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Soil stress as affected by wheel load and tyre inflation pressure
Soil & Tillage Research 96 (2007) 284–291 www.elsevier.com/locate/still
Soil stress as affected by wheel load and tyre inflation pressure Johan Arvidsson *, Thomas Keller Department of Soil Sciences, Swedish University of Agricultural Sciences, P.O. Box 7014, SE-750 07 Uppsala, Sweden Received 2 May 2007; accepted 22 June 2007
Abstract The relative importance of wheel load and tyre inflation pressure on topsoil and subsoil stresses has long been disputed in soil compaction research. The objectives of the experiment presented here were to (1) measure maximum soil stresses and stress distribution in the topsoil for different wheel loads at the same recommended tyre inflation pressure; (2) measure soil stresses at different inflation pressures for the given wheel loads; and (3) measure subsoil stresses and compare measured and simulated values. Measurements were made with the wheel loads 11, 15 and 33 kN at inflation pressures of 70, 100 and 150 kPa. Topsoil stresses were measured at 10 cm depth with five stress sensors installed in disturbed soil, perpendicular to driving direction. Contact area was measured on a hard surface. Subsoil stresses were measured at 30, 50 and 70 cm depth with sensors installed in undisturbed soil. The mean ground contact pressure could be approximated by the tyre inflation pressure (only) when the recommended inflation pressure was used. The maximum stress at 10 cm depth was considerably higher than the inflation pressure (39% on average) and also increased with increasing wheel load. While tyre inflation pressure had a large influence on soil stresses measured at 10 cm depth, it had very little influence in the subsoil (30 cm and deeper). In contrast, wheel load had a very large influence on subsoil stresses. Measured and simulated values agreed reasonably well in terms of relative differences between treatments, but the effect of inflation pressure on subsoil stresses was overestimated in the simulations. To reduce soil stresses exerted by tyres in agriculture, the results show the need to further study the distribution of stresses under tyres. For calculation of subsoil stresses, further validations of commonly used models for stress propagation are needed. # 2007 Elsevier B.V. All rights reserved. Keywords: Compaction; Soil stress; Subsoil; Topsoil; Tyre inflation pressure; Wheel load
1. Introduction Soil compaction is the result of stresses acting upon the soil. One of the farmer’s main options to reduce compaction is to reduce these stresses. For agricultural vehicles, this can mainly be done in two ways: by reducing the load or by increasing the contact area. For tyres, stresses in the contact area and the topsoil are closely connected to the inflation pressure (e.g. Bailey et al., 1992; Erbach and Knoll, 1992; Raper et al., 1995; Arvidsson and Ristic, 1996). The mean contact * Corresponding author. E-mail address: [email protected] (J. Arvidsson). 0167-1987/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.still.2007.06.012
stress can often be approximated by the inflation pressure (Plackett, 1984; Johnson and Burt, 1990; Burt et al., 1992; Van den Akker, 1994; Arvidsson et al., 2002). Koolen et al. (1992) assumed the mean normal stress in the contact surface to be 1.2–1.3 times the inflation pressure due to the stiffness of the tyre carcass. Karafiath and Nowatski (1978) presented an equation in which the mean contact pressure is calculated from the inflation pressure and tyre characteristics: pm ¼ c i pi þ pc
(1)
where pm is the mean contact pressure; ci the tyre stiffness constant; pi, the in flation pressure and pc the pressure exerted by the tyre carcass when pi = 0.
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Plackett (1984) measured the carcass stiffness and found it to be in the range 0.2–0.5 bar. There are also several reports in the literature where the measured average contact stress was lower than the inflation pressure (e.g. Gysi et al., 1999; Arvidsson et al., 2002; Alakukku et al., 2002). However, maximum stresses can be considerably higher than the mean contact stress, sometimes by a factor of two to four (Burt et al., 1992; Gysi et al., 2001, Alakukku et al., 2002). For a description of the stress distribution in the contact area, So¨hne (1958) proposed a parabolic distribution over the tyre imprint, while Hammel (1994) suggested a trapezoidal distribution. Whereas the effect of inflation pressure on stresses in the topsoil has been clearly demonstrated, the effect of wheel load is less clear. Stress measurements with different loads have often been carried out using the same tyre (e.g. Bailey et al., 1992; Erbach and Knoll, 1992; Burt et al., 1992; Raper et al., 1995; Way et al., 2000; Way and Kishimoto, 2003). Since increasing wheel load increases the recommended tyre inflation pressure, this means that the effect of load and inflation pressure cannot be studied independently. Stresses in the subsoil can be calculated from the stress distribution in the contact area. Most widely used are the equations formulated by Boussinesq (1885) and later modified by Fro¨hlich (1934), in which the vertical stress under a point load is calculated. By dividing the contact area into subareas representing point loads, stresses beneath a tyre can be simulated (So¨hne, 1958). Due to the interaction of stresses, increasing wheel load results in higher simulated stresses in the subsoil. This has also been confirmed in measurements of stresses and compaction in the subsoil (e.g. Eriksson et al., 1974, Arvidsson et al., 2001, Trautner and Arvidsson, 2003). Olsen (1994), based on calculations according to Eq. (1), stated that the soil stress in the 0.1–1 m layer depends both on the load and the contact area stress. For high wheel loads (>80 kN), Arvidsson et al. (2002) and Keller and Arvidsson (2004) demonstrated a large influence of tyre inflation pressure on soil stress and displacement at 0.3 m depth. However, at greater depths, the influence of inflation pressure was small. Danfors (1994) found no effect of inflation pressure on compaction in the subsoil. Despite a large amount of research in the area of subsoil compaction (Ha˚kansson, 1994; Van den Akker et al., 2003), there are very few validated simulations of subsoil stresses that are based on measured contact area stresses. The objectives of the experiment presented here were to (1) measure maximum soil stresses and stress distribution in the topsoil for different wheel loads at the
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same recommended tyre inflation pressure; (2) measure soil stresses at different inflation pressures for the given wheel loads; and (3) measure subsoil stresses and compare measured and simulated values. 2. Materials and methods 2.1. Stress distribution in the topsoil Measurements of stress distribution in the topsoil were made on a loam soil (308 g kg1 clay, 18 g kg1 organic matter content) in Uppsala, Sweden (59.98N, 17.68E), in November 2002 at a water content close to field capacity (250 g kg1). Stress sensors were constructed from load cells (DS Europe Series BS 302) with a diameter of 17.5 mm, which were mounted in a circular plate, 15 mm high and 70 mm in diameter. Before the measurements, 10 cm of topsoil were removed and five stress sensors were placed at 90 mm intervals, perpendicular to the driving direction. The topsoil was then backfilled over the sensors. During wheeling, the centre of the tyre was run over the outermost sensor, and the stress distribution was assumed to be symmetrical along the centre line of the wheel track. Four separate installations were made, which were considered as replicates. For each installation, wheelings were made with all combinations of wheel loads and inflation pressures, without removing the soil between the passes. Stress measurements seem to be little influenced by the number of passes when deformations are small (Van den Akker et al., 1994; Alakukku et al., 2002). For each installation, the wheel loads were driven in a randomized order over the sensors. There was no clear difference in stress recordings due to the number of passes over the sensors. Wheelings were made with two tractors, MF 6290 and MF 4245. The intention was to have different wheel loads, but with the same recommended tyre inflation pressure of 100 kPa. This was achieved for the front and rear tyre of the MF 4245, and the rear tyre of the MF 6290. In addition to the recommended inflation pressure of 100 kPa, wheelings were also made at tyre inflation pressures of 70 and 150 kPa. Wheel loads, tyre sizes and recommended wheel load for different inflation pressures are presented in Table 1. 2.2. Tyre contact area on hard surface The different tyres were driven onto paper sheets lying on a concrete floor, and a spray paint was used to outline the tyre imprint onto the paper. Thereafter, the tyre imprint was cut out of the paper and weighed to
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Table 1 Tyre dimensions, wheel load and recommended inflation pressure for the wheels used in the experiment Wheel
Wheel load (kN)
Tyre size
Unloaded radius (mm)
Recommended wheel loada (kN) at 70 kPa
100 kPa
150 kPa
MF 6290 Rear
33.3
650/65 R 38
906
28.5
34.8
45.4
MF 4245 Front Rear
10.5 14.5
11.2 R 28 13.6 R 38
600 775
9.0 13.1
10.4 14.7
12.7 18.6
a
Recommended by the tyre manufacturer for a speed of 30 km h1.
