- Email: [email protected]
A numerical–statistical hybrid modelling scheme for evaluation of draught requirements of a subsoiler cutting a sandy loam soil, as affected by moisture content, bulk density and depth
Soil & Tillage Research 63 (2002) 155±165
A numerical±statistical hybrid modelling scheme for evaluation of draught requirements of a subsoiler cutting a sandy loam soil, as affected by moisture content, bulk density and depth Abdul Mounem Mouazena,*, Herman Ramonb a
Faculty of Agriculture, Department of Rural Engineering, University of Aleppo, P.O. Box 12214, Aleppo, Syria Faculty of Agricultural and Applied Biological Sciences, Laboratory of Agricultural Machinery and Processing, Department of Agro-Engineering and-Economics, Kasteelpark Arenberg 30, B-3001 Leuven, Belgium
b
Received 13 October 2000; received in revised form 13 August 2001; accepted 16 August 2001
Abstract The development of simple regression relationships, based on ®nite element (FEM) analyses of cutting a sandy loam soil by medium±deep subsoiler will provide con®dential and quick tools to predict the subsoiler draught requirement for any combination of moisture content w, wet bulk density rw and tillage depth (d). Large number of FEM analyses were performed to assess the effect of w, d and rw on subsoiler draught. This draught was calculated from the output of 126 FEM modelling analyses. The model variations were selected based on the interaction among the studied variables, namely, six moisture contents ranging from 0.03 to 0.22 m3 m 3, ®ve wet bulk densities ranging from 1.3 to 2.0 Mg/m3 and six tillage depths ranging from 0.10 to 0.37 m. The interaction among these three variables was also taken into consideration, and a multiple linear regression analysis was performed aiming at establishing a mathematical relationship for simulating the draught variation as a function of these variables. Further relationship was developed for relating the variation in draught with w, d and dry bulk density (rd). The FEM showed that subsoiler draught increased with d, rw and rd, whereas it decreased with w. The decrease in draught with w did not extend beyond a w of 0.17 m3 m 3, since the draught calculated for 0.22 m3 m 3 w was very close to that calculated for a w of 0.17 m3 m 3. Regression equations developed to relate the subsoiler draught with w, d, rw and rd were of quite simple forms, and had high determination coef®cients (R2) close to 0.95. These equations indicated that the horizontal force varied linearly with w and non-linearly with d, rw and rd. This non-linear variation of draught was found to be a quadratic function of d and rw , and a cubic function of rd. A comparison of the calculated and measured draught for cutting a similar sandy loam soil with a similarly designed subsoiler, showed a good approximation. The small divergence between the calculated and measured draught was attributed to the difference in soil texture and subsoiler chisel length. Thus, the regression equation developed proved to be a capable tool of predicting the draught requirements of the selected tillage tool design, when cutting sandy loam soils under any combination of w, d and rw . # 2002 Elsevier Science B.V. All rights reserved. Keywords: Tillage tool draught; Moisture content; Bulk density; Depth; Linear regression analysis
1. Introduction
*
Corresponding author. Tel.: 963-21-3631-958. E-mail address: [email protected] (A.M. Mouazen).
Draught is directly related to the energy requirement of tillage tools. It may re¯ect the soil physical condition and the degree of compaction of agricultural
0167-1987/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 1 9 8 7 ( 0 1 ) 0 0 2 4 3 - 4
156
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
soils. For a unique soil type, tillage speed and tool design, draught varies with bulk density (r), w and d. These in¯uencing factors were the main axis of interest of previous research, which adapted ®eld experiments to understand how these factors affect draught requirements of tillage tools. If d and speed of tillage tools could be controlled during ®eld experiment, a representative relationship relating draught with r and w can be introduced. However, the effect of tillage system on r and w has been widely studied (Gameda et al., 1987; Bernier et al., 1989; Erbach et al., 1992; Evans et al., 1996), whereas the effect of r and w on draught requirements has been less studied. The shortage of research can be attributed to the heterogeneity of agricultural soils. In fact, draught is affected by the variation of soil properties within the ®eld (spatial variability). This includes soil type, r and w, which vary considerably, along with the vertical and horizontal directions. Moreover, no reports performed dynamic measurement of w and r, required for establishing relationship between these two variables and draught. Therefore, r and w have been related to the variation in the soil strength, expressed as penetration resistance (Ayers and Perumpral, 1982; Busscher and Sojka, 1987; Tabatabaeefar et al., 1998; Mapfumo and Chanasyk, 1998; Unger and Jones, 1998), or to soil shear strength coef®cients, namely cohesion and internal friction angle (Ayers, 1987; Mouazen et al., 2000). Even equations established for draught prediction have ignored one of these independent variables. Upadhyaya et al. (1984) published the following equation for the draught requirement of a subsoiler: D B0 CI Wd B1 rw d W S2
(1)
where D is the draught, CI the cone index, W the width of subsoiler cutting edge, d the depth, rw the wet bulk density, S the travel speed and B0, B1 the constants. It is clear that w is ignored in Eq. (1), which affects draught requirements, especially when tilling compactable soils. Other researchers also eliminated w in their general function for implement draught prediction (Sprinkle et al., 1970; Glancey et al., 1996). Koolen and Kuipers (1983) introduced several techniques for prediction of tool forces based on observations and relationships between independent and dependent variables. However, these techniques depended upon data collected arbitrarily from the ®eld, and mean values of draught and the independent
variables were taken into consideration for developing an equation for the draught requirement. These mean values do not con®rm that the predicted draught at any point within the ®eld is a re¯ection of the soil physical condition at that point. Even the single ®eld measurement of draught cannot be related with the real value of w and r at the same position where draught was measured. Kydd et al. (1984) developed equations for draught prediction of tillage tools, realising that the variations in climatic conditions, w, soil hardness and soil type made it dif®cult to obtain repeatable draught data. Therefore, it is essential to develop a proper technique capable to simulate the interaction between the draught, r, w and d. Utilising the ®nite element method (FEM) will allow draught to be related to r and w, as a new technique used for accomplishing such an objective. This method has been reported to be a proper technique to predict the horizontal and vertical forces of tillage tools. It also predicts tool forces at any combination of r and w, based on mechanical coef®cients measured for the corresponding soil physical and soil±metal interaction conditions. These coef®cients arecohesion,friction angle, Young's modulus, Poisson's ratio, adhesion and soil±metal friction. Sprinkle et al. (1970) introduced an equation for draught prediction, which involved eight independent variables, except w, and three dimensions of force, length and time. Generally, the number of independent variables can be reduced by means of the FEM analysis. Tool geometry, soil cohesion, internal friction angle and soil±metal friction angle can be eliminated from the regression equations, since they are used as input data for the FEM analysis. Tilling with low speed may allow for further reduction in the number of the independent variables by excluding speed from the draught regression equations. However, draught has to be estimated from the FEM analysis for given tillage tool geometry, soil type, r and w. Involving the cutting d as an important variable affecting draught, a multiple linear regression analysis will yield a simple equation capable to compute draught for any combination of r, w and d. This paper aims to develop simple regression equations based on the output of a large number of FEM analyses, which are capable to compute the subsoiler draught requirements as functions of w, r and d. It also tries to assess the effect of w, r and d on subsoiler draught, based on FEM analyses of cutting of a sandy loam soil with the subsoiler.
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165 Table 1 Soil texture de®ned according to the USDA Soil Classi®cationa Property
Zoutleeuw field (g kg 1)
Soil bin (g kg 1)
Sand (>50 mm) Silt (2±50 mm) Clay (<2 mm)
569 340 91
578 288 134
a
Soil texture of Zoutleeuw ®eld was measured at the Soil Survey Department, Catholic University of Leuven, Belgium, while soil texture of soil bin was measured at the Geotechnical Department, Faculty of Civil Engineering, Technical University of Budapest, Hungary.
