DEM simulation of stress transmission under agricultural traffic Part 3: Evaluation with field experiment

doi:10.1016/j.still.2020.104606

Soil and Tillage Research

Volume 200, June 2020, 104606

https://doi.org/10.1016/j.still.2020.104606 Get rights and content

Abstract

In a concurrent paper, we compared a continuum model and a discrete element method (DEM) model in simulating stress transmission in soil under a wheel. Here, those models are evaluated with measurements of vertical normal stress (σ_z) under the wheels of a tractor-slurry spreader setup. It was found that the variation in the measured σ_z could be explained by the heterogeneous stress distribution in our structured soil, similar to what is observed in the DEM simulation. Furthermore, comparison of the continuum and DEM model showed that the lack of horizontal forces and dynamic load transfer at the boundary condition in the continuum model lead to a systematic underestimation of the measured σ_z. Traction and drawbar forces have a significant impact on the stress state under a wheel. The continuum model and its boundary conditions should be modified to include these forces accurately.

Introduction

Soil cultivation is associated with traffic of agricultural vehicles on fields, which might cause soil compaction. It is one of the major forms of soil degradation and can lead to persistent damage of soil quality (Håkansson and Reeder, 1994, Alaoui et al., 2011, Berisso et al., 2012). In a concurrent paper, we applied the discrete element method (DEM) to simulate stress transmission under agricultural traffic. The model was compared to the pseudo-analytical continuum model of Söhne (1953) (hereafter referred to as the Söhne model) and the influence of the material parameters on the stress transmission was evaluated (De Pue and Cornelis, 2019).

The Söhne model is based on the Boussinesq (1885) solution for stress propagation in an elastic material, combined with a boundary condition which describes the stress distribution at the tyre-soil interface. It is a well-established model, which forms the foundation of multiple popular risk assessment models for soil compaction, such as SoCoMo (Van den Akker, 2004), SoilFlex (Keller et al., 2007) and Terranimo (Stettler et al., 2014).

In contrast to the Söhne model, the DEM model does not simulate the soil as a continuum, but as an assembly of granular particles. Stress is transmitted through interactions between those particles, resulting in a heterogeneous pattern. It was shown by De Pue and Cornelis (2019) that both methods yield similar results for the vertical normal stress (σ_z), despite their fundamentally different concept to calculate stress transmission. However, significant differences in horizontal stress were found, as well as a considerable effect of traction and drawbar forces on the stress state in the soil. In the present study, we evaluate the Söhne model and the DEM model with data from a previous study by Lamandé and Schjønning (2018).

The measurement and simulation of stress in soil is a challenging task. In situ measurements of stresses in soil are typically performed with load cells or bolling probes, installed at one or more depths. The accuracy of the measurement largely depends on the design and installation of the sensor. The shape and stiffness of the sensor, as well as the disturbance of the soil or poor contact between soil and sensor can cause errors in the stress measurements (Kirby, 1999, Lamandé et al., 2007). Furthermore, various studies have suggested that stress propagates in a heterogeneous way through a structured soil (Dexter et al., 1988, Trautner and Arvidsson, 2003, Lamandé et al., 2015, Keller et al., 2016, Naveed et al., 2016) and that soil deformation is associated with shear failure (Chancellor et al., 1962, Gupta et al., 1989, Raper et al., 1994). These aspects of stress transmission are not included in the Söhne model. Consequently, the evaluation of stress transmission simulations with field experiments showed variable success (Smith et al., 2000, Lamandé and Schjønning, 2011a, Lamandé and Schjønning, 2018, Keller et al., 2016).

Another poorly understood element of vehicle-induced soil compaction is the effect of traction and drawbar forces. Although it has been demonstrated that this horizontal stress at the tyre-soil interface causes significant damage to the soil, it is rarely included in the modelling of soil compaction (Davies et al., 1973, Raghavan et al., 1977, Battiato et al., 2015). In a second concurrent paper, it was found that the current formulations of horizontal stress boundary conditions in the Söhne model had limited effect on the vertical stress (σ_z) in the soil profile. Contrary to the DEM simulations, the effect of traction remained limited to the upper soil layer (De Pue et al., 2020b).