determine the area. Finally, the imprints of the lugs were cut out separately to determine the area of the lugs. One replicate was made for each tyre and inflation pressure. 2.3. Measurements of stress in the subsoil In May 2004, measurements of vertical stresses in the subsoil were conducted on the same field as the measurements in the topsoil. The soil was a clay soil, (546 g kg1 clay and 38 g kg1 organic matter in 0– 20 cm, 561 g kg1 clay and 7 g kg1 organic matter in 30–50 cm). Wheelings were made at a water content close to field capacity throughout the soil profile (305 g kg1 in 0–20 cm). Stress sensors were installed horizontally from a dug pit at 30, 50 and 70 cm depth, as described by Arvidsson and Andersson (1997). Wheelings were made with the same wheel loads and tyre inflation pressures as for the measurements of topsoil stresses. Three installations were made, which were considered as replicates. For each installation, wheelings were made with all combinations of wheel loads and inflation pressures. As for the topsoil, for each installation the wheel loads were driven in a randomized order over the sensors. Only two installations gave satisfactory readings at 50 cm depth and one at 70 cm depth, probably due to problems in getting contact between the soil and the stress sensor when there is little soil deformation.
A concentration factor of 5 (soft soil) was used for all simulations. Stresses were calculated by use of a spreadsheet in which the wheel load was divided into point loads in a 40 40 mm2 grid. The stress calculations were made using three distributions of stress (s) in the contact area: Sim U, uniform stress distribution; s, inflation pressure; Sim P, parabolic stress distribution; smax = 1.5 inflainflation pressure; Sim M: s = measured stress at 10 cm depth. 3. Results 3.1. Maximum stress at 10 cm depth, contact area stresses The maximum measured stresses at the different depths are presented in Table 2. At 10 cm depth, the stress increased with increasing inflation pressure and with increasing wheel load (P < 0.05). Soil stress at 10 cm depth as a function of inflation pressure is shown in Fig. 1. The intercept of the regression line for all tyres is 52 kPa, and the slope 0.8. Regression lines for the individual tyres had the following coefficients: 33 kN wheel loads s max ¼ 1:16 pinfl þ 40 11 kN wheel loads s max ¼ 0:49 pinfl þ 67
2.4. Stress calculations
R2 ¼ 0:97
Vertical stresses sz at a certain depth z were calculated according to So¨hne (1958):
15 kN wheel loads s max ¼ 0:75 pinfl þ 51
s v ðZÞ ¼
i¼n X i¼0
ðs v Þi ¼
i¼n X i¼0
vPi cosvþ2 ui 2pZ 2
(2)
where v is the concentration factor, P the point load and u the angle between the normal load vector and the position vector from the point load to the desired point.
R2 ¼ 1:0 (3)
R2 ¼ 0:98
(4)
(5)
where smax is the maximum measured stress at 10 cm depth and pinfl the tyre inflation pressure. There were statistically significant differences in the regression equations for the different tyres (P < 0.05). The mean stress calculated from the contact area measured on a hard surface is also presented in Table 2,
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Table 2 Maximum measured stress at 10, 30, 50 and 70 cm depth, mean stress calculated from the tyre contact area and mean stress calculated for the tyre lugs Wheel load, inflation pressure
Maximum stress (kPa) at depth
Mean stress (kPa)
Mean stress (kPa)
10 cm
30 cma
50 cm a
70 cm a
Contact area
Lugs
33 kN 150 kPa 100 kPa 70 kPa
214 a 156 bc 129 cde
164 a 159 a 135 b
33 48 46
36 39 36
142 112 92
521 412 349
15 kN 150 kPa 100 kPa 70 kPa
161 b 139 bcd 102 ef
80 c 73 c 78 c
18 18 18
13 12 13
102 94 81
582 509 431
11 kN 150 kPa 100 kPa 70 kPa
139 bcd 123 def 99 f
87 c 83 c 88 c
20 17 20
11 11 11
125 114 105
716 585 474
34 kN 15 kN 11 kN
166 a 134 b 120 b
153 a 77 b 86 b
42 a 19 b 18 b
37 a 11 b 13 b
150 kPa 100 kPa 70 kPa
171 a 139 b 110 c
110 105 100
24 28 28
20 21 20
Values not followed by the same letter are significantly different (P < 0.05). a Measurements at 30–70 cm depth were made at a different site compared to 10 cm depth.
which also shows that the stress increased with increasing inflation pressure, but at a lower rate. Mean stress under the lugs ranged from 349 to 716 kPa (Table 2). 3.2. Stress distribution in the topsoil The stress distribution for the 33 kN wheel load perpendicular to the driving direction is presented in Fig. 2. Increasing inflation pressure increased the
measured stress for all load cells. The highest stress was recorded between the edge and the centre of the tyre. The stress distribution for all wheel loads at 100 kPa inflation pressure, i.e., at the recommended tyre inflation pressure, is presented in Fig. 3. For the 11 kN wheel load, the stress was highest under the centre of the tyre, whereas there was a rather uniform stress distribution under the 15 kN wheel load. 3.3. Subsoil stresses The maximum measured stress at 30, 50 and 70 cm depth is presented in Table 2. The stress was highest for
Fig. 1. Measured vertical stress at 10 cm depth as a function of tyre inflation pressure.
