Discrete Element Modelling and Simulation Parameter Calibration for the Growing Media of Seedling Nursery Blocks

Abstract

Using the discrete element method to simulate the interaction between growing media and machinery is an effective method to design seedling machinery and improve the precision of facility horticultural operations. In order to further improve the accuracy of the study on the interaction between seedling block-forming machines and growing media, the growing media used in the production of seedling nursery blocks was taken as the research object, and the Plackett–Burman screening test and Box–Behnken test were conducted based on the discrete element method using the EEPA model to conduct the calibration of discrete element parameters of the growing media. Optimization was conducted with an actual repose angle as the target value, and the optimal combination is as follows: the interparticle collision-recovery coefficient is 0.5066, the collision-recovery coefficient between particles and the geometric model is 0.714, the interparticle dynamic-friction coefficient is 0.381, and the tangential stiffness factor is 0.375. Finally, the soil uniaxial closed compression test was conducted with optimized calibration parameters. The relative error between the maximum axial load on the punch and the measured value in the simulation process was 4.23%, which verified the accuracy and reliability of parameter calibration of the growing media and provided support for the simulation of growing media and optimization of seedling nursery block-forming machine.

1. Introduction

China is a significant player in the field of facility horticulture, with the area of facility horticulture accounting for over 80% of the total area of facilities worldwide [1]. As the scale and intensity of facility horticulture continue to grow, there are increasing demands for advanced seedling operation machinery (including transportation, pallet loading/molding, media digging for plug trays, etc.) [2,3]. The discrete element method is frequently utilized to accurately represent the motion behavior of materials and simulate their interactions with machinery [4,5]. The application of this method in studying the interaction between seedling substrates and working machinery has the potential to enhance work efficiency, minimize research and development costs, and provide valuable theoretical insights for optimizing the design of seedling substrate production and working machinery [6]. An accurate and reliable simulation is contingent upon the selection of appropriate discrete element-simulation parameters (such as eigenparameters, basic contact parameters, and contact models), which serve as essential prerequisites for effective simulation [7]. However, due to the diverse materials, particle-size distribution, and shapes of the objects being studied, it is essential to select an appropriate contact model and parameters that align with the characteristics of the research objects to enhance the simulation’s accuracy [8,9].

Currently, numerous scholars have conducted comprehensive research on agricultural granular particles using the discrete element method. The discrete element simulation parameters of fallen jujube fruit were calibrated using the Hertz–Mindlin (no slip) contact model [10]. Wang et al. [11] recommended selecting soil particles with a radius of 7 mm for Hertz–Mindlin with a bonding model when conducting research on soil subsoiling. Discrete element models of soil particles have been widely reported. For instance, discrete element-simulation models were developed based on Edinburgh Elasto-Plastic Adhesion (EEPA) for consolidated soil [12], no-tillage soil [13], broken soil [14], and sandy loam soil [15], which has been established that the discrete element method can be effectively utilized in simulating agricultural machinery operations and optimizing agricultural machinery design. However, there are relatively few simulation studies on growing media. Tong et al. [16] selected Hertz–Mindlin with the bonding model when the end efferent of the simulated transplanter captured the growing media (composed of peat, perlite, and vermiculite with a moisture content of ~50–72%) and used the soil parameter as an alternative to achieve a qualitative analysis of the cohesion between the growing media. Wang et al. [17] modeled and calibrated one of the growing media’s raw materials (coconut husk particles) based on the Hertz–Mindlin (no slip) contact model with the discrete element method, providing a reference for the design of special equipment for mixing coconut husk-growing media. Ding et al. [18] conducted a discrete element parameter calibration for the plug tray-growing media (mainly composed of peat, wood chips, etc., with a moisture content of about 31%), and selected the EEPA model.

