Numerical Simulation of Soil-Tool Interaction by Discrete Element Method

Simulación Numérica de la Interacción Suelo-Apero Mediante el Método de Elementos Discreto

M.Sc. Elvis López Bravo¹, Dr. C. Miguel Herrera Suárez¹, Dr. C. Omar González Cueto¹,  Prof. Engelbert Tijskens, Herman Ramon²

I. Universidad Central de Las Villas, Dpto. Mecanización Agropecuaria, Villa Clara, Cuba.
II. Division of Mechatronics, Biostatistics and Sensors (MeBioS), Department of Biosystems, Faculty of Bioscience Engineering, Kasteelpark Arenberg 30, B-3001 Heverlee, Belgium.

ABSTRAC

Discrete Element Method (DEM) was used to simulate the soil-tool interaction. The model is based on the action of normal, shear, cohesion and friction forces into the cohesive granular medium, calculated as a function of micro-mechanical properties. Macro-mechanical properties of soil-soil and soil-metal were used to determining the micro parameters on the model. In order simulate the tillage operations a soil virtual block was generated in hexagonal compacted array using 45 000 spherical particles forming a cohesive block. A soil-bin installation was conditioned to measuring the draft force in hard-dry and soft-wet soil condition to compare the results with simulation tests. The comparison showed a small under predicted behavior of the model for soft-wet soil; however the results become more accurate toward hard-dry soil conditions. The density changes during simulations and pressures distributions below the tillage tool path is showed, given a dynamic representation of soil internal tension and loosening after tillage operation.

Keywords: Tillage, modeling, draft force, density.

RESUMEN

El método de elementos discretos (DEM) fue utilizado para simular la interacción del suelo con la herramienta de labranza. El mismo se basa en la acción que ejercen las fuerzas normal, tangencial, cohesión y fricción en un medio granular cohesivo, a partir de su determinación a escala micro-mecánicas. Las propiedades macroscópicas que intervienen en el contacto suelo-suelo sirven como parámetros macros los cuales son usados para determinar los parámetros micros del modelo. Para la simulación de la labranza se realizó la generación virtual de un bloque de suelo con un total de 45 000 partículas esféricas, formando un bloque cohesivo. Para verificar los resultados de la simulación se acondicionó un canal de suelo para dos condiciones extremas: seco-endurecido y húmedo-suelto. Los resultados mostraron una tendencia del modelo a sobreestimar la magnitud de la fuerza de tiro para el suelo suelto y con alta humedad, Sin embargo el modelo resultó más preciso para la condición de alta densidad. Se obtuvieron además las distribuciones de densidad del suelo en las diferentes secciones del bloque virtual así como los resultados de la distribución de fuerzas en las capas comprimidas debido al paso de la herramienta de labranza.

Palabras clave: labranza, modelo, fuerza de tiro, densidad.

INTRODUCTION

Draft force prediction, clod sizes distribution and damages by erosion have been some of the motivation topics for modeling soil-tillage interaction. Data from field process and lab experiments are combined on mathematical models; supporting by the increment on informatics resources more accurate, fasters and extended prognostics are performed. Computational techniques as well as finite element methods (FEM), discrete element methods (DEM), artificial neural network (ANN) and computational fluid dynamics (CFD) are indistinctly used with different purposes in soil simulation. Important approaching of rheological soil behavior is the result of transition from quasi-static to dynamic analysis (Karmakar & Kushwaha, 2006). Optimization for tillage tools focused on geometrical modification has been carried out on moldboard ploughs, obtaining significant draft force reduction required to move the tool through different soil conditions (Shrestha et al., 2001; Godwin, 2007). Field performance of the implements for futures applications in soil-ecosystem were evaluated in the nineties decade, testing several variant of tools shapes and operations speed and getting the draft forces requirement. The most efficient tools designs were evaluated at farm level correlating the energy supply and seedbed quality (Perdok & Kouwenhoven, 1994). Prediction of draught requirements by ANN for three designs of moldboard plows, tested in sandy loam soil under different operating ranges and soil conditions, showed a good correlation in comparison with results obtaining from prediction equations (Roul et al., 2009). Considering the soil as a continuum medium, several constitutive models have been created and improved. Modified Cam-Clay model was implemented focus on deriving time dependent effect, the model included soil anisotropic and creep behavior, as a result gyration and expansion of load affected the principal stress redirection, confirmation of simulation was made using un-drained shear and creep test (Ahmari & Ahmadi, 2009). Von-Mises yield criterion on perfectly plastic model was applied using Lagrangian method; including strain-softening and rate dependent, the authors present a numerical model for cone penetration into soft clay soil, the influence of stiffness index, in-situ stress anisotropy and roughness were theoretically correlated and compared with the cavity expansion theory (Liyanapathirana, 2009).

