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Changes in soil stress during repeated wheeling: A comparison of measured and simulated values.


Soil compaction is generally defined as a reduction in soil total porosity and, conversely, an increase in bulk density. It can occur as a result of natural processes, but the main concern in modern agriculture is field-traffic-induced soil compaction. This not only decreases total porosity, but also negatively alters vital soil production functions (e.g. root growth and plant development, with an associated reduction in crop yield) and is regarded as one of the greatest current threats to soil fertility (Batey 2009). The weight of modern agricultural machines tends to exceed the bearing capacity of most soils and thus field traffic is a major factor in land degradation by soil compaction (Hamza and Anderson 2005; Peth and Horn 2006). The soil surface is subjected to several passes by machinery tyres during a season or year and the stress applied on the surface propagates through the soil profile. The degree of soil deformation or compaction induced may vary from soil to soil depending on the soil conditions (soil strength) and the specifications of the traction device (e.g. tyre vs track, tyre or track size and type, tyre inflation pressure and wheel load), the loading time (i.e. travel speed) and the frequency of wheeling (i.e. the number of passes).

Although soil compaction is a relatively well studied topic, there are still gaps in the current understanding of the soil compaction process, for example, regarding the impacts of soil strength and loading time on stress transmission and soil stress changes during repeated loading (Keller and Lamande 2010). Moreover, the literature is not unanimous on how soil mechanical characteristics (which in turn are affected by soil water content and bulk density) affect stress transmission. Boussinesq's theory (Boussinesq 1885) on stress transmission in elastic media implies that the vertical stress is not affected by mechanical properties of the material (e.g. soil), but that other stress components are a function of material properties (e.g. Poisson ratio) (see also Keller e? al. 2016). However, the general concept based on the modified elasticity model (Frohlich 1934) is that the vertical stress is also a function of material properties (i.e. the concentration factor in the Frohlich model). It has been widely reported that the vertical stresses are more concentrated under the centre of the soil-tyre interface in wet soil (with lower soil strength) than in dry soil, resulting in deeper propagation of stresses in wet soil than in dry soil, and thus that vertical stresses decrease more rapidly with depth in dry soil (Sohne 1953; Hakansson 2005; Lamande and Schjonning 2011). However, Arvidsson et al. (2001) showed that vertical stresses and resulting compaction effects in the subsoil at depths >0.5 m were often greater in dry soil than in wet soil.

Loading time, which is directly related to vehicle travel speed, is not expected to considerably changc the stress as long as the loading rate is much smaller than the velocity of stress propagation in unsaturated soil (i.e. 10-12 m [s.sup.-1]) (Koolen and Kuipers 1983). However, the resulting soil deformation depends strongly on the loading time (Koolen and Kuipers 1983). The amount of energy dissipated by viscous flow of soil, resulting in permanent deformation during transient loading, is determined by the loading time (Or and Ghezzehei 2002). Karczewski (1978) and Horn et al. (1989) reported an inverse influence of soil deformation speed on subsoil stress (at 0.35 m depth), i.e. the higher the deformation speed, the lower the subsoil stress. It has been argued that faster passage of a tyre on a soil surface causes less intensive stress propagation in subsoil, i.e. the shorter period of stress application at faster speeds gives a smaller time for subsoil to experience the maximum stress (Horn et al. 1989; Pytka 2012). The action of a suddenly applied stress is not transmitted at once to all parts of the soil sample (Koolen and Kuipers 1983). However, a different effect has been found for the topsoil (at 0.2 m), with Horn et al. (1989) reporting that the total vertical stress increases with travel speed, in particular for soil at high water content. This can be explained by excessive pore water pressure caused by high deformation rate of topsoil (Horn et al. 1989).

Several studies have investigated the effect of repeated wheeling on soil stress (e.g. Horn et al. 1994; Riggert et al. 2016), soil stress and strain (e.g. Wiermann et al. 1999; Horn et al. 2003; Pytka 2005) and changes in soil macro properties including bulk density, hydraulic conductivity and cone index (e.g. Botta et al. 2009). Repeated short-term stress application (e.g. passage of several wheels after each other) results in an increase in degree of saturation and therefore an increase in matric potential, resulting in strain softening (i.e. the soil becomes weaker due to deformation) (e.g. Richards et al. 1997; Huang et al. 2012). In a study involving 50 consecutive wheeling events with a 3.7 Mg tractor, Semmel (1993) found that strain softening due to repeated wheeling decreased the minor principal stress and increased the major principal (i.e. vertical) stress. Lipiec et al. (1992) found the vertical deformation of a silty loam soil at two water contents to be a linear function of the logarithm of the number of wheel passes, with a steeper slope for the wetter soil.

