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Soil mechanical stresses in high wheel load agricultural field traffic: a case study.


Soil compaction is an increasing threat to soil functions in modem agriculture (e.g. Hamza and Anderson 2005). Recent decades have experienced a marked increase in wheel loads (WLs; Vermeulen et al. 2013). In addition, the size of tyres has increased considerably, with the net effect being a significant increase in the stresses the soil profile is subjected to (Schjonning et al. 20156). Plastic deformation of subsoils has been proven to persist over the long term, if not permanently (e.g. Berisso et al. 2012; 2013a). Engineering solutions in terms of subsoil loosening have been disappointing (Soane et al. 1987; Munkholm et al. 2005). Subsoil compaction is a hidden damage but threatens important soil ecosystem services, including crop yields and soil functions that, in turn, can affect the environment. In the scientific literature there is an increasing focus on so-called 'non-use values' or 'bequest values' (e.g. de Groot et al. 2010), which include ecosystem services that we may still not be aware of but may turn out to be affected by compaction. Thus, the persistent nature of subsoil compaction requires urgent consideration in terms of precautionary measures and quantification of the threat that we are facing (Schjonning et al. 2015b).

Measurements of soil stresses in undisturbed soil are problematic and very time consuming. Most often, only the vertical stress or the mean normal stress components are available (Keller et al. 2016). However, it is evident that soil deformation is determined by the total stress field (Horn et al. 1989) and that deviatoric stresses may contribute considerably to soil damage (e.g. Berisso et al. 2013b). Hence, our knowledge of stresses exerted on the soil, especially on undisturbed subsoil, is limited, although some studies do exist. For example, Dexter et al. (1988) reported stress in an undisturbed sandy loam soil, but only to a depth of 0.5 m. In that study, the WLs tested were in the range 11-38 kN, with inflation pressures (IPs) ranging from approximately 100 to 280 kPa. In other studies, Horn et al. (1989) performed stress measurements below a tractor with a WL of 40.5 kN and an IP of 140 kPa to a maximum depth of 0.35 m, and Harris and Bakker (1994) reported stresses ranging from 150 to 220 kPa measured at 0.15, 0.25 and 0.3 m depths below various agricultural machinery, with unspecified WLs and IPs. More recently, Seehusen et al. (2014) measured stresses down to 0.6 m depth below two slurry spreaders in Norway. However, the most comprehensive dataset with stress measurements in the subsoil was assembled by Keller et al. (2012). Vertical stress was measured at 0.3, 0.5 and 0.7 m depths for a range of soil types in Sweden and Denmark (clay content 0.18-0.67 kg [kg.sup.-1]) and the wheeling tests included WLs ranging from 17 to 82 kN, but the majority of data were for loads <45 kN. IPs ranged from 50 to 250 kPa and all tests were performed at a water content close to field capacity. Under these conditions, vertical stresses ranged up to ~350 kPa (Keller et al. 2012). Lamande and Schjonning (2011a, 20116) investigated vertical stress in a silty clay loam soil at field capacity water conditions and at 0.3, 0.6 and 0.9 m depths, testing WLs of approximately 30 and 60 kN, and found vertical stress up to -330 kPa.

Much field traffic in modern agriculture can apply WLs up to 120 kN at field capacity water conditions or even wetter (e.g. VDI 2007; Vermeulen et al. 2013). The aim of the present study was to increase our knowledge of the level of vertical stress from agricultural vehicles at high WLs. To that end, we tested a tractor-trailer combination for slurry application typically used in Danish agriculture. Our investigation should be seen as a case study, where we modified the trailer to induce WLs as high as approximately 70 kN. In addition to quantification of stress levels to a depth of 0.9 m, we aimed to identify the loading characteristics that contributed to the stresses observed.