To sum up, the research object of seedling breeding substrate by researchers at home and abroad is mainly a certain growing media material or plug tray-growing media. In actual seedling breeding practices, due to the inherent limitations in the physical and chemical properties of individual growing media, it is often necessary to utilize a composite growing media that combines both organic materials (such as peat, straw, organic fertilizer, coconut bran, etc.) and inorganic materials (such as perlite and vermiculite) to achieve optimal seedling breeding results [19,20]. Furthermore, currently, there is a lack of simulation analysis on the flow behavior and compression molding of growing media in the preparation of seedling nursery blocks.

According to the previous study, it has been proved that the rabbit manure compost-growing media has good physical and chemical properties and a seedling-rearing effect [21]. The growing media, being a typical granular particle, exhibit a notable rebound following compression molding, accompanied by a certain degree of cohesiveness and elastoplasticity. Therefore, compared to the Hertz–Mindlin (no slip) model, which is suitable for incompressible non-viscous particles [10], the Hertz–Mindlin-with-JKR model, which is suitable for incompressible viscous particles [22], the Hysteretic Spring model, which is suitable for compressible non-viscous particles [23], and the Hertz–Mindlin-with-bonding model, which is suitable for materials such as rocks and concrete that do not rebound after breaking [24], the EEPA model may be more suitable for simulating this growing media [14,15]. When calibrating the parameters of the EEPA model, the Plackett–Burman screening test is considered to be able to quickly identify parameters that have a significant impact, while the Box–Behnken test can further find the optimal parameter combination, thereby achieving accurate simulation of the growing media [12,13].

In this study, the growing media used in the production of seedling nursery blocks were selected as the focus object. The discrete element method was utilized, with the EEPA model employed, to conduct Plackett–Burman (PB) screening tests and Box–Behnken (BB) tests for the calibration and optimization of the discrete element parameters of the growing media. After verifying the maximum forming load during the uniaxial closed compression test, the construction of a discrete element model for the growing media was finally completed, providing valuable data references for the design and optimization of the molding device for seedling nursery blocks.

2. Materials and Methods

2.1. Test Material

The growing media used in this study were mainly composed of rabbit manure compost, peat, vermiculite, and straw, with a volume ratio of 40:10:25:25 and a moisture content of 33.5%. After random sampling, the test was repeated three times using a standard ring knife of 100 cm³ (50.46 × 50 mm), and the bulk weight of the growing media was 304 kg/m³. The density of growing media measured by gravity bottle method was 1080 kg/m³ and was used for subsequent simulation tests. The particle size distribution of growing media was measured by layer-screen method, which showed that 93% of growing media particle size was ~0.11–1.7 mm, and the geometric average diameter was 0.43 mm.

2.2. Test Methods

Through the combination of accumulation and compression test of growing media and simulation of discrete element model, the relevant parameters of the established growing media were calibrated, as shown in Figure 1. The static repose angle of growing media was obtained by cylinder-lifting method and used as the target value for parameter calibration of the growing media. The values or ranges of simulation parameters were obtained through literature research (see Section 2.2.5), PB screening tests were designed using Design Expert 10 software, and the growing media-accumulation simulation tests were conducted using EDEM 2020 to obtain parameters that had a significant impact on the repose angle. BB test method was used to establish a regression model of growing media static repose angle and significance parameters, and the actual static repose angle was taken as the target value, and the parameters were optimized by Design Expert software. The optimized simulation parameters were used to conduct growing media-accumulation tests, and the accuracy of the simulation model was compared. The maximum axial load during the forming process of growing media was obtained through the uniaxial closed-compression test of growing media, and the discrete element-simulation test was conducted simultaneously with the optimized simulation parameters. By comparing the difference between the actual and simulated maximum axial load, the reliability of the discrete element model of growing media was further verified.

2.2.1. Growing Media-Accumulation Test

The test device of growing media is shown in Figure 2, which consists of cylinder, chassis, screw, and push-rod motors (SY-A02B, Wuxi Ouruide Transmission Technology Co., Ltd., Wuxi, China). Among them, the diameter of the cylinder is 70 mm, and the height is 245 mm. After the growing media filled the cylinder, the push-rod motor drove the cylinder to lift at a constant speed of 5 mm/s, and the growing media naturally accumulated to form the pile. After the reactor was stabilized, three sets of images were collected from the front and side, respectively, and the data of base angle were obtained by using Image J software 1.54j [25]. The accumulation test was repeated five times, and the repose angle of growing media was 44.64°.