Several studies by FEM have been conducted using simples and complexes geometries of tools projected in two and three dimensions, with the objective of determining the effect of cutting speed and blade angles related to draft force variation during soil-tool interaction (Mouazen & Neményi, 1999; Mootaz et al., 2003; Abo-Elnor et al., 2004; Sahu & Raheman, 2006; Gebregziabher et al., 2007; Davoudi et al., 2008).

Several studies have been carried out to simulating the soil behavior in Cuban soil focus in tillage operation and soil management. The methodology to determine from mechanical soil test the parameters needed to fill the FEM model was used to predicting the result of soil tensional state(Herrera, 2001). The parameters of the model for soil tool interaction was determined and proof the accurate of elastic-plastics formulation obtaining best results using a Drucker-Prager model (Herrera et al., 2008). Triaxial compression test and shear test have been simulated in different Cuban soils to predict the soil behavior related to compaction by the action of the inflate wheel pressures and transporting load (Gonzalez et al., 2007; Gonzalez et al., 2009).

Discrete medium is widely applied for simulation of dynamic process, having an extend field in soils engineering applications. The principal vantage over continuum methods is the capacity to represent the interaction among particles happen in granular medium (Tadesse, 2004). Many contact models can be included depending on how each element interacts with each other, these contacts models rules the behavior of the overall medium, the micro-properties parameters for the model will be deduced from soil mechanical properties. The rheological simulation can result on an accurate prognostic about soil behavior and draft force requirements.
]]> The goal for the present study is to simulate the soil-tool interaction to predicting the draft forces and soil particles behavior in tillage operations by mean of macro-scale model implemented on Discrete Element Method.

METHODS

Model description. Classical DEM model proposed by Cundall and Strack (Cundall & Strack, 1979), is used to compute the interaction between soil particles and tillage tool, two kinds of contacts were implemented: soil-soil and soil-tool, for both calculations the same contact scheme is applied, changing only cause of mechanical properties which are obtained from regression equation according to the specifics soil physical desire condition (López, 2011), The macroscopic parameters included in the model bring a physic-mechanical characterization of the soil namely: Elastic Young’s modulus (E), Poisson ratio (n), cohesion (c), adhesion (ca), internal friction (f) and metal-soil friction (d). The model dealing with normal, shear, gravity, cohesion and friction forces (Figure 1).

The micro parameters for the model are dynamic calculated from equations that working with geometrical elements and macro-properties of the particles in contact at each time step using. The force in normal direction is calculated by:

Where kn mean the normal spring, Dun is the variation of normal overlapping, hn is the viscous damping and Dt is the time step variation.

Where Eab is the equivalent Young’s modulus of the two contact materials, Aint is the interior area of the contact and Deq is the equivalent distance between the two objects, the other part of the equation is the relationship between poison’s ratio n with loading path coefficient ak, softening factor bk and interaction range gk (Hentz et al., 2004).

The force in tangential direction is calculated by:

Where ks is the shear spring, Dus is the variation of tangential overlapping and hs represents the viscous damping in tangential direction. The value of ks depends on kn, been obtained by:

The viscous damping in normal and tangential direction is determined by:

Where b is the viscous damping coefficient; ma and mb are the mass of the two objects in contact.

Where c is the cohesion between two objects in contact from lab experiment, fm is micro-friction coefficient, k3 and k4 are two material constants related with porosity and particles sizes distribution in the simulated medium.

Soil block generation

Soil block at 650 x 400 x 300 mm was generated filling a rectangular box with 45 000 spherical particles (Figure 2a). The hexagonal compacted spatial array was used as the methods to get the efficient distribute of particles. The whole particles were submitted to free fall into the mentioned box, the second step was pressing from the top to the bottom. The horizontal press (red color plane) is moved at constant velocity at 0,2 m/min reducing the space into the container and getting the desire specimen density (Figure 2b). Sizes of particles were distributed on three different layers with radius at 8-10; 6-5 and 3-4 mm at the top, center, and bottom respectively.

The soil block was generated in three different physical condition by mean of modifies in water contents (u) and soil bulk densities (g). The conditions obtained by simulation represent soft-wet (r = 1,1 g/cm3, u = 30%), friable (r = 1,2 g/cm3, u = 18%) and hard-dry soil (r = 1,4, g/cm3, u = 10%). The parameters used for each simulation is showing in Table1.