Materials and methods


A sandy loam soil at Flakkebjerg, Denmark (55[degrees]19'42"N, 11[degrees]24'28"E; 33 m) was selected for experimental traffic. The soil is a Luvisol derived from glacial tills of the Weichsel glacial period. The textural composition of the topsoil includes clay (<2 [micro]m; ~14%), silt (2-20 [micro]m; ~13%), fine sand (20-200 [micro]m; ~41%) and coarse sand (0.2-2 mm; ~32%) fractions. The soil was ploughed annually to a depth of 0.25 m and grown with small-grain cereals. The experimental tests took place in the spring following autumn ploughing but before secondary tillage. More details regarding the soil have been reported elsewhere (Schjonning et al. 2011, 2016, 2017; Obour et al. 2017).

Experimental traffic

A tractor-trailer combination for slurry application was used as the experimental traffic. The total weight of the machinery was -52 Mg, which included a fully loaded slurry tank. The trailer was equipped with three axles. During the experimental tests, the front trailer axle was lifted hydraulically, which resulted in WLs of approximately 70 kN for the tractor rear axle and approximately 68 kN for the middle and rearmost axles of the trailer. The wheels of the front trailer axle carried a minor load. The WLs were recorded on a weighbridge. The tractor front wheel tyres and all tyres on the trailer were generally inflated to much higher pressures than those recommended by the manufacturers (Table 1). This reflects our strategy that the study should provide information on the actual practice in modern day farming; the contractor delivering the machinery for our tests was asked not to change the IPs used when trafficking nearby farmers' fields. The reason for the use of high IPs in practical agriculture is the need to travel public roads at higher speeds than used in the field. An exception to the generally higher IPs was the tyres on the rear tractor axle, in which the IP was slightly lower than recommended for the load. Experimental traffic was applied to the field in spring 2010 at a water content close to field capacity. Two replicate tests were performed. More details of the compaction experiment have been reported elsewhere (Schjonning et al. 2016, 2017), with the tests described herein corresponding to Treatment M8 in the previous publications.

Vertical stress near the tyre-soil interface

Seventeen stress transducers glued in a line onto a 6-mm thick rubber strip were placed at a depth of 0.1 m across the driving direction and covered by rotovated soil. Cylindrical steel transducer housings were located in a row, 0.06 m from centre to centre. The signals from load cells (DS Europe Series 302; DS Europe, Milan, Italy) activated by a piston in the centre of the transducer housings were monitored at a high frequency by a computer that simultaneously recorded the position of the wheel using a laser sensor. The combination of detailed data from the laser sensor and the load cells enabled detection of the periphery, and hence the area of contact between the tyre and soil. Two replicate measurements were performed. More details regarding the test procedure are available elsewhere (Schjonning et al. 2006, 2008; Lamande et al. 2015).

Vertical stress in the soil profile

Vertical stresses were measured in two dimensions (for the depth below the centre of the tyres and in the driving direction) in the soil profile during passage of the machinery (combined with the measurements of the tyre-soil interface stresses described above). Stress transducers were inserted horizontally from a pit at three depths (0.3, 0.6 and 0.9 m) at a distance of 1 m from the pit (Fig. 1). Horizontal holes (54 mm diameter) were bored using a hydraulic jack. The transducers were constructed as cylindrical metal housings (52 mm diameter, 80 mm length), each encasing a load cell (DS Europe Series 302; DS Europe). A wedge system integrated in the transducers enabled good contact between the soil and load cell. As for the surface stresses, two replicate measurements were made. Details regarding the transducers, their calibration and the insertion and measurement procedures have been reported elsewhere (Lamande et al. 2007, 2015; Lamande and Schjonning 2011a).

Modelling of stresses

The distribution of vertical stress in the tyre-soil contact area can be estimated from the loading characteristics (Schjonning et al. 2015a). We used tyre dimensions, the IP characteristics and WLs to perform these calculations for each tyre on the tractor-trailer system. The stress distribution in the contact area was then used as an input in the analytical Sohne (1953) model for stress transmission in the soil profile, as described by Keller and Arvidsson (2004). In the present study, we used a concentration factor of v = 5, which is often used for moist soil at field capacity (e.g. Keller and Arvidsson 2004).