2. Materials and methods 2.1. Site description The selected experimental ®eld was located at Zoutleeuw region, southeast of Brussels, Belgium. Soil texture fractions were determined by combination of wet sieve and hydrometer tests, using the USDA Soil Classi®cation, as shown in Table 1. The soil was an Arenic Cambisol, according to the FAO classi®cation. Soil samples were collected from 16 different points that were randomly distributed in the ®eld. These samples were taken from different depths down to a maximum depth of 0.32 m. Samples were carefully mixed in order to have a uniform soil material, which represents the ®eld soil at different positions and different depths. Experiments were then carried out to determine the soil and soil±metal interaction properties needed for the FEM analyses, as described below. 2.2. Measurement of soil mechanical properties The standard triaxial compression apparatus was used to obtain the soil mechanical properties, namely, cohesion, internal friction angle, Young's modulus of elasticity and Poisson's ratio. A more detailed description of the equipment is available in many resources (KeÂzdi, 1980; McKyes, 1989). Remoulded soil specimens were prepared in a cylindrical shape after controlling rw and w. The dimensions of the cylindrical samples were 75 mm height and 38 mm in diameter with a total volume of 85 cm3. The soil cylinders were then surrounded by a membrane and con®ned by water pressure (s3) in the water-®lled load cell. During the
157
tests, the axial principal stress (s1) was generated on the top of the cylinder by moving the top piston rod downward. The difference between the lateral and axial principal stresses (s1 s3) generated shear stresses on various planes. Drained tests were carried out with three different con®ning pressures (s3) of 30, 60 and 90 kPa, at a low speed of 1 mm/min. The selection of relatively low con®ning pressures satis®es the demands of the agricultural soil mechanical processes, working at shallow depths. The required mechanical coef®cients were evaluated based on measured principal stress difference (s1 s3) versus axial strain (e1) diagrams obtained. The coef®cients measured for various combinations of w, rd and rw , are summarised in Table 2. 2.3. Measurement of soil±metal interaction properties Soil±metal interaction properties, namely, adhesion and external friction angle were determined by using a modi®ed shear box. The apparatus consisted of two square rings. The dimensions of the rings were 60 mm long, 60 mm wide and 15 mm height with a total area of 36 cm2. A piece of the same metal used to manufacture the subsoiler was placed in the lower ring, whereas soil was placed in the upper ring. During the test, normal pressures were applied to the soil in the upper ring, while the bottom ring was moved horizontally. The shear force versus relative displacement was plotted and the soil shear strength properties were estimated based on the Mohr±Coulomb criterion. Identical tests to those performed with the standard triaxial compression test were repeated here. Tests were conducted with a low speed of 1 mm/min. Soil± metal external friction angle values are given in Table 2. Soil±metal adhesion was ignored, since its value for different combinations of w and rw was small, and was even equal to zero in some cases. 2.4. Finite element analysis The following hypotheses have been considered during the FEM modelling of subsoiler cutting of the sandy loam soil: negligible speed effect; finite subsoiler two-part widths and angles;
158
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
Table 2 Soil and soil±metal interaction properties measured for various combinations of moisture content w and bulk density (r)a Number
w (m3 m 3)
rw (Mg/m3)
rd (Mg/m3)
Cohesion (kPa)
Internal friction (8)
Young's modulus (kPa)
Poisson's ratio
External friction (8)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
0.07 0.10 0.13 0.03 0.07 0.10 0.13 0.17 0.22 0.03 0.07 0.10 0.13 0.17 0.22 0.10 0.13 0.17 0.22 0.13 0.17
1.30 1.30 1.30 1.50 1.50 1.50 1.50 1.50 1.50 1.65 1.65 1.65 1.65 1.65 1.65 1.80 1.80 1.80 1.80 2.00 2.00
1.21 1.18 1.15 1.46 1.40 1.36 1.32 1.28 1.26 1.60 1.54 1.50 1.46 1.41 1.38 1.64 1.59 1.54 1.49 1.77 1.71
8.6 7.0 9.3 22.7 17.0 16.0 11.7 8.1 9.2 19.5 30.7 20.3 18.6 13.2 13.9 16.7 22.0 12.8 11.6 29.9 21.3
32.6 31.4 29.2 29.3 30.6 30.9 30.8 31.4 30.8 37.6 26.6 30.8 27.4 28.4 29.1 33.5 29.2 29.8 30.9 28.8 27.1
1920 1910 2090 3460 3330 3150 2440 2480 2330 12170 6470 5780 3410 3180 2450 9130 6170 4560 3140 10030 5722
0.020 0.059 0.067 0.380 0.202 0.091 0.150 0.045 0.245 0.459 0.373 0.300 0.244 0.162 0.136 0.437 0.377 0.277 0.285 0.446 0.445
22.4 13.1 14.4 16.0 18.9 15.6 25.0 19.8 18.3 11.9 13.3 24.0 24.1 21.6 20.9 23.0 15.9 17.2 18.8 19.9 14.8
a These mechanical properties were measured using standard apparatus at the Geotechnical Department, Faculty of Civil Engineering, Technical University of Budapest (KeÂzdi, 1980).
unique soil texture (sandy loam soil); negligible soil±metal adhesion; homogeneous soil body; elasto-plastic soil material behaviour defined fully by cohesion, friction angle, Young's modulus of elasticity and Poisson's ratio; varied rw , w and d. A three-dimensional FEM model of subsoiler cutting was utilised, which was previously developed for cutting of homogeneous soil materials (Mouazen and NemeÂnyi, 1999a), and non-homogeneous soil materials (Mouazen and NemeÂnyi, 1999b). The subsoiler consisted of two parts; the chisel of 0.06 m width, and the shank of 0.03 m width. Mouazen et al. (1999) found by the theoretical FEM modelling and soil bin measurements that a subsoiler, having a 758 rake angle shank and 158 angle chisel, required the lowest draught. Thus, this design was adapted in this study. A three-dimensional FEM mesh was generated within a hexahedron of 2.0 m long, 0.54 m wide and 0.5 m deep below the chisel tip. The FEM mesh of the soil± subsoiler system in two- and three-dimensional views
is shown in Fig. 1. Linear and isoparametric rectangular prism elements with eight nodes were selected to represent the soil material. The element nodes were situated at the corner of the rectangular prism. Three translational and three rotational degrees of freedom were considered per node. The total number of nodal points and elements for various depth-model variations are given in Table 3. The model considered the soil as elastic±perfectly plastic material. Hence, the Drucker±Prager elastic±perfectly plastic material model was adapted for simulating the material Table 3 Number of elements and nodal points for different cutting depths of the FEM model Cutting depth (m)
Elements
Nodal points
0.37 0.32 0.27 0.22 0.15 0.10
1040 948 856 764 672 580
1435 1323 1211 1099 987 875
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
159
Fig. 1. The two- and three-dimensional FEM model views.