Wheeling experiments by Wiermann et al. (1999) in a soil bin (with a Norfolk sandy loam soil) with two wheel passes showed significantly higher stresses (in particular the major principal stress) for the second pass compared with the first pass. This can be explained by the smaller tyre footprint area for the second pass, where the wheel travelled on a more rigid soil surface (Way et al. 1995), and better contact between stress transducer and compacted soil for the second pass (see also Horn et al. 1996). In a soil bin study with a dry Hiwassee clay, Horn et al. (2003) found that the major principal stress and the octahedral stresses (both measured at 0.15 m depth) increased with increasing number of wheel passes, while the mean normal stress ([[sigma].sub.m]) remained almost the same. Pytka (2005) showed a considerable increase in stress and rut depth during the first two passes of a tractor, with the increase in soil stress being higher for a sandy soil than for a loess soil.

The aim of the present study was to evaluate the change in [[sigma].sub.m] in the soil profile during repeated passes of a two-wheel-drive (2WD) tractor. Repeated wheeling was conducted at two soil water contents, two travel speeds and two rear wheel loads of the tractor. The hypotheses tested were that (i) the change in measured stress as a function of number of wheel passes is mainly the result of a reduction in the distance between probe and soil surface due to increasing rut depth with repeated wheel passes, and (ii) the increase in rut depth, soil bulk density and cone index is smaller at higher vehicle speed and lower wheel load.

Materials and methods

Study site and soil

Field measurements were carried out in autumn 2016 in a field in Ghahderijan, Isfahan province, Iran (32[degrees]34'N, 51[degrees]26'E, 1615m above sea level). Mean annual temperature at the site is 15.6[degrees]C and mean annual precipitation is 125 mm. The soil (fine-clay, mixed, thermic Typic Haplargid) is formed from alluvial sediments of the Zayandehroud river and is low in organic matter (OM content <0.5%). The site has a history of intensive conventional tillage (Mosaddeghi et al. 2000). The textural composition of the soil was analysed before the experiments (Table 1). Soil particle size distribution was analysed using the pipette method and OM concentration was calculated from the loss on ignition (Schulte and Hopkins 1996). The plastic limit (PL) was determined according to the Casagrande PL test, i.e. as the gravimetric water content at which a rolled thread of freshly moulded soil with a diameter of 3 mm just begins to crack (British Standard 1377, 1975). The liquid limit (LL) was estimated using the traditional Casagrande LL apparatus (ASTM Standard D4318, 2012). A standard Proctor test (ASTM Standard D698, 2012) was performed on disturbed soil from the field collected from 0-0.35 m depth. The disturbed soil was sieved at 8 mm and dried at 105[degrees]C for 48 h to ensure zero water content. Samples with different water contents were prepared by spraying a calculated mass of water onto the soil and gently mixing to achieve a uniform water distribution. The samples were then tightly covered with plastic sheeting and stored in a cool room for 24 h to allow for water redistribution and ensure uniform water content. The Proctor test was carried out using a hand compaction device (mould volume 942 [cm.sup.3], mould inner diameter 105 mm, hammer weight 24.5 N, falling height 305 mm, with 25 blows on each layer) with a compaction energy of 0.6 MJ [m.sup.-3].

Wheeling experiments

The field was mouldboard-ploughed to 0.4 m depth, followed by disc harrowing (to 0.2 m depth) in autumn 2016 (two months before the experiment). The field was subdivided into two subplots (each 32 m wide and 40 m long) and irrigated three times with subsequent natural drying cycles. This allowed for sufficient settling of the freshly ploughed soil and an associated increase in soil strength. The two subplots were then prepared at two different water contents. This was achieved by drying for different periods of time after the last irrigation. The average water content (WC) of the tilled layer (0-0.4 m) was 0.18 g [g.sup.-1] (corresponding to WC = 0.9 PL, where PL is the water content at the plastic limit) and 0.25 g [g.sup.-1] (i.e. 1.35 PL), hereafter called "dry soil" and "wet soil" respectively. Table 2 shows the water content and bulk density profiles of the two water content conditions.

Wheeling experiments were carried out with a MF285-2WD tractor (Table 3). In each soil condition (dry and wet), experiments were performed for two travel speeds (0.5 and 1 m [s.sup.-1]) combined with two rear axle loads (17 and 26 kN, hereafter referred to as "light" and "heavy") (Table 3). Each combination comprised eight repeated passes (all in the same track) with the tractor. The four combinations (travel speed x wheel load) within each soil condition were carried out in different tracks (i.e. in unwheeled tracks).

For the heavy rear wheel, a mouldboard plough was mounted on the tractor's three-point hitch and bags of sand were put on the plough frame. The plough was lifted to the highest possible height to cause the maximum weight transfer from the front axle. As shown in Table 3, this resulted in rear axle loads of 26.1 and 17.2 kN for the heavy and light rear axles respectively. The soil-tyre contact area was measured only in dry soil by spreading chalk powder around the contact area and then measuring the large and small diameter of the footprint oval (Table 3). The calculated mean ground pressure of the front and rear wheels was not significantly different for the heavy and light rear axle configurations, because of the larger contact area for the heavier wheel (Table 3).