Fig. 2. Measured vertical stress at 10 cm depth perpendicular to driving direction for 33 kN wheel load.
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estimated, while the agreement between simulated and measured stresses was increased by using a parabolic (Sim P) or the measured (Sim M) stress distribution. With increasing depth, stresses calculated with the different stress distributions at the soil surface (Sim U, Sim P and Sim M) become more and more similar, i.e., the stress distribution at the soil surface became less important with increasing depth. Fig. 4 shows measured and simulated stresses (Sim M stress distribution) for the wheel loads of 15 and 11 kN relative to the respective measured and simulated stresses for the wheel load of 33 kN. The model satisfactorily predicted the influence of wheel load on soil stresses. Fig. 5 shows measured and simulated stresses for the tyre inflation pressures of 70 and 150 kPa relative to the respective measured and simulated stresses for the tyre inflation pressure of 100 kPa. For the highest wheel load (33 kN), the model predicted the effect of tyre inflation pressure on soil stress in accordance with the measurements (Fig. 5a). However, for the lower wheel loads (11 and 15 kN), the model predicted effects of tyre inflation pressure but these were not observed in the field (Fig. 5b and c).
Fig. 3. Measured vertical stress at 10 cm depth perpendicular to driving direction for all wheel loads at 100 kPa tyre inflation pressure.
the highest wheel load at all three depths (P < 0.001). On average for all wheel loads, tyre inflation pressure had no significant effect on soil stresses measured in the subsoil. However, when all combinations of wheel loads and inflation pressures were analysed as separate treatments, inflation pressure had a significant effect on the measured soil stress at 30 cm depth for the highest wheel load (Table 2). 3.4. Calculated subsoil stresses The calculated stresses are shown in Table 3. Generally, simulated stresses were higher than measured stresses at 50 cm depth. At 30 and 70 cm depth the agreement between simulated and measured stresses was better. With a uniform stress distribution at the soil surface (Sim U), stresses at 30 cm depth were under-
4. Discussion The mean contact stress at the recommended tyre inflation pressure, calculated from the contact area on a hard surface, was close to the tyre inflation pressure
Table 3 Simulated and measured stresses at 30, 50 and 70 cm depth Load,
Maximum stress (kPa) at depth
inflation
30 cm
140 111 85
146 120 101
33 48 46
80 73 78
76 64 49
89 75 59
106 92 73
87 83 88
68 52 40
72 61 49
82 71 58
164 159 135
15 kN 150 kPa 100 kPa 70 kPa 11 kN 150 kPa 100 kPa 70 kPa
c d
d
113 86 64
33 kN 150 kPa 100 kPa 70 kPa
Sim U
c
Sim M
Meas.
a
50 cm b
Sim P
pressure
b
a
Meas.
a
70 cm Sim U
b
c
Meas.a
Sim Ub
Sim Pc
Sim M d
84 81 73
36 39 36
43 40 35
46 43 38
49 51 50
41 37 33
54 47 38
13 12 13
20 21 18
22 21 20
30 26 21
31 29 26
38 33 29
11 11 11
17 15 13
17 16 15
20 18 16
Sim P
Sim M
69 60 48
77 68 57
18 18 18
36 35 29
20 17 20
31 26 22
Measured values. Simulated value, uniform stress distribution, s = inflation pressure. Simulated value, parabolic stress distribution, smax = 1.5 inflation pressure. Simulated value, measured stress distribution at 10 cm depth.
d
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Fig. 4. Measured stresses (symbols) for the wheel loads of 15 and 11 kN relative to the measured stress for the wheel load of 33 kN; and simulated stresses (curves) for the wheel loads of 15 and 11 kN relative to the simulated stress for the wheel load of 33 kN. (a) 100 kPa, (b) 70 kPa and (c) 150 kPa tyre inflation pressure.
Fig. 5. Measured stresses (symbols) for the tyre inflation pressures of 70 and 150 kPa relative to the measured stress for the tyre inflation pressure of 100 kPa; and simulated stresses (curves) for the tyre inflation pressures of 70 and 150 kPa relative to the simulated stress for the tyre inflation pressure of 100 kPa. (a) 33 kN, (b) 15 kN and (c) 11 kN wheel load.
(within 15%, Table 2). This is in agreement with earlier studies (Johnson and Burt, 1990; Burt et al., 1992; Van den Akker, 1994; Arvidsson et al., 2002). A change in tyre inflation pressure gave a smaller change in contact area stress (Table 2). This was especially pronounced for the smallest tyres, perhaps due to their smaller tyre diameter and volume. The results could be well described using Eq. (1), with an intercept around 70 kPa accounting for carcass stiffness. At the highest inflation pressure, the mean contact stress was lower than the inflation pressure. Similar results have been obtained by Alakukku et al. (2002) and Arvidsson et al. (2002). A possible explanation is an uneven stress distribution in the tyre carcass due to the high stresses acting on the lugs. The mean stresses under lugs ranged from 350 to over 700 kPa. This also means that when soil deformation is small, the stresses exerted on the soil can be expected to attain very high values (Gupta and Raper, 1994). The measured maximum vertical soil stress at 10 cm depth was generally higher than the tyre inflation pressure; on average, it was 39% higher at the
recommended inflation pressure of 100 kPa (Table 2). For the different wheel loads, the maximum stress was well described as a function of tyre inflation pressure, (Eq. (3)–(5), Fig. 1). The intercept, corresponding to carcass stiffness, was approximately 50 kPa. The measured soil stress at 10 cm depth was highest for the highest wheel load, indicating an effect not only of inflation pressure but also of wheel load on vertical soil stresses close to the soil surface. While most models to calculate mean contact stress or stress distribution in the contact area do not include wheel load, Steiner and So¨hne (1979) included this parameter to predict mean contact stress. Keller (2005) predicts the maximum stress below a tyre as a function of tyre inflation pressure, the ratio of tyre inflation pressure to recommended tyre inflation pressure, and wheel load. For the highest wheel load, the highest stress was measured between the centre and the edge of the tyre. Therefore, stresses under this tyre could not be described by, for example, a parabolic stress distribution (So¨hne, 1958), but can be described by the recently developed model of Keller (2005). The results show that