Soil Bin test

RESULTS AND DISCUSSION

Comparison between soil-bin and simulation test

The average draft force obtained during the soil-bin test in soft-wet condition represented by the dash blue line in Figure 4, shows the small under-prediction quality of the model for relative low range of force demanding system. The draft force measured by the measuring system (red color line) in the lab condition was bigger than the force obtained in simulation test. Nevertheless the error of 97 N is an acceptable value considering the spatial huge variation of soil physical properties and the corresponding over-dimension of tiller in agricultural practices. On the other hand 1,41 kN draft force average measured in hard-dry soil condition (green dash line), shows more close force prediction by the model exhibiting a standard error of 34 N.

One of the reasons why draft force decrease is the particle packing which affects the strength of the simulated soil. The cylindrical shapes for all particles and a limited sizes distribution increase the empties spaces into the virtual block of soil, it is coherent with soil porosity, however in real soil large amount of small particles are filled a considerable intergranular spaces what increase the soil stiffness. For hard-soil the overlap become larger and bulk density also increase obtaining a proportional pore homogenization and a consequently strength increment.

Tillage simulation for different soil conditions

Particles compression and decompression take places during movement of the tool through the soil, as a result the fluctuation forces patter with different proportion for each soil conditions appear, the amount of bonds broken up at the same time determine the minimum and maximum values of the force. The fluctuation force on hard-dry condition is also larger than two other treatments, caused by more fragility among particles. Patter of plastic flow characterizes the soil movement on soft-wet condition, while fragile patter is more representative on hard-dry soil followed by larger number of clods formation.

Variation on particles bulk density calculated from seven parallels blocks (Figure 6a), arranged in longitudinal direction after tillage simulation shows a different patter of increment (Figure 6b).

In hard-dry soil condition bulk density decrease mainly at the center of the section (Figure 6b), by the action of the main body of the tool, for the section above lateral blades bulk density remain with discrete reduction. That behavior is also showed for simulation in friable soil condition, though more uniform density was obtained along transversal section of the tool meaning a rising in the soil loosing index. Under wet-soil condition the action of the lateral blades become nil, only small amount of particles loosening were found at the wedge position section of the tool while the other part of the block remain undisturbed.

Graphical representation of particles forces on the horizontal plane below the tool path in the trajectory of 600mm from left to right obtained in the simulation of dry-hard and friable soil condition highlight the bigger particles tension register in the most compacted soil (Figure 7a), the amount of particles submitted to pressure also grown up and some picks are obtaining at the current tool position.

Less forces values and quite reduction in pressured area characterize the resultant forces for soil in friable conditions (Figure 7b).Accordingly the bigger particles force the consequent increment on internal tension and plow pan formation.

CONCLUSIONS

The discrete element method provides the fundamental formulation and geometrical tools to implementing the particles contacts in a macro-scale representation, deriving from soil macro-properties the micro properties for the model.

The experimental measurements in a soil-bin using a tool designed according to agricultural treatments of soil cultivation allow determining the draft forces requirement for a tool in tillage operations submitted to different conditions of moistures and bulk densities.

Comparison between tillage draft forces obtained from soil-bin and discrete simulation in soft-wet (r = 1,1 g/cm3, u = 30%), and hard-dry (r = 1,4, g/cm3, u = 10%) soil conditions showed an adequate prediction forces with standard error at 97 and 34 N respectively, the model tended to under-predict the magnitude of the force in soft-wet condition attributable to larger amount of pores wish reduces the soil strength.

By mean of soil tillage simulation by cultivator tool in soft-wet, friable and hard-dry soil conditions can be evaluated the variation of draft forces, the results obtained by simulation are consistent with the soil physical conditions giving a criteria of soil fragility and plasticity according to the pattern of force-displacement curve.
]]> Soil loosening depending on the position of the implement shows a maximum level in friable (r = 1,2 g/cm3, u = 18%) soil, the bulk density level off from 1,2 to 1,12g/cm3 at the center of the tool decreasing gradually toward both sides, a different pattern was found in soft-wet soil where the bulk density decrease slightly only at the center tool path.

Particles forces distribution obtained in the plane below to the path of the tool in the simulated soil block show rising values for dry-hard soil, denoting maximum pressures at the current tool position, also the tension surface increase in comparison with friable soil condition becoming this area prone to plow pan formation.

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Recibido: 15 de mayo de 2011
Aprobado: 20 de julio de 2012

Elvis López Bravo, Prof. Auxiliar, Universidad Central de Las Villas, Dpto. Mecanización Agropecuaria, Villa Clara, CP: 54830. Correo electrónico: elvislb@uclv.edu.cu