During each pass, soil [[sigma].sub.m] was measured at 0.15, 0.25 and 0.35 m depth using Boiling probes. After each pass, the rut depth was measured by a calliper and an indicator ruler from the initial soil surface. An average of five rut depth measurements was recorded for each pass. Cone index was measured using a hand-pushed non-commercial penetrometer inserted to a depth of 0.45 m, with three random insertions on the track after each pass. After the eight passes, core samples (100 mm diameter, 60 mm height) were taken from the compacted track at 0.15, 0.25 and 0.35 m depth (i.e. at the same depths at which the Boiling probes were installed) to determine the total change in bulk density. Additional core samples were taken from undisturbed (i.e. unwheeled) areas in both the wet and dry soil for soil mechanical laboratory tests and determination of the Poisson ratio.

Stress measurements

Stress measurements were made at 0.15, 0.25 and 0.35 m depth using cylindrical Boiling probes (Boiling 1987; Berli et al. 2006). The Boiling probe has a rubber membrane head (10 mm inner diameter, 150 mm length) connected to a pressure gauge (600 kPa, ECT 8472, Trafag Co., Switzerland) through a 1500 mm PVC tube. The probe is filled with an incompressible fluid (e.g. water) and measures [[sigma].sub.m] around the rubber head. An advantage of the Boiling probe in comparison with stress-state transducers is the easier installation with minimal soil disturbance and the good contact achieved between the probe head and surrounding soil by applying an inclusion pressure (Keller et al. 2016). The probes were installed by drilling holes at predetermined angles using a frame designed for this purpose. The centre of the probe heads was located beneath the centre of the track (see Fig. 1 for a schematic diagram of the field measurement set-up). In order to ensure good contact between the probe and the surrounding soil, an initial inclusion pressure of 125 kPa was applied (Keller et al. 2016). The pressure gauges of the probes were connected to a data logger for data collection at a 500 Hz sampling rate.

The inclusion pressure of the Boiling probe (Pi) is proportional to [[sigma].sub.m] in the surrounding soil. The proportionality coefficient ([k.sub.s]; Eqn 1) has been experimentally derived (Boiling 1987) and analytically related to the soil's Poisson ratio such that [k.sub.s] is primarily a function of the soil's Poisson ratio, v (Berli et al. 2006):

[[sigma].sub.m] = [k.sub.s][P.sub.i] = [[1 + [upsilon]]/3(1 - [upsilon]] [P.sub.i] (1)

The Poisson ratio of the experimental soils was determined according to Eggers et al. (2006) from confined and unconfined uniaxial compression tests on undisturbed samples taken from each water content condition. For the confined compression tests, the samples were subjected to stepwise increasing stress from 10 to 200 kPa, unloaded, and reloaded to 250 kPa in six steps. Axial strain was obtained by dividing the deformation measured at the end of each load step by the sample initial height. For the unconfined tests, the soil specimen was cut on the inner wall of the cylinder and carefully removed with a Teflon piston. Stresses were applied stepwise up to 50kPa (in four steps) to ensure that the maximum stress was within the elastic range (i.e. below the precomprcssion stress determined from the confined uniaxial tests). The samples were then unloaded and stepwise reloaded to 80kPa (see also Naderi-Boldaji et al. 2014). The slope of the unloading path in unconfined test was used as an estimation of Young's modulus (E). Poisson ratio was calculated from E and the slope of unloading path of the confined test (Eggers et al. 2006).

Stress simulations

The stress beneath the heavy rear wheel was simulated using the semi-empirical model SoilFlex (Keller et al. 2007). The model is based on the classical solution of Boussinesq (1885) with pure elastic (i.e. a concentration factor of 3) and incompressible (i.e. a Poisson ratio of 0.5) assumptions for soil mechanical behaviour. The soil-tyre contact area was divided into i small elements, [A.sub.i], each carrying an incremental load depending on the stress applied on the element, [P.sub.i] = [A.sub.i] [[sigma].sub.i], which was treated as a point load. The normal stress components at a given point at depth z were then expressed as:

[[sigma].sub.z] = [i=n.summation over (i=0)] [3[P.sub.i]/2[pi][r.sup.2.sub.i]] [cos.sup.3][[theta].sub.i] (2)

[[sigma].sub.x] = [i=n.summation over (i=0)] [3[P.sub.i]/2[pi][r.sup.2.sub.i]] cos [[theta].sub.i][sin.sup.2][[theta].sub.i][cos.sup.2][[delta].sub.i] (3)

[[sigma].sub.y] = [i=n.summation over (i=0)] [3[P.sub.i]/2[pi][r.sup.2.sub.i]] cos [[theta].sub.i][sin.sup.2][[theta].sub.i][cos.sup.2][[delta].sub.i] (4)

where r is the distance from the point load to the desired point, [theta] is the angle between the normal load vector and the position vector from the point load to the desired point, and [delta] is the angle between the x-axis and the vertical plane that contains the position vector to the desired point. It should be noted that the horizontal stresses at the soil-tyre contact area were neglected in our stress simulations, because no drawbar pull was applied on the tractor during the tests (i.e. the shear stress at the soil-tyre interface was negligible). The mean normal stress is:

[[sigma].sub.m] = 1/3 ([[sigma].sub.x] + [[sigma].sub.y] + [[sigma].sub.z]) (5)

The boundary condition at the soil-tyre contact (i.e. the shape of the contact area and respective normal stress distribution) was assumed to be elliptical with a parabolic stress distribution.