Statistical analysis

Simple linear regression was used to relate measured mechanical stresses to loading characteristics (PROC REG model in SAS version 9.3; SAS Institute, Cary, NC, USA).

Results and discussion

Vertical stress near the tyre-soil interface

The contact area between tyre and soil increased with tyre volume (Table 1). For tyres with comparable volumes, the contact area was smallest for high ratios of actual to load-recommended IP (front wheel of the slurry spreader vs the middle and rear wheels). These observations are in line with those reported previously (Schjonning et al. 2008, 2015a). The maximum stresses at the tyre-soil interface ([[sigma].sub.max-surface]) for the slurry spreader wheels and the rear tractor wheel were approximately 60-90 kPa higher than the IP, which is in close agreement with previous observations (Keller 2005; Lamande and Schjonning 2008). We note that the trailer wheels exerted maximum contact stresses as high as ~340 kPa.

An example of the stress distribution in the contact area is shown in Fig. 2. The maximum measured stress was generally much higher than the mean ground pressure (MGP), which indicates a highly uneven stress distribution at the tyre-soil interface (Fig. 3). This is in line with previous observations for loosened soils (Burt et al. 1992; Filipovic et al. 2016) and undisturbed soils (e.g. Gysi et al. 2001; Keller 2005; Lamande and Schjonning 2008). In addition, omax_surfacc was linearly related to MGP (Fig. 3). However, the front trailer tyre deviated from this relationship to some degree. This probably relates to the fact that the wheel carried only 27.3 kN, but at an IP approximately 4.7-fold higher the recommended IP (Table 1). Under such conditions, the tyre loses its flexibility and acts more like a rigid drum than an elastic tube (Schjonning and Lamande 2010). Thus, we excluded the front trailer tyre from regression analyses of the two loading characteristics. The slope of this relationship, 2.44 (Fig. 3), was smaller than the 3.29 reported by Lamande and Schjonning (2008) for a range of tyres, WLs and IPs. However, the results of the present study support the above observation that the maximum stresses in the contact area between the tyre and soil cannot be estimated as a factor 1.5-fold the MGP as suggested by Rusanov (1994).

Vertical stress in the soil profile

Vertical stresses measured at three depths for one of the replicate measurements are shown in Fig. 4. For each wheel, the mean maximum vertical stress ([[sigma].sub.max-soil]) of both replicates is given in Table 1, together with the distance of the two individual recorded values from the mean. The front wheel of the trailer was raised but still had contact with the soil surface, as shown by the stress measurements for both installations. At all depths, comparable levels of stress were recorded below the rear wheel of the tractor and the middle and rear wheels of the slurry spreader. Stresses below the tractor rear tyre may have been expected to be lower than for the middle and rear tyres of the slurry spreader because of a lower IP and a higher contact area, but they were all loaded with approximately 70 kN.

Regression analyses that included data from all five tyres indicated that the WL effect was significant for all depths and explained 94-99% of the variation in the maximum stress data (Fig. 5), at 0.3, 0.6, and 0.9 m depths ([[sigma].sub.0.3], [[sigma].sub.0.6] and [[sigma].sub.0.9] respectively):

[[sigma].sub.0.3](kPa) = 95.8 * + 2.88 ** x WL(kN), [R.sup.2] = 0.94, s = 17.9 (1)

[[sigma].sub.0.6] (kPa) = -[10.6.sup.ns] + 3.46 *** x WL(kN), [R.sup.2] = 0.99, s = 3.11 (2)

