Mathematical simulation and calculation of the soil compaction under dynamic loads

The deformation and compaction of loamy sandy soddy-podzolic soils under linear dynamic changes in the compressive stresses and in the course of the soil creeping were studied in field experiments. The rheological properties of these soils occurring in the viscoelastic state were described by a first-order differential equation relating the compressive stresses, the rates of their changes, and the velocities of the relative vertical compressive deformation. Regression equations were derived for the viscoelastic properties of the studied soil as functions of its density, moisture, and linear compaction velocity. Methods were proposed for the calculation of indices of the stress-strain state and the compaction of soils under specified conditions of changes in their compressive stresses with time and in the course of the soil creeping after the initial linear increase in load. Corresponding computer programs were developed. The effect of the main factors due to the linear increase in the compressive loads and in the course of the soil creeping on the rheological properties, the stress-strain state, and the density of soils was quantitatively estimated. The calculation showed that the values of the soil deformation and the density under compressive stresses lower than the ultimate strength were stabilized with time, and the properties of the viscoelastic soil approached elastic ones.     

Changes in the rheological properties and bulk density of soddy-podzolic soils under dynamic loads

Field studies of the rheological properties of loamy sandy soddy-podzolic soils were performed. Within the studied ranges of the soil moistening and bulk density values, the soils behaved as viscoelastic bodies. The dynamic deformation of such soils under compressive stress was modeled by a differential equation of the first order linking the compressive stress, the rate of its changes, and the relative soil deformation in the vertical direction. Correlative relationships between the viscoelastic soil properties, the soil bulk density, the soil water content, and the angular frequency of the harmonic law of the soil deformation were obtained. The methods of calculation of the soil bulk density as dependent on the initial bulk density and the mode of the soil deformation upon cyclic loads by rigid cylinders and by elastic wheels were developed. These methods were realized in a computer program for the quantitative assessment of the effect of the major factors on the changes in the rheological properties, the indices of the soil deformation, and the soil bulk density under the impact of compressive loads. It was shown that an increase in the number of loading-unloading cycles leads to the transformation of the viscoelastic soil properties into elastic properties.     

Mathematical modeling of the processes of soil deformation and soil compaction

The regularities of the dynamic deformation of soils with viscoelastic properties have been studied. The methods to calculate soil rheological parameters, the stress state of deformed soils, and soil compaction upon a gradual increase in pressure loads and upon cyclic sinusoidal loads created by consecutive passage of a rolling cylinder over the soil surface are suggested. The corresponding parameters have been calculated for soddy-podzolic and chernozemic soils. The quantitative assessment of the effect of a number of factors on changes in the bulk density and in the rheological properties of the soil at different depths upon the soil deformation is given.     

轮式和履带式车辆行走对农田土壤的压实作用分析

由履带式行走机构代替轮胎被认为是减缓大型农业车辆对土壤压实的有效手段之一。与轮胎相比,履带具有更大的接地面积,能够有效减小车辆对土壤的平均压力。然而履带与土壤接触面间的应力分布极不均匀,应力主要集中在各承重轮下方,履带减缓土壤压实的能力是目前有待研究的问题。该研究通过在土壤内埋设压力传感器,测试比较了相近载质量的轮胎和履带式车辆作用下,0.15和0.35 m深度土壤内的最大垂直及水平应力,同时研究了车辆行驶速度对土壤内垂直及水平应力大小的影响。基于土壤压实分析模型计算了轮胎和履带压实的0.1~0.7m深度土壤内的最大垂直及水平应力分布。通过对0.15和0.35 m深度的土样进行室内测试,比较了轮胎和履带式车辆压实对土壤透气率、先期固结压力及干容重大小的影响。结果表明,履带相比较于轮胎,能够减小土壤内的垂直及水平应力,但垂直应力的减小量比水平应力大;轮胎对0.15和0.35m深度土壤作用的平均最大垂直应力分别约为履带的2.2及2.0倍,而平均最大水平应力仅分别约为履带的1.2及1.1倍。轮胎作用下的最大垂直及水平应力在表层土壤内明显大于履带,但两者的应力差值随着土壤深度的增加逐渐减小,分别在0.7和0.4 m深度时无明显差别。轮胎和履带压实作用下,0.15和0.35 m深度土壤内的垂直及水平应力均随车辆行驶速度的增加而减小,履带作用下的应力减小速度大于轮胎。履带作用下0.15和0.35 m深度内土壤的透气率均明显小于轮胎,但土壤的先期固结压力及干容重无显著区别。研究结果为可为农业车辆行走机构的选择及使用提供参考。     