Data analysis

The variations in rut depth were evaluated with linear regressions against the number of passes. Cone index was compared before and after eight repeated passes for wet and dry soil conditions. The stress average of the eight passes was used in comparisons of the combinations of soil water content, axle load and travel speed at 0.15, 0.25 and 0.35 m depth.

Results and discussion

Soil characterisation

The plastic and liquid limits, Proctor test results and mechanical properties of the experimental soil are shown in Table 4. The wet soil resulted in smaller Young's modulus (E) and Poisson ratio (v). A minor difference in v was found between the two soil conditions, resulting in a difference of 0.06 in the stress conversion factor ([k.sub.s]). Decreasing v with increasing soil water content is in agreement with previous findings by Naderi-Boldaji et al. (2014) and Keller et al. (2016).

Rut depth and bulk density

Rut depth as a function of number of passes in the experiments is shown in Fig. 2. Rut depth increased linearly with number of passes, with a larger increase for the wet soil. As explained by Botta et al. (2009), soil deformation under traffic is governed by ground stiffness and tyre stiffness (i.e. the sum of tyre inflation pressure and tyre carcass stiffness pressure, which is approximately the equivalent pressure resulting at zero tyre inflation pressure) (Wong 2008; Misiewicz et al. 2016). If the ground is relatively firm (e.g. for the dry soil), the ground stiffness is larger than the tyre stiffness and the tyre deformation is expected to be larger than the soil deformation. No clear effect of travel speed or rear wheel load was found for the wet soil, but the heavy wheel on the dry soil caused larger rut depths than the light wheel. The first pass of the tractor resulted in similar rut depth in all cases, but the subsequent passes increased the rut depth differently.

The total increase in bulk density at 0.15, 0.25 and 0.35 m depth is shown in Fig. 3. At 0.15 and 0.25 m depth, the dry-heavy combination caused the maximum increase in bulk density, with no effect of travel speed. This can be explained by the water content of the dry soil, which was close to the optimum water content for compaction obtained from the Proctor test. Moreover, the largest stress was measured at 0.15 m depth in the dry soil, which may explain the largest bulk density increase at 0.15 m depth in the dry soil. However, at 0.35 m depth, the maximum increase in bulk density was found for the wet-heavy combination. Travel speed affected the increase in bulk density at 0.35 depth (smaller increase with higher speed). Furthermore, the increase in bulk density at 0.35 m depth was greater for the wet-heavy than the wet-light combination. This suggests a more severe effect of traffic on the subsoil of the wet soil, which is in agreement with findings reported by Botta et al. (2002, 2009) and Arvidsson and Keller (2007). These authors concluded that subsoil compaction due to tractor traffic is basically related to wheel load, independently of tyre ground pressure (i.e. stress obtained as the wheel load divided by the soil-tyre contact area). The mean ground pressure for the light and heavy rear wheels was similar in the present study (Table 3).

The increase in bulk density decreased with depth for the dty soil, but was approximately constant or even slightly increased with depth for the wet soil. This can be related to the stronger attenuation of stress with depth for the dry soil than the wet soil, as discussed later.

Cone index

No significant difference was found between the average initial (i.e. before traffic) cone index of the wet (2.97 MPa) and dry (3.01 MPa) soil within 0-0.45 m depth, although the water content difference was noticeable. Cone index generally increased linearly with the number of passes for all experiments (not shown). The average cone index before traffic and after eight passes for all the combinations at the three depth intervals is shown in Table 5 and the increase in cone index after eight passes is shown in Fig. 4. The wet soil showed a more pronounced increase in cone index than the dry soil within 0.3-0.45 m depth. The heavier real wheel load caused an increase in cone index in the wet subsoil (0.3-0.45 m), but a decrease in the dry subsoil. Similarly, higher speed caused an increase in cone index in the wet soil, but a decrease in the dry soil.

Mean normal stress

The peak values of [[sigma].sub.m] at 0.15, 0.25 and 0.35 m depth for all combinations of factors and repeated passes arc presented in Table 6. In general, [[sigma].sub.m] increased with number of passes. This is in agreement with findings by Wiermann et al. (1999), Horn et al. (2003) and Pytka (2005). As discussed by Riggert et al. (2016), denser soil due to the deterioration of soil aggregates and the rearrangement of particles could be the reason for an increase in stress with repeated wheeling. Another reason, as will be discussed below, might be the decreasing distance between stress transducer and soil surface with increasing rut depth.

