A Discrete Element Model for Characterizing Soil-Cotton Seeding Equipment Interactions Using the JKR and Bonding Contact Models

Abstract

Due to the increasing demand for agricultural water, the water availability for winter and spring irrigation of cotton fields has decreased. Consequently, dry seeding followed by irrigation (DSSI) has become a widespread cotton cultivation technique in Xinjiang. This study focused on the interaction between soil particles and cotton seeding equipment under DSSI in Xinjiang. The discrete element method (DEM) simulation framework was employed to compare the performance of the Johnson-Kendall-Roberts (JKR) model and Bonding model in simulating contact between soil particles. The models’ ability to simulate the angle of repose was investigated, and shear tests were conducted. The simulation results showed that both models had comparable repose angles, with relative errors of 0.59% for the JKR model and 0.36% for the contact model. However, the contact model demonstrated superior predictive accuracy in simulating direct shear test results, predicting an internal friction angle of 35.8°, with a relative error of 5.8% compared to experimental measurements. In contrast, the JKR model exhibited a larger error. The Bonding model provides a more accurate description of soil particle contact. Subsoiler penetration tests showed that the maximum penetration force was 467.2 N, closely matching the simulation result of 485.3 N, which validates the reliability of the model parameters. The proposed soil simulation framework and calibrated parameters accurately represented soil mechanical properties, providing a robust basis for discrete element modeling and structural optimization of soil-tool interactions in cotton field tillage machinery.

1. Introduction

Due to its unique geographical location and natural environment, Xinjiang has become China’s most productive cotton-producing region [1,2]. Increased agricultural water demands have led to a shortage of winter and spring irrigation water for cotton fields, making water conservation and efficiency enhancement imperative. Widespread soil amendments and upgrades to sowing machinery have been implemented in most cotton-growing areas. Dry seeding followed by irrigation (DSSI) has become widespread in recent years in Xinjiang. This technique requires specific field preparation and a soil structure with a firm topsoil layer, a loose subsoil layer, fine tilth, and a level surface to ensure reliable seedling emergence after drip irrigation. The discrete element method (DEM) has distinct advantages in optimizing agricultural machinery components [3] and investigating the interaction between agricultural machinery and soil particles [4,5]. Consequently, an accurate DEM model of cotton field soil under DSSI is vital for optimizing the components of cotton seeders.

The DEM enables the precise analysis of the motion of granular materials and interactions. It has been widely used to investigate soil physical properties [6,7,8,9,10]. The critical parameters of soil particles must be calibrated to optimize the design of hole formers in hole seeders and enhance their applicability in complex soil environments. These parameters include soil density, moisture content, shear strength, angle of repose, and the inter-particle coefficients of restitution and friction [11,12,13]. The accurate calibration of these parameters enables the DEM simulation of the interaction between hole seeders and soil under working conditions, providing a scientific basis for optimizing the design of seeding equipment. Several studies employed DEM simulations and experiments to calibrate the parameters of various soil types. Qiu et al. [14] established a DEM model for cinnamon soil using the Hertz-Mindlin model and the Johnson-Kendall-Roberts (JKR) cohesive contact model, but their study focused on simulating the cutting resistance of soil-engaging components without optimizing parameters for soil particle movement characteristics during the seeding process. Xiang et al. [15] analyzed southern China’s clay loam using the JKR model and calibrated the parameters through angle of repose tests. However, there are significant differences in mechanical properties between southern clay loam and sandy soils in Xinjiang cotton fields, making their parameter system not directly transferable. Chen et al. [16] simulated the deep loosening process in three soil types (coarse sand, loam, and sandy loam) using the Parallel Bond Model (PBM). Although the model reliability was verified, the interaction between soil-engaging components and soil was not thoroughly investigated. Ucgul et al. [17] determined DEM parameters for tillage simulation through angle of repose and cone penetration tests. However, their study focused on non-cohesive soils and did not address the cohesive effects between soil particles under drip irrigation conditions. Bravo et al. [18] obtained macroscopic geotechnical parameters through direct shear tests. Although the derived microscopic parameters are applicable to geotechnical engineering simulations, they have not been modified to account for the characteristics of shallow soil disturbance in agricultural sowing processes.