The objectives of the present study are twofold: (1) to evaluate the DEM model with field measurements of σ_z and (2) to compare σ_z simulated with the Söhne model and the DEM model with field measured σ_z to evaluate the effect of traction on σ_z.

Section snippets

Test field

The wheeling tests were conducted on a test field in Flakkebjerg, Denmark (55°19′42″ N, 11°24′28″ E), which exhibits a large spatial variability in soil texture (Schjønning et al., 2016). Intrinsic properties of soils developed from glacial tills usually show spatial heterogeneity (e.g. Berisso et al., 2012), and especially texture can vary considerably within short distances. More details regarding the soil have been reported extensively (Schjønning et al., 2011, Schjønning et al., 2016, Obour

Results

A comparison of σ_z simulated with the Söhne and DEM model is shown in Fig. 4. Despite the fundamentally different approach to simulate the stress under a wheel, the results are similar. However, some important differences can be observed. The wheel shown here is the rear wheel of the tractor, and exerts traction force on the soil. The Söhne model did not include a horizontal stress boundary condition (since it has been demonstrated to have limited influence on σ_z; De Pue et al., 2020b). The DEM

Discussion

From Fig. 6, Fig. 7, two main observations can be made: the distribution of the observed σ_z exhibited large variation and both models underestimated the observed σ_z, in particular in the shallow layer. These observations are in accordance with previous studies that compared measured and simulated stress induced by agricultural traffic.

Some authors refer to the difficulty to measure the stress state of the soil correctly (Keller et al., 2014, Keller et al., 2016). The uncertainty of the stress

Conclusion

The variability in σ_z measurements indicates a heterogeneous stress distribution which cannot be simulated with continuum models. DEM can be tool to quantify this phenomenon, and to investigate its importance for soil compaction.

Overall, the simulation of σ_z had the same accuracy with both methods in this study. However, the bias between the measured and simulated stress with the Söhne model under wheels with traction was consistently larger than for wheels without traction. This was not the

Conflicts of interest

The authors declare no conflicts of interest.

Acknowledgements

The intensive fieldwork which made this study possible was done by the researchers and technicians from the Department of Agroecology, Aarhus University. This work stands on the shoulders of the many who offer free, open source knowledge and tools. The authors gratefully acknowledge the work of all collaborators who developed YADE and maintain it to be free and open source, and the people of HPC-UGent for their technical support. Lastly, we thank Sci-hub for making scientific knowledge

References (68)

N.H. Abu-Hamdeh et al.
Measuring and predicting stress distribution under tractive devices in undisturbed soils
Biosyst. Eng.
(2003)
J. Van den Akker
SOCOMO: a soil compaction model to calculate soil stresses and the subsoil carrying capacity
Soil Tillage Res.
(2004)
A. Alaoui et al.
A review of the changes in the soil pore system due to soil deformation: a hydrodynamic perspective
Soil Tillage Res.
(2011)
A. Bailey et al.
Soil stresses under a tractor tire at various loads and inflation pressures
J. Terramech.
(1996)
A. Battiato et al.
Tractor traction performance simulation on differently textured soils and validation: a basic study to make traction and energy requirements accessible to the practice
Soil Tillage Res.
(2017)
F.E. Berisso et al.
Persistent effects of subsoil compaction on pore size distribution and gas transport in a loamy soil
Soil Tillage Res.
(2012)
F. Bourrier et al.
Discrete modeling of granular soils reinforcement by plant roots
Ecol. Eng.
(2013)
C. Coetzee
Calibration of the discrete element method
Powder Technol.
(2017)
J. De Pue et al.
Dem simulation of stress transmission under agricultural traffic part 1: comparison with continuum model and parametric study
Soil Tillage Res.
(2019)
J. De Pue et al.
Calibration of dem material parameters to simulate stress-strain behaviour of unsaturated soils during uniaxial compression
Soil Tillage Res.
(2019)

A. Dexter et al.

Pressure transmission beneath wheels in soils on the eyre peninsula of south australia

J. Terramech.

(1988)

I. Håkansson et al.

Subsoil compaction by vehicles with high axle load-extent, persistence and crop response

Soil Tillage Res.

(1994)

T. Keller et al.

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

Soil Tillage Res.