During the first pass of the tractor, the higher travel speed generally resulted in a larger stress at 0.15 m depth. This agrees with Horn et al. (1989), who attributed the higher stress at higher speed with excessive pore water pressure due to the higher deformation rate at the higher speed.

The value of [[sigma].sub.m] (average of eight repeated passes) at 0.15, 0.25 and 0.35 m depth under the rear wheel is shown in Fig. 5, where the bars show the standard error of the eight repeated passes. The stress at 0.15 m depth (Fig. 5a) was larger for the dry soil than the wet soil. Moreover, the stress was greater for the heavy rear wheel. The higher stress for the dry soil at 0.15 m can be attributed to smaller soil-tyre contact area and larger mean ground pressure compared with the wet soil. The maximum stress and stress distribution at the soil-tyre interface is highly affected by the soil strength at the interface. In general. the harder the soil surface, the higher the maximum stress at the soil-tyre interface (Keller and Lamande 2010).

A greater difference between the stress under heavy and light rear wheels was found in the dry soil than in the wet soil. This can be explained by the soil-tyre contact area, which seemed not to change considerably in dry soil, resulting in larger contact stress with increasing wheel load, whereas it increased with increasing rut depth in wet soil (i.e. due to deeper tyre sinkage).

In contrast to 0.15 m depth, [[sigma].sub.m] was larger for the wet soil than the dry soil. At 0.25 (Fig. 5b) and 0.35 m (Fig. 5c), the stress under the light rear wheel was lower in the dry soil than the wet soil, i.e. the stress attenuated faster with depth in the dry soil, whereas the stresses were similar in the dry and wet soil under the heavy wheel. Similarly to the 0.15 depth, a larger difference between the stress under the heavy and light rear wheels was found in dry soil than in wet soil at 0.25 and 0.35 m depth.

The effect of speed was found to be more pronounced under the heavy wheel than the light wheel. The stress was generally higher for the faster travel speed. This contradicts findings by Horn et al. (1989), who observed an 85% decrease in subsoil vertical stress with increasing travel speed. However, the travel speeds examined in that study covered a larger range (0.7, 4.5 and 8 km [h.sup.-1)] than those investigated in this study (0.5 and 1 m [s.sup.-1]). Another difference could lie in the sampling rate of stress measurements, which is not reported by Horn et al. (1989). With a low sampling rate, the peak stress may be missed when the vehicle speed is high.

A strong correlation was found between [[sigma].sub.m] and the increase in bulk density for the dry soil at all depths (Fig. 6). However, there was no correlation between applied stress and the increase in bulk density for the wet soil (Fig. 6). This may be because the dry soil had sufficient air-filled pore space, allowing for soil particle rearrangement and compaction, whereas soil volume change may have been limited in the wet soil (WC = 1.35 PL) due to the relatively high degree of saturation.

Comparison of measured and simulated mean normal stress

The simulated and measured [[sigma].sub.m] under the front and rear tyres of the tractor are shown in Fig. 7. The simulated values in that diagram are those obtained by simulating the heavy rear axle configuration in the first tractor pass, whereas the measured data are the average of measurements in wet and dry soils at 0.5 and 1 m [s.sup.-1] travel speed. The simulations did not account for soil water content or travel speed. The simulated stress close to the soil surface beneath the front wheel was higher than that under the rear wheel, which is the result of the higher inflation pressure of the front tyre (cf. Table 3). Higher stresses under the rear wheel in the subsoil are explained by the higher load of the rear wheel. The simulations seemed realistic and correctly reflected the differences between front and rear tyre, but both the front and rear stresses were overestimated by the simulations at all three depths studied, by 87% and 82% respectively. One potential reason could be the difference in Poisson ratio of the test soil (v = 0.4 to 0.44; Table 4) and simulated soil (i.e. 0.5). The Poisson ratio affects the horizontal stress components and hence [[sigma].sub.m]. The analytical solution by Frohlich (1934) assumes the soil is an incompressible material (i.e. with Poisson ratio 0.5), which is not realistic. Thus the 'original' Boussinesq equations that include Poisson ratio should probably be used when simulation of stress components other than vertical stress (here, [[sigma].sub.m]) is of interest. Another reason for the stress overestimation by simulations could be the difference in soil-tyre contact stress between the model and real conditions.

Fig. 8 shows [[sigma].sub.m], as a function of rut depth for all depths and all wheeling experiments. In most of the experiments, stress increased with rut depth. This supports the hypothesis that the variation in stress with repeated wheeling is mainly because of decreasing distance between the soil-tyre contact area and the Boiling probes. As can be seen, the correlations were often stronger at 0.25 and 0.35 m depth, in particular for the wet soil. One reason for the poor correlation at 0.15 m depth in some experiments could be dislocation of the Boiling probes with increasing rut depth.