behaviour of the soil under subsoiler loading, whose yield function (f) is given as f 3asm s
k0
(2)
where a, k are the parameters, sm the mean compressive stress and s the effective stress. To study the interaction and sliding characteristics of the soil±subsoiler system, Coulomb's criterion of dry friction is utilised, which can be expressed (Mohsenin, 1970) as F (3) tan d W
where tan d is the coef®cient of external friction, d the angle of soil±metal friction, F the frictional or tangential force to the interface plane and W the normal force to the contact surface. For its simplicity in connecting two materials with complex geometric interface, two-node, gap elements were inserted between each couple of nodes of the soil and front edges of the subsoiler. A commercially available COSMOS/DesignSTAR 1.0 FEM program was used to perform the numerical analysis. One hundred and twenty six FEM analyses were performed for various combinations among six
160
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
moisture contents: 0.03, 0.07, 0.10, 0.13, 0.17 and 0.22 m3 m 3, ®ve wet bulk densities: 1.3, 1.5, 1.65, 1.8 and 2.0 Mg/m3 and six depths: 0.10, 0.17, 0.22, 0.27, 0.32 and 0.37 m. Soil was loaded by a 0.1 m subsoiler displacement in the travel direction. Subsoiler draught was calculated from the summation of the horizontal components of the interface element forces one for every three-displacement steps. 2.5. Statistical analysis Multiple linear regression analyses were performed on draught values obtained from the FEM analyses to establish mathematical relationships for estimating the draught (dependent variable) as a function of the three main independent variables: w, r and d. These regression analyses were performed with SPLUS, 4.5 statistical software at a con®dence level of 0.95. The draught values calculated from the FEM analyses were ®rst reduced by a correction factor of 15%. This is because a previous study, conducted by Mouazen et al. (1999), found an over-prediction of draught estimation of 15% in comparison with the measured draught in a soil bin. This over-prediction was recorded for cutting of a similar sandy loam soil with a similarly designed subsoiler. Therefore, 126 corrected readings were taken into account before running the regression analysis. 2.6. Soil bin test In order to verify the results calculated by the FEM, a soil bin experiment was carried out at the Institute of Agricultural Machinery, Technical University of Munich (Mouazen et al., 1999). The soil bin was 25 m long, 2.5 m wide and 0.6 m deep, and was being used to conduct experiments related to soil compaction by wheel traction (Schwanghart and Zweier, 1993). The experimental soil was a sandy loam with the texture given in Table 1. Soil preparation consisted of soil loosening and compaction. The detailed process was: 1. Soil loosening: Deep cultivation was carried out by winged tines set at 0.32 m depth, whereas shallow cultivation was done by a rotary cultivator (rotavator) set at 0.18 m. After loosening, the soil was watered and covered with a sheet of plastic
during the night in order to achieve uniform moisture distribution throughout the whole soil material. 2. Soil compaction: As in the soil loosening, deep and shallow soil compaction procedures were carried out. The soil was ®rst compacted by a Campbell packer, with the aid of weights, down to 0.18 m depth. Then a smooth roller ®lled with water was used to pack the surface soil. Finally, a frog vibrator was used in order to improve the subsoil compaction. The experiment was carried out with a relatively slow speed of 0.165 m/s to measure the subsoiler draught. The selection of a slow speed was because of ignoring the dynamic effect during the FEM analysis. One test was run without replication to measure the subsoiler draught. 3. Results and discussion 3.1. Variation of FEM calculated draught with d, w, rw and rd The subsoiler draught, calculated from the FEM model, is found to increase with displacement until reaching almost peak value. After the major peak, secondary draught peaks appear in a similar way to ®eld draught measurement, as shown in Fig. 2. However, the draught value at the major peak is considered as the required draught of the subsoiler, at which soil failure occurs. Fig. 2 also demonstrates the draught variation with rw , estimated for a constant w of 0.13 m3 m 3, as an example. It is also clearly shown from Fig. 3 that the subsoiler draught increases with rw , for all levels of w. This increase in draught is attributed to the increase in the soil mechanical properties, which increase with rw , as reported by Mouazen et al. (2000). This is because the soil mechanical properties, applied as input data for the FEM analyses represent the hardness and shear strength of the soil. The higher the mechanical property values, the higher are the subsoiler forces needed to overcome the soil shear strength. However, small decreases in draught occur only at a rw of 1.8 Mg/m3 for w of 0.17 and 0.22 m3 m 3 (Fig. 3). A similar tendency of draught variation with rw is also found with rd, as shown in Fig. 4. This ®gure
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
161
Fig. 2. Draught variation with displacement, calculated for various wet bulk densities rw and a moisture content w of 0.13 m3 m 3.
demonstrates the variation of draught with rd, for different rw levels and 0.37 m d. It is well known that rd is one of the important indicators of soil compaction, in addition to the cone index measured by penetrometers. The higher the degree of compaction (higher rd), the higher is the draught needed for cutting the soil by the subsoiler studied, as shown clearly in Fig. 4. Draught calculated for all combinations of rw and w, also augments with d. This classical increase in draught with d was also reported previously by other researchers (Garner et al., 1987; Stafford and Hendrick, 1988; Khalilian et al., 1988; Shinners et al.,
1990). However, the subsoiler draught increased nonlinearly with d, as shown in Fig. 5. The overall curve inclinations differ, according to the different combination of r and w selected. The w also seems to be an important factor in¯uencing draught. A comparison of draught curves calculated from the FEM model for different w is shown in Fig. 6. This ®gure demonstrates the variation in subsoiler draught with w, estimated for a constant rw , of 1.3 Mg/m3, as an example. It is shown clearly that the draught decreases with w. Fielke et al. (1993) also reported a draught reduction of a cultivator by 30±50% under wet soil conditions in comparison with dry soil
Fig. 3. Draught variation with wet bulk density rw , shown for different moisture contents w.
162
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
Fig. 4. Draught variation with dry bulk density (rd) for various wet bulk densities rw and 0.37 m d.
conditions. This result can be extended to include all draught values calculated for different rw considered in this study, as shown in Fig. 7. The decrease in draught, however, is limited to a w level of 0.17 m3 m 3. Beyond this w level, draught has either a higher or lower value, but no big differences in draught are found between the w of 0.17 and 0.22 m3 m 3. At a constant rw , of 1.3 Mg/m3, draught calculated for a w of 0.22 m3 m 3 has higher value than that calculated for a w of 0.17 m3 m 3, along with subsoiler displacement up to nearly 0.05 m, after
which draught has almost equal values for both w levels (Fig. 6). SoÈhne (1958) reported that compactibility increases very strongly with w, which was limited by a large amount of water between 0.209 and 0.241 m3 m 3. An optimum w close to 0.15 m3 m 3 for soil compaction occurrence was determined for a sandy loam soil by Raghavan et al. (1977). Below the optimum w, the degree of soil compaction became proportional to w. This may indicate a positive correlation between the tillage tool draught and w, when tillage is carried out after a
Fig. 5. Draught variation with cutting depth (d).
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
163
Fig. 6. A comparison of subsoiler draught calculated for different moisture contents w and a wet bulk density rw of 1.3 Mg/m3.
compaction occurrence. However, this study aims to assess the in¯uence of w on the soil at the moment of soil tilling, regardless of w during occurrence of soil compaction. Soil compactibility augments with w up to the optimum w, whereas draught requirement decreases with w up to the maximum w. 3.2. Development of draught regression equations The regression analysis showed that the draught varies linearly with w and non-linearly with rw and d, as expressed by the following regression equation: D
33:74w 73:253d 2 2:5649r2w ;
R2 0:9434
where D is the draught (kN), d the tillage depth (m), rw the wet bulk density (Mg/m3) and w the moisture content, dry basis (d.b.) (m3 m 3). The high determination coef®cient of 0.9434 indicates that theoretical draught can be estimated as a function of w, rw and d, with a high degree of accuracy. A multiple linear regression analysis was also performed, considering the draught as dependent variable and w, rd and d as independent variables. Similarly, the developed regression formula established linear variation of draught with w and non-linear variation with rd and d: D
(4)
21:36w 73:9313d2 1:6734r3d ;
R2 0:9494
Fig. 7. Draught variation with moisture content w shown for different wet bulk densities rw .