(2004)

T. Keller et al.

Transmission of vertical soil stress under agricultural tyres: comparing measurements with simulations

Soil Tillage Res.

(2014)

T. Keller et al.

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

Soil Tillage Res.

(2007)

T. Keller et al.

Challenges in the development of analytical soil compaction models

Soil Tillage Res.

(2010)

L.R. Khot et al.

Experimental validation of distinct element simulation for dynamic wheel-soil interaction

J. Terramech.

(2007)

J. Kirby

Soil stress measurement: part I. Transducer in a uniform stress field

J. Agric. Eng. Res.

(1999)

A. Koolen

A method for soil compactibility determination

J. Agric. Eng. Res.

(1974)

M. Lamandé et al.

Accuracy of soil stress measurements as affected by transducer dimensions and shape

Soil Tillage Res.

(2015)

M. Lamandé et al.

Transmission of vertical stress in a real soil profile. Part I: Site description, evaluation of the söhne model, and the effect of topsoil tillage

Soil Tillage Res.

(2011)

M. Lamandé et al.

Transmission of vertical stress in a real soil profile. Part II: Effect of tyre size, inflation pressure and wheel load

Soil Tillage Res.

(2011)

M. Lamandé et al.

Mechanical behaviour of an undisturbed soil subjected to loadings: effects of load and contact area

Soil Tillage Res.

(2007)

M. Michael et al.

DEM-fem coupling simulations of the interactions between a tire tread and granular terrain

Comput. Methods Appl. Mech. Eng.

(2015)

M. Naveed et al.

Quantifying vertical stress transmission and compaction-induced soil structure using sensor mat and X-ray computed tomography

Soil Tillage Res.

(2016)

V. Nguyen et al.

Experimental analysis of vertical soil reaction and soil stress distribution under off-road tires

J. Terramech.

(2008)

K. Nishiyama et al.

2d fe-DEM analysis of tractive performance of an elastic wheel for planetary rovers

J. Terramech.

(2016)

P.B. Obour et al.

Subsoil compaction assessed by visual evaluation and laboratory methods

Soil Tillage Res.

(2017)

M. Oda et al.

Experimental micromechanical evaluation of strength of granular materials: effects of particle rolling

Mech. Mater.

(1982)

G. Raghavan et al.

Effect of wheel slip on soil compaction

J. Agric. Eng. Res.

(1977)

P. Schjønning et al.

Soil precompression stress, penetration resistance and crop yields in relation to differently-trafficked, temperate-region sandy loam soils

Soil Tillage Res.

(2016)

P. Schjønning et al.

Modelling effects of tyre inflation pressure on the stress distribution near the soil-tyre interface

Biosyst. Eng.

(2008)

P. Schjønning et al.

Predicted tyre-soil interface area and vertical stress distribution based on loading characteristics

Soil Tillage Res.

(2015)

I. Shmulevich et al.

Traction performance of a pushed/pulled drive wheel

J. Terramech.

(2003)

Cited by (15)