In order to test the hypothesis that the increase in stress with repeated wheeling is largely due to decreasing distance between soil surface and stress probe with increasing rut depth, the stress was calculated as a function of rut depth and compared with measured values. The calculated and measured stresses were associated to the rut depth based on the assumption that the first pass ran on the soil surface (i.e. with no rut formed previously). The simulated stress data were used for the heavy rear wheel, as shown in Fig. 7. For a better comparison, the stress was normalised with respect to the stress for the first pass (i.e. the reference stress), and relative stresses were obtained for the measured and simulated stress variations with respect to rut depth (Fig. 9). The 0.15m depth in the wet soil was excluded from the analysis, as the measured stress decreased with increasing rut depth (cf. Table 6). The measured relative stress increase as a function of rut depth was larger than the simulated relative stress increase for 0.15 (Fig. 9) and 0.35 m depth (Fig. 9) in dry soil. For 0.25 m depth (Fig. 9), the simulated and measured increase in stress with rut depth was similar under dry conditions, whereas the measured increase was lower than the simulated increase under wet conditions (Fig. 9). The generally larger increase in measured relative stress with increasing rut depth may suggest that factors other than decreasing distance between soil surface and sensor probe also contribute.

Conclusions and implications for further studies

Repeated wheeling experiments were carried out on an Iranian clay soil at two different soil water contents, two rear wheel loads of a 2WD tractor and two travel speeds. Mean normal stress, cone index and rut depth were measured for eight repeated passes of the tractor for each combination of the experimental factors. The following general findings were made:

(1) Rut depth increased linearly with number of passes, with a larger increase on wet soil.

(2) The largest increase in cone index was observed at 0.3-0.45 m depth in wet soil under the heavy rear wheel. However, the largest increase in bulk density was observed at 0.15 m depth in dry soil, most likely because soil water content was close to the Proctor optimum water content. This suggests that faster speed in a heavy wheel pass may result in less intensive subsoil compaction in wet soil than dry soil.

(3) Mean normal stress was higher at 0.15 m depth in dry soil and the stress attenuation with respect to depth was more pronounced for dry soil.

(4) Stress increased with increasing rut depth due to repeated wheeling in most of the experiments. Stress simulations confirmed the increase in stress with rut depth due to decreasing distance between the soil-tyre interface and stress sensors with increasing rut depth. However, this could not fully explain the increase in stress with rut depth, and thus additional factors (e.g. soil strength) must have contributed. Further studies should examine soils with different initial compaction and look at independent effects of soil strength around the sensor and repeated wheeling.

Field experiments with larger tractors and agricultural machines and with larger differences in the parameters studied here are needed in order to understand and potentially model stress propagation as affected by repeated wheeling. The present simulations reveal that changes in soil strength due to repeated wheeling and changes in soil Poisson ratio predominantly due to change in soil water content are factors that need to be accounted for in soil stress propagation models, but are currently not adequately considered in widely used semi-empirical models.

Conflicts of interest

The authors declare no conflicts of interest. Acknowledgements

The authors would like to thank Matthias Stettler from the School of Agricultural, Forest and Food Sciences (HAFL), Bern University of Applied Sciences, Bern, Switzerland, for providing the technical information to construct the Boiling probes. Dr Ehsan Shahbazi from the Department of Agronomic Sciences, Shahrckord University, is thanked for his help in statistical analyses.


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Mojtaba Naderi-Boldaji (A,E), Ali Kazemzadeh (A), Abbas Hemmat (B), Sajad Rostami (A), and Thomas Keller (C,D)

(A) Department of Mechanical Engineering of Biosystems, Shahrekord University, Shahrekord 88186-34141, Iran,

(B) Department of Biosystems Engineering, Faculty of Agriculture, Isfahan University of Technology, Isfahan 84156-83111, Iran.

(C) Agroscope, Department of Agroecology and Environment, Reckenholzstrasse 191, CH-8046, Zurich, Switzerland.

(D) Department of Soil and Environment, Swedish University of Agricultural Sciences, Box 7014, SE-75007, Uppsala, Sweden.

(E) Corresponding author. Email:;

Received 26 March 2017, accepted 24 August 2017, published online 10 November 2017

Caption: Fig. 1. Field measurement setup.

Caption: Fig. 2. Rut depth as a function of the number of passes for dry (D) and wet (W) soil, heavy (H) and light (L) real wheel at travel speeds of 0.5 and m [s.sup.-1] .

Caption: Fig. 3. Total increase (after eight passes) in bulk density for dry (D) and wet (W) soils, heavy (H) and light (L) real wheels at travel speeds of 0.5 and 1 m [s.sup.-1] for 0.15, 0.25 and 0.35 m depths.

Caption: Fig. 4. Total difference in cone index before and after eight passes for all the treatments.

