DEM simulation of stress transmission under agricultural traffic Part 2: Shear stress at the tyre-soil interface

Highlights

• Horizontal stress transmission in Söhne was similar for all boundary conditions

• Vertical stress in Söhne was not influenced by shear stress boundary condition

• Horizontal stress was transmitted to deeper layers, according to the DEM model

Abstract

Although it has been proven to be of considerable importance, it remains unclear how to model the effect of traction on soil compaction. This study used multiple approaches to simulate the stress under an active wheel with the pseudo-continuous Söhne model, and compared it to a discrete element method (DEM) model of the same scenario. It was found that the differences in normal horizontal stress (σ_y) due to these different boundary conditions in the Söhne model were limited. According to these simulations, the effect on normal vertical stress (σ_z) was negligible. This was in contrast with the DEM simulations, where the impact of traction on σ_y was also stronger and less shallow. Advanced numerical models can be used to gain insight in the importance of traction, and could be used to improve the boundary condition of the Söhne model. However, further experimental validation is needed.

Introduction

The traffic of machinery on a field is usually related to operations with high draught requirements, such as tillage or the towing of heavy trailers (Arvidsson et al., 2004, Håkansson, 2005). The strong drawbar pull force that is associated with these activities causes horizontal stress on the soil, in addition to the vertical load of the machines. This can result in substantial additional damage to the soil, and needs to be considered in the risk assessment of soil compaction (Soane et al., 1980, Håkansson et al., 1988, Alakukku et al., 2003).

Davies et al. (1973) and Raghavan et al., 1977, Raghavan et al., 1978 reported an increase in soil compaction at higher traction or wheel slip. More recently Battiato et al. (2015) found a significant decrease in topsoil saturated hydraulic conductivity when trafficking at higher slip rates. Pulido-Moncada et al. (2019) compared the soil impacts of a high-wheel load, self-propelled machine and a tractor-trailer system, and speculated that traction-induced shear failure is one of the reasons for the observed intenser soil compaction by the tractor-trailer system. Although the damage of soil structure due to shear stress is repeatedly documented (Berisso et al., 2013, Schjønning et al., 2013), the effect of traction and soil slip still forms a blind spot in many soil compaction risk assessment studies.

On the other hand, shear stress at the tyre-soil interface has been studied intensively in a terramechanical context. Terramechanics is ‘the study of the overall performance of a machine in relation to its operating environment - the terrain’ (Muro and O’Brien, 2006, Wong, 2009). In contrast to soil physics and soil mechanics, the main focus of terramechanics is thus the traction that a wheel will generate under certain circumstances, rather than the stress it causes in the soil profile. Theories have been developed for the stress distribution at the wheel-tyre interface for driven and towed rigid wheels (Wong and Reece, 1967a, Wong and Reece, 1967b), as well as deformable wheels (Karafiath and Nowatzki, 1978, Shmulevich and Osetinsky, 2003, Senatore and Sandu, 2011). The analytical predictions of traction and stress distribution have been validated with soil-bin and field experiments (e.g. Onafeko and Reece, 1967, Battiato and Diserens, 2017) and stress measurements at the tyre-soil interface (e.g. Krick, 1969, Senatore and Iagnemma, 2014, Higa et al., 2015).

Yet, these insights are rarely included in the modelling of soil compaction. SOCOMO and SoilFlex include a shear stress boundary condition (van den Akker, 2004, Keller et al., 2007), but this has not been validated. One of the few studies that validate the analytical simulation of soil compaction with both horizontal and vertical stresses is by Wulfsohn and Upadhyaya (1992). A 3D model to simulate the interface between the soil and tyre allowed an accurate prediction of traction, but the validation of soil compaction was inconclusive since the stress state was not measured and the change in measured bulk density due to wheeling was not significant.

Numerical methods, such as finite element method (FEM) or discrete element method (DEM) also allow to simulate the performance of a flexible wheel on a deformable soil (Asaf et al., 2006, Smith et al., 2014, Zhao and Zang, 2014, Nishiyama et al., 2016). FEM is a widely accepted technique to simulate soil compaction (Perumpral et al., 1971, Defossez and Richard, 2002, Keller et al., 2013, Nawaz et al., 2013). Still, in most soil compaction simulations, the boundary condition either is a vertical load (Defossez and Richard, 2002), or a wheel without realistic slip or traction (Fervers, 2004, Xia, 2011, Moslem and Hossein, 2014, Cueto et al., 2016, Silva et al., 2018). Raper et al. (1995) used the radial normal stress at the wheel-soil interface as boundary condition in the FEM simulation of stress transmission, but acknowledged that the missing tangential component could be one of the reasons for the underestimated stress in the validation. Abu-Hamdeh and Reeder (2003) found a good agreement between measured and simulated soil stress with FEM, but faced difficulties to validate the model at higher traction due to movement of the stress transducers.

In a concurrent study, the stress transmission under a tractor-trailer setup was simulated with a pseudo-analytical continuum model (Söhne (1953); hereafter referred to as the Söhne model) and a DEM model (De Pue and Cornelis, 2019). The DEM model was designed in such a manner that the tractor wheels were actively rotating and towing the (passive) trailer wheels, thus simulating realistic traction and drawbar pull forces. Whilst a good agreement was found between the Söhne and DEM simulations for vertical stress under the trailer wheels, the Söhne model simulated lower stress for the tractor wheels. These simulations were compared to measurements of vertical stress (σ_z) in the soil profile during a field experiment (De Pue et al., 2019b). The evaluation indicated that both models performed similar, but a consistently higher underestimation was found in the Söhne simulations of σ_z under the (rear) tractor wheels.

Advanced numerical models provide fundamental insight in the stress propagation under a wheel, and can be used to improve simplified models. This approach was used in this study to evaluate three existing methods to include traction-induced horizontal stress in the boundary condition of the Söhne model. The resulting simulations of horizontal and vertical normal stress were compared to a DEM simulation of a wheel with traction. Additionally, the tyre/soil interface stress from the DEM simulation was used as a boundary condition in the Söhne model. The objective of this study is to evaluate 1) the influence of the different horizontal stress boundary conditions in Söhne and 2) differences in traction-induced stress transmission between the models.