Discrete element modelling of stress propagation in soil under a rigid wheel in a soil bin։ a simulation of probe inducing stress deviation and wheel speed
2023, Biosystems Engineering
Discrete element method (DEM) is a suitable technique for simulation of stress propagation in soils, particularly with freshly tilled or aggregated structures. Measurement of true stress, in the absence of a stress-measuring probe inserted in the soil, is not experimentally possible. Stress probes may therefore under- or over-estimate true soil stress. Building on previous work simulating vertical stress propagation under plate sinkage loading, the study modelled stress propagation under a moving rigid wheel. The aim was to determine how vertical stress, with and without a probe, at a given depth may differ under dynamic loading vs. static plate sinkage loading and with varying wheel speed. DEM parameters of the hysteretic spring-linear cohesion contact model were calibrated by a cone penetration test which was validated by wheel sinkage into the soil. Two tests were conducted in a soil bin at a water content of 11% d.b; at a bulk density of 1200 kg m⁻³ and a wheel loading of 600 N, and at a bulk density of 1350 kg m⁻³ and wheel loading of 1200 N. Vertical soil stress was measured at 0.15 m depth using a cylindrical load cell probe. The DEM simulation underestimated the measured stress by an average 13%. Average stress overestimation ratio (with/without probe stress) was found to be 1.12, which agreed with measurements beneath the plate during plate sinkage loading. Increasing wheel speed from 0.2 to 6 m s⁻¹ showed a 7% increase in DEM-simulated with-probe stress.
Extended terramechanics model for machine--soil interaction: Representation of change in the ground shape and property via cellular automata
2023, Soil and Tillage Research
Citation Excerpt :
Recently, terramechanics concepts have attracted interest for application in extreme environments such as disaster response robots and lunar and planetary exploration rovers (Zhou et al., 2014; Tadokoro, 2019; Schäfer et al., 2010; Trease et al., 2011; Sharma et al., 2018; Sutoh et al., 2013. Notably, terramechanics analyses for rough terrains can be classified into multibody dynamics analysis using semi-empirical models (Zhou et al., 2014; Arvidson et al., 2017; Raymond and Jayakumar, 2015; Li et al., 2013b) and numerical analysis using the finite element method (Ozaki et al., 2015; Ozaki and Kondo, 2016; Nishiyama et al., 2016; Fervers, 2004; Cueto et al., 2016; Chiroux et al., 2005) or discrete element method (Nishiyama et al., 2016; Nakashima et al., 2007, 2010; Johnson et al., 2015; Knuth et al., 2012; Smith and Peng, 2013; Li et al., 2010; De Pue and Cornelis, 2019; De Pue et al., 2020a; 2020b). In particular, multibody dynamics analyses for rough terrains represent a powerful tool to enhance the performance of off-road vehicles and robots and formulate efficient and safe working plans.
Terramechanics, as an interdisciplinary field, focuses on the interaction between the ground and vehicles. Terramechanics concepts can be used to realize the design of underbodies and pass-planning of off-road vehicles, among other applications. However, conventional semi-empirical terramechanics models cannot accurately evaluate the terrain surface deformation associated with the interaction between the solid object and ground. Therefore, this article proposes an extended terramechanics model, which incorporates the terrain surface deformation mechanism based on cellular automata. First, to examine the effectiveness of the proposed model to capture variations in the terrain surface deformation and draft force, an analysis of a vertical plate drag test was conducted based on the proposed model. Next, a single-wheel traveling analysis was performed. The experimentally obtained drawbar-pull and sinkage could be reasonably simulated, which cannot be easily realized using conventional methods.
The challenge in estimating soil compressive strength for use in risk assessment of soil compaction in field traffic
2023, Advances in Agronomy
Citation Excerpt :
Moreover, Naveed et al. (2016) observed that the discrete nature of stress transmission was found to be more pronounced at lower ratios of applied stress to strength, while at higher ratios, a stress propagation pattern as expected from continuum mechanics, such as described by the classical Boussinesq (1885) equation, predominated. The aspect of stress transmission in (structured) soil is a subject in itself, and the opportunities and challenges in taking soil heterogeneity into account in predictions of stress from machinery have been discussed in a range of papers (e.g., De Pue and Cornelis, 2019; De Pue et al., 2020b). In the present context, the above emphasizes that the normal load applied in a uniaxial, confined compression test is probably not uniformly transmitted through the soil.