Caption: Fig. 5. Averaged (eight repeated passes for each treatment) mean normal stress ([[sigma].sub.m]) with standard error bars at (a) 0.15, (b) 0.25 and (c) 0.35 m depths under the tractor rear wheel.

Caption: Fig. 6. Increase in bulk density as a function of applied stress.

Caption:Fig. 7. Measured and simulated mean normal stress ([[sigma].sub.m]) for front and rear tyre of the heavy rear axle treatment. The measured data show the averaged [[sigma].sub.m] for wet and dry soil at travel speeds of 0.5 and 1 m [s.sup.-1]. The horizontal bars show the standard error.

Caption: Fig. 8. Variations in mean normal stress ([[sigma].sub.m]) as a function of rut depth for all the wheeling treatments. D: dry soil; W: wet soil; H: heavy rear wheel; L: light rear wheel.

Caption: Fig. 9. Measured v. simulated relative stress as a function of rut depth. D: dry soil; W: wet soil; H; heavy rear wheel; L: light rear wheel, at 0.15, 0.25 and 0.35 m depths.
Table 1. Textural composition of the experimental soil
(0-0.35 m depth)

Sand: sand concentration (0.05-0.2 mm); Silt: silt concentration
(0.002-0.05 mm); Clay: clay concentration (<0.002 mm); OM:
organic matter concentration

Textural composition

Sand (g [kg.sup-1])      180
Silt (g [kg.sup-1])      320
Clay (g [kg.sup-1])      500
OM (g [kg.sup-1])         <5

Table 2. Soil water content (WC) and dry bulk density (BD) of the
'dry' and 'wet' soil before wheel traffic

The values are averages of four core samples per soil wetness

                           Dry soil

Depth (m)     WC(g [g.sup.-1])     BD (Mg [m.sup.-3])

0.15        0.185 [+ or -] 0.012   1.41 [+ or -] 0.1
0.25         0.18 [+ or -] 0.005   1.46 [+ or -] 0.04
0.35         0.15 [+ or -] 0.016   1.57 [+ or -] 0.12

                           Wet soil

Depth (m)    WC (g [g.sup.-1])     BD (Mg [m.sup.-3])

0.15        0.272 [+ or -] 0.015   1.46 [+ or -] 0.08
0.25        0.261 [+ or -] 0.008   1.52 [+ or -] 0.05
0.35        0.234 [+ or -] 0.011   1.52 [+ or -] 0.09

Table 3. Tractor characteristics for the heavy and light rear axle

Tractor                                       MF285-2WD

Engine power (kW)                                 55
Front tyre size                                7.5-19
Rear tyre size                        18.4-15-30, 10 PLY RATING

                                  Heavy Rear Axle   Light Rear Axle

Inflation pressure (front, kPa)         228               214
Inflation pressure (Rear, kPa)          145               131
Total weight (kN)                      36.0              30.2
Front axle weight (kN)                  9.9              13.0
Rear axle weight (kN)                  26.1              17.2
Contact area front ([m.sup.2])         0.20              0.24
Contact area rear ([m.sup.2])          0.57              0.40
Ground pressure front (kPa)            25.0              27.3
Ground pressure rear (kPa)             23.0              21.7

Table 4. Atterberg limits. Proctor test results and mechanical
properties of the experimental soil

PL: plastic limit; LL: liquid limit; PI: plasticity index; WC: water
content; BD: bulk density; E: Young's modulus; v: Poisson's ratio;
[k.sub.s]: stress conversion factor.

Atterberg limits

PL (g [g.sup.-1])              0.191
LL (g [g.sup.-1])              0.328
PI (g [g.sup.-1])              0.137

                            Proctor test

Optimum WC (g [g.sup.-1])      0.16
Maximum BD (Mg [m.sup.3])      1.66

Mechanical properties and stress conversion factor

                            WC = 0.9 PL   WC = 1.35 PL

E (kPa)                       3915.6        1802.2
[upsilon]                      0.44           0.4
[k.sub.s]                      0.85          0.79

Table 5. Averaged cone index (MPa) with standard error for dry (D)
and wet (W), light (L) and heavy (H) rear wheel loads and travel
speeds of 0.5 and 1 m [s.sup.-1] within 0-0.15, 0.15-0.3 and
0.3-0.45 m depths before and after eight passes

Depth (m)                   0-0.15

                  Before                 After

D-L-0.5     1.22 [+ or -] 0.04    2.01 [+ or -] 0.06
D-L-l       1.31 [+ or -] 0.15    2.11 [+ or -] 0.47
D-H-0.5     1.14 [+ or -] 0.18    1.97 [+ or -] 0.13
D-H-l       1.26 [+ or -] 0.06    1.94 [+ or -] 0.51
W-L-0.5     1.14 [+ or -] 0.06    2.27 [+ or -] 0.19
W-L-l       1.20 [+ or -] 0.17    2.33 [+ or -] 0.20
W-H-0.5     0.84 [+ or -] 0.11    1.83 [+ or -] 0.15
W-H-l       1.29 [+ or -] 0.44    2.25 [+ or -] 0.24