(5)
164
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
Comparing Eq. (4) with Eq. (5) emphasises that the non-linear variation of the draught was found to be a quadratic function of rw , and a cubic function of rd. 3.3. Validation of regression equations To validate the accuracy of Eq. (4) in estimating the draught requirement of the subsoiler studied, the calculated draught is compared to the measured value. Draught of a similarly designed subsoiler, operating in a sandy loam soil was previously measured in a soil bin (Mouazen et al., 1999). This measurement was carried out under a rw of 1.73 Mg/m3 and w of 0.145 m3 m 3. Substitution of these values in Eq. (4), draught was calculated for two depths of 0.32 and 0.37 m. A comparison of the FEM calculated and soil bin measured draught is given in Table 4. As shown in the table, the calculated draught from the FEM model exceeds the measured value. This overprediction of the draught can be attributed to the slight divergence in the chisel length between the FEM model subsoiler and the subsoiler used during the soil bin experiment. The longer chisel (0.37 m) of the subsoiler considered in the FEM model than that of the subsoiler used in the soil bin (0.34 m) might cause the increase in the predicted draught over the measured one. It could be concluded that Eq. (4) can predict the draught requirement of the selected tillage tool design, operating in sandy loam soils under any combination of w, d and rw . Similar equations can be developed for different soil types and tillage tool designs. Moreover, Eq. (5) might be utilised to perform on-line detection of the variation in the ®eld soil compaction. The online measurement of the subsoiler draught and w with controlled d will satisfy the requirements of obtaining the spatial variation of rd, as one of the important indicators of soil compaction. Table 4 A comparison of the calculated and measured subsoiler draught for two cutting depths (d) and a moisture content w of 0.145 m3 m 3 Number
Depth (m)
Calculated draught (kN)
Measured draught (kN)
1 2
0.32 0.37
10.28 12.81
9.18 11.20
4. Conclusions The FEM was used to model subsoiler cutting of a sandy loam soil, and understanding the effect of the w, d and r on the draught requirement of the studied subsoiler. The advantage of this technique is its capability of estimation of the draught requirement of a given tillage tool design, needed to cut a given soil texture at known values of d, w and r. This is because the ®eld measurement fails to provide clear and accurate information about the draught variation, especially as a function of r and w. It was found that draught increased with variables d, rw and rd, whereas it decreased with w. The decrease in draught with w did not extend beyond a w of 0.17 m3 m 3, as the draught calculated for a w of 0.22 m3 m 3 was very close to that calculated for a w of 0.17 m3 m 3. Multiple regression analysis was carried out to establish formulae capable to predict the subsoiler draught at any combination of d, w, rw and rd. These equations were of quite simple forms, and had high determination coef®cients (R2) close to 0.95. They indicated that the theoretical subsoiler horizontal force varied linearly with w and non-linearly with d, rw and rd. The non-linear variation of draught was found to be a quadratic function of d and rw , and a cubic function of rd. A comparison of the FEM calculated subsoiler draught and soil bin measured draught showed small over-prediction in the calculated draught forces over the measured values. This over-prediction was attributed to the slight divergence in soil texture and subsoiler chisel length. Thus, the regression equation developed proved to be a capable tool of predicting the draught requirements of a selected tillage tool design, when cutting sandy loam soils under any combination of w, d and rw . This encourages developing similar equations capable to handle different soil types and tillage tool designs. The equation developed to relate the draught to w, rd and d might be utilised to perform on-line detection of the variation in the ®eld soil compaction. On-line measurement of subsoiler draught and w with controlling d will satisfy the requirements of obtaining the spatial variation of the rd, as one of the important indicators of soil compaction.
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
References Ayers, P.D., 1987. Moisture and bulk density effects on soil shear strength parameters for coarse grained soils. Trans. Am. Soc. Agric. Eng. 31 (2), 1282±1287. Ayers, P.D., Perumpral, J.V., 1982. Moisture and density effect on cone index. Trans. Am. Soc. Agric. Eng. 25 (5), 1169±1172. Bernier, H., Bostock, G., Raghavan, S.V., Broughton, R.S., 1989. Subsoiling effects on moisture content and bulk density in the soil pro®le. ASAE Paper. Appl. Eng. Agric. 5 (1), 24±28. Busscher, W.J., Sojka, R.E., 1987. Enhancement of subsoiling effect on soil strength by conservation tillage. Trans. Am. Soc. Agric. Eng. 30 (4), 888±892. Erbach, D.C., Benjamin, J.G., Cruse, R.M., Elamin, M.A., Mukhtar, S., Choi, C.-H., 1992. Soil and corn response to tillage with paraplow. Trans. Am. Soc. Agric. Eng. 35 (5), 1354±1374. Evans, S.D., Lindstrom, M.J., Voorhees, W.B., Moncrief, J.F., Nelson, G.A., 1996. Effect of subsoiling and subsequent tillage on soil bulk density, soil moisture and corn yield. Soil Till. Res. 38, 35±46. Fielke, J.M., Riley, T.W., Slattery, M.G., Fitzpatrick, R.W., 1993. Comparison of tillage forces and wear rates of pressed and cast cultivator shares. Soil Till. Res. 25, 317±328. Gameda, S., Raghavan, G.S.V., McKyes, E., Watson, A.K., Mehuys, G., 1987. Response of grain corn to subsoiling and chemical wetting of a compacted clay subsoil. Soil Till. Res. 29, 179±187. Garner, T.H., Reynolds, W.R., Musen, H.L., Miles, G.E., Davis, J.W., Peiper, U.M., 1987. Energy requirement for subsoiling coastal plain soils. Trans. Am. Soc. Agric. Eng. 30 (2), 343± 350. Glancey, J.L., Upadhyaya, S.K., Chancellor, W.J., Rumsey, J.W., 1996. Prediction of agricultural implement draft using an instrumented analog tillage tool. Soil Till. Res. 37, 47±65. Â ., 1980. Handbook of Soil Mechanics, Vol. 2: Soil Testing. KeÂzdi, A Elsevier, Amsterdam. Khalilian, A., Garner, T.H., Musen, H.L., Dodd, R.B., Hale, S.A., 1988. Energy for conservation tillage in coastal plain soils. Trans. Am. Soc. Agric. Eng. 31 (5), 1333±1338. Koolen, A.J., Kuipers, H., 1983. Agricultural Soil Mechanics. Springer, Berlin. Kydd, H.D., Frehlich, G.E., Boyden, A.R., 1984. Tillage power requirement in Western Canada. ASAE Paper No. 84-1027. ASAE, St. Joseph, MI, USA. Mapfumo, E., Chanasyk, D.S., 1998. Guidelines for save traf®cking and cultivation, and resistance±density±moisture relations
165
of three disturbed soils from Alberta. Soil Till. Res. 47, 193± 202. McKyes, E., 1989. Agricultural Engineering Soil Mechanics. Elsevier, Amsterdam. Mohsenin, N.N., 1970. Physical Properties of Plant and Animal Materials. Gordon and Breach, New York. Mouazen, A.M., NemeÂnyi, M., 1999a. Tillage tool design by the ®nite element method. Part I. Finite element modelling of soil plastic behaviour. J. Agric. Eng. Res. 72, 37±51. Mouazen, A.M., NemeÂnyi, M., 1999b. Finite element analysis of subsoiler cutting in non-homogeneous sandy loam soil. Soil Till. Res. 51, 1±15. Mouazen, A.M., NemeÂnyi, M., Schwanghart, H., Rempfer, M., 1999. Tillage tool design by the ®nite element method. Part II. Experimental validation of the ®nite element results with soil bin test. J. Agric. Eng. Res. 72, 53±58. Mouazen, A.M., Ramon, H., De Baerdemaeker, J., 2000. Variation in the mechanical properties of an agricultural sandy loam soil with bulk density and moisture content. J. Agric. Eng. Res., submitted for publication. Raghavan, G.S.V., McKyes, E., Beaulieu, B., 1977. Prediction of clay soil compaction. J. Terramech. 14, 31±38. Schwanghart, H., Zweier, A., 1993. In¯uence of tread on drawbar pull of tires for small off-road vehicles. In: Proceedings of the 11th International Conference on Int. Society for Terrain Vehicle Systems, Lake Tahoe, USA, pp. 233±244. Shinners, K.J., Alcock, R., Wilkes, J.M., 1990. Combining active and passive tillage elements to reduce draft requirement. Trans. Am. Soc. Agric. Eng. 33 (2), 400±404. SoÈhne, W., 1958. Fundamentals of pressure distribution and soil compaction under tractor tires. Agric. Eng. 39, 276±281. Sprinkle, L.W., Langston, T.D., Weber, J.A., Sharon, N.M., 1970. A similitude study with static and dynamic parameters in an arti®cial soil. Trans. Am. Soc. Agric. Eng. 29, 580±586. Stafford, J.V., Hendrick, J.G., 1988. Dynamic sensing of soil pans. Trans. Am. Soc. Agric. Eng. 31 (1), 9±13. Tabatabaeefar, A., Solhjoo, A., Alimardanee, R., 1998. Mathematical model for soil cone index in Zarghan Fars, Iran. In: Proceedings of the International Conference on Agricultural Engineering, Oslo, Norway, No. 98-C-090. Unger, P.W., Jones, O.R., 1998. Long-term tillage and cropping systems affect bulk density and penetration resistance of soil cropped to dryland wheat and grain sorghum. Soil Till. Res. 45, 39±57. Upadhyaya, S.K., Williams, T.H., Kemble, L.J., Collins, N.E., 1984. Energy requirement for chiselling in coastal plain soils. Trans. Am. Soc. Agric. Eng. 27 (6), 1643±1649.