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to attain low stresses in the topsoil, much attention has to be given to the stress distribution in the contact area. The maximum stress in the subsoil (30 cm and deeper) was mainly determined by wheel load, and little influenced by tyre inflation pressure. Only at the highest wheel load was there a certain influence of inflation pressure. Arvidsson et al. (2002) and Keller and Arvidsson (2004) found a large effect of tyre inflation pressure on soil stress at 30 cm depth, although not at greater depth. However, their investigations were made with much higher wheel loads (>80 kN) than in the present study. According to the equations of Fro¨hlich (1934), contact stresses have a larger influence on subsoil stresses the larger the wheel load. Van den Akker (1994) also measured a small effect of tyre inflation pressure on stress at 30 cm depth, using a wheel load of 32 kN. The correlation between simulated and measured values was reasonable in relative terms. The effect of wheel load on stress propagation was well predicted by the model (Fig. 4). However, the model predicted a relatively strong effect of tyre inflation pressure on subsoil stresses, which was only observed for the highest wheel load, but not for the lower wheel loads (Fig. 5). The agreement between absolute values of simulated and measured stresses was worse, especially at 50 cm depth. This might be due to the following reasons. First, the model cannot account for different soil layers. Therefore, the effect of a soft soil layer overlaying a hard soil layer (or vice versa) on stress propagation may not be predicted accurately with an analytical model as used in this study. However, the effect of material (i.e., soil) stiffness on vertical stress propagation may be small when deformations are small, which was the case for our experiments. Second, and probably most important, the absolute values of the subsoil measurements were not fully reliable. This is due to problems in getting contact between the sensor and the soil when deformation is small, and/or due to the differences in stiffness between soil and the transducer (Kirby, 1999a,b). Although it is difficult to measure absolute values, differences between treatments may still be reliable since all combinations of wheel loads and inflation pressure were measured with each installation. The stress distribution at the soil surface not only had an effect on simulated stresses in the topsoil, but also on stresses in the subsoil. A uniform stress distribution at the soil surface resulted in an underestimation of stresses in the upper subsoil, which is in accordance with Keller and Arvidsson (2004) and Keller (2005). With increasing tyre inflation pressure, the under-
estimation became less pronounced. This is due to the fact that the ratio of maximum measured stress to tyre inflation pressure decreased with increasing ratio of tyre inflation pressure to recommended tyre inflation pressure (Table 2), which was also observed by Keller and Arvidsson (2004). Therefore, it is essential in soil compaction modelling to have an accurate prediction of the stress distribution at the tyre–soil interface. 5. Conclusions The mean ground contact pressure could be approximated by the tyre inflation pressure when the recommended inflation pressure was used. The maximum stress at 10 cm depth was considerably higher than the inflation pressure, and also increased with increasing wheel load. For the largest tyre, stress was highest between the edge and the centre, which cannot be described by the most commonly used shapes (i.e., uniform, parabolic and trapezoidal) for stress distribution over a tyre imprint, but can be described by a decay function as proposed by Keller (2005). While tyre inflation pressure had a large influence on soil stresses measured at 10 cm depth, it had very little influence in the subsoil (30 cm and deeper). In contrast, wheel load had a very large influence on subsoil stresses. The results demonstrate that stress in the topsoil is not simply a function of tyre inflation pressure and that stress in the subsoil is not simply a function of wheel load. Soil stress is always a function of the stress at the tyre–soil interface, which is a function of both tyre inflation pressure and wheel load, as well as tyre properties and soil conditions. Simulated stresses agreed reasonably well with measured values in relative terms. However, the effect of inflation pressure on subsoil stresses was overestimated by the model. The results show that in order to reduce soil stresses exerted by tyres in agriculture, there is a need to further study the distribution of stresses under tyres. For calculation of subsoil stresses, further validations of commonly used models for stress propagation are needed. References Alakukku, L., Ahokas, J., Ristolainen, A., 2002. Response of clay soil macroporosity to stress caused by tracked tractors. In: Pagliai, M., Jones, R. (Eds.), Sustainable and Management—Environmental Protection. Advances in GeoEcology, 35. Catena Verlag, Reiskirchen, pp. 319–330. Arvidsson, J., Ristic, S., 1996. Soil stress and compaction effects for four tractor tyres. J. Terramech. 33 (5), 223–232.
J. Arvidsson, T. Keller / Soil & Tillage Research 96 (2007) 284–291 Arvidsson, J., Andersson, S., 1997. Determination of soil displacement by measuring the pressure of a column of liquid. In: Proceedings of 14th International Conference of ISTRO, Pulawy, Poland. Arvidsson, J., Trautner, A., van den Akker, J.J.H., Schjønning, P., 2001. Subsoil compaction caused by heavy sugarbeet harvesters in southern Sweden.II Soil displacement during wheeling and model computations of compaction. Soil Till. Res. 60, 79–89. Arvidsson, J., Trautner, A., Keller, T., 2002. Influence of tyre inflation pressure on stress and displacement in the subsoil. In: Pagliai, M., Jones, R. (Eds.), Sustainable Land Management—Environmental Protection. Advances in GeoEcology, 35. Catena Verlag, Reiskirchen, pp. 331–338. Bailey, A.C., Raper, R.L., Burt, E.C., Johnson, C.E., Way, T.R. 1992. Soil Stresses under Tires with low Inflation Pressure. ASAE Meeting Presentation No. 92-1581. Boussinesq, J., 1885. Applications des potentials a` l’e´tude de l’equilibre et du movement des solides elastique. Gauthier-Villais, Paris. Burt, E.C., Wood, R.K., Bailey, A.C., 1992. Some comparisons of average to peak soil–tire contact pressures. Trans. ASAE 35, 401– 404. Danfors, B., 1994. Changes in subsoil porosity caused by heavy vehicles. Soil Till. Res. 29, 135–144. Erbach, D.C., Knoll, K.K. 1992. Inflation Pressure Effect on Soil Compaction. ASAE Meeting Presentation No. 92-1582. Eriksson, J., Ha˚kansson, I., Danfors, B. 1974. Jordpackning – markstruktur – gro¨da. (The effect of soil compaction on soil structure and crop yields.) Swed. Inst. Agric. Eng., Uppsala, Rep. 354, 88 pp. (In Swedish. Translated into English 1975 by J.K. Aase, U.S.D.A.–A.R.S., Washington, DC, USA). Fro¨hlich, O.K., 1934. Druckverteilung im Baugrunde. Springer Verlag, Wien, 178 pp. Gupta, S.C., Raper, R.L., 1994. Prediction of soil compaction under vehicles. In: Soane, B.D., van Ouwerkerk, C. (Eds.),Soil Compaction in Crop Production. Elsevier, Amsterdam. Gysi, M., Ott, A., Flu¨hler, H., 1999. Influence of single passes with high wheel load on a structured, unploughed sandy loam soil. Soil Till. Res. 52, 141–151. Gysi, M., Maeder, V., Weisskopf, P., 2001. Pressure distribution underneath tires of agricultural vehicles. Trans. Am. Soc. Agric. Eng. 44, 1385–1389. Hammel, K., 1994. Soil stress distribution under lugged tires. Soil Till. Res. 32, 163–181. Ha˚kansson, I. (Ed.), 1994. Subsoil compaction by high axle load traffic. Soil Till. Res. 29, 105–306 (special issue). Johnson, C.E., Burt, E.C., 1990. A method of predicting soil stress state under tires. Trans. ASAE 33, 713–717. Karafiath, L.L., Nowatski, E.A., 1978. Soil Mechanics for Off-road Vehicle Engineering. Trans Tech Publications, Clausthal, Germany, pp. 515.