This study obtained soil samples from cotton fields under the DSSI regime in Alaer City, Xinjiang, and conducted simulation-based calibration and validation of the parameters using the DEM. The experimental and simulation results were compared to calibrate the DEM parameters of cotton field soil. The results can be used to optimize the design of the hole former in hole seeders and develop prototypes.

2. Materials and Methods

2.1. Experimental Materials

Soil samples were collected from cotton fields under the DSSI regime in Tanan Town, Alaer City, Xinjiang (81°18′ E, 40°30′ N). The samples were obtained during the optimal cotton sowing period (early April) to ensure consistency between simulations and experiments. A five-point sampling method was employed, and samples were collected at a depth of approximately 10 cm. This sampling depth corresponds to the typical tillage layer (<10 cm depth) in agricultural production and the primary root zone of cotton plants (0–10 cm soil layer), enabling the accurate assessment of soil tillage conditions and the soil management efficacy.

2.2. Soil Moisture Content and Density

The soil moisture content was determined using constant-temperature oven-drying. The experimental apparatus included a forced-air drying oven, an electronic balance (precision: 0.01 g), and a vacuum desiccator. Ten labeled aluminum moisture cans were weighed. The soil samples were placed into the cans, and the cans were weighed before being transferred to the drying oven (105 °C). The cans were removed at 2 h intervals, cooled in the desiccator, and weighed until a constant weight was achieved. The final weight was recorded. The soil moisture content (%) was calculated using Equation (1):

$$\omega ={\displaystyle \frac{m_0-m_1}{m_0}}\times 100\%$$

(1)

where $\omega$ is the soil moisture content (%); $m_0$ is the mass of the fresh soil sample (g); $m_1$ the mass of the oven-dried soil sample at constant weight (g).

Soil moisture content tests were conducted in triplicate, yielding an average moisture content of 16.92% in the topsoil layer (0–10 cm depth).

Soil density was determined using core sampling during the optimal sowing period. A standard cutting ring sampler (100 cm³ volume) was used to extract undisturbed soil cores from the 10 cm tillage layer in cotton fields. The soil cores were immediately transferred to weighed aluminum containers. The total mass of the container and the soil core was measured, and the net soil mass was obtained by subtracting the tare mass of the container. Soil bulk density ($\rho$, g/cm³) was calculated using Equation (2):

$${\rho }_s={\displaystyle \frac{m}{v}}={\displaystyle \frac{m_a-m_b}{v}}$$

(2)

where ${\rho }_s$ is the soil density (g/cm³); $m$ is the net mass of oven-dried soil (g); $m_a$ is the total mass of the aluminum container and fresh soil (g); $m_b$ is the tare mass of the aluminum container (g); $v$ is the volume of the cutting ring sampler (cm³).

Soil density measurements were conducted in triplicate. The mean soil density in the cotton field tillage layer (0–10 cm depth) during the optimal sowing period was 1.225 g/cm³

2.3. Angle of Repose Measurement

The angle of repose test was used to calibrate the particle contact model parameters in the DEM framework. The DEM parameters were iteratively adjusted, and the experimental and simulated angles of repose and the Engineering Discrete Element Method (EDEM) simulation results were compared to ensure the physical congruence between the simulated and actual soil behavior. This experimental approach provides critical reference data for EDEM parameter calibration, significantly enhancing the accuracy of the soil property simulations.

The angle of repose test was conducted using a lift cylinder. The cylinder was a steel tube with an inner diameter of 70 mm and a height of 100 mm. It was placed on a base plate. The cylinder was filled with soil, and the lifting mechanism was used to lift the cylinder at a constant speed of approximately 10 mm/s. As the cylinder moved upward, the soil flowed downward and outward relative to the cylinder, forming a conical pile. A protractor was used to measure the angle in four directions around the soil pile, and the average value of the test results was used as the angle of repose, as shown in Figure 1. The angle of repose test was repeated for five groups.

