factor expressed over a working depth range, % deviation of sample mean from population mean, % ratio, S/P C penetration force, N geometrical factor, m tool index soil moisture content dry basis, % number of single tillage tools in a multi-tool implement
n N ,N A A P P C r R R ? s S t < w X z d c
Subscripts s standard tine t single tillage tool w multi tool tillage implement i imaginary tine
The expression for G is valid for any standard Q tine working above its critical depth. The soil strength factor S (in the reference soil condition) can be estimated empirically at a given depth d by using any standard tine of width w as a measuring device, from the knowledge of its draught D . Q D Q S" (4) 0)707w#1)225d The prediction methodology was developed and validated1 for single tillage tools operating at a low velocity (e.g. 2 km/h) to re#ect the quasi-static conditions dictated by the analytical model.2 It consists of two stages, namely (1) to establish in a reference soil condition some comparative relationships (i.e. tool index I) linking the draught of the standard tine D to that of each tillage Q tool D and (2) to measure the draught of the standard R tine D in the "eld. The tool draught D in that "eld Q R condition is predicted from Eqn (5): where
number of required replications in CI data samples dimensionless N-factors probability level speci"c cone penetration energy parameter, kJ/m or kN/m coe$cient of linear correlation, % coe$cient of multiple correlation, % adjusted coe$cient of determination of the regression, % standard error of the regression, regression units soil strength factor, kN/m statistical Student's t value statistical coe$cient of variation, % standard tine width, m tine inner spacing on an implement, m statistical z value soil}tool interface friction angle, deg soil bulk unit weight, kN/m soil internal friction angle, deg
D "I;D R Q
(5)
D I" R D Q
(6)
This method was shown to provide predictions typically within 15% of the measured draught for a range of single tillage tines operating under four soil conditions.1 However, constraints associated with such methodology are: (1) the need for speci"c "eld equipment to acquire the standard tine draught data (i.e. force measurement equipment, standard tine and hitch frame, tractive machinery) and (2) the invasive aspects of carrying out the measurements in the intended "eld conditions with regard to the soil conditions and growing crops. The practicality of implementing this methodology could, therefore, be enhanced if the soil strength data in the "eld was obtained by using a quick, simple and non-destructive alternative method. Investigations were carried out to determine the suitability of the cone penetrometer in this context, this device being widely used as a practical tool to provide estimates of soil strength.3,4 The soil strength estimate in kPa, often referred to as cone index C , is a composite soil parameter, strongly in#uenced by G soil type, soil structural state and soil water content.5+8 The cone penetration resistance has often been used to predict the draught requirement of, principally, plough implements,9+11 where either C values at median working G depth or average C value over the working depth zone, G
P R ED I CT I O N O F TI LLA G E I M PL E ME N T D RA U G H T
have been used as in situ soil strength data. The approach followed here is di!erent as correlations were sought between the cone penetration resistance data and the soil strength factor S as measured by the standard tine [Eqn (4)] rather than with its draught itself. A general relationship between the parameter C and the factor S was G anticipated (see Fig. 1) since various aspects of soil}soil and soil}metal failure are known to in#uence both the C parameter3 and the soil strength factor S, as implied by G the soil mechanical properties d, c, c and in the theoretical model of Eqn (2). Additionally, the draught of 453 rake angle tines (and therefore the soil strength factor S) and the cone penetration resistance have been shown to display comparable trends8,12 with soil moisture content in frictional-cohesive soils. A fundamental di!erence, however, was also expected as S represents a bulk strength value which is in#uenced by the state of the soil over the whole depth pro"le (from the soil surface down to the working depth), as opposed to the C parameter comparG ing as a point estimate of soil strength at a given depth. As a result, a cone penetration energy criterion P C was de"ned, involving all the cone penetrometer readings within the soil pro"le and was expected to be conceptually similar to the soil strength factor S (see Fig. 1). The P parameter is given by the area enclosed under the C curve of the C versus depth relationship down to the G depth of work (Fig. 1) and is obtained from simple mathematical integration of the &&best "t'' C regression G equation with respect to working depth d [Eqn (7)]: B
P " C ) dd G C M
(7)
The units of P represent an energy per unit crossC sectional area of the cone (i.e. kPa;m,kJ/m) which
67
characterize a speci"c cone penetration energy. These units are equivalent to the fundamental units of S (i.e. force/length). As a practical alternative in the "eld, P can C easily be approximated from the product of the average C value over a depth pro"le multiplied by the value of G the working depth d. The objectives of the study reported below were as follows: (i) to investigate the correlations between S and P for C a range of soil types, soil water contents, and across a typical working depth range, and to quantify some empirical relationships linking S to P ; C (ii) to assess the merit of relying upon the cone penetrometer to estimate the soil strength factor S, and ultimately to predict the in situ draught of the standard tine D , by validating these Q empirical relationships in a separate range of "eld conditions; (iii) to predict the draught of four primary tillage implements operating at a low speed and a typical working depth, using the standard tine prediction methodology [e.g. Eqn (5)] with the standard tine draught D either measured or predicted from cone Q penetrometer data. The results corresponding to each objective are reported in Sections 2, 3 and 4 respectively. 2. Correlations between soil strength factor and cone penetration energy 2.1. Materials and methods Cone penetrometer resistance data was acquired at four di!erent sites (two sandy-loam, soils A and C, and two clay soils, soils B and D) on six separate occasions
Fig. 1. Conceptual relationship between the soil strength factor S and the cone penetration energy P C
68
J . M. A. D ES B IOL L ES E ¹ A ¸.