Compaction of loamy soils due to tractor traffic in vineyards and orchards and its effect on infiltration in southern France

Viticulture and fruit culture in Mediterranean areas demand frequent tractor traffic in vineyards and orchards for tillage and for the application of herbicides and pesticides, resulting in soil compaction. The aim of this study was to investigate the extent of soil compaction and its effect on infiltration in vineyards and orchards in an area in southern France, known for its wine and fruit production (Vaucluse). Compaction of both the topsoil and the subsoil was demonstrated with measurements of bulk density, penetration resistance and water retention characteristics. Subsoil compaction was attributed to wheel load, not to tillage, and was alleviated within 5 years after termination of tillage operations in vineyards. No effects of topsoil compaction on infiltration were expected on account of the slight differences in the values of infiltration parameters between wheel tracks and inter-rill areas. Effects of subsoil compaction on infiltration were examined with rainfall simulation tests. Under wet initial conditions and high rain intensities, no effect of soil compaction on infiltration was observed. This implies that the frequent tractor traffic associated with viticulture and fruit culture does not enhance run-off on loamy soils in Mediterranean areas.     

履带式行走机构压实作用下土壤应力分布均匀性分析

履带式行走机构因具有较小的接地压力而被逐渐应用在大型农业车辆上,以减小对土壤的压实。然而由于履带下应力分布的不均匀,导致农业车辆对土壤的最大应力并未有效减小,对土壤较长的压力作用时间反而增加了土壤被压实的风险。应力分布的不均匀还会造成履带沉陷量的增大,降低车辆在软土地面的通过性能。为了研究履带式行走机构压实作用下土壤内的应力分布规律以及如何提高应力分布的均匀性,以缓解履带车辆对土壤压实作用、提高履带车辆软地通过能力,该文采用侧断面水平钻孔埋设压力传感器的方法,测得了履带式行走机构压实作用下履带中心线横截面内0.35 m深度土壤内沿履带长度方向上的垂直及水平应力分布;同时研究了履带张紧力大小对应力分布均匀性的影响。结果表明,履带式行走机构下的垂直应力在各负重轮的轴线处呈现一个应力峰值;水平应力在各负重轮轴线的前、后方分别呈现一个应力峰值,且最小应力在轴线处。各负重轮下的应力峰值大小不同。最大垂直应力出现在履带式行走机构后端的导向轮处;最大水平应力出现在后支重轮与导向轮之间。适当减小履带张紧力能够提高垂直及水平应力分布的均匀性。履带张紧力由1.8×10~4k Pa减小至1.6×10~4k Pa时,履带下的最大垂直及水平应力分别减小了约37.3%和21.7%;平均最大垂直及水平应力分别减小了约26.4%和20.4%。研究结果可为履带式行走机构结构的优化提供理论依据,以期提高履带下应力分布的均匀性。     

土壤压实对土壤物理性质及小麦氮磷钾吸收的影响

为了研究土壤压实对土壤物理性质以及小麦养分吸收情况的影响,在2006和2007年进行了两轮田间试验.试验中,先用旋耕机对田块进行旋耕,耕深10cm,然后使用手扶式、轮式、履带式拖拉机在旋耕后的田块中通过1次(T1)、2次(T2)、4次(T3)以对土壤进行压实处理,对照组(T4)不作任何压实处理.压实处理后再次对土壤表层进行浅旋耕,耕深5 cm,耕后用播种机进行小麦播种,小麦品种为南京-601.试验结果发现,次表层土壤的压实处理显著影响次表层土壤的容重,孔隙度,小麦蛋白质含量以及植物中N、P、K的含量.除次表层的土壤容重在T3组中最大,T4组中最小外,其他参数值在T4组中最大,T3组中最小.并且,随着次表层土壤压实程度的增加,几乎所有的参数(土壤容重除外)都有所减少.不过,与第一年相比,参数值在第二年略有增加.总之,土壤压实严重破坏土壤结构,不利于小麦对养分的吸收.     