[[sigma].sub.0.9](kPa) = -[3.51.sup.ns] + 0.71 *** x WL(kN), [R.sup.2] = 0.98, s = 2.64 (3)

where 5 is the s.d. of the estimate and asterisks indicate the level of significance of the coefficients (*** P<0.001, ** P<0.01, * P<0.05). Care should be taken when interpreting results from regression analyses in which the distribution of the independent variable is uneven. In this case, the WL tends to group at two levels: approximately 20-27 kN and 67-70 kN (Fig. 5). However, for the 0.6 and 0.9 m depths, all data points fit nicely with the trend line and thus support the regression as a reliable estimate of the relationship between the loading conditions (tyres and soil) in the present study. Neither tyre IP nor MGP turned out to be significant in such simple tests of drivers of soil stresses observed (data not shown). The lack of a correlation with IPs may have been due to the generally high ratios of actual to recommended IPs (Table 1). However, from previous studies, we know that IP (expressed as the ratio of actual to load-recommended pressures) also affects tyre behaviour and stress distribution at ratios well above unity (Schjonning et al. 2015a). Keller and Arvidsson (2004) found that decreasing IPs for a specific tyre when carrying the same load affected vertical stress measured at 0.3 m, but not at 0.5 and 0.7 m depths. In a previous study, we observed that doubling the contact area for a given load affected stresses and strains in the upper soil horizons, but not deeper in the subsoil (Lamande et al. 2007). Keller and Arvidsson (2004) emphasised the importance in distinguishing between load per se and the combination of contact area and stresses acting in that contact area. They pointed out the benefit of distributing the load to a larger contact area by, for example, using dual wheels. However, for commonly used tyres that are used singly, the results of the present study indicate that the WL is the main driver for the level of stress in the subsoil. This is in accordance with findings of previous studies (e.g. Dexter et al. 1988; Lamande and Schjonning 2011 6).

We note that the intercept term in Eqns 2 and 3 is not significantly different from zero. If forcing the regression through origin, the coefficient for the WL regressor for 0.9 m depth is 0.65 (data not shown). This means that at a depth of 0.9 m, the vertical stress will increase by 0.65 kPa for each 1-kN increase in WL (corresponding to ~6.6 kPa for each additional 1 Mg put on the wheel). This is in close accordance with model estimates for tyres mounted on combine harvesters in the period 1960-2010 (Schjonning et al. 20156).

Modelling vertical stress in the soil profile

The Boussinesq (1885) model for stress transmission assumes fully elastic properties of the material addressed. The wellknown Sohne (1953) model for stress transmission in soil is often used to predict stresses in the soil profile. The so-called concentration factor, v, accounts for empirical observations that stress penetration in depth is more pronounced than expected from the Boussinesq (1885) model. Fig. 6 shows measured [[sigma].sub.max-soil] in relation to the Sohne-predicted vertical stress, assuming v = 5 in the calculations. Model predictions are fairly close to the measured values for the 0.6 and 0.9 m depths (Fig. 5). In contrast, at a depth of 0.3 m, the Sohne model underpredicts the stress below all wheels. This has been observed before (e.g. Blackwell and Soane 1978; Dexter et al. 1988; Richards et al. 1997; Lamande and Scanning 201 la, 201 lb). The deviation may relate to the structural conditions of the plough layer. A tilled soil typically exhibits a hierarchical structure of aggregates, the strength of which is size dependent (Dexter 1988; Schjonning et al. 2012a). Naveed et al. (2016) showed that for such soil structures, discrete stress transmission patterns were observed at moderate stress levels, whereas continuum-like (elastic) stress transmission prevailed when the hierarchical levels had, most likely, been destroyed at 620 kPa vertical stress.

Soil stress and strength

In a previous study, we reported soil precompression stress ([[sigma].sub.pc]) for the Flakkebjerg soil (Schjonning et al. 2016). At a matric potential of -100 hPa, corresponding to field capacity (at which the compaction tests were performed), soil at 0.3, 0.5 and 0.8 m depths had [[sigma].sub.pc] values of 44, 58 and 81kPa respectively. Theoretically, soil will deform elastically up to stresses comparable to [[sigma].sub.pc], and plastically for higher stresses (e.g. Lebert and Horn 1991). Based on this concept, we should expect compaction effects at least to a depth of 0.6 m (compare the abovementioned [[sigma].sub.pc]-values with maximum stresses in Table 1). Significant compaction effects on pore volumes and air permeability to a depth of 0.7 m have actually been reported for exactly the experimental traffic tested herein (Obour et al. 2017, fig. 1). Similarly, we observed a considerable increase in cone penetration resistance to 0.7 m, statistically significant to 0.45 m (Schjonning et al. 2016, fig. 3b). Keller et al. (2012) found a vertical stress of -40 kPa to be critical for plastic deformation of subsoil across a range of different soils loaded at field capacity. This is less than but of the same magnitude as the abovementioned [[sigma].sub.pc] values monitored at the Flakkebjerg soil.