A numerical±statistical hybrid modelling scheme for evaluation of draught requirements of a subsoiler cutting a sandy loam soil, as affected by moisture content, bulk density and depth Abdul Mounem Mouazena,*, Herman Ramonb a
Faculty of Agriculture, Department of Rural Engineering, University of Aleppo, P.O. Box 12214, Aleppo, Syria Faculty of Agricultural and Applied Biological Sciences, Laboratory of Agricultural Machinery and Processing, Department of Agro-Engineering and-Economics, Kasteelpark Arenberg 30, B-3001 Leuven, Belgium
b
Received 13 October 2000; received in revised form 13 August 2001; accepted 16 August 2001
Abstract The development of simple regression relationships, based on ®nite element (FEM) analyses of cutting a sandy loam soil by medium±deep subsoiler will provide con®dential and quick tools to predict the subsoiler draught requirement for any combination of moisture content w, wet bulk density rw and tillage depth (d). Large number of FEM analyses were performed to assess the effect of w, d and rw on subsoiler draught. This draught was calculated from the output of 126 FEM modelling analyses. The model variations were selected based on the interaction among the studied variables, namely, six moisture contents ranging from 0.03 to 0.22 m3 m 3, ®ve wet bulk densities ranging from 1.3 to 2.0 Mg/m3 and six tillage depths ranging from 0.10 to 0.37 m. The interaction among these three variables was also taken into consideration, and a multiple linear regression analysis was performed aiming at establishing a mathematical relationship for simulating the draught variation as a function of these variables. Further relationship was developed for relating the variation in draught with w, d and dry bulk density (rd). The FEM showed that subsoiler draught increased with d, rw and rd, whereas it decreased with w. The decrease in draught with w did not extend beyond a w of 0.17 m3 m 3, since the draught calculated for 0.22 m3 m 3 w was very close to that calculated for a w of 0.17 m3 m 3. Regression equations developed to relate the subsoiler draught with w, d, rw and rd were of quite simple forms, and had high determination coef®cients (R2) close to 0.95. These equations indicated that the horizontal force varied linearly with w and non-linearly with d, rw and rd. This non-linear variation of draught was found to be a quadratic function of d and rw , and a cubic function of rd. A comparison of the calculated and measured draught for cutting a similar sandy loam soil with a similarly designed subsoiler, showed a good approximation. The small divergence between the calculated and measured draught was attributed to the difference in soil texture and subsoiler chisel length. Thus, the regression equation developed proved to be a capable tool of predicting the draught requirements of the selected tillage tool design, when cutting sandy loam soils under any combination of w, d and rw . # 2002 Elsevier Science B.V. All rights reserved. Keywords: Tillage tool draught; Moisture content; Bulk density; Depth; Linear regression analysis
1. Introduction
*
Corresponding author. Tel.: 963-21-3631-958. E-mail address: [email protected] (A.M. Mouazen).
Draught is directly related to the energy requirement of tillage tools. It may re¯ect the soil physical condition and the degree of compaction of agricultural
0167-1987/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 1 9 8 7 ( 0 1 ) 0 0 2 4 3 - 4
156
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
soils. For a unique soil type, tillage speed and tool design, draught varies with bulk density (r), w and d. These in¯uencing factors were the main axis of interest of previous research, which adapted ®eld experiments to understand how these factors affect draught requirements of tillage tools. If d and speed of tillage tools could be controlled during ®eld experiment, a representative relationship relating draught with r and w can be introduced. However, the effect of tillage system on r and w has been widely studied (Gameda et al., 1987; Bernier et al., 1989; Erbach et al., 1992; Evans et al., 1996), whereas the effect of r and w on draught requirements has been less studied. The shortage of research can be attributed to the heterogeneity of agricultural soils. In fact, draught is affected by the variation of soil properties within the ®eld (spatial variability). This includes soil type, r and w, which vary considerably, along with the vertical and horizontal directions. Moreover, no reports performed dynamic measurement of w and r, required for establishing relationship between these two variables and draught. Therefore, r and w have been related to the variation in the soil strength, expressed as penetration resistance (Ayers and Perumpral, 1982; Busscher and Sojka, 1987; Tabatabaeefar et al., 1998; Mapfumo and Chanasyk, 1998; Unger and Jones, 1998), or to soil shear strength coef®cients, namely cohesion and internal friction angle (Ayers, 1987; Mouazen et al., 2000). Even equations established for draught prediction have ignored one of these independent variables. Upadhyaya et al. (1984) published the following equation for the draught requirement of a subsoiler: D B0 CI Wd B1 rw d W S2
(1)
where D is the draught, CI the cone index, W the width of subsoiler cutting edge, d the depth, rw the wet bulk density, S the travel speed and B0, B1 the constants. It is clear that w is ignored in Eq. (1), which affects draught requirements, especially when tilling compactable soils. Other researchers also eliminated w in their general function for implement draught prediction (Sprinkle et al., 1970; Glancey et al., 1996). Koolen and Kuipers (1983) introduced several techniques for prediction of tool forces based on observations and relationships between independent and dependent variables. However, these techniques depended upon data collected arbitrarily from the ®eld, and mean values of draught and the independent
variables were taken into consideration for developing an equation for the draught requirement. These mean values do not con®rm that the predicted draught at any point within the ®eld is a re¯ection of the soil physical condition at that point. Even the single ®eld measurement of draught cannot be related with the real value of w and r at the same position where draught was measured. Kydd et al. (1984) developed equations for draught prediction of tillage tools, realising that the variations in climatic conditions, w, soil hardness and soil type made it dif®cult to obtain repeatable draught data. Therefore, it is essential to develop a proper technique capable to simulate the interaction between the draught, r, w and d. Utilising the ®nite element method (FEM) will allow draught to be related to r and w, as a new technique used for accomplishing such an objective. This method has been reported to be a proper technique to predict the horizontal and vertical forces of tillage tools. It also predicts tool forces at any combination of r and w, based on mechanical coef®cients measured for the corresponding soil physical and soil±metal interaction conditions. These coef®cients arecohesion,friction angle, Young's modulus, Poisson's ratio, adhesion and soil±metal friction. Sprinkle et al. (1970) introduced an equation for draught prediction, which involved eight independent variables, except w, and three dimensions of force, length and time. Generally, the number of independent variables can be reduced by means of the FEM analysis. Tool geometry, soil cohesion, internal friction angle and soil±metal friction angle can be eliminated from the regression equations, since they are used as input data for the FEM analysis. Tilling with low speed may allow for further reduction in the number of the independent variables by excluding speed from the draught regression equations. However, draught has to be estimated from the FEM analysis for given tillage tool geometry, soil type, r and w. Involving the cutting d as an important variable affecting draught, a multiple linear regression analysis will yield a simple equation capable to compute draught for any combination of r, w and d. This paper aims to develop simple regression equations based on the output of a large number of FEM analyses, which are capable to compute the subsoiler draught requirements as functions of w, r and d. It also tries to assess the effect of w, r and d on subsoiler draught, based on FEM analyses of cutting of a sandy loam soil with the subsoiler.
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165 Table 1 Soil texture de®ned according to the USDA Soil Classi®cationa Property
Zoutleeuw field (g kg 1)
Soil bin (g kg 1)
Sand (>50 mm) Silt (2±50 mm) Clay (<2 mm)
569 340 91
578 288 134
a
Soil texture of Zoutleeuw ®eld was measured at the Soil Survey Department, Catholic University of Leuven, Belgium, while soil texture of soil bin was measured at the Geotechnical Department, Faculty of Civil Engineering, Technical University of Budapest, Hungary.