Table 1 Field conditions (a) referred to in the correlation analyses and (b) for the veri5cation of the models Mechanical analysis Soil reference
Texture
Sand,%
Silt,%
Clay,%
Soil moisture content in 0)1}0)2 m layer, % dry basis
(a) Soil conditions for correlation analyses Soil A Sandy-loam Soil B Clay Soil C Sandy-loam Soil D Clay
69 25 67 13
15 26 18 21
16 49 15 66
13)7}20)5* 23)0}29)0* 14)6}17)8* 30)2}43)3*
(b) Soil conditions for model veri,cations Soil E Sandy-loam Soil F Clay Soil G Sandy-loam
69 15 59
15 25 25
16 60 16
13)8R 34.6R 13)8R
* Soil moisture range encountered over trial period (six experiments/soil type). R Soil moisture at time of trial (1 experiment/ soil type).
providing a range of soil textures and moisture contents (i.e. 24 soil conditions) summarized in Table 1(a). Under these same soil conditions, the draught requirement of a 70 mm wide standard tine was measured over a comparable range of depths. The cone penetration data was collected with a handheld electronic penetrometer following the general procedure outlined13 in the ASAE Standard S 313)2. A 303 apex angle, 12)83 mm diameter cone was used, whose base was set as the depth reference. The penetration resistance readings were recorded at regular depth intervals (every 30 mm for tillage tines, 20 mm for shallower working plough tools) over a working depth range matching that of the standard tine. The force output readings were transformed into pressure units of kPa using appropriate conversion factors to quantify the soil cone index values. The very "rst reading of each data set was systematically discarded as unrepresentative of stress conditions close to the soil surface, and the next following reading was then assumed to be representative of the soil condition up to the soil surface. Care was taken to ensure that any potential drag resistance from the cone shaft was minimized in moist sticky soil conditions (soil D) by ensuring any soil build-up was removed from the penetrometer rod at the start of each sampling. At least 50 sets of cone penetration readings were acquired at random locations within each experimental plot, which satis"ed the minimum replication requirement (n "47) as determined by the following formula, after Neville and Kennedy,14 assuming the cone penetrometer data to be independent15 and normally distributed:16
n "
(8)
where the expected coe$cient of variation < of the mean cone penetration at a given depth (i.e. standard deviation over mean ratio in %) was taken as 35%, later con"rmed by subsequent readings; the admissible level of deviation E of the sample mean from the unknown population mean, also expressed on a percentage basis, was set at 10%; and the limit value t of the Student's t distribution from the assumption of normality, was chosen at a given risk level (i.e. t"z"1)96 at the 5% level for large samples). The coe$cients of variation (i.e. ratios of standard deviation over mean) of the mean cone penetrometer readings varied between 20 and 40%, with the lowest variation observed in the plastic clay soil D, and the highest in the dry, compact soil B. The cone penetration resistance data acquired in the more compact soil conditions (soils A, B and C) typically depicted a maximum at approximately 0)25 m depth (clay soil B, e.g. Fig. 2) or deeper, at 0)35 m depth (sandy loam soils A and C). In the wetter clay soil D, the cone penetrometer values tended to continually increase with sampling depth. Regression analyses were applied to the cone penetration data sets with the aim of establishing the characteristic C versus depth relationships in each soil type and G condition. The regression equations (polynomial functions of depth) based upon the least-squares method were selected from their goodness of "t17 such that they best represented the experimental data sets. This was achieved with the lowest error mean square values (i.e. higher values of the adjusted coe$cient of determination of the regression R and adequate Mallows C statistic17) which ? N also provided closest to normally distributed residuals. Simple mathematical integration of the C equations G