The minimum and maximum repose static angles of the cotton field soil during the sowing period were determined as 35.30° and 42.26°, respectively, and the soil accumulation was 38.80 ± 3.46°.

2.4. Direct Shear Test of Soil

The direct shear test of the soil provides the internal friction angle and cohesive force between soil particles at the test site. The instruments included a YJRB-B type automatic soil direct shear tester, a φ 61.8 × 20 mm consolidation shear box, and a 100 cm³ soil sampling ring knife, as shown in Figure 2. The YJRB-B type automatic soil direct shear tester consists of a test host, a normal load pressure regulating cabinet, a controller, an air source, and a computer control system. The consolidation shear box has an area of 30 cm², with a maximum shear stroke of 30 mm and an accuracy of 0.01 mm. The soil was subjected to different normal compressive stresses (100 kPa, 200 kPa, 300 kPa, and 400 kPa) and the same horizontal stress. The shear rate was 2 mm/s, and three tests were conducted under the same normal compressive stress.

The shear strength of the soil was derived under different normal compressive stresses. The relationship curve between the soil’s shear strength and the normal compressive stress was created using Origin 2022 software. The Mohr-Coulomb failure envelope of the soil sample is shown in Figure 3. The cohesion and internal friction angle of the soil derived from the fitted data and the Coulomb Equation (3) were 23.33 kPa and 38°, respectively [19].

$$\tau =c+\sigma \mathit{tan}\Phi$$

(3)

where $\tau$ is the soil shear strength (kPa); $c$ is the cohesion (kPa); $\sigma$ is the normal compressive stress (kPa); $\Phi$ is the internal friction angle (°).

2.5. Calibration of Soil Contact Parameters via Simulation

2.5.1. Contact Model

A simulation was conducted using EDEM 2020 software to model the interaction between the seeding equipment and the soil and between soil particles. Contact models were used to simulate the interactions. The EDEM software includes the Hertz-Mindlin (no slip) model, Hertz-Mindlin with Bonding model, JKR model, LCM, linear spring model, moving plane model, and others [20,21,22].

The JKR model and the Hertz-Mindlin with Bonding model have been widely used for soil parameter calibrations. The JKR normal elastic contact force is based on the JKR theory, which characterizes the overlap, interaction parameters, and surface energy between particles [23,24,25,26] (Figure 4). R_i and R_j represent the radii of the particles.

The calculation methods for other forces are the same as those of the Hertz-Mindlin (no-slip) contact model. The JKR normal elastic forces are defined in Equations (4) and (5):

$$F_{JKR}=-4\sqrt{\pi \gamma E_{eq}}{\alpha }^{{\displaystyle \frac{3}{2}}}+{\displaystyle \frac{4E_{eq}}{3R_{eq}}}{\alpha }^3$$

(4)

$$\delta ={\displaystyle \frac{{\alpha }^2}{R_{eq}}}-\sqrt{{\displaystyle \frac{4\pi \gamma \alpha }{E_{eq}}}}$$

(5)

where $F_{JKR}$ is the JKR normal elastic force (N); $E_{eq}$ is the equivalent elastic modulus, (Pa); $R_{eq}$ is the equivalent contact radius (m); $\alpha$ is the radius of the contact circles of the two particles (m); $\delta$ is the normal distance between particles (m); $\gamma$ is the surface energy (J/m²).

This contact model can be used to calculate the cohesive force between particles when a gap exists between two particles. The maximum distance between two particles with a non-zero adhesive force is calculated using Equations (6) and (7):

$${\delta }_c={\displaystyle \frac{{{\alpha }_c}^2}{R_{eq}}}-\sqrt{{\displaystyle \frac{4\pi \gamma {\alpha }_c}{E_{eq}}}}$$

(6)

$${\alpha }_c={\left[{\displaystyle \frac{9\pi \gamma {R_{eq}}^2}{2E_{eq}}}\left({\displaystyle \frac{3}{4}}-{\displaystyle \frac{1}{\sqrt{2}}}\right)\right]}^{{\displaystyle \frac{1}{3}}}$$

(7)

where ${\delta }_c$ is the maximum distance between particles (m); ${\alpha }_c$ is the maximum contact circle radius between contacting particles (m).