2. Materials and methods 2.1. Site description The selected experimental ®eld was located at Zoutleeuw region, southeast of Brussels, Belgium. Soil texture fractions were determined by combination of wet sieve and hydrometer tests, using the USDA Soil Classi®cation, as shown in Table 1. The soil was an Arenic Cambisol, according to the FAO classi®cation. Soil samples were collected from 16 different points that were randomly distributed in the ®eld. These samples were taken from different depths down to a maximum depth of 0.32 m. Samples were carefully mixed in order to have a uniform soil material, which represents the ®eld soil at different positions and different depths. Experiments were then carried out to determine the soil and soil±metal interaction properties needed for the FEM analyses, as described below. 2.2. Measurement of soil mechanical properties The standard triaxial compression apparatus was used to obtain the soil mechanical properties, namely, cohesion, internal friction angle, Young's modulus of elasticity and Poisson's ratio. A more detailed description of the equipment is available in many resources (KeÂzdi, 1980; McKyes, 1989). Remoulded soil specimens were prepared in a cylindrical shape after controlling rw and w. The dimensions of the cylindrical samples were 75 mm height and 38 mm in diameter with a total volume of 85 cm3. The soil cylinders were then surrounded by a membrane and con®ned by water pressure (s3) in the water-®lled load cell. During the
157
tests, the axial principal stress (s1) was generated on the top of the cylinder by moving the top piston rod downward. The difference between the lateral and axial principal stresses (s1 s3) generated shear stresses on various planes. Drained tests were carried out with three different con®ning pressures (s3) of 30, 60 and 90 kPa, at a low speed of 1 mm/min. The selection of relatively low con®ning pressures satis®es the demands of the agricultural soil mechanical processes, working at shallow depths. The required mechanical coef®cients were evaluated based on measured principal stress difference (s1 s3) versus axial strain (e1) diagrams obtained. The coef®cients measured for various combinations of w, rd and rw , are summarised in Table 2. 2.3. Measurement of soil±metal interaction properties Soil±metal interaction properties, namely, adhesion and external friction angle were determined by using a modi®ed shear box. The apparatus consisted of two square rings. The dimensions of the rings were 60 mm long, 60 mm wide and 15 mm height with a total area of 36 cm2. A piece of the same metal used to manufacture the subsoiler was placed in the lower ring, whereas soil was placed in the upper ring. During the test, normal pressures were applied to the soil in the upper ring, while the bottom ring was moved horizontally. The shear force versus relative displacement was plotted and the soil shear strength properties were estimated based on the Mohr±Coulomb criterion. Identical tests to those performed with the standard triaxial compression test were repeated here. Tests were conducted with a low speed of 1 mm/min. Soil± metal external friction angle values are given in Table 2. Soil±metal adhesion was ignored, since its value for different combinations of w and rw was small, and was even equal to zero in some cases. 2.4. Finite element analysis The following hypotheses have been considered during the FEM modelling of subsoiler cutting of the sandy loam soil: negligible speed effect; finite subsoiler two-part widths and angles;
158
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
Table 2 Soil and soil±metal interaction properties measured for various combinations of moisture content w and bulk density (r)a Number
w (m3 m 3)
rw (Mg/m3)
rd (Mg/m3)
Cohesion (kPa)
Internal friction (8)
Young's modulus (kPa)
Poisson's ratio
External friction (8)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
0.07 0.10 0.13 0.03 0.07 0.10 0.13 0.17 0.22 0.03 0.07 0.10 0.13 0.17 0.22 0.10 0.13 0.17 0.22 0.13 0.17
1.30 1.30 1.30 1.50 1.50 1.50 1.50 1.50 1.50 1.65 1.65 1.65 1.65 1.65 1.65 1.80 1.80 1.80 1.80 2.00 2.00
1.21 1.18 1.15 1.46 1.40 1.36 1.32 1.28 1.26 1.60 1.54 1.50 1.46 1.41 1.38 1.64 1.59 1.54 1.49 1.77 1.71
8.6 7.0 9.3 22.7 17.0 16.0 11.7 8.1 9.2 19.5 30.7 20.3 18.6 13.2 13.9 16.7 22.0 12.8 11.6 29.9 21.3
32.6 31.4 29.2 29.3 30.6 30.9 30.8 31.4 30.8 37.6 26.6 30.8 27.4 28.4 29.1 33.5 29.2 29.8 30.9 28.8 27.1
1920 1910 2090 3460 3330 3150 2440 2480 2330 12170 6470 5780 3410 3180 2450 9130 6170 4560 3140 10030 5722
0.020 0.059 0.067 0.380 0.202 0.091 0.150 0.045 0.245 0.459 0.373 0.300 0.244 0.162 0.136 0.437 0.377 0.277 0.285 0.446 0.445
22.4 13.1 14.4 16.0 18.9 15.6 25.0 19.8 18.3 11.9 13.3 24.0 24.1 21.6 20.9 23.0 15.9 17.2 18.8 19.9 14.8
a These mechanical properties were measured using standard apparatus at the Geotechnical Department, Faculty of Civil Engineering, Technical University of Budapest (KeÂzdi, 1980).
unique soil texture (sandy loam soil); negligible soil±metal adhesion; homogeneous soil body; elasto-plastic soil material behaviour defined fully by cohesion, friction angle, Young's modulus of elasticity and Poisson's ratio; varied rw , w and d. A three-dimensional FEM model of subsoiler cutting was utilised, which was previously developed for cutting of homogeneous soil materials (Mouazen and NemeÂnyi, 1999a), and non-homogeneous soil materials (Mouazen and NemeÂnyi, 1999b). The subsoiler consisted of two parts; the chisel of 0.06 m width, and the shank of 0.03 m width. Mouazen et al. (1999) found by the theoretical FEM modelling and soil bin measurements that a subsoiler, having a 758 rake angle shank and 158 angle chisel, required the lowest draught. Thus, this design was adapted in this study. A three-dimensional FEM mesh was generated within a hexahedron of 2.0 m long, 0.54 m wide and 0.5 m deep below the chisel tip. The FEM mesh of the soil± subsoiler system in two- and three-dimensional views
is shown in Fig. 1. Linear and isoparametric rectangular prism elements with eight nodes were selected to represent the soil material. The element nodes were situated at the corner of the rectangular prism. Three translational and three rotational degrees of freedom were considered per node. The total number of nodal points and elements for various depth-model variations are given in Table 3. The model considered the soil as elastic±perfectly plastic material. Hence, the Drucker±Prager elastic±perfectly plastic material model was adapted for simulating the material Table 3 Number of elements and nodal points for different cutting depths of the FEM model Cutting depth (m)
Elements
Nodal points
0.37 0.32 0.27 0.22 0.15 0.10
1040 948 856 764 672 580
1435 1323 1211 1099 987 875
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
159
Fig. 1. The two- and three-dimensional FEM model views.