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Keller, T., 2005. A model for the prediction of the contact area and the distribution of vertical stress below agricultural tyres from readily available tyre parameters. Biosyst. Eng. 92, 85–96. Keller, T., Arvidsson, J., 2004. Technical solutions to reduce the risk of subsoil compaction: effect of dual wheels, tandem wheels and tyre inflation pressure on stress propagation in soil. Soil Till. Res. 79, 191–205. Kirby, J.M., 1999a. Soil stress measurement: Part 1. Transducer beneath a circular loaded area. J. Agric. Eng. Res. 72, 151–160. Kirby, J.M., 1999b. Soil stress measurement: Part 2. Transducer in a uniform stress field. J. Agric. Eng. Res. 72, 141–149. Koolen, A.J., Lerink, P., Kurstjens, D.A.G., van den Akker, J.J.H., Arts, W.B.M., 1992. Prediction of aspects of soil–wheel systems. Soil Till. Res. 24, 381–396. Olsen, H.J., 1994. Calculation of subsoil stresses. Soil Till. Res. 29, 11–124. Plackett, C.W., 1984. The ground pressure of some agricultural tyres at low load with zero sinkage. J. Agric. Eng. Res. 29, 159–166. Raper, R.L., Bailey, A.C., Burt, E.C., Way, T.R., Liberati, P., 1995. Inflation pressure and dynamic load effects on soil deformation and soil–tire interface stresses. Trans. ASAE 38, 685–689. Steiner, M., So¨hne, W., 1979. Berechnung der Tragfa¨higkeit von Ackerschlepperreifen sowie des Kontaktfla¨chenmitteldruckes und des Rollwiderstandes auf starrer Fahrbahn. (Calculation of the load capacity of tractor tires as well as the medium pressure in the contact area and the rolling resistance on a rigid surface. Grundl. Landtech. 29, 145–152. So¨hne, W., 1958. Fundamentals of pressure distribution and compaction under tractor tires. Agric. Eng. 39, 276–281 290. Trautner, A., Arvidsson, J., 2003. Subsoil compaction caused by machinery traffic on a Swedish Eutric Cambisol at different soil water contents. Soil Till. Res. 73, 107–118. Van den Akker, J.J.H., 1994. Prevention of subsoil compaction by tuning the wheel load to the bearing capacity of the subsoil. In: Proceedings of 13th International Conference of ISTRO, Denmark, pp. 537–542. Van den Akker, J.J.H., Arts, W.B.M., Koolen, A.J., Stuiver, H.J., 1994. Comparisons of stresses, compactions and increase of penetration resistance caused by a low ground pressure tyre and a normal tyre. Soil Till. Res. 29, 125–134. Van den Akker, J.J.H., Arvidsson, J., Horn, R. (Eds.), 2003. Experiences with the impact and prevention of subsoil compaction in the European Union. Soil Till. Res. 73, 1–186 (special issue). Way, T.R., Kishimoto, T., Burt, E.C., Bailey, A.C., 2000. Soil tyre interfaces pressures of a low aspect ratio tractor tyre. In: Horn, R., van den Akker, J.J.H., Arvidsson, J. (Eds.), Subsoil Compaction–Distribution, Processes and Consequences. Advances in GeoEcology, 32. Catena Verlag, Reiskirchen, pp. 82–92. Way, T.R., Kishimoto, T., 2003. Interface pressures of a tractor drive tyre on structured and loose soils. Biosyst. Eng. 87, 375–386.
Soil stress as affected by wheel load and tyre inflation pressure Johan Arvidsson *, Thomas Keller Department of Soil Sciences, Swedish University of Agricultural Sciences, P.O. Box 7014, SE-750 07 Uppsala, Sweden Received 2 May 2007; accepted 22 June 2007
Abstract The relative importance of wheel load and tyre inflation pressure on topsoil and subsoil stresses has long been disputed in soil compaction research. The objectives of the experiment presented here were to (1) measure maximum soil stresses and stress distribution in the topsoil for different wheel loads at the same recommended tyre inflation pressure; (2) measure soil stresses at different inflation pressures for the given wheel loads; and (3) measure subsoil stresses and compare measured and simulated values. Measurements were made with the wheel loads 11, 15 and 33 kN at inflation pressures of 70, 100 and 150 kPa. Topsoil stresses were measured at 10 cm depth with five stress sensors installed in disturbed soil, perpendicular to driving direction. Contact area was measured on a hard surface. Subsoil stresses were measured at 30, 50 and 70 cm depth with sensors installed in undisturbed soil. The mean ground contact pressure could be approximated by the tyre inflation pressure (only) when the recommended inflation pressure was used. The maximum stress at 10 cm depth was considerably higher than the inflation pressure (39% on average) and also increased with increasing wheel load. While tyre inflation pressure had a large influence on soil stresses measured at 10 cm depth, it had very little influence in the subsoil (30 cm and deeper). In contrast, wheel load had a very large influence on subsoil stresses. Measured and simulated values agreed reasonably well in terms of relative differences between treatments, but the effect of inflation pressure on subsoil stresses was overestimated in the simulations. To reduce soil stresses exerted by tyres in agriculture, the results show the need to further study the distribution of stresses under tyres. For calculation of subsoil stresses, further validations of commonly used models for stress propagation are needed. # 2007 Elsevier B.V. All rights reserved. Keywords: Compaction; Soil stress; Subsoil; Topsoil; Tyre inflation pressure; Wheel load
1. Introduction Soil compaction is the result of stresses acting upon the soil. One of the farmer’s main options to reduce compaction is to reduce these stresses. For agricultural vehicles, this can mainly be done in two ways: by reducing the load or by increasing the contact area. For tyres, stresses in the contact area and the topsoil are closely connected to the inflation pressure (e.g. Bailey et al., 1992; Erbach and Knoll, 1992; Raper et al., 1995; Arvidsson and Ristic, 1996). The mean contact * Corresponding author. E-mail address: [email protected] (J. Arvidsson). 0167-1987/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.still.2007.06.012
stress can often be approximated by the inflation pressure (Plackett, 1984; Johnson and Burt, 1990; Burt et al., 1992; Van den Akker, 1994; Arvidsson et al., 2002). Koolen et al. (1992) assumed the mean normal stress in the contact surface to be 1.2–1.3 times the inflation pressure due to the stiffness of the tyre carcass. Karafiath and Nowatski (1978) presented an equation in which the mean contact pressure is calculated from the inflation pressure and tyre characteristics: pm ¼ c i pi þ pc
(1)
where pm is the mean contact pressure; ci the tyre stiffness constant; pi, the in flation pressure and pc the pressure exerted by the tyre carcass when pi = 0.