The adhesive force is zero when the normal gap between particles exceeds ${\delta }_c$. If no contact exists between the particles, and the normal gap is smaller than ${\delta }_c$, the maximum adhesive force is calculated by Equation (8):

$$F_{pullout}=-{\displaystyle \frac{2}{3}}\pi \gamma R_{eq}$$

(8)

where $F_{pullout}$ is the maximum adhesive force (N).

The JKR model provides the frictional force of the large adhesive component in the normal contact direction, enabling the accurate simulation of soil mechanical behavior.

The Hertz-Mindlin with Bonding model is shown in Figure 5. R_P denotes the radius of the particles, R_b denotes the bonding radius, and R_C denotes the contact radius. The cohesive force between soil particles exists due to bonds between deformable particles. This bond can withstand normal and tangential forces and transmit forces and moments. The contact behavior between particles before the preset bonding time follows the standard Hertz-Mindlin (no slip) model [27,28,29].

After a bond has been established, the adhesive force and the moment of soil particles increase from zero with the time step [30], which can be expressed using Equation (9):

$$\left\{\begin{array}{c}\mathsf{\Delta }{F}_n=-v_n{S}_{n}A\mathsf{\Delta }t\\ \mathsf{\Delta }{F}_{\tau }=-v_{\tau }{S}_{\tau }A\mathsf{\Delta }t\\ \mathsf{\Delta }{M}_n=-{\omega }_n{S}_{n}J\mathsf{\Delta }t\\ \mathsf{\Delta }{M}_{\tau }=-{\omega }_{\tau }{S}_{\tau }{\displaystyle \frac{J}{2}}\mathsf{\Delta }t\\ A=\pi {R_b}^2\\ J={\displaystyle \frac{1}{2}}\pi {R_b}^2\end{array}\right.$$

(9)

where A is the contact area of soil particles (m²); $R_b$ is the bonding radius of soil particles (m); J is the polar moment of inertia of the particle cross-section (m⁴); $S_n$ is the normal stiffness of bonded particles (N/m); $v_n$,$v_{\tau }$ is the normal and tangential components of particle velocity (m/s); ${\omega }_n$,${\omega }_{\tau }$ is the normal and tangential components of particle angular velocity (rad/s); $\mathsf{\Delta }t$ time step (s).

The bond breaks when the applied external force exceeds a preset value. The critical normal stress ${\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ and the critical tangential stress ${\tau }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ are defined using Equations (10) and (11), respectively:

$${\sigma }_{\mathrm{m}\mathrm{a}\mathrm{x}}<{\displaystyle \frac{-F_n}{A}}+{\displaystyle \frac{2M_{\tau }}{J}}{R}_b$$

(10)

$${\tau }_{\mathrm{m}\mathrm{a}\mathrm{x}}<{\displaystyle \frac{-F_{\tau }}{A}}+{\displaystyle \frac{M_{\tau }}{J}}{R}_b$$

(11)

2.5.2. Simulation of the Angle of Repose of Soil Particles

The contact model parameters significantly influence the simulation results; thus, accurate model parameters are crucial. The required parameters include material and contact parameters. The DEM software EDEM was used to calibrate the angle of repose parameters.

Experiments and DEM simulations were used to calibrate and optimize the simulation parameters of the cotton field soil. The significant factors affecting the angle of repose were determined using the Plackett-Burman design (P-BD). Subsequently, climbing tests were conducted for significant factors to determine their optimal range. A Box-Behnken Design (B-BD) response surface methodology was used to establish a calibration model for cotton field soil. The model was validated by experiments to determine the optimal parameters for the DEM simulation of cotton field soil.