69
P R ED I CT I O N O F TI LLA G E I M PL E ME N T D RA U G H T
according to Eqn (7) was then carried out to de"ne the corresponding cone penetration energy P equations over C the depth range. The trend of the P curves is dependent C upon that of their respective C curves, and overall exG hibit some linearity in their relationship with depth (e.g. Fig. 2). Details of the methodology and materials used to acquire draught data D for a 70 mm wide standard tine Q were reported by Desbiolles et al.1 Also reported were the corresponding 24 regression equations and their respective R coe$cients ranging from 64 to 98%. The values of ? the in situ soil strength factor S were then computed over the depth range using Eqn (4), assuming that its validity could be extended to "eld soil conditions (the validity of this assumption was to be tested in the accuracy achieved by the prediction methodology). The general &®ression equation approach'' adopted in the study had the practical advantage of allowing P and S values to be easily C determined at any required depths for use in the prediction methodology. In each of the 24 soil conditions, sampling for soil moisture content was also organised at "ve random locations within each plot, and was restricted to the
0)1}0)2 m depth layer, representing a highly #uctuating layer under both rainfall input and drying sun-rays. Moisture contents were determined using the oven dry technique at 1053C for 48 h and were expressed on a percentage dry basis.
2.2. Correlation analysis Figure 2 gives an example of the data collected in the clay soil B, at 24)6% moisture content (dry basis), showing the relationships obtained for C , P and D , S. The G C Q correlation coe$cients between S and C or S and G P parameters are summarised in Table 2. The most C reliable correlation was found between S and P as anC ticipated, with highly signi"cant positive coe$cients of 0)929 and 0)752 in the sandy-loam (soils A and C) and clay (soils B and D) soil categories, respectively. The level of correlation in soil B and in soil D was lessened when pooling the data sets of these two soils together, possibly as a consequence of the high in#uence of soil moisture upon both soil strength factor S and cone penetration resistance C , being a likely source of discrepancies. In G order to quantify the correlation between S and P , a C ratio F was de"ned as given by Eqn (9) S F" P C
Fig. 2. Sample standard tine and cone penetrometer xeld data (soil B, 24)6% moisture content)
(9)
The values of the F ratios were computed at 50 mm depth intervals over the 0)05}0)45 m depth range using "tted values of S and P obtained from their respective C regression equations under the 24 soil conditions. The F ratio plots are shown as line curves in Fig. 3 and Fig. 4 for two soil categories, namely predominantly frictional (sandy soils A and C) and predominantly cohesive (clay soils B and D) soils, respectively. The empirical F ratio relationships are strongly in#uenced by working depth (i.e. exponential decay relationship), particularly in the shallow range. This depth e!ect was anticipated since the slopes of the S and P curves di!ered signi"cantly, as is C exampli"ed in Fig. 2. Additionally, some e!ect of soil moisture content can clearly be observed among the family of curves in the clay soil category (Fig. 4), with a trend for greater F ratio values observed at higher moisture contents. This highlights the fact that the standard tine draught sensitivity to soil moisture content is di!erent from that of the cone penetration resistance. Overall, the e!ect of soil moisture content is less obvious in the sandy-loam class (Fig. 3) and at the deeper depths in both soil categories. The more pronounced interaction with soil moisture content in the clay soil category is not surprising since the in#uence of soil moisture on soil strength is typically greatest in cohesive soils which, as
70
J . M. A. D ES B IOL L ES E ¹ A ¸.