Society calls for protection of agricultural soils in order to sustain the production of foods for a growing population. Compaction of subsoil layers is an increasing problem in modern agriculture and a cause of serious concern because of the poor resilience in natural amelioration. The concept of soil precompression stress has been adapted from civil engineering, although in soil science it is applied to unsaturated soils that have developed a secondary structure from the action of weather, biota and tillage. It assumes strain is elastic at loads up to the precompression stress, while plastic deformation is expected at higher stresses. To determine this threshold we performed uniaxial, confined compression tests for a total of 584 minimally disturbed soil cores sampled at three subsoil layers on nine Danish soils ranging in clay content from 0.02 to 0.38 kg kg⁻¹. The cores were drained to either of three matric potentials (−50, −100 or − 300 hPa) prior to loading. Stress was applied by a constant-strain rate method. We estimated the point of maximum curvature of the strain-log₁₀(normal stress) relation by a numerical procedure. This point is considered here as a compactive stress threshold, typically labeled the soil precompression stress, σ_pc. The preload suction stress (PSS) was calculated as the product of initial (i.e., before loading) water suction and initial degree of pore water saturation. Multiple regressions were performed to evaluate the effect of soil properties (textural classes, volumetric water content, bulk density (BD), soil organic matter (SOM), and PSS) on σ_pc. The best model explained 39% of the variation in σ_pc, and indicated that σ_pc increases with increasing PSS, BD and SOM. For a given combination of clay, BD and SOM, PSS affected σ_pc negatively. We recommend our regression model for use in risk assessment tools for estimating sustainable traffic on agricultural soils. The model was validated by five independent data sets from the literature. Our study shows that caution should be applied when regarding σ_pc as a fixed threshold for compressive strength. We hypothesize that plastic deformation is initiated over a range of stress rather than at a distinctive single value. Further studies are needed to better understand—and potentially quantify—to what extent the predicted σ_pc can be regarded a central estimate of allowable stress for a given soil.
Simulation of soil stress under plate sinkage loading: A comparison of finite element and discrete element methods
2022, Soil and Tillage Research
Citation Excerpt :
The results showed an overall agreement between the vertical stresses simulated by the DEM model and calculated using the Söhne model except for an active traction wheel where slightly higher DEM-simulated soil stress was discussed to be attributed to shear stresses at soil-tire interface which affects the results of DEM simulations but not similarly the Söhne model calculations (De Pue et al., 2020a). Measurements of vertical stress under the wheels of a tractor-slurry spreader setup indicated that both Söhne and DEM models overestimated the measured stress in particular in shallow layers (De Pue et al., 2020b). This was referred to the uncertainty in true stress measurement by stress transducers.
Stress propagation in soil under vehicular traffic can be simulated either analytically based on the laws of continuum mechanics or numerically using finite element (FEM) and discrete element methods (DEM). Soil stress measured by a stress probe may differ from the "true" stress (i.e. the stress without the probe), as probes under- or over-estimate soil stress. No instrument has yet been developed to enable true stress measurement, while simulated stress can only be validated by comparing with measured stress. Hence, it is important to model the interaction of soil with a load cell probe to understand the difference between "with probe" and "without probe" soil stress. This study aimed at modelling the interaction of a load cell stress probe and soil under circular surface loading (i.e. by plate sinkage test) using FEM and DEM to understand the differences of the two methods, and to address whether arable soil is a continuum or a discrete media with regard to stress propagation. Simulated stress was compared with experimental stress (i.e. the stress measured by the probe). Experimental stress measurements were made in a clay loam soil at a gravimetric water content of 11% (corresponding to 0.5 PL, the lower plastic limit) and bulk densities of 1000 and 1150 kg m⁻³ corresponding to loose to slightly compacted soil, respectively. The load cell probe was installed at 0.15 m depth within a soil column, and varying surface loads were applied by a circular plate. The measured stress as a function of applied load was compared with simulated stress using either FEM or DEM. Simulations underestimated the measured stress, with an RMSE of 22.8 kPa for DEM and 40.1 kPa for FEM. The difference in soil stress between simulations with and without a probe were small for DEM, but significant for FEM. For FEM simulations, embedding a stress probe into the soil resulted in an overestimation of the “true” stress by 94% for the soil and boundary conditions tested. For DEM, the average overestimation was only 11%. Differences between FEM and DEM simulations with and without a probe were discussed and attributed to the sponge effect in FEM, and to differences in stress distribution at the soil-loading plate interface caused by the arching effect. Simulations showed that increasing the ratio of probe housing diameter to sensing surface decreased the stress overestimation for both DEM and FEM methods. More research is needed to address how stress propagation and the stress readings by a sensor probe are influenced in continuum and granular media, and how soil stress should be best modelled (as a continuum or granular material) depending on soil properties and characteristics.