Preliminary soil particle size analysis showed mass fraction distributions of 12.96% (0–0.5 mm), 35.17% (0.5–1 mm), 33.18% (1–1.5 mm), and 18.69% (>1.5 mm). For simulation accuracy, median diameters representing each size range were selected: 0.25 mm, 0.75 mm, 1.25 mm, and 1.75 mm, respectively. The JKR and Bonding models shared the same nine basic parameters (T1–T9) in the angle of repose simulation, whereas the JKR model included an additional surface energy parameter (T10). The unique parameters of the Bonding model included normal stiffness, tangential stiffness, critical normal stress, critical tangential stress, and bonding radius. Based on existing studies, the normal bonding stiffness was 1 × 10⁸ N/m³, the tangential bonding stiffness was 5 × 10⁷ N/m³ [31], and the particle contact radius was 1.2 times the particle radius [32]. The critical normal and tangential stresses were parameters T11 and T12. According to extensive preliminary tests and the literature, the Poisson’s ratio of steel was 0.3, and the density was 7800 kg/m³. The parameters of the P-BD are listed in

Table 1. Parameters required for angle of repose simulation.

Parameter Types	Parameter Designations	Parameters	Parameter Levels
			−1	0	1
Basic Parameters	T1	Poisson’s Ratio	0.3	0.35	0.4
	T2	Density (kg/m3)	1200	1250	1300
	T3	Shear Modulus (MPa)	1	1.25	1.5
	T4	Soil-Soil Restitution Coefficient	0.15	0.4	0.65
	T5	Soil-Soil Static Friction Coefficient	0.2	0.5	0.8
	T6	Soil-Soil Dynamic Friction Coefficient	0.1	0.4	0.7
	T7	Soil-Steel Restitution Coefficient	0.3	0.5	0.7
	T8	Soil-Steel Static Friction Coefficient	0.3	0.6	0.9
	T9	Soil-Steel Dynamic Friction Coefficient	0	0.25	0.5
JKR Model Parameters	T10	Surface Energy (J/m2)	0	0.15	0.3
Bonding Model Parameter	T11	Critical Normal Stress (kPa)	1	10	100
	T12	Critical Tangential Stress (kPa)	1	10	100

.

Screening experiments were conducted using Design-Expert 13 software, and 13 simulations were performed for each contact model configuration: (a) the JKR model and (b) the Bonding model. Standardized Pareto charts (Figure 6) indicated three statistically significant parameters for each model: parameters T10, T5, and T4 in the JKR model and T5, T8 and T6 in the bonding model.

Based on the results of the climb test, the B-BD was implemented using Design-Expert 13 software with the angle of repose as the response variable [33]. Fifteen experimental runs were conducted for the JKR model simulation, yielding a coefficient of determination (R²) of 0.9672 and an adjusted R² of 0.8689. Both values indicate an excellent model fit to the empirical data. Non-significant influencing factors were eliminated through analysis of variance. Subsequently, a second-order regression Equation (12) was established:

$$Y_1=41.706-36.133T_4-9.392T_5+58.461T_{10}+70.667T_4{T}_5-86.889T_5{T}_{10}$$

(12)

For the Bonding model, fifteen experimental trials were conducted, achieving an R² of 0.9903 and an adjusted R² of 0.9612. A second-order regression equation for soil relative error was subsequently established as presented in Equation (13).

$$Y_2=52.993-38.045T_5+8.55T_6-38.967T_8+49.107{T_6}^2+36.107{T_8}^2$$

(13)

The optimal parameter combination is listed in

Table 2. Optimal Parameter Combination.

Contact Model	T4	T5	T6	T8
JKR Model	0.585	0.45	-	-
Bonding Model	-	0.54	0.31	0.51

.

The validation of the optimized parameter combinations demonstrated an excellent agreement with the empirical data. The simulated angle of repose for the JKR model was 38.57° (Figure 7a), showing a 0.59% relative error compared to experimental measurements. The Hertz-Mindlin with Bonding model yielded a simulated angle of 38.94° (Figure 7b), with a lower relative error (0.36%). These results confirm that both contact parameter sets are suitable for soil shear modeling experiments.