Table 2 Correlation coe7cients r between soil strength factor S and cone penetrometer variables Ci or Pe Correlation coezcient Pooled results Paired data set
Soil A
Soil B
Soil C
Soil D
Soils A, C
Soils B, D
(C , S) (P , S) C n
0)816 0)934 47
0)167* 0)888 47
0)483 0)947 45
0)717 0)904 47
0)736 0)929 92
0)112* 0)752 94
Soils A, B, C, D 0)365 0)787 186
Note: All coe$cients of linear correlation r are signi"cant at the 1% level (*not signi"cant at the 5% level). n is sample size of paired data set (C , S) or (P , S) from which r was determined. S, C and P data (n values) were obtained over a range of soil C C moisture content and working depths in each of the four soil conditions (A, B, C, D).
a result, exhibit a wide range of soil failures18 and of physical states (i.e. cemented, friable, plastic or liquid). The above observations translated in correlation coef"cients r"0)59 and r"0)31 between the F ratio and the soil moisture content data in the clay and sandy soil categories, respectively, and r"0)53 and r"0)68 be-
tween the F ratio and the exponential of working depth d in the clay and sandy soil categories, respectively. Multiple regression analyses carried out separately for the clay (soils B and D) and sandy (soils A and C) categories de"ned the following empirical relationships between the F ratio values, soil moisture content m on A
Fig. 3. Ewects of soil moisture content and working depth on F ratio relationships (sandy soil category, soils A and C): , 13}15%; , 15}17%; , 17}19%; , 19}21%
Fig. 4. Ewects of soil moisture content and working depth on F ratio relationships (clay soil category, soils B and D): , 20}25%; , 25}30%; , 30}35%; , 40}45%
P R ED I CT I O N O F TI LLA G E I M PL E ME N T D RA U G H T
% dry basis, and working depth d in metres: F "!0)2764#0)0573 ln(m )#0)1543e\B AJ?W A (R"59)1%, s"0)0051)
(10)
F "!0)054#0)00153m #0)0694e\B Q?LBW A (R"62)8%, s"0)0129)
(11)
where R is the coe$cient of multiple correlation and s is the standard error. These relationships are valid over the experimental depth range (i.e. 0)05}0)45 m) and soil moisture content range expressed on a dry basis (13}21% and 23}43% in the sandy and clay soil categories, respectively). The coe$cients of determination of the regression equations are moderate, possibly as a result of the limited set of soil moisture data, which was acquired within the 0)1}0)2 m depth layer only. A more extensive set of soil moisture content data acquired by layer within the whole soil pro"le could possibly have generated more accurate relationships. All regression coe$cients are highly signi"cant (probability P"0)001), with the exponential depth parameter contributing 49% of the regression sums of squares in the clay soil category, and 84% in the sandy soil category. The F ratio relationships [Eqns (10) and (11)] can be used to estimate the soil strength factor S in a "eld soil condition by applying Eqn (9), from the knowledge of (i) the cone penetration resistance pro"le down to the working depth d of the standard tine, upon which to estimate the speci"c cone penetration energy P at depth d apC plying Eqn (7) and (ii) the soil moisture content (dry basis) within the 0)1}0)2 m depth layer, to compute the empirical F ratio estimate at the working depth d in the relevant soil category. The standard tine draught D can Q then be estimated from cone penetrometer data from D "F;P ;G (12) Q C Q which, combined with Eqn (5), now provides an alternative estimate of the tillage tool draught D : R D "I;F;P ;G (13) R C Q 3. Field validation of ratio of soil strength to speci5c cone penetration energy 3.1. Experimental method Three additional "eld conditions were considered, namely two friable sandy loam (soils E and G) and a compact clay (soil F), whose textures and moisture contents are also given in Table 1(b). Sampling for soil moisture content was carried out using the method detailed in Section 2.1. The standard tine draught data was acquired at a low velocity (1)5}2 km/h) in a replicated
71
and randomized manner at several depths within the 0)1}0)4 m depth range, using an instrumented four wheel drive tractor and a three point hitched frame onto which a 70 mm wide standard tine was "tted. Gauge wheels provided depth settings at 25 mm intervals. The actual depth of work of each run was measured at four locations and the mean value calculated and matched to the corresponding standard tine draught reading. The force measurements were conducted using an extended octagonal ring transducer, previously described by Godwin,19 sampling the transducer output signals at a frequency of 100 Hz. Multiple regression analyses (polynomial functions of depth) were conducted on each data set, in a similar fashion to that reported in Section 2.1, to establish the characteristic standard tine draught versus depth relationships under the three soil conditions (see Fig. 5). Fitted draught values at selected depths were then referred to as the measured standard tine draught data. Cone penetration resistance data were also acquired in a similar manner to that outlined in Section 2.1, and led to the formulation of speci"c cone penetration energy P equaC tions for the three soil conditions (soils E to G) by applying Eqn (7). The standard tine draught D operating Q at a depth d was predicted following the model of Eqn (12), and the predicted relationships are shown in Fig. 5.