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Plackett (1984) measured the carcass stiffness and found it to be in the range 0.2–0.5 bar. There are also several reports in the literature where the measured average contact stress was lower than the inflation pressure (e.g. Gysi et al., 1999; Arvidsson et al., 2002; Alakukku et al., 2002). However, maximum stresses can be considerably higher than the mean contact stress, sometimes by a factor of two to four (Burt et al., 1992; Gysi et al., 2001, Alakukku et al., 2002). For a description of the stress distribution in the contact area, So¨hne (1958) proposed a parabolic distribution over the tyre imprint, while Hammel (1994) suggested a trapezoidal distribution. Whereas the effect of inflation pressure on stresses in the topsoil has been clearly demonstrated, the effect of wheel load is less clear. Stress measurements with different loads have often been carried out using the same tyre (e.g. Bailey et al., 1992; Erbach and Knoll, 1992; Burt et al., 1992; Raper et al., 1995; Way et al., 2000; Way and Kishimoto, 2003). Since increasing wheel load increases the recommended tyre inflation pressure, this means that the effect of load and inflation pressure cannot be studied independently. Stresses in the subsoil can be calculated from the stress distribution in the contact area. Most widely used are the equations formulated by Boussinesq (1885) and later modified by Fro¨hlich (1934), in which the vertical stress under a point load is calculated. By dividing the contact area into subareas representing point loads, stresses beneath a tyre can be simulated (So¨hne, 1958). Due to the interaction of stresses, increasing wheel load results in higher simulated stresses in the subsoil. This has also been confirmed in measurements of stresses and compaction in the subsoil (e.g. Eriksson et al., 1974, Arvidsson et al., 2001, Trautner and Arvidsson, 2003). Olsen (1994), based on calculations according to Eq. (1), stated that the soil stress in the 0.1–1 m layer depends both on the load and the contact area stress. For high wheel loads (>80 kN), Arvidsson et al. (2002) and Keller and Arvidsson (2004) demonstrated a large influence of tyre inflation pressure on soil stress and displacement at 0.3 m depth. However, at greater depths, the influence of inflation pressure was small. Danfors (1994) found no effect of inflation pressure on compaction in the subsoil. Despite a large amount of research in the area of subsoil compaction (Ha˚kansson, 1994; Van den Akker et al., 2003), there are very few validated simulations of subsoil stresses that are based on measured contact area stresses. The objectives of the experiment presented here were to (1) measure maximum soil stresses and stress distribution in the topsoil for different wheel loads at the
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same recommended tyre inflation pressure; (2) measure soil stresses at different inflation pressures for the given wheel loads; and (3) measure subsoil stresses and compare measured and simulated values. 2. Materials and methods 2.1. Stress distribution in the topsoil Measurements of stress distribution in the topsoil were made on a loam soil (308 g kg1 clay, 18 g kg1 organic matter content) in Uppsala, Sweden (59.98N, 17.68E), in November 2002 at a water content close to field capacity (250 g kg1). Stress sensors were constructed from load cells (DS Europe Series BS 302) with a diameter of 17.5 mm, which were mounted in a circular plate, 15 mm high and 70 mm in diameter. Before the measurements, 10 cm of topsoil were removed and five stress sensors were placed at 90 mm intervals, perpendicular to the driving direction. The topsoil was then backfilled over the sensors. During wheeling, the centre of the tyre was run over the outermost sensor, and the stress distribution was assumed to be symmetrical along the centre line of the wheel track. Four separate installations were made, which were considered as replicates. For each installation, wheelings were made with all combinations of wheel loads and inflation pressures, without removing the soil between the passes. Stress measurements seem to be little influenced by the number of passes when deformations are small (Van den Akker et al., 1994; Alakukku et al., 2002). For each installation, the wheel loads were driven in a randomized order over the sensors. There was no clear difference in stress recordings due to the number of passes over the sensors. Wheelings were made with two tractors, MF 6290 and MF 4245. The intention was to have different wheel loads, but with the same recommended tyre inflation pressure of 100 kPa. This was achieved for the front and rear tyre of the MF 4245, and the rear tyre of the MF 6290. In addition to the recommended inflation pressure of 100 kPa, wheelings were also made at tyre inflation pressures of 70 and 150 kPa. Wheel loads, tyre sizes and recommended wheel load for different inflation pressures are presented in Table 1. 2.2. Tyre contact area on hard surface The different tyres were driven onto paper sheets lying on a concrete floor, and a spray paint was used to outline the tyre imprint onto the paper. Thereafter, the tyre imprint was cut out of the paper and weighed to
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Table 1 Tyre dimensions, wheel load and recommended inflation pressure for the wheels used in the experiment Wheel
Wheel load (kN)
Tyre size
Unloaded radius (mm)
Recommended wheel loada (kN) at 70 kPa
100 kPa
150 kPa
MF 6290 Rear
33.3
650/65 R 38
906
28.5
34.8
45.4
MF 4245 Front Rear
10.5 14.5
11.2 R 28 13.6 R 38
600 775
9.0 13.1
10.4 14.7
12.7 18.6
a
Recommended by the tyre manufacturer for a speed of 30 km h1.
determine the area. Finally, the imprints of the lugs were cut out separately to determine the area of the lugs. One replicate was made for each tyre and inflation pressure. 2.3. Measurements of stress in the subsoil In May 2004, measurements of vertical stresses in the subsoil were conducted on the same field as the measurements in the topsoil. The soil was a clay soil, (546 g kg1 clay and 38 g kg1 organic matter in 0– 20 cm, 561 g kg1 clay and 7 g kg1 organic matter in 30–50 cm). Wheelings were made at a water content close to field capacity throughout the soil profile (305 g kg1 in 0–20 cm). Stress sensors were installed horizontally from a dug pit at 30, 50 and 70 cm depth, as described by Arvidsson and Andersson (1997). Wheelings were made with the same wheel loads and tyre inflation pressures as for the measurements of topsoil stresses. Three installations were made, which were considered as replicates. For each installation, wheelings were made with all combinations of wheel loads and inflation pressures. As for the topsoil, for each installation the wheel loads were driven in a randomized order over the sensors. Only two installations gave satisfactory readings at 50 cm depth and one at 70 cm depth, probably due to problems in getting contact between the soil and the stress sensor when there is little soil deformation.
A concentration factor of 5 (soft soil) was used for all simulations. Stresses were calculated by use of a spreadsheet in which the wheel load was divided into point loads in a 40 40 mm2 grid. The stress calculations were made using three distributions of stress (s) in the contact area: Sim U, uniform stress distribution; s, inflation pressure; Sim P, parabolic stress distribution; smax = 1.5 inflainflation pressure; Sim M: s = measured stress at 10 cm depth. 3. Results 3.1. Maximum stress at 10 cm depth, contact area stresses The maximum measured stresses at the different depths are presented in Table 2. At 10 cm depth, the stress increased with increasing inflation pressure and with increasing wheel load (P < 0.05). Soil stress at 10 cm depth as a function of inflation pressure is shown in Fig. 1. The intercept of the regression line for all tyres is 52 kPa, and the slope 0.8. Regression lines for the individual tyres had the following coefficients: 33 kN wheel loads s max ¼ 1:16 pinfl þ 40 11 kN wheel loads s max ¼ 0:49 pinfl þ 67
2.4. Stress calculations
R2 ¼ 0:97
Vertical stresses sz at a certain depth z were calculated according to So¨hne (1958):
15 kN wheel loads s max ¼ 0:75 pinfl þ 51
s v ðZÞ ¼
i¼n X i¼0
ðs v Þi ¼
i¼n X i¼0
vPi cosvþ2 ui 2pZ 2
(2)
where v is the concentration factor, P the point load and u the angle between the normal load vector and the position vector from the point load to the desired point.