behaviour of the soil under subsoiler loading, whose yield function (f) is given as f 3asm s
k0
(2)
where a, k are the parameters, sm the mean compressive stress and s the effective stress. To study the interaction and sliding characteristics of the soil±subsoiler system, Coulomb's criterion of dry friction is utilised, which can be expressed (Mohsenin, 1970) as F (3) tan d W
where tan d is the coef®cient of external friction, d the angle of soil±metal friction, F the frictional or tangential force to the interface plane and W the normal force to the contact surface. For its simplicity in connecting two materials with complex geometric interface, two-node, gap elements were inserted between each couple of nodes of the soil and front edges of the subsoiler. A commercially available COSMOS/DesignSTAR 1.0 FEM program was used to perform the numerical analysis. One hundred and twenty six FEM analyses were performed for various combinations among six
160
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
moisture contents: 0.03, 0.07, 0.10, 0.13, 0.17 and 0.22 m3 m 3, ®ve wet bulk densities: 1.3, 1.5, 1.65, 1.8 and 2.0 Mg/m3 and six depths: 0.10, 0.17, 0.22, 0.27, 0.32 and 0.37 m. Soil was loaded by a 0.1 m subsoiler displacement in the travel direction. Subsoiler draught was calculated from the summation of the horizontal components of the interface element forces one for every three-displacement steps. 2.5. Statistical analysis Multiple linear regression analyses were performed on draught values obtained from the FEM analyses to establish mathematical relationships for estimating the draught (dependent variable) as a function of the three main independent variables: w, r and d. These regression analyses were performed with SPLUS, 4.5 statistical software at a con®dence level of 0.95. The draught values calculated from the FEM analyses were ®rst reduced by a correction factor of 15%. This is because a previous study, conducted by Mouazen et al. (1999), found an over-prediction of draught estimation of 15% in comparison with the measured draught in a soil bin. This over-prediction was recorded for cutting of a similar sandy loam soil with a similarly designed subsoiler. Therefore, 126 corrected readings were taken into account before running the regression analysis. 2.6. Soil bin test In order to verify the results calculated by the FEM, a soil bin experiment was carried out at the Institute of Agricultural Machinery, Technical University of Munich (Mouazen et al., 1999). The soil bin was 25 m long, 2.5 m wide and 0.6 m deep, and was being used to conduct experiments related to soil compaction by wheel traction (Schwanghart and Zweier, 1993). The experimental soil was a sandy loam with the texture given in Table 1. Soil preparation consisted of soil loosening and compaction. The detailed process was: 1. Soil loosening: Deep cultivation was carried out by winged tines set at 0.32 m depth, whereas shallow cultivation was done by a rotary cultivator (rotavator) set at 0.18 m. After loosening, the soil was watered and covered with a sheet of plastic
during the night in order to achieve uniform moisture distribution throughout the whole soil material. 2. Soil compaction: As in the soil loosening, deep and shallow soil compaction procedures were carried out. The soil was ®rst compacted by a Campbell packer, with the aid of weights, down to 0.18 m depth. Then a smooth roller ®lled with water was used to pack the surface soil. Finally, a frog vibrator was used in order to improve the subsoil compaction. The experiment was carried out with a relatively slow speed of 0.165 m/s to measure the subsoiler draught. The selection of a slow speed was because of ignoring the dynamic effect during the FEM analysis. One test was run without replication to measure the subsoiler draught. 3. Results and discussion 3.1. Variation of FEM calculated draught with d, w, rw and rd The subsoiler draught, calculated from the FEM model, is found to increase with displacement until reaching almost peak value. After the major peak, secondary draught peaks appear in a similar way to ®eld draught measurement, as shown in Fig. 2. However, the draught value at the major peak is considered as the required draught of the subsoiler, at which soil failure occurs. Fig. 2 also demonstrates the draught variation with rw , estimated for a constant w of 0.13 m3 m 3, as an example. It is also clearly shown from Fig. 3 that the subsoiler draught increases with rw , for all levels of w. This increase in draught is attributed to the increase in the soil mechanical properties, which increase with rw , as reported by Mouazen et al. (2000). This is because the soil mechanical properties, applied as input data for the FEM analyses represent the hardness and shear strength of the soil. The higher the mechanical property values, the higher are the subsoiler forces needed to overcome the soil shear strength. However, small decreases in draught occur only at a rw of 1.8 Mg/m3 for w of 0.17 and 0.22 m3 m 3 (Fig. 3). A similar tendency of draught variation with rw is also found with rd, as shown in Fig. 4. This ®gure
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
161
Fig. 2. Draught variation with displacement, calculated for various wet bulk densities rw and a moisture content w of 0.13 m3 m 3.
demonstrates the variation of draught with rd, for different rw levels and 0.37 m d. It is well known that rd is one of the important indicators of soil compaction, in addition to the cone index measured by penetrometers. The higher the degree of compaction (higher rd), the higher is the draught needed for cutting the soil by the subsoiler studied, as shown clearly in Fig. 4. Draught calculated for all combinations of rw and w, also augments with d. This classical increase in draught with d was also reported previously by other researchers (Garner et al., 1987; Stafford and Hendrick, 1988; Khalilian et al., 1988; Shinners et al.,
1990). However, the subsoiler draught increased nonlinearly with d, as shown in Fig. 5. The overall curve inclinations differ, according to the different combination of r and w selected. The w also seems to be an important factor in¯uencing draught. A comparison of draught curves calculated from the FEM model for different w is shown in Fig. 6. This ®gure demonstrates the variation in subsoiler draught with w, estimated for a constant rw , of 1.3 Mg/m3, as an example. It is shown clearly that the draught decreases with w. Fielke et al. (1993) also reported a draught reduction of a cultivator by 30±50% under wet soil conditions in comparison with dry soil
Fig. 3. Draught variation with wet bulk density rw , shown for different moisture contents w.
162
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
Fig. 4. Draught variation with dry bulk density (rd) for various wet bulk densities rw and 0.37 m d.
conditions. This result can be extended to include all draught values calculated for different rw considered in this study, as shown in Fig. 7. The decrease in draught, however, is limited to a w level of 0.17 m3 m 3. Beyond this w level, draught has either a higher or lower value, but no big differences in draught are found between the w of 0.17 and 0.22 m3 m 3. At a constant rw , of 1.3 Mg/m3, draught calculated for a w of 0.22 m3 m 3 has higher value than that calculated for a w of 0.17 m3 m 3, along with subsoiler displacement up to nearly 0.05 m, after
which draught has almost equal values for both w levels (Fig. 6). SoÈhne (1958) reported that compactibility increases very strongly with w, which was limited by a large amount of water between 0.209 and 0.241 m3 m 3. An optimum w close to 0.15 m3 m 3 for soil compaction occurrence was determined for a sandy loam soil by Raghavan et al. (1977). Below the optimum w, the degree of soil compaction became proportional to w. This may indicate a positive correlation between the tillage tool draught and w, when tillage is carried out after a
Fig. 5. Draught variation with cutting depth (d).
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
163
Fig. 6. A comparison of subsoiler draught calculated for different moisture contents w and a wet bulk density rw of 1.3 Mg/m3.
compaction occurrence. However, this study aims to assess the in¯uence of w on the soil at the moment of soil tilling, regardless of w during occurrence of soil compaction. Soil compactibility augments with w up to the optimum w, whereas draught requirement decreases with w up to the maximum w. 3.2. Development of draught regression equations The regression analysis showed that the draught varies linearly with w and non-linearly with rw and d, as expressed by the following regression equation: D
33:74w 73:253d 2 2:5649r2w ;
R2 0:9434
where D is the draught (kN), d the tillage depth (m), rw the wet bulk density (Mg/m3) and w the moisture content, dry basis (d.b.) (m3 m 3). The high determination coef®cient of 0.9434 indicates that theoretical draught can be estimated as a function of w, rw and d, with a high degree of accuracy. A multiple linear regression analysis was also performed, considering the draught as dependent variable and w, rd and d as independent variables. Similarly, the developed regression formula established linear variation of draught with w and non-linear variation with rd and d: D
(4)
21:36w 73:9313d2 1:6734r3d ;
R2 0:9494
Fig. 7. Draught variation with moisture content w shown for different wet bulk densities rw .