3. Result and Discussion

3.1. Direct Shear Simulation Test of Soil

The same normal stresses as in the physical experiments were applied in the simulations for both contact models. The soil particles were compacted under normal stresses of 100 kPa, 200 kPa, 300 kPa, and 400 kPa.

A numerical shear test model was established using SolidWorks 2023 software based on the results of the direct shear test, as shown in Figure 8. The model dimensions were identical to those of the experiment. The model consisted of upper and lower shear boxes. The upper shear box had a height of 60 mm and an inner diameter of 61.8 mm, and the lower shear box had a height of 10 mm and an inner diameter of 61.8 mm. The two shear boxes were placed concentrically, with the lower box open at the top and closed at the bottom, and the upper box open at both ends. A normal stress platen was installed at the top to apply normal compressive stress. The shear model was imported into EDEM software, and the material was steel. Soil particles with the same mass as in the experiment were added. The vertical load on the soil model was applied by imposing a downward velocity on the pressure platen in the upper shear box. The contact force between the soil particles and the pressure platen in the vertical direction was used as the normal compressive stress in the simulated direct shear test.

The simulation applied a shear velocity of 2 mm/s to the lower shear box, with the direction of movement as shown by the red arrow in Figure 8, and the relative direction of movement of the upper shear box as shown by the blue arrow, consistent with the shear rate used in the experiments. The total shear simulation duration was 5 s, and the simulation terminated when the horizontal displacement of the lower shear box reached 10 mm.

To calibrate the critical normal and tangential stresses and reduce the number of calibration parameters, these two stresses were assigned the same values [34]. Iterative shear simulations were conducted using critical normal and tangential stress values of 70 kPa. A direct shear simulation was performed with the Hertz-Mindlin with Bonding model, resulting in a simulated internal friction angle of 35.8°, with a relative error of 5.8% compared to the physical test. The direct shear simulation data for the JKR model were determined based on the optimal parameter combination derived from the soil angle of repose simulation tests. The simulation results indicated that the JKR model yielded a simulated internal friction angle of 18.81°. The significant deviation between the JKR model results and the experimental values may be attributed to the model’s simplification of particle shape and friction mechanisms, the limitations of cross-scenario parameter reuse, and differences between simulation conditions and experimental conditions, which collectively lead to a significant underestimation of the internal friction angle. In contrast, the Hertz-Mindlin model (with bonding), which focuses more on the synergistic effect of friction and bonding, yields simulation results (35.8°) that are closer to the experimental values. This also confirms the limitations of the JKR model in describing the shear friction characteristics of soil.

The shear stress-displacement relationship for both contact models at a normal compressive stress of 200 kPa and the experimental results are shown in Figure 9.

The results of the experiment and the bonding model simulations exhibited three phases in the shear stress response: an increase, a steady-state phase, and a decrease. In the physical tests, segment 0–a₁ represents the ascending phase, where the shear stress increases with the displacement due to the combined effects of soil cohesion and internal frictional resistance. The intact physical bonds between the soil particles ensure structural integrity during this phase.

The system enters the steady-state phase when the displacement reaches point a1 (a₁–a₂), characterized by bond rupture. However, particle rearrangement and frictional interlocking result in new load-bearing paths, resulting in stable shear stress. The descending phase starts after reaching point a₂, and the soil exhibits complete failure. The cohesion is lost, and only residual frictional resistance remains, reducing the stress. The Bonding model closely describes this physical behavior. Segment 0–b₁ corresponds to the increasing trend, in which elastic deformation occurs under shear forces. Segment b₁–b₂ reflects the steady-state phase, demonstrating the dynamic equilibrium between bond rupture and bond reinforcement and corresponding closely to the stress plateau observed experimentally. A descending trend occurs after point b₂, and the bond failure rate exceeds the system’s load-bearing capacity. In contrast, the JKR model demonstrates different shear behavior, exhibiting a monotonic stress increase without the subsequent phases, significantly deviating from the experimental observations. This discrepancy highlights substantial mechanistic differences in the shear responses derived from the models.