Depth (m)                  0.15-0.3

                  Before                 After

D-L-0.5      2.81 [+ or -] 0.2    3.55 [+ or -] 0.53
D-L-l        2.6 [+ or -] 0.35    3.36 [+ or -] 0.41
D-H-0.5     3.25 [+ or -] 0.43    4.01 [+ or -] 0.39
D-H-l       3.78 [+ or -] 0.28    4.57 [+ or -] 0.61
W-L-0.5     3.63 [+ or -] 0.23    4.36 [+ or -] 0.21
W-L-l       3.54 [+ or -] 0.92    4.40 [+ or -] 0.03
W-H-0.5     2.48 [+ or -] 0.27    4.43 [+ or -] 0.09
W-H-l       3.74 [+ or -] 0.28    4.37 [+ or -] 0.37

Depth (m)                  0.3-0.45

                  Before                 Atter

D-L-0.5     4.63 [+ or -] 0.22    6.08 [+ or -] 0.73
D-L-l       3.85 [+ or -] 0.21    4.30 [+ or -] 0.40
D-H-0.5     4.58 [+ or -] 0.16    5.61 [+ or -] 0.42
D-H-l       5.73 [+ or -] 0.17    6.02 [+ or -] 1.02
W-L-0.5     5.05 [+ or -] 0.25    5.82 [+ or -] 0.28
W-L-l       4.71 [+ or -] 0.76    5.77 [+ or -] 0.11
W-H-0.5     3.75 [+ or -] 0.29    5.26 [+ or -] 0.14
W-H-l       4.38 [+ or -] 0.39    6.41 [+ or -] 0.27

Table 6. Mean normal stress at 0.15, 0.25 and 0.35 m depth under the
rear wheel for all the treatments

No. of   Soil water content = 0.9 PL
         Light rear            Heavy rear
         wheel                 wheel

         Slow (A)   Fast (A)   Slow   Fast

         0.15 m depth

1          23.1       40.2     34.4   54.4
2          41.7       37.8     62.6   65.1
3          47.5       44.2     68.3   52.7
4          46.7       23.5     71.2   64.2
5          25.7       31.9     77.9   63.2
6          40.0       30.2     75.7   61.1
7          49.5       54.8     76.5   60.4
8          55.0       46.7     75.2   48.0

         0.25 m depth

1           4.5        4.7     28.8   35.1
2           6.3        3.1     33.0   52.9
3           6.9        7.0     35.4   52.4
4           7.8        5.4     37.6   54.5
5           4.8        5.4     38.9   51.7
6           6.5        4.8     37.0   52.0
7           7.1       10.7     34.2   48.1
8           8.4       14.4     36.3   58.7

         0.35 m depth

1           1.6        1.0     11.1   13.7
2           1.9        0.8     16.1   21.9
3           2.4        1.4     17.4   22.5
4           2.2        1.0     20.0   26.5
5           1.1        1.3     21.5   26.6
6           1.7        1.3     22.5   28.1
7           3.0        1.9     21.3   28.6
8           3.3        1.9     21.6   30.2

No. of   Soil water content = 1.35 PL
         Light  rear   Heavy rear
         wheel         wheel

         Slow   Fast   Slow   Fast

         0.15 m depth

1        18.7   35.6   47.4   39.5
2        20.0   32.3   48.7   44.3
3        18.5   33.7   53.7   40.8
4        22.8   34.0   52.1   37.4
5        28.7   43.1   36.0   35.7
6        30.5   33.7   32.5   40.3
7        38.2   32.2   37.8   39.8
8        38.3   33.6   34.4   33.6

         0.25 m depth

1        19.4   23.1   31.4   34.3
2        20.1   22.0   37.6   36.3
3        18.7   19.3   42.4   27.9
4        21.9   19.6   48.0   36.9
5        26.8   24.9   32.2   39.6
6        27.4   22.8   33.2   41.6
7        31.7   24.8   40.7   40.8
8        34.0   24.9   38.2   39.2

         0.35 m depth

1         4.9   10.9    4.3   14.9
2         7.9   15.8    6.5   21.0
3         9.0   17.1   10.8   26.6
4        12.0   19.1   16.2   26.2
5        13.2   19.1   11.0   28.8
6        16.4   19.3   12.9   31.0
7        19.2   20.0   17.1   29.6
8        20.2   20.5   16.9   30.8

(A) Slow and fast correspond to 0.5 and 1 m s 1 travel
speed respectively.
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Author:Naderi-Boldaji, Mojtaba; Kazemzadeh, Ali; Hemmat, Abbas; Rostami, Sajad; Keller, Thomas
Publication:Soil Research
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Date:Mar 1, 2018
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