3.2. Prediction of standard tine draught An error factor e was arbitrarily de"ned to assess the performance of the cone penetrometer based predictions of the standard tine draught. The error factor e is characterized over a depth range and is computed as the area contained between the curves of the predicted and measured draught}depth relationships, expressed as a proportion (percentage) of the corresponding area contained under the curve of the measured draught}depth relationship. The factor e is estimated on an area basis and is therefore not sensitive to the e!ect of positive and negative prediction errors at speci"c depths and, being de"ned over a depth range, is a direct measure of the di!erence between the predicted and measured curves being easily quanti"ed with the available regression equations. The standard tine draught D was predicted with Q a 15)5% error over the 0)1}0)4 m depth range in the two sandy-loam soils (soils E and G), representing a 0)6}0)8 kN average prediction error. The standard tine draught was predicted with a 13)4% overall error over the same depth range in the clay soil F, corresponding to a 1)6 kN prediction error on average. A tendency to under-predict consistently at the deeper depths was noted. These data suggest that the correlations established between S and
72
J . M. A. D ES B IOL L ES E ¹ A ¸.
by rede"ning the F ratio relationships based upon a more extensive soil moisture content data set, sampled by depth layer over the working depth pro"le.
4. Draught predictions for tillage implements 4.1. Multi-tool tillage implement prediction models Multi-tool tillage implements were considered as an association of n single tillage tools. The implement draught D can thus be approximated as n times the U draught D of a single tool, subsequently corrected to R account for (1) the tool interactions within the implement frame, depending upon working depth and tool spacing, and (2) the e!ects of any additional attachment or accessories "tted. In a model for tool interaction, reported by Godwin et al.,20 the interaction between two adjacent tines is modelled from the overlap between the assumed areas of disturbance, and results in a decrease in the draughts of the two tines. This force reduction is assumed to equate to the draught D of an imaginary tine produG cing the corresponding soil disturbance in the interacting zone (Fig. 6). In particular, the model is characterized by the following assumptions: 1. The soil failure boundaries slope sideways at 453 (see Fig. 6). 2. The imaginary tine has negligible width, thus creating side crescent failures only, and is inclined at the rake angle of the main tines.
Fig. 5. Measured and predicted standard tine draught in three soil conditions: , predicted, , xtted; , measured data
P have the potential to become a useful empirical link C between in-"eld soil strength data, as measured by the standard tine, and cone penetrometer data, in the form of speci"c cone penetration energy. These correlations can be used to enhance the practicality of the empirical draught prediction methodology for tillage implements operating in "eld conditions, as described in Section 1. Possible improvements in the predictions may be obtained
Fig. 6. Tool interaction model for multi-tine implements (adapted from Godwin et al.20)
73
P R ED I CT I O N O F TI LLA G E I M PL E ME N T D RA U G H T
3. The working depth d of the imaginary tine is given by G the intersection point of the 453 theoretical failure boundaries (see Fig. 6), which is a function of the tine inner spacing X and of the tine working depth d: X d "d! G 2
(14)
In this study, the imaginary tines were assumed to be at 453 rake angle and treated as imaginary standard tines (w"0) whose draught D was modelled by applying the G concept of Eqn (1): D "S;G G G
(15)
where, from Eqn (3), G "1)225;d (16) G G and S is the soil strength factor at the depth d , and is G obtained from the standard tine draught data. The total draught reduction D due to tool interaction on an impleP ment comprising n equally spaced tines working at a depth d, is thus given by D "(n!1);D (17) P G The implement draught D is thus estimated by U D "n;D !D #D (18) U R P ? where D is the additional draught due to "tted accessor? ies or attachments, either measured or estimated from relevant literature data. In the model of Eqn (18), D can R either be estimated from Eqn (5) (i.e. standard tine or ST method) or from Eqn (13) (i.e. cone penetrometer or CP method).