Calibration of discrete element parameters and experimental verification for modelling subsurface soils
2021, Biosystems Engineering
Citation Excerpt :
Sweep cultivation can mitigate the negative impact of the plough layer (subsurface soils), whose cultivation performance is dependent on the dynamic interaction between subsurface soil and sweep tool (Li, Chen, & Chen, 2016). The discrete element method (DEM) has been shown to have considerable advantages in soil-tool interaction simulation, such as simulating the interaction mechanism intuitively to optimise tool geometry parameters (e.g. (Barr, Desbiolles, Ucgul, & Fielke, 2020; Hang, Gao, Yuan, Huang, & Zhu, 2018; Saunders, Ucgul, & Godwin, 2021; Y.; Wang et al., 2020; Zeng, Chen, & Zhang, 2017)), reducing experimental design costs (e.g. (Barr, Desbiolles, Fielke, & Ucgul, 2019; Barr, Ucgul, Desbiolles, & Fielke, 2018; Ucgul, Fielke, & Saunders, 2014a,b)) and studying soil stress from a microscopic perspective (e.g. (De Pue, Lamandé, & Cornelis, 2020; De Pue, Lamandé, Schjønning, & Cornelis, 2020)). The accuracy and reliability of DEM modelling significantly depend on selections of suitable contact model and reasonable DEM parameter calibration approach (Coetzee, 2017).
The discrete element method (DEM) has shown considerable advantages for the simulation of soil-tool interaction simulation. To develop reliable DEM simulations, the selection of an appropriate contact model and its parameter calibration are critical. A DEM model of cohesive subsurface soils was established to predict the draught of sweep cultivation by using the Edinburgh elasto-plastic adhesion (EEPA) contact model. Firstly, the DEM parameters were used for calibration, which were significant for the results of the uniaxial confined compression test and the unconfined compressive strength test. Then, the mapping relationship between other DEM parameters and the soil stress–strain behaviour was calculated to obtain a solution matching the stress–strain measurement results. Finally, cone penetration resistance (penetration rate of 8 mm s⁻¹) and the draught of sweep tillage (depth of 200 mm and speed of 1.67 m s⁻¹) were used to evaluate the accuracy of the parameters. The results showed that the penetration resistance in the elastic phase of the simulation was in close agreement (R² = 0.9964) with the measurements, and the total relative error and the average relative error between the predicted sweep draft and the measurement were 9.4% and 4.77%, respectively. Thus, it was shown that the developed calibration method can effectively predict the development of the sweeping draught and the penetration stress.
Discrete element modelling of large soil deformations under heavy vehicles
2021, Journal of Terramechanics
Citation Excerpt :
The authors use spherical particles with blocked rotations in a porous soil representation. In a concurrent paper the normal vertical stress was evaluated with field experiments (De Pue et al., 2020). A study of wheel rutting and mobility of heavy vehicles using particle-based terrain modelling in three dimension is presented in Recuero et al. (2017).
This paper addresses the challenges of creating realistic models of soil for simulations of heavy vehicles on weak terrain. We modelled dense soils using the discrete element method with variable parameters for surface friction, normal cohesion, and rolling resistance. To find out what type of soils can be represented, we measured the internal friction and bulk cohesion of over 100 different virtual samples. To test the model, we simulated rut formation from a heavy vehicle with different loads and soil strengths. We conclude that the relevant space of dense frictional and frictional-cohesive soils can be represented and that the model is applicable for simulation of large deformations induced by heavy vehicles on weak terrain.

View all citing articles on Scopus

View full text

DEM simulation of stress transmission under agricultural traffic Part 3: Evaluation with field experiment

Abstract

Introduction

Section snippets

Test field

Results

Discussion

Conclusion

Conflicts of interest

Acknowledgements

Biosyst. Eng.

Soil Tillage Res.

Soil Tillage Res.

J. Terramech.

Soil Tillage Res.

Soil Tillage Res.

Ecol. Eng.

Powder Technol.

Soil Tillage Res.

Soil Tillage Res.

J. Terramech.

Soil Tillage Res.

Soil Tillage Res.

Soil Tillage Res.

Soil Tillage Res.

Soil Tillage Res.

J. Terramech.

J. Agric. Eng. Res.

J. Agric. Eng. Res.

Soil Tillage Res.

Soil Tillage Res.

Soil Tillage Res.

Soil Tillage Res.

Comput. Methods Appl. Mech. Eng.

Soil Tillage Res.

J. Terramech.

J. Terramech.

Soil Tillage Res.

Mech. Mater.

J. Agric. Eng. Res.

Soil Tillage Res.

Biosyst. Eng.

Soil Tillage Res.

J. Terramech.