拖拉机田间行走对土壤特性及冬小麦生长的影响

农业机械的过度使用、密集轮作以及不适当管理等都会造成土壤压实。试验研究了拖拉机行走对土壤特性和小麦生长的影响。试验所使用的耕作机械包括轮式、履带式和手扶式三种拖拉机,分析了土壤压实对小麦生长以及土壤结构不连续性的影响。试验数据表明,土壤密度、土壤阻力以及土壤水分一般会随拖拉机行走次数增加而增大。同时,文中给出了小麦根系与秸秆间蕴涵的机理关系。试验数据还表明,小麦发芽率在显著性水平P≤0.05时,不同处理组之间无明显差异。但是,2、4、6、8、10、12、18周以及收割时的小麦秸秆高度在显著性水平P≤0.01时,各处理组之间却存在显著差异,其中轮式和手扶式拖拉机处理组高于履带式拖拉机处理组。当显著性水平分别为P≤0.05和 P≤0.01时,不同处理组的小麦根长度和密度间也存在显著差异,其中轮式和手扶式拖拉机处理组同样表现出更好的结果。总之,拖拉机行走会显著影响干物质、谷物产量等小麦生长参数。然而,作物产量不仅受土壤压实的影响,同时很大程度上也取决于天气以及土壤初始压实等因素。     

Prevention strategies for field traffic-induced subsoil compaction: a review: Part 1. Machine/soil interactions

Subsoil compaction is a severe problem mainly because its effects have been found to be long-lasting and difficult to correct. It is better to avoid subsoil compaction than to rely on alleviating the compacted structure afterwards. Before recommendations to avoid subsoil compaction can be given, the key variables and processes involved in the machinery–subsoil system must be known and understood. Field traffic-induced subsoil compaction is discussed to determine the variables important to the prevention of the compaction capability of running gear. Likewise, technical choices to minimise the risk of subsoil compaction are reviewed. According to analytical solutions and experimental results the stress in the soil under a loaded wheel decreases with depth. The risk of subsoil compaction is high when the exerted stresses are higher than the bearing capacity of the subsoil. Soil wetness decreases the bearing capacity of soil. The most serious sources of subsoil compaction are ploughing in the furrow and heavy wheel loads applied at high pressure in soft conditions. To prevent (sub)soil compaction, the machines and equipment used on the field in critical conditions should be adjusted to actual strength of the subsoil by controlling wheel/track loads and using low tyre inflation pressures. Recommendations based on quantitative guidelines for machine/soil interactions should be available for different wheel load/ground pressure combinations and soil conditions.     

Traffic alternatives for harvesting soybean (Glycine max L.): Effect on yields and soil under a direct sowing system

This initially high level of soil compaction in some direct sowing systems might suggest that the impact of subsequent traffic would be minimal, but data have not been consistent. Soil compaction is caused by the high traffic intensity and weight of tractor and combines in harvest operations, especially when these operations are carried out on wet soil or with high-pressure tyres. Traffic effects on the yield of soybean and on some physical soil properties were studied over a period of 3 years. After this period, the reduction of traffic intensity from 38 to 15 Mg km⁻¹ ha⁻¹ produced an increase on the yields of 29.2% from the base year improving the incomes by US$134 ha⁻¹ besides the reduction of fuel consumption of 35.5%. With the results obtained in this work it can be assumed that traffic reduction at harvest has a good potential to increase yields and reduce soil compaction under direct sowing system on the Rolling Pampa Region, Argentina.     

Rules of thumb for minimizing subsoil compaction

Subsoil compaction is persistent and can affect important soil functions including soil productivity. The aim of this study was to develop recommendations on how to avoid subsoil compaction for soils exposed to traffic by machinery at field capacity. We measured the vertical stress in the tyre–soil contact area for two traction tyres at ca. 30‐ and 60‐kN wheel loads on a loamy sand at field capacity. Data on resulting stress distributions were combined with those from the literature for five implement tyres tested at a range of inflation pressures and wheel loads. The vertical stress in the soil profile was then predicted using the Söhne model for all tests in the combined data set. The predicted stress at 20 cm depth correlated with the maximum stress in the contact area, tyre inflation pressure, tyre–soil contact area and mean ground pressure. At 100 cm depth, the predicted vertical stress was primarily determined by wheel load, but an effect of the other factors was also detected. Based on published recommendations for allowable stresses in the soil profile, we propose the ‘50‐50 rule’: At water contents around field capacity, traffic on agricultural soil should not exert vertical stresses in excess of 50 kPa at depths >50 cm. Our combined data provide the basis for the ‘8‐8 rule’: The depth of the 50‐kPa stress isobar increases by 8 cm for each additional tonne increase in wheel load and by 8 cm for each doubling of the tyre inflation pressure. We suggest that farmers use this simple rule for evaluating the sustainability of any planned traffic over moist soil.     