As noted, the present study did not find a significant correlation between IP and soil stresses, although such a relationship has been observed previously (e.g. Keller and Arvidsson 2004). The so-called 8-8 rule combines the IP and WL in predictions of the depth of 50-kPa vertical stress ([d.sub.50]) in the soil profile (Schjonning et al. 2012b). Fig. 7 confirms the validity of this rule of thumb for estimating [d.sub.50]:

[d.sub.50](cm) = 30 + 8 x WL + 8 x [log.sub.2](IP) (4)

where WL is wheel load in Mg and IP is inflation pressure in bar. The [d.sub.50] seems a relevant approximate measure in risk assessment of soil compaction because our data, in accordance with Keller et al. (2012), indicate approximately 50 kPa to be a critical threshold of vertical stress for soil at field capacity.

Schjonning et al. (20156) evaluated the potential of increasing the size of single tyres in order to increase the contact area and decrease contact stresses to levels yielding [d.sub.50] < 50 cm when carrying high loads. Their exercise indicated that a contact area as large as approximately 1.8 [m.sup.2] would be required to carry the approximately 70 kN load tested in the present study. This is more than double the contact area observed for the large rear tractor tyre (Table 1). If sticking to the loads used in practical agriculture today, our results urgently call for the distribution of loads across larger contact areas by means of tracks or dual or tandem wheels.


The results of the present study demonstrate that wheel loads around 70 kN applied to soil at field capacity water may induce vertical stresses of around 300, 100 and 45kPa at soil depths of 0.3, 0.6 and 0.9 m respectively. Maximum stresses in the tyre-soil contact area were as high as approximately 345 kPa.

At all subsoil depths, the stresses were correlated with the WL. For similar conditions as in the present study, the vertical stress at 0.9 m may be expected to increase linearly with the WL, adding approximately 6.6 kPa for each additional 1 Mg on the wheel.

The results of the present study confirmed the simple rule of thumb for the prediction of [d.sub.50] vertical stress from the WL and IP.

Previously published results have shown that the stresses quantified in the present study induced significant, plastic deformation of soil to depths of at least 0.7 m.

Conflicts of interest

The authors declare no conflicts of interest. Acknowledgements

The authors thank Feto E. Berisso and Stig T. Rasmussen for assistance with the field measurements of soil stress. The experimental work was supported financially by Promilleafgiftsfonden and Landdistriktsmidlerne, whereas interpretation of the data and the creation of this paper were funded, in part, by the Danish Council for Independent Research | Technology and Production Sciences via the StressSoil project (Contract no. 11-106471) and, in part, by the Ministry of Environment and Food of Denmark via the COMMIT project (GUDP Grant no. 34009-16-1086).


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Mathieu Lamande (A), and Per Schjonning (A,B)

(A) Aarhus University, Department of Agroecology, Research Centre Foulum, Blichers Alle 20, PO Box 50, DK-8830 Tjele, Denmark.

(B) Corresponding author. Email:

Received 25 April 2017, accepted 26 July 2017, published online 12 September 2017

Caption: Fig. 1. Instrumentation for measuring the stress distribution in the tyre-soil contact area and vertical stress at depths of 0.3, 0.6 and 0.9 m. Note that the first trailer wheels are hydraulically lifted, hence loading the soil less than the other wheels (cf. Fig. 4). Driving speed during measurements was approximately 0.5 [ms.sup.-1]. Photograph taken by Janne Aalborg Nielsen.