R2 ¼ 1:0 (3)
R2 ¼ 0:98
(4)
(5)
where smax is the maximum measured stress at 10 cm depth and pinfl the tyre inflation pressure. There were statistically significant differences in the regression equations for the different tyres (P < 0.05). The mean stress calculated from the contact area measured on a hard surface is also presented in Table 2,
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Table 2 Maximum measured stress at 10, 30, 50 and 70 cm depth, mean stress calculated from the tyre contact area and mean stress calculated for the tyre lugs Wheel load, inflation pressure
Maximum stress (kPa) at depth
Mean stress (kPa)
Mean stress (kPa)
10 cm
30 cma
50 cm a
70 cm a
Contact area
Lugs
33 kN 150 kPa 100 kPa 70 kPa
214 a 156 bc 129 cde
164 a 159 a 135 b
33 48 46
36 39 36
142 112 92
521 412 349
15 kN 150 kPa 100 kPa 70 kPa
161 b 139 bcd 102 ef
80 c 73 c 78 c
18 18 18
13 12 13
102 94 81
582 509 431
11 kN 150 kPa 100 kPa 70 kPa
139 bcd 123 def 99 f
87 c 83 c 88 c
20 17 20
11 11 11
125 114 105
716 585 474
34 kN 15 kN 11 kN
166 a 134 b 120 b
153 a 77 b 86 b
42 a 19 b 18 b
37 a 11 b 13 b
150 kPa 100 kPa 70 kPa
171 a 139 b 110 c
110 105 100
24 28 28
20 21 20
Values not followed by the same letter are significantly different (P < 0.05). a Measurements at 30–70 cm depth were made at a different site compared to 10 cm depth.
which also shows that the stress increased with increasing inflation pressure, but at a lower rate. Mean stress under the lugs ranged from 349 to 716 kPa (Table 2). 3.2. Stress distribution in the topsoil The stress distribution for the 33 kN wheel load perpendicular to the driving direction is presented in Fig. 2. Increasing inflation pressure increased the
measured stress for all load cells. The highest stress was recorded between the edge and the centre of the tyre. The stress distribution for all wheel loads at 100 kPa inflation pressure, i.e., at the recommended tyre inflation pressure, is presented in Fig. 3. For the 11 kN wheel load, the stress was highest under the centre of the tyre, whereas there was a rather uniform stress distribution under the 15 kN wheel load. 3.3. Subsoil stresses The maximum measured stress at 30, 50 and 70 cm depth is presented in Table 2. The stress was highest for
Fig. 1. Measured vertical stress at 10 cm depth as a function of tyre inflation pressure.
Fig. 2. Measured vertical stress at 10 cm depth perpendicular to driving direction for 33 kN wheel load.
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estimated, while the agreement between simulated and measured stresses was increased by using a parabolic (Sim P) or the measured (Sim M) stress distribution. With increasing depth, stresses calculated with the different stress distributions at the soil surface (Sim U, Sim P and Sim M) become more and more similar, i.e., the stress distribution at the soil surface became less important with increasing depth. Fig. 4 shows measured and simulated stresses (Sim M stress distribution) for the wheel loads of 15 and 11 kN relative to the respective measured and simulated stresses for the wheel load of 33 kN. The model satisfactorily predicted the influence of wheel load on soil stresses. Fig. 5 shows measured and simulated stresses for the tyre inflation pressures of 70 and 150 kPa relative to the respective measured and simulated stresses for the tyre inflation pressure of 100 kPa. For the highest wheel load (33 kN), the model predicted the effect of tyre inflation pressure on soil stress in accordance with the measurements (Fig. 5a). However, for the lower wheel loads (11 and 15 kN), the model predicted effects of tyre inflation pressure but these were not observed in the field (Fig. 5b and c).
Fig. 3. Measured vertical stress at 10 cm depth perpendicular to driving direction for all wheel loads at 100 kPa tyre inflation pressure.
the highest wheel load at all three depths (P < 0.001). On average for all wheel loads, tyre inflation pressure had no significant effect on soil stresses measured in the subsoil. However, when all combinations of wheel loads and inflation pressures were analysed as separate treatments, inflation pressure had a significant effect on the measured soil stress at 30 cm depth for the highest wheel load (Table 2). 3.4. Calculated subsoil stresses The calculated stresses are shown in Table 3. Generally, simulated stresses were higher than measured stresses at 50 cm depth. At 30 and 70 cm depth the agreement between simulated and measured stresses was better. With a uniform stress distribution at the soil surface (Sim U), stresses at 30 cm depth were under-
4. Discussion The mean contact stress at the recommended tyre inflation pressure, calculated from the contact area on a hard surface, was close to the tyre inflation pressure
Table 3 Simulated and measured stresses at 30, 50 and 70 cm depth Load,
Maximum stress (kPa) at depth
inflation
30 cm
140 111 85
146 120 101
33 48 46
80 73 78
76 64 49
89 75 59
106 92 73
87 83 88
68 52 40
72 61 49
82 71 58
164 159 135
15 kN 150 kPa 100 kPa 70 kPa 11 kN 150 kPa 100 kPa 70 kPa
c d
d
113 86 64
33 kN 150 kPa 100 kPa 70 kPa
Sim U
c
Sim M
Meas.
a
50 cm b
Sim P
pressure
b
a
Meas.
a
70 cm Sim U
b
c
Meas.a
Sim Ub
Sim Pc
Sim M d
84 81 73
36 39 36
43 40 35
46 43 38
49 51 50
41 37 33
54 47 38
13 12 13
20 21 18
22 21 20
30 26 21
31 29 26
38 33 29
11 11 11
17 15 13
17 16 15
20 18 16
Sim P
Sim M
69 60 48
77 68 57
18 18 18
36 35 29
20 17 20
31 26 22
Measured values. Simulated value, uniform stress distribution, s = inflation pressure. Simulated value, parabolic stress distribution, smax = 1.5 inflation pressure. Simulated value, measured stress distribution at 10 cm depth.
d
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Fig. 4. Measured stresses (symbols) for the wheel loads of 15 and 11 kN relative to the measured stress for the wheel load of 33 kN; and simulated stresses (curves) for the wheel loads of 15 and 11 kN relative to the simulated stress for the wheel load of 33 kN. (a) 100 kPa, (b) 70 kPa and (c) 150 kPa tyre inflation pressure.