4.2. Field experiment methodology Four primary tillage implements were considered, namely: (i) a chisel implement ("ve curved blade tines); (ii) a high lift winged subsoiler (single shank); (iii) an one way
disc plough (three furrows); and (iv) a reversible mouldboard plough (three furrows). The implement draught measurements were carried out in a random and replicated manner and at a low velocity (1)5}2 km/h) in soils E to G as part of a separate investigation,21 but were conducted simultaneously while acquiring the standard tine draught and cone penetrometer data, reported in Section 3. The implement draught was measured with two tractors using a shear pin dynamometer mounted on the drawbar of the leading tractor towing the implement mounted on the second tractor. Force values were obtained by subtracting the rolling resistance of the second tractor with the implement raised, from the overall force of the tractor with the implement working at the required depth. The working depths were measured at several locations along each run, their mean calculated and matched to the corresponding draught. The transducer output signals were sampled at a frequency of 100 Hz. Details of the draught readings and working depth data were reported by Kirisci21 and the mean draught values with their standard deviations are reproduced in Table 3. The chisel and subsoiler implements consisted of single tillage units for which the tool index relationships I had already been established and reported by Desbiolles et al.1 The inner tine spacing X on the chisel implement was 0)32 m. The mouldboard plough comprised three bodies of a similar type (semi-helical) and at a similar furrow spacing (0)356 m) to that previously investigated by the authors.1 Added accessories included (1) mouldboard extensions, (2) skimmers and (3) coulters on share, each one with a particular pulling requirement. However, the overall draught of the combination of mouldboard body and coulter was expected to be less than that of a (less e$cient) mouldboard body by itself, as is supported in the existing literature.22,23 For simplicity, the di!erence in draught requirement was assumed to be compensated by the pull requirement of accessories (1), (2), and of a rear gauge wheel. The tool index values I of
Table 3 Mean measured draught (standard deviation) of four tillage implements operating at typical working depths, adapted after Kirisci21 Draught, kN Tillage implement Chisel implement Subsoiler tine Disc plough Mouldboard plough
Soil E sandy-loam 33)3 15)7 12)9 14)1
(1)6) (1)4) (1)3) (1)4)
Soil F clay 40)0 22)8 18)7 33)1
(2)4) (1)3) (1)9) (1)8)
Working depth, m Soil G sandy-loam 8)7 12)4 9)5 12)6
(0)9) (1)9) (2)4) (1)8)
Soil E sandy-loam
Soil F clay
Soil G sandy-loam
0)31 0)40 0)17 0)20
0)17 0)33 0)14 0)19
0)17 0)42 0)15 0)23
74
J . M. A. D ES B IOL L ES E ¹ A ¸.
the mouldboard body previously investigated and reported by the authors were referred to in the predictions. The disc plough comprised three disc units of similar characteristics to those of a single plough disc previously investigated and for which tool index relationships I had been established.1 The 20% wider furrow spacing on the plough implement (i.e. 0)305 m as opposed to 0)254 m) was accounted for by incorporating a multiplying factor of 1)2 (i.e. 0)305/0)254 ratio) into Eqn (18), assuming near-constant ploughing resistance per unit width. Disc plough accessories included (1) disc scrapers and (2) a side thrust wheel. The additional draught requirement due to disc scrapers, whose function is to increase the turning over ability of the disc plough, is mainly a function of operating speed and working depth, and that of the side thrust wheel is a function of the magnitude of the soil/disc force reaction (e.g. soil strength). To account for their e!ect, and where no information could be isolated in the literature available to the authors, the added draught value D was arbitrarily set at 10% of the overall ? implement draught. Draught predictions for the four implements were computed in line with the comments above based upon the measured standard tine and cone penetrometer methods, and the prediction errors were evaluated and expressed as a percentage proportion of the measured draught values.