Caption: Fig. 2. Example of the measured distribution of vertical stress in the tyre-soil contact area for the rear trailer axle in one of the plots. Distance across the tyre is given relative to the middle of the tyre. Distance in driving direction is relative to the axle of the tractor front tyre (see Fig. 4). Note that stress transducers are situated below a 10-cm layer of loose soil as part of the measuring procedure.

Caption: Fig. 3. Measured maximum stress at the tyre-soil interface ([[sigma].sub.max-surface]) plotted against mean ground pressure (MGP) averaged for the five wheels. Data show the mean across the two replicate tests. Note that stress transducers are situated below a 10-cm layer of loose soil as part of the measuring procedure.

Caption: Fig. 4. Vertical soil stresses at three soil depths (0.3, 0.6 and 0.9 m) during passage of the machinery in one of the plots. The abscissa gives distance in m from the front axle of the tractor and hence provides the laser sensor-derived true distance between wheels.

Caption: Fig. 5. Measured maximum vertical stress ([[sigma].sub.max-soil]) at three soil depths (0.3 m, open symbols; 0.6 m, light grey shading; 0.9 m, dark grey shading) as related to the wheel loads. Data are mean values across the two replicate tests. Lines indicate simple linear regression.

Caption: Fig. 6. Model-calculated (Sohne) and measured vertical stress ([[sigma].sub.max-soil]) for all combinations of wheels and soil depths (0.3 m, open symbols; 0.6 m, light grey shading; 0.9 m, dark grey shading).

Caption: Fig. 7. Depth of 50kPa vertical stress ([d.sub.50]) predicted using the rule of thumb given in Eqn 4 plotted against measured (interpolated) values of soil depths experiencing 50kPa stress. The line gives the 1:1 relationship.
Table 1. Characteristics of the machine used for experimental traffic

Mean tyre-soil contact area, maximum vertical stresses at the
tyre-soil interface ([[sigma].sub.max-surface]) and maximum
vertical stresses ([[sigma].sub.max-soil]) at three depths
below the wheels for each axle are shown. Figures in parentheses
are the distance to the mean (n = 2). Mean ground pressure is
the ratio of the wheel load to contact area


                                   Front         Rear          Front

Technical name of tyre           600/70R30     650/85R38     710/55R34
Tyre width (m)                      0.6          0.692         0.71
Tyre diameter (m)                  1.585         2.05          1.645
Tyre volume ([m.sup.3])            0.63          1.23          0.75
Actual inflation pressure           170           170           280
Load-rated inflation                60            192           60
  pressure (kPa)
Wheel load (kN)                    19.9          70.5          27.3
Tyre-soil contact area          0.35 (0.01)   0.81 (0.05)   0.30 (0.03)
Mean ground pressure (kPa)         57(1)        87 (5)        92 (11)
[[sigma].sub.max-surface]        200 (14)       262 (6)       344 (4)
[[sigma].sub.max-soil] (kPa)
  0.3 m                          173 (43)      298 (40)      151 (39)
  0.6 m                            19(4)       106 (36)       37 (22)
  0.9 m                            8 (2)        45 (1)         19(4)

                                Slurry spreader

                                  Middle         Rear

Technical name of tyre           710/55R34     710/55R34
Tyre width (m)                     0.71          0.71
Tyre diameter (m)                  1.645         1.645
Tyre volume ([m.sup.3])            0.75          0.75
Actual inflation pressure           280           280
Load-rated inflation                151           151
  pressure (kPa)
Wheel load (kN)                    67.8          67.8
Tyre-soil contact area          0.60 (0.04)   0.57 (0.01)
Mean ground pressure (kPa)        114 (8)       118 (3)
[[sigma].sub.max-surface]         338 (6)      346 (35)
[[sigma].sub.max-soil] (kPa)
  0.3 m                          294 (30)      293 (42)
  0.6 m                           97 (47)       99 (46)
  0.9 m                           46 (4)        45 (2)
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Author:Lamande, Mathieu; Schjonning, Per
Publication:Soil Research
Geographic Code:4EUDE
Date:Mar 1, 2018
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