Measuring and predicting Stress Distribution under Tractive Devices in Undisturbed Soils

The objective of this study was to compare predicted stresses with measured stresses within the soil profile underneath a tractor rear tyre as affected by soil type, dynamic load, and contact pressure. The major principal stress, octahedral normal stress, and octahedral shearing stress were compared. A three-dimensional non-linear finite element model was used to predict soil profile stresses while stress state transducers were used to measure soil stresses beneath a moving tyre in the field. Principal stresses, octahedral normal stresses, and octahedral shearing stresses were calculated from the measured stresses. Predicted values of soil stress obtained from the finite element model were compared against measured values obtained from field experiments. Generally, the results from the finite element model were found to be compatible with the experimental results. The study of compaction on two soils indicated that, at the same dynamic load, compaction of clay soils was far more severe than that of coarsely textured soils.     

TECHNIQUES FOR MEASURING CHANGES IN THE PACKING STATE AND CONE RESISTANCE OF SOIL AFTER THE PASSAGE OF WHEELS AND TRACKS

Methods are described for measuring the changes in the horizontal and vertical distribution of packing state and cone resistance following the passage of wheels and tracks over prepared beds of soil. A gamma-ray transmission system was employed with automatically controlled scanning in a 2 × 2 cm grid in soil sections of 1.08 m length by 0.3 m depth, using a scintillator/photomultiplier detector assembly with stabilized pulse-height analysis and magnetic tape recording. Changes in cone resistance were measured in a 2 cm (vertical) by JO cm (horizontal) grid in a section 1.4 m length by 0.5 m depth using an electrically driven penetrometer with load and displacement simultaneously recorded on an XY plotter and magnetic tape. Results were analysed and displayed graphically by computer with packing state expressed by a number of optional properties (dry bulk density, total porosity, air-filled porosity, void ratio, or specific volume). Pronounced differences in packing state and soil strength were observed as a result of the passage of a two-wheel-drive tractor, with and without cage wheels, and a crawler tractor. Adding a cage wheel decreased slightly the compaction below the rubber tyre, but formed a partially compacted zone below the cage wheel. Increases of dry bulk density and soil strength were recorded below the crawler track but the values for these properties did not reach the maximum values found below the rubber tyre.     

Technical solutions to reduce the risk of subsoil compaction: effects of dual wheels, tandem wheels and tyre inflation pressure on stress propagation in soil

The use of heavy machinery is increasing in agriculture, which induces increased risks of subsoil compaction. Hence, there is a need for technical solutions that reduce the compaction risk at high total machine loads. Three field experiments were performed in order to study the effects of dual wheels, tandem wheels and tyre inflation pressure on stress propagation in soil. Vertical soil stress was measured at three different depths by installing probes into the soil horizontally from a dug pit. In one experiment, also the stress distribution below the tyre was measured. Beneath the dual wheels, vertical stresses at 0.15 and 0.3 m depth were lower between the two wheels than under the centre of each wheel, despite the gap between the wheels being small (0.1 m). At 0.5 m depth, vertical stress beneath the wheels was the same as between the two wheels. The stress interaction from the two wheels was weak, even in the subsoil. Accordingly, measured stresses at 0.3, 0.5 and 0.7 m depth were highest under the centre of each axle centre line of tandem wheels, and much lower between the axles. For a wheel load of 86 kN, tyre inflation pressure significantly affected stress at 0.3 m depth, but not at greater depths. Stress directly below the tyre, measured at 0.1 m depth, was unevenly distributed, both in driving direction and perpendicular to driving direction, and maximum stress was considerably higher than tyre inflation pressure. Calculations of vertical stress based on Boussinesq's equation for elastic materials agreed well with measurements. A parabolic or linear contact stress distribution (stress declines from the centre to the edge of the contact area) was a better approximation of the contact stress than a uniform stress distribution. The results demonstrate that stress in the soil at different depths is a function of the stress on the surface and the contact area, which in turn are functions of wheel load, wheel arrangement, tyre inflation pressure, contact stress distribution and soil conditions. Soil stress and soil compaction are a function of neither axle load nor total vehicle load. This is of great importance for practical purposes. Reducing wheel load, e.g. by using dual or tandem wheels, also allows tyre inflation pressure to be reduced. This reduces the risk of subsoil compaction.     