4.3. Prediction of implement draught The overall prediction performance of the models is shown in Table 4. These prediction accuracies are to be assessed in light of the variability in the measured draught values, such as the coe$cients of variation (stan-
dard deviation/mean) of the mean measured draught shown in Table 3 and ranging from 5}26%. The standard tine (ST) models predicted the implement draught within 15}19% on average over the three soil conditions. As expected, the prediction error increased to within 11}41% range with the cone penetrometer (CP) models due to the additional link (F ratio) used in the prediction model. Overall, the standard tine and cone penetrometer models predicted within 17 and 26% of the measured draught, respectively, comparing favourably with the accuracy for in situ draught predictions reported in the literature.2,20,24 Table 4 shows in particular that the ST model predictions fell well within two standard deviations (i.e. 95% con"dence interval) of the mean measured draught values. The best overall performance (16)3 and 10)9% error for the standard tine and cone penetrometer models, respectively) was achieved with the disc plough. Improved predictions on average were obtained with the cone penetrometer models, which in the authors' opinion illustrates the potential case where the prediction errors (in both the predicted D and predicted D ) are compensaQ R tory rather than additive (e.g. in this case, a signi"cant compensation occurred in soil G). The standard tine model performance with the mouldboard plough implement was also satisfactory with a below 15% average prediction error (compared to a 25% error on average with the cone penetrometer models, mainly due to additive e!ects in prediction errors found in soil G). A similar situation was observed with the subsoiler tine (18)7 and 28)5% errors on an average for the standard tine and cone penetrometer models, respectively). The performance of the multi-tine chisel implement was least satisfactory (18)4 and 41)1% respective average errors). The larger prediction errors observed
Table 4 Prediction error of standard tine (ST) and cone penetrometer (CP) models for four tillage implements operating in three soil conditions Error, % Tillage implement
Chisel implement Subsoiler tine Disc plough Mouldboard plough Mean (all tools)
Soil E sandy-loam
Soil G sandy-loam
Mean sandy-loam
Soil F clay
Mean all soils
ST
CP
ST
CP
ST
CP
ST
CP
ST
CP
!17)9 !24)6 !10)2 18)7 17)9
!36)0 !49)7 !12)4 14)7 28)2
4)4 16)1 !36)6 17)9 18)8
46)2 !11)2 !6)0 44)1 26)9
11)2 20)4 23)4 18)3 18)3
41)1 30)5 9)2 29)4 27)6
!32)8 !15)4 2)0 !6)6 14)2
!41)2 !24)6 14)4 !16)2 24)1
18)4 18)7 16)3 14)4 16)9
41)1 28)5 10)9 25)0 26)4
Note: ST: Standard tine model [Eqn (5)], CP: Cone penetrometer model [Eqn (13)], all means are computed from absolute values.
P R ED I CT I O N O F TI LLA G E I M PL E ME N T D RA U G H T
with this multi-tine implement may be explained by potentially signi"cant #uctuations in working depth due to the lack of gauge wheels on that implement (i.e. sensitivity to tractor pitch and roll) which may have rendered the working depth estimates less accurate. No e!ect of soil type on the prediction performance was detected. The overall performance of the standard tine based models for predicting the in situ draught of multi-tool tillage implements is encouraging, characterised with similar prediction error levels to those reported for single tools.1 Conversely, whilst the cone penetrometer is attractive for its practicality and rapidity in acquiring in situ soil strength data for input into the models, the study has shown that its use typically comes at the cost of prediction accuracy. This was expected due to the additional F ratio parameter input into the models. However, the authors believe that more accurate F ratio relationships could be de"ned based upon a more extensive set of soil moisture data sampled by layers within the soil pro"le. The usefulness of the cone penetrometer models should be assessed in light of the signi"cant di$culties associated in applying the current analytical methods to in situ force predictions (relying upon fundamental soil mechanical properties c, c, , d and c ) for complex tool shapes. ? 5. Conclusions (1) The investigation has produced a novel approach for using cone penetrometer data to predict the in situ draught of tillage implements, by highlighting signi"cant correlations between speci"c cone penetration energy and an in situ soil strength parameter as measured by a standard time. (2) The draught requirement of a 70 mm wide standard tine was predicted successfully from cone penetrometer data in three soil conditions within 15% error over the 0)1}0)4 m working depth range. These prediction results compare very favourably with the accuracy for draught measurements reported in the literature and with the typical variability observed within this study. (3) The investigations also showed that an existing prediction methodology, previously developed and validated for single tillage tools, could predict within 17% on average the draught of four di!erent multitool tillage implements, from the knowledge of the standard tine draught measured in situ. (4) When using the standard tine draught values estimated from cone penetrometer data, the tillage implement draught could be predicted within 26% on average. This performance level is still useful as the cone penetrometer method provides quicker results in a practical manner.
75
Acknowledgements This research work was partly funded by the Ministry of Agriculture, Fisheries and Food, UK, and by Silsoe College of Cran"eld University. The authors are especially grateful to the technical sta! of the College for their helpful participation.
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