The bond failure is shown in the stress cloud diagrams (Figure 10) perpendicular to the normal stress and shear displacement directions at t = 3.5 s under 200 kPa normal stress. These diagrams illustrate the force distribution and bond rupture for both contact models during shear simulations.

The stress cloud diagrams reveal different mechanical responses for the two contact models. In the JKR model, the stress distribution across cohesive bonds is relatively stable at t = 3.5 s, without significant redistribution, indicating the model’s inability to accurately describe shear-induced interfacial mechanical behavior. In contrast, the Bonding model demonstrates characteristic mechanical responses. The leftward displacement of the lower shear box causes coordinated particle movement through bond interactions, resulting in systematic tensile-compressive alternation of interparticle bonds. This mechanical process results in progressive stress distribution from the lower right to the upper left in the cloud diagram. Initial stress concentration occurs in the lower right, followed by stress wave propagation toward the upper left, forming stress gradient bands, which demonstrate the dynamic evolution of force chain networks during shear.

The relationship between particle displacement and shear strength for both contact models is shown in Figure 11. The Hertz-Mindlin with Bonding model shows excellent agreement between the experimental and simulated shear force evolution, whereas the Hertz-Mindlin with the JKR model exhibits significant deviations. These results demonstrate that the Hertz-Mindlin with Bonding model provides superior characterization of soil shear behavior.

In summary, the angle of repose simulations and direct shear tests demonstrate that the Hertz-Mindlin with Bonding model more accurately characterizes interparticle contact in granular soil systems than the JKR model.

3.2. Soil Penetration Test and Simulation Verification of Hole Creation

As a core component of cotton precision seeding equipment, the hole former creates precise seed cavities through mechanical soil penetration. Its duckbill structure creates seed cavities with a consistent depth (1.5–2.5 cm) and optimal diameter (20–30 mm). This mechanism works in synchronization with a precision metering system to deposit one or two cotton seeds accurately into each cavity, followed by soil covering and compaction to ensure optimal seed-soil contact. The experimental simulation replicates the soil penetration during seeding, where the interaction between the hole former and the soil generates measurable soil disturbance and force feedback.

The most commonly employed hole former configurations in cotton planting include square and conical duckbill designs, with 20–30 mm cavity diameters and 80–120 mm lengths. A conical duckbill design was used in the simulation (Figure 12). It minimizes soil resistance during penetration and ensures sufficient cavity wall stability.

The soil penetration test apparatus consisted of three primary components: a pressure measurement system, the hole former, and a standardized soil bin. The soil bin was a rectangular container with dimensions of 200 mm (length) × 150 mm (width) × 150 mm (height). It was filled with prepared soil samples with different bulk densities. The former was rigidly attached to the compression testing apparatus and moved downward at a constant penetration rate of 60 mm/min until reaching the target depth of 60 mm, as illustrated in Figure 13. The movable duckbill components moved to the right due to increasing soil resistance. The duckbill achieved full deployment at the maximum penetration depth of 60 mm, with a sufficient opening angle to enable seed release. This mechanical behavior was carefully monitored to ensure the appropriate synchronization between soil penetration and seed release timing, critical for achieving precision seed placement. The experimental configuration enabled the measurement of the vertical penetration force and lateral soil reaction force acting on the opener surfaces.

The duckbill device did not open the soil in the simulation in EDEM. Thus, it was necessary to utilize the multi-body dynamics simulation software Recurdyn 2024 to achieve the soil penetration simulation. In EDEM, the soil particles and their properties are based on the calibrated parameters, and the soil particles fill the soil box, whose volume is the same as in the experiment. The model was established in Recurdyn with the same size as in the experiment, and EDEM was coupled with Recurdyn. The downward movement occurred at a speed of 60 mm/min, and the final soil penetration depth was 60 mm.