三七育苗播种压轮仿形开沟装置的设计与试验

为满足三七行株距小、播深浅且对播种深度一致性要求高的特殊播种农艺,该研究依据二力杠杆原理设计了一种适于三七育苗播种的压轮仿形开沟装置。该装置能实现横、纵向仿形且对疏松土壤有一定的紧实作用。借助ANSYS软件对压轮连接板进行应力、应变分析,验证该结构的可靠性。以土壤紧实度、播种机前进速度、弹簧预拉力为试验因素,以开沟深度稳定性为试验指标,开展二次正交旋转组合试验,建立试验因素与开沟深度稳定性之间的回归数学模型并进行显著性检验。借助Design Expert 10.0.3软件对试验因素进行响应曲面分析,并对参数进行系统优化,得到开沟深度稳定性最佳的工作参数组合为:土壤紧实度259.50 kPa,播种机前进速度6.40 m/min,弹簧预拉力211.90 N,此时,开沟深度稳定性为89.41%。用最优工作参数进行土槽试验验证,验证结果表明:试验开沟深度稳定性平均值与优化模型求解结果基本一致。该研究设计的压轮仿形开沟装置满足三七育苗播种要求,且开沟深度稳定性较好,该研究可为三七育苗播种开沟装置的设计提供依据。     

Subsoil compaction caused by machinery traffic on a Swedish Eutric Cambisol at different soil water contents

Field traffic may reduce the amount of air-filled pores and cavities in the soil thus affecting a large range of physical soil properties and processes, such as infiltration, soil water flow and water retention. Furthermore, soil compaction may increase the mechanical strength of the soil and thereby impede root growth.

The objective of this research was to test the hypotheses that: (1) the degree of soil displacement during field traffic depends largely on the soil water content, and (2) the depth to which the soil is displaced during field traffic can be predicted on the basis of the soil precompression stress and calculated soil stresses. In 1999, field measurements were carried out on a Swedish swelling/shrinking clay loam of stresses and vertical soil displacement during traffic with wheel loads of 2, 3, 5 and 7 Mg at soil water contents of between 11 and 35% (w/w). This was combined with determinations of soil precompression stress at the time of the traffic and predictions of the soil compaction with the soil compaction model SOCOMO. Vertical soil displacement increased with increased axle load. In May, the soil precompression stress was approximately 100 kPa at 0.3, 0.5 and 0.7 m depth. In August and September, the soil precompression stress at 0.3, 0.5 and 0.7 m depth was 550–1245 kPa. However, when traffic with a wheel load of 7 Mg was applied, the soil displacements at 0.5 m depth were several times larger in August and September than in May, and even more at 0.7 m depth. An implication of the results is that the precompression stress does not always provide a good indication of the risk for subsoil compaction. A practical consequence is that subsoil compaction in some soils may occur even when the soil is very dry. The SOCOMO model predicted the soil displacement relatively well when the soil precompression stress was low. However, for all other wheeling treatments, the model failed to predict that any soil compaction would occur, even at high axle loads.

The measured soil stresses were generally higher than the stresses calculated with the SOCOMO model. Neither the application of a parabolic surface load distribution nor an increased concentration factor could account for this difference. This was probably because the stress distribution in a very dry and strongly structured soil is different from the stress distribution in more homogeneous soils.     

Changes in some physical properties of a clay soil in Central Italy following the passage of rubber tracked and wheeled tractors of medium power