(5)
164
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
Comparing Eq. (4) with Eq. (5) emphasises that the non-linear variation of the draught was found to be a quadratic function of rw , and a cubic function of rd. 3.3. Validation of regression equations To validate the accuracy of Eq. (4) in estimating the draught requirement of the subsoiler studied, the calculated draught is compared to the measured value. Draught of a similarly designed subsoiler, operating in a sandy loam soil was previously measured in a soil bin (Mouazen et al., 1999). This measurement was carried out under a rw of 1.73 Mg/m3 and w of 0.145 m3 m 3. Substitution of these values in Eq. (4), draught was calculated for two depths of 0.32 and 0.37 m. A comparison of the FEM calculated and soil bin measured draught is given in Table 4. As shown in the table, the calculated draught from the FEM model exceeds the measured value. This overprediction of the draught can be attributed to the slight divergence in the chisel length between the FEM model subsoiler and the subsoiler used during the soil bin experiment. The longer chisel (0.37 m) of the subsoiler considered in the FEM model than that of the subsoiler used in the soil bin (0.34 m) might cause the increase in the predicted draught over the measured one. It could be concluded that Eq. (4) can predict the draught requirement of the selected tillage tool design, operating in sandy loam soils under any combination of w, d and rw . Similar equations can be developed for different soil types and tillage tool designs. Moreover, Eq. (5) might be utilised to perform on-line detection of the variation in the ®eld soil compaction. The online measurement of the subsoiler draught and w with controlled d will satisfy the requirements of obtaining the spatial variation of rd, as one of the important indicators of soil compaction. Table 4 A comparison of the calculated and measured subsoiler draught for two cutting depths (d) and a moisture content w of 0.145 m3 m 3 Number
Depth (m)
Calculated draught (kN)
Measured draught (kN)
1 2
0.32 0.37
10.28 12.81
9.18 11.20
4. Conclusions The FEM was used to model subsoiler cutting of a sandy loam soil, and understanding the effect of the w, d and r on the draught requirement of the studied subsoiler. The advantage of this technique is its capability of estimation of the draught requirement of a given tillage tool design, needed to cut a given soil texture at known values of d, w and r. This is because the ®eld measurement fails to provide clear and accurate information about the draught variation, especially as a function of r and w. It was found that draught increased with variables d, rw and rd, whereas it decreased with w. The decrease in draught with w did not extend beyond a w of 0.17 m3 m 3, as the draught calculated for a w of 0.22 m3 m 3 was very close to that calculated for a w of 0.17 m3 m 3. Multiple regression analysis was carried out to establish formulae capable to predict the subsoiler draught at any combination of d, w, rw and rd. These equations were of quite simple forms, and had high determination coef®cients (R2) close to 0.95. They indicated that the theoretical subsoiler horizontal force varied linearly with w and non-linearly with d, rw and rd. The non-linear variation of draught was found to be a quadratic function of d and rw , and a cubic function of rd. A comparison of the FEM calculated subsoiler draught and soil bin measured draught showed small over-prediction in the calculated draught forces over the measured values. This over-prediction was attributed to the slight divergence in soil texture and subsoiler chisel length. Thus, the regression equation developed proved to be a capable tool of predicting the draught requirements of a selected tillage tool design, when cutting sandy loam soils under any combination of w, d and rw . This encourages developing similar equations capable to handle different soil types and tillage tool designs. The equation developed to relate the draught to w, rd and d might be utilised to perform on-line detection of the variation in the ®eld soil compaction. On-line measurement of subsoiler draught and w with controlling d will satisfy the requirements of obtaining the spatial variation of the rd, as one of the important indicators of soil compaction.
A.M. Mouazen, H. Ramon / Soil & Tillage Research 63 (2002) 155±165
References Ayers, P.D., 1987. Moisture and bulk density effects on soil shear strength parameters for coarse grained soils. Trans. Am. Soc. Agric. Eng. 31 (2), 1282±1287. Ayers, P.D., Perumpral, J.V., 1982. Moisture and density effect on cone index. Trans. Am. Soc. Agric. Eng. 25 (5), 1169±1172. Bernier, H., Bostock, G., Raghavan, S.V., Broughton, R.S., 1989. Subsoiling effects on moisture content and bulk density in the soil pro®le. ASAE Paper. Appl. Eng. Agric. 5 (1), 24±28. Busscher, W.J., Sojka, R.E., 1987. Enhancement of subsoiling effect on soil strength by conservation tillage. Trans. Am. Soc. Agric. Eng. 30 (4), 888±892. Erbach, D.C., Benjamin, J.G., Cruse, R.M., Elamin, M.A., Mukhtar, S., Choi, C.-H., 1992. Soil and corn response to tillage with paraplow. Trans. Am. Soc. Agric. Eng. 35 (5), 1354±1374. Evans, S.D., Lindstrom, M.J., Voorhees, W.B., Moncrief, J.F., Nelson, G.A., 1996. Effect of subsoiling and subsequent tillage on soil bulk density, soil moisture and corn yield. Soil Till. Res. 38, 35±46. Fielke, J.M., Riley, T.W., Slattery, M.G., Fitzpatrick, R.W., 1993. Comparison of tillage forces and wear rates of pressed and cast cultivator shares. Soil Till. Res. 25, 317±328. Gameda, S., Raghavan, G.S.V., McKyes, E., Watson, A.K., Mehuys, G., 1987. Response of grain corn to subsoiling and chemical wetting of a compacted clay subsoil. Soil Till. Res. 29, 179±187. Garner, T.H., Reynolds, W.R., Musen, H.L., Miles, G.E., Davis, J.W., Peiper, U.M., 1987. Energy requirement for subsoiling coastal plain soils. Trans. Am. Soc. Agric. Eng. 30 (2), 343± 350. Glancey, J.L., Upadhyaya, S.K., Chancellor, W.J., Rumsey, J.W., 1996. Prediction of agricultural implement draft using an instrumented analog tillage tool. Soil Till. Res. 37, 47±65. Â ., 1980. Handbook of Soil Mechanics, Vol. 2: Soil Testing. KeÂzdi, A Elsevier, Amsterdam. Khalilian, A., Garner, T.H., Musen, H.L., Dodd, R.B., Hale, S.A., 1988. Energy for conservation tillage in coastal plain soils. Trans. Am. Soc. Agric. Eng. 31 (5), 1333±1338. Koolen, A.J., Kuipers, H., 1983. Agricultural Soil Mechanics. Springer, Berlin. Kydd, H.D., Frehlich, G.E., Boyden, A.R., 1984. Tillage power requirement in Western Canada. ASAE Paper No. 84-1027. ASAE, St. Joseph, MI, USA. Mapfumo, E., Chanasyk, D.S., 1998. Guidelines for save traf®cking and cultivation, and resistance±density±moisture relations
165
of three disturbed soils from Alberta. Soil Till. Res. 47, 193± 202. McKyes, E., 1989. Agricultural Engineering Soil Mechanics. Elsevier, Amsterdam. Mohsenin, N.N., 1970. Physical Properties of Plant and Animal Materials. Gordon and Breach, New York. Mouazen, A.M., NemeÂnyi, M., 1999a. Tillage tool design by the ®nite element method. Part I. Finite element modelling of soil plastic behaviour. J. Agric. Eng. Res. 72, 37±51. Mouazen, A.M., NemeÂnyi, M., 1999b. Finite element analysis of subsoiler cutting in non-homogeneous sandy loam soil. Soil Till. Res. 51, 1±15. Mouazen, A.M., NemeÂnyi, M., Schwanghart, H., Rempfer, M., 1999. Tillage tool design by the ®nite element method. Part II. Experimental validation of the ®nite element results with soil bin test. J. Agric. Eng. Res. 72, 53±58. Mouazen, A.M., Ramon, H., De Baerdemaeker, J., 2000. Variation in the mechanical properties of an agricultural sandy loam soil with bulk density and moisture content. J. Agric. Eng. Res., submitted for publication. Raghavan, G.S.V., McKyes, E., Beaulieu, B., 1977. Prediction of clay soil compaction. J. Terramech. 14, 31±38. Schwanghart, H., Zweier, A., 1993. In¯uence of tread on drawbar pull of tires for small off-road vehicles. In: Proceedings of the 11th International Conference on Int. Society for Terrain Vehicle Systems, Lake Tahoe, USA, pp. 233±244. Shinners, K.J., Alcock, R., Wilkes, J.M., 1990. Combining active and passive tillage elements to reduce draft requirement. Trans. Am. Soc. Agric. Eng. 33 (2), 400±404. SoÈhne, W., 1958. Fundamentals of pressure distribution and soil compaction under tractor tires. Agric. Eng. 39, 276±281. Sprinkle, L.W., Langston, T.D., Weber, J.A., Sharon, N.M., 1970. A similitude study with static and dynamic parameters in an arti®cial soil. Trans. Am. Soc. Agric. Eng. 29, 580±586. Stafford, J.V., Hendrick, J.G., 1988. Dynamic sensing of soil pans. Trans. Am. Soc. Agric. Eng. 31 (1), 9±13. Tabatabaeefar, A., Solhjoo, A., Alimardanee, R., 1998. Mathematical model for soil cone index in Zarghan Fars, Iran. In: Proceedings of the International Conference on Agricultural Engineering, Oslo, Norway, No. 98-C-090. Unger, P.W., Jones, O.R., 1998. Long-term tillage and cropping systems affect bulk density and penetration resistance of soil cropped to dryland wheat and grain sorghum. Soil Till. Res. 45, 39±57. Upadhyaya, S.K., Williams, T.H., Kemble, L.J., Collins, N.E., 1984. Energy requirement for chiselling in coastal plain soils. Trans. Am. Soc. Agric. Eng. 27 (6), 1643±1649.