Fig. 5. Measured stresses (symbols) for the tyre inflation pressures of 70 and 150 kPa relative to the measured stress for the tyre inflation pressure of 100 kPa; and simulated stresses (curves) for the tyre inflation pressures of 70 and 150 kPa relative to the simulated stress for the tyre inflation pressure of 100 kPa. (a) 33 kN, (b) 15 kN and (c) 11 kN wheel load.
(within 15%, Table 2). This is in agreement with earlier studies (Johnson and Burt, 1990; Burt et al., 1992; Van den Akker, 1994; Arvidsson et al., 2002). A change in tyre inflation pressure gave a smaller change in contact area stress (Table 2). This was especially pronounced for the smallest tyres, perhaps due to their smaller tyre diameter and volume. The results could be well described using Eq. (1), with an intercept around 70 kPa accounting for carcass stiffness. At the highest inflation pressure, the mean contact stress was lower than the inflation pressure. Similar results have been obtained by Alakukku et al. (2002) and Arvidsson et al. (2002). A possible explanation is an uneven stress distribution in the tyre carcass due to the high stresses acting on the lugs. The mean stresses under lugs ranged from 350 to over 700 kPa. This also means that when soil deformation is small, the stresses exerted on the soil can be expected to attain very high values (Gupta and Raper, 1994). The measured maximum vertical soil stress at 10 cm depth was generally higher than the tyre inflation pressure; on average, it was 39% higher at the
recommended inflation pressure of 100 kPa (Table 2). For the different wheel loads, the maximum stress was well described as a function of tyre inflation pressure, (Eq. (3)–(5), Fig. 1). The intercept, corresponding to carcass stiffness, was approximately 50 kPa. The measured soil stress at 10 cm depth was highest for the highest wheel load, indicating an effect not only of inflation pressure but also of wheel load on vertical soil stresses close to the soil surface. While most models to calculate mean contact stress or stress distribution in the contact area do not include wheel load, Steiner and So¨hne (1979) included this parameter to predict mean contact stress. Keller (2005) predicts the maximum stress below a tyre as a function of tyre inflation pressure, the ratio of tyre inflation pressure to recommended tyre inflation pressure, and wheel load. For the highest wheel load, the highest stress was measured between the centre and the edge of the tyre. Therefore, stresses under this tyre could not be described by, for example, a parabolic stress distribution (So¨hne, 1958), but can be described by the recently developed model of Keller (2005). The results show that
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to attain low stresses in the topsoil, much attention has to be given to the stress distribution in the contact area. The maximum stress in the subsoil (30 cm and deeper) was mainly determined by wheel load, and little influenced by tyre inflation pressure. Only at the highest wheel load was there a certain influence of inflation pressure. Arvidsson et al. (2002) and Keller and Arvidsson (2004) found a large effect of tyre inflation pressure on soil stress at 30 cm depth, although not at greater depth. However, their investigations were made with much higher wheel loads (>80 kN) than in the present study. According to the equations of Fro¨hlich (1934), contact stresses have a larger influence on subsoil stresses the larger the wheel load. Van den Akker (1994) also measured a small effect of tyre inflation pressure on stress at 30 cm depth, using a wheel load of 32 kN. The correlation between simulated and measured values was reasonable in relative terms. The effect of wheel load on stress propagation was well predicted by the model (Fig. 4). However, the model predicted a relatively strong effect of tyre inflation pressure on subsoil stresses, which was only observed for the highest wheel load, but not for the lower wheel loads (Fig. 5). The agreement between absolute values of simulated and measured stresses was worse, especially at 50 cm depth. This might be due to the following reasons. First, the model cannot account for different soil layers. Therefore, the effect of a soft soil layer overlaying a hard soil layer (or vice versa) on stress propagation may not be predicted accurately with an analytical model as used in this study. However, the effect of material (i.e., soil) stiffness on vertical stress propagation may be small when deformations are small, which was the case for our experiments. Second, and probably most important, the absolute values of the subsoil measurements were not fully reliable. This is due to problems in getting contact between the sensor and the soil when deformation is small, and/or due to the differences in stiffness between soil and the transducer (Kirby, 1999a,b). Although it is difficult to measure absolute values, differences between treatments may still be reliable since all combinations of wheel loads and inflation pressure were measured with each installation. The stress distribution at the soil surface not only had an effect on simulated stresses in the topsoil, but also on stresses in the subsoil. A uniform stress distribution at the soil surface resulted in an underestimation of stresses in the upper subsoil, which is in accordance with Keller and Arvidsson (2004) and Keller (2005). With increasing tyre inflation pressure, the under-
estimation became less pronounced. This is due to the fact that the ratio of maximum measured stress to tyre inflation pressure decreased with increasing ratio of tyre inflation pressure to recommended tyre inflation pressure (Table 2), which was also observed by Keller and Arvidsson (2004). Therefore, it is essential in soil compaction modelling to have an accurate prediction of the stress distribution at the tyre–soil interface. 5. Conclusions The mean ground contact pressure could be approximated by the tyre inflation pressure when the recommended inflation pressure was used. The maximum stress at 10 cm depth was considerably higher than the inflation pressure, and also increased with increasing wheel load. For the largest tyre, stress was highest between the edge and the centre, which cannot be described by the most commonly used shapes (i.e., uniform, parabolic and trapezoidal) for stress distribution over a tyre imprint, but can be described by a decay function as proposed by Keller (2005). While tyre inflation pressure had a large influence on soil stresses measured at 10 cm depth, it had very little influence in the subsoil (30 cm and deeper). In contrast, wheel load had a very large influence on subsoil stresses. The results demonstrate that stress in the topsoil is not simply a function of tyre inflation pressure and that stress in the subsoil is not simply a function of wheel load. Soil stress is always a function of the stress at the tyre–soil interface, which is a function of both tyre inflation pressure and wheel load, as well as tyre properties and soil conditions. Simulated stresses agreed reasonably well with measured values in relative terms. However, the effect of inflation pressure on subsoil stresses was overestimated by the model. The results show that in order to reduce soil stresses exerted by tyres in agriculture, there is a need to further study the distribution of stresses under tyres. For calculation of subsoil stresses, further validations of commonly used models for stress propagation are needed. References Alakukku, L., Ahokas, J., Ristolainen, A., 2002. Response of clay soil macroporosity to stress caused by tracked tractors. In: Pagliai, M., Jones, R. (Eds.), Sustainable and Management—Environmental Protection. Advances in GeoEcology, 35. Catena Verlag, Reiskirchen, pp. 319–330. Arvidsson, J., Ristic, S., 1996. Soil stress and compaction effects for four tractor tyres. J. Terramech. 33 (5), 223–232.
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