The aim of this study was to evaluate the compacting effect of rubber tracked tractors in comparison to that of the traditional wheeled tractors. Macroporosity, pore shape and size distribution, bulk density, penetration resistance and saturated hydraulic conductivity were analysed in a clay soil (Vertic Cambisol) near Rome (Italy) following one and four passes on the same track of rubber tracked and wheeled tractors of medium power. The soil structure attributes were evaluated by characterising porosity by means of image analysis of soil thin sections prepared from undisturbed samples. Macroporosity decreased in the 0–10 cm layer of compacted soil, particularly after four tractor passes, due to a large reduction in the proportion of elongated pores and in their vertical continuity. The rubber tracked tractor had a more pronounced compaction effect in the surface layer (0–10 cm) than the wheeled tractor both after one and four passes; the latter treatment producing the lowest soil porosity. The same trend was observed for hydraulic conductivity, which showed a highly significant correlation with elongated pores. In the 10–20 cm layer the porosity was significantly decreased following traffic, apart from in the soil under one pass of the rubber tracked tractor. Again in this layer, the lowest values of porosity were found in soil after four passes of the rubber tracked tractor. Single and multiple passes made by the two tractors induced different effects regarding soil penetration resistance and bulk density. Increment ratio of penetration resistance after tractor passes with respect to the control was: 12.5 and 49.9% with the wheeled and 34.4 and 39.8% with the tracked after one and four passes, respectively. Increment ratio of dry bulk density values after tractor passes with respect to the control was 7.9 and 11.7% with the wheeled and 7.5 and 8.3% with the tracked after one and four passes, respectively. The tractor passes transformed the initial subangular blocky structure into a massive structure with sometimes a platy structure in the upper few centimetres. The results indicated that soil compaction following traffic with the rubber tracked tractor was generally the more pronounced. However the compacting effect of this tractor after one pass seemed to be limited to the surface layer only.     

Changes in the properties of a Vertisol and responses of wheat after compaction with harvester traffic

Soil compaction has been recognised as the greatest problem in terms of damage to Australia’s soil resource. Compaction by tractor and harvester tyres, related to trafficking of wet soil, is one source of the problem. In this paper an array of soil properties was measured before and immediately after the application of a known compaction force to a wet Vertisol. A local grain harvester was used on soil that was just trafficable; a common scenario at harvest. The primary aim was to determine the changes in various soil properties in order to provide a “benchmark” against which the effectiveness of future remedial treatments could be evaluated. A secondary aim was a comparison of the measurements’ efficiency to assess a soil’s structural degradation status. Also assessed was the subsequent effect of the applied compaction on wheat growth and yield in the following cropping season. Nine of the soil properties measured gave statistically significant differences as a result of the soil compaction. Differences were mostly restricted to the top 0.2 m of the soil. The greatest measured depth of effect was decreased soil porosity to 0.4 m measured from intact soil clods. There was 72% emergence of the wheat crop planted into the compact soil and 93% in the uncompact soil. Wheat yield, however, was not affected by the compaction. This may demonstrate that wheat, growing on a full profile of stored soil water as did the current crop, may be little affected by compaction. Also, wheat may have potential to facilitate rapid repair of the damage in a Vertisol such as the current soil by drying the topsoil between rainfall events so increasing shrinking and swelling cycles. If this is true, then sowing a suitable crop species in a Vertisol may be a better option than tillage for repairing compaction damage by agricultural traffic.     

Soil stress as affected by wheel load and tyre inflation pressure

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.     

SoilFlex: A model for prediction of soil stresses and soil compaction due to agricultural field traffic including a synthesis of analytical approaches

Soil compaction is one of the most important factors responsible for soil physical degradation. Soil compaction models are important tools for controlling traffic-induced soil compaction in agriculture. A two-dimensional model for calculation of soil stresses and soil compaction due to agricultural field traffic is presented. It is written as a spreadsheet that is easy to use and therefore intended for use not only by experts in soil mechanics, but also by e.g. agricultural advisers. The model allows for a realistic prediction of the contact area and the stress distribution in the contact area from readily available tyre parameters. It is possible to simulate the passage of several machines, including e.g. tractors with dual wheels and trailers with tandem wheels. The model is based on analytical equations for stress propagation in soil. The load is applied incrementally, thus keeping the strains small for each increment. Several stress–strain relationships describing the compressive behaviour of agricultural soils are incorporated. Mechanical properties of soil can be estimated by means of pedo-transfer functions. The model includes two options for calculation of vertical displacement and rut depth, either from volumetric strains only or from both volumetric and shear strains. We show in examples that the model provides satisfactory predictions of stress propagation and changes in bulk density. However, computation results of soil deformation strongly depend on soil mechanical properties that are labour-intensive to measure and difficult to estimate and thus not readily available. Therefore, prediction of deformation might not be easily handled in practice. The model presented is called SoilFlex, because it is a soil compaction model that is flexible in terms of the model inputs, the constitutive equations describing the stress–strain relationships and the model outputs.