The mechanical response of the soil during the hole former’s penetration was analyzed. Figure 14 shows the force on the soil particles at a penetration depth of 60 mm.

As the hole formed penetrated the soil, the front ends of its fixed duckbill and active duckbill began to contact the soil mass, causing shear and compressive stresses to intensify locally. The particle color transitioned from blue to green (Figure 14), and the orientation shifted away from the hole former, indicating that the particle forces increased and slippage occurred. The bonds experienced tensile-shear effects, resulting in directional deformation, and damage occurred.

As the depth of the hole former increased, the active duckbill of the hole former was subjected to the reaction force of the soil, causing the active duckbill to open to the right and gradually separate from the fixed duckbill. The high-stress area (red in Figure 14) increased at the leading edge and on both sides of the hole former. The arrow directions indicate a fan-shaped trend. The relative movement between particles intensified, and bond fractures occurred in multiple regions. A change in the directionality of particle slippage reflected changes in the stress transfer path. Tensile cracking, slippage, and complete failure were observed in stress-concentrated areas, and the soil structure deteriorated.

At a depth of 60 mm, the active duckbill of the hole former moved to the right to the maximum displacement, and the entire duckbill was fully opened. The red particles were dominant. Many arrows and directional consistency indicate substantial movement between particles. The forces affecting the bonds reached the limit, and fractures or slippage occurred in most areas. The force direction showed radial diffusion, local damage, structural loosening, and stress release. The particle force intensity and direction show the evolution of the bonds from stability to tension, slippage, and fracture during penetration. The change in the particle movement direction reflects the force transmission and reveals alterations in the soil structure due to disturbance, exhibiting significant nonlinear responses and cumulative damage.

The simulation and experimental results were compared to verify the models’ accuracy (Figure 15). The test results show that the peak soil pressure was 467.2 N in the experiment and 485.3 N in the simulation. The force curves of the hole former during soil penetration are consistent in the simulation and experiment, verifying the accuracy of the Bonding model and parameter calibration. Thus, the proposed contact model accurately characterizes the mechanical response during the hole former’s soil penetration, confirming the rationality and reliability of the model parameter configuration and the constitutive relationship.

4. Conclusions

The DEM was used for simulations, and experiments were conducted to determine the physical parameters of the soil in the cotton-planting area in southern Xinjiang. The following conclusions were obtained:

(1)

A simulation test of the soil’s angle of repose was performed, and the simulation parameters were obtained using two contact models. The relative error between the simulated and actual angles of repose of the soil was 0.59% for the JKR model and 0.36% for the Hertz-Mindlin with Bonding model

(2)

In the soil shear test, the Bonding model showed higher accuracy than the JKR model. The internal friction angle obtained by the Bonding model was 35.8° with a relative error of 5.8°, while that by the JKR model was 18.81°. This reveals that in dynamic mechanical processes such as soil shearing, when the simulation involves relative sliding and separation of particle groups, contact models (e.g., the Bonding model) that can simultaneously characterize both the bonding force and friction force between particles are more consistent with the mechanical response laws of actual soil.

(3)

The maximum penetration force of the hole former in the experiment was 467.2 N, and the simulated value was 485.3 N, showing a high degree of agreement. The simulated parameter values are close to the actual ones, indicating that the proposed calibration method and parameter values can be applied to the discrete element simulation of the interaction between the soil-contacting components of the cotton seeder and the soil under the Dry Seeding followed by Irrigation (DSSI) regime, as well as its structural optimization. Meanwhile, it also verifies the applicability of the above-mentioned law regarding the selection of contact models in the scenario of agricultural machinery—soil interaction.

This study is helpful for the discrete element simulation analysis of the interaction between soil-engaging components of cotton field tillage machinery and soil, as well as their structural optimization. However, there is still some discrepancy between the results of the simulation experiment and the actual field operation. Future work will explore the performance of hole-forming devices and the interaction mechanism between hole-forming devices and soil under different soil conditions through field experiments.