2.2.2. Growing Media Uniaxial Closed-Compression Test

The growing media uniaxial closed-compression test platform, as shown in Figure 3, was mainly composed of universal material testing machine (INSTRon-3367, Instron, Norwood, MA, USA), punch die, concave die, die pad, stripper, control, and display system. The inner diameter of the die was 50 mm, the height was 90 mm, and the inner wall was polished to reduce the forming energy consumption. The system can control the compression process (adjust the compression load, displacement, time, speed, and other parameters) and record the load and displacement of the growing media in real time. In the test, the growing media were filled with the concave die, and then the universal material testing machine was started to drive the punch downward at a speed of 35 mm/min. The motion displacement was 72.2 mm; that is, the compression ratio was 4:1. The maximum axial load on the punch during compression test was recorded by the universal material testing machine system. The test was repeated five times, and the maximum axial load was 2644.41 N.

2.2.3. Contact Model Selection

In the preliminary test, it was found that the growing media have a certain elastic-plastic property, and there is a certain degree of rebound after compression molding, so it is suitable to choose the EEPA model as the contact model of the growing media particles [26]. The model can reflect nonlinear elastoplasticity and bonding properties and can effectively simulate the growing media particle-compression molding process. EEPA model normal contact force-normal overlap curve is shown in Figure 4, and the calculation method is shown in Formula (1) [27].

$$f_n=\left\{\begin{array}{c}{f}_o+K_1{\delta }^{\mathrm{n}}\\ f_o+K_2({\delta }^{\mathrm{n}}-{\delta }_p^n)\\ f_o-K_{\mathrm{adh}}{\delta }^{\mathrm{X}}\end{array}\right.\begin{array}{cc}& \end{array}\begin{array}{c}{K}_2({\delta }^{\mathrm{n}}-{\delta }_p^n)\ge K_1{\delta }^{\mathrm{n}}\\ K_1{\delta }^{\mathrm{n}}>K_2({\delta }^{\mathrm{n}}-{\delta }_p^n)>K_{adh}{\delta }^X\\ -K_{adh}{\delta }^X\ge K_2({\delta }^{\mathrm{n}}-{\delta }_p^n)\end{array}$$

(1)

where $f_n$ and $f_0$ are normal contact force (N) and constant initial bond strength (N), respectively; $\delta$ and ${\delta }_p$ are normal overlap (m) and plastic deformation (m), respectively. $K_1$, $K_2$_, and $K_{adh}$ are the loading branch stiffness (N/m), unloading branch stiffness (N/m), and bonding branch stiffness (N/m), respectively. n and X are loading branch index and bonding branch index, respectively.

2.2.4. Simulation Model Building

Before the simulation test, it is necessary to establish the geometric model of growing media particle and accumulation test and uniaxial closed-compression test. A single-ball model with an average particle radius of 0.9 mm was selected as the simulation model of the growing media in order to improve the speed of simulation calculation due to the small particle size (0.43 mm) of growing media [28].

SolidWorks software 2023 was used to establish the simplified geometric model of pile test and the geometric model of uniaxial closed-compression test (such as concave die, punch die, and scraper), respectively, and saved as IGS format for import into EDEM, as shown in Figure 5.

2.2.5. Simulation Parameter Setting

The Poisson’s ratio of the growing media was 0.38 [15,29], and the shear modulus was 1 MPa [15,30] by referring to similar materials such as potted flower matrix and soft clay. The steel geometric model has a Poisson ratio of 0.3, a density of 7850 kg/m³, and a shear modulus of 7 × 10⁴ MPa, as reported in literature [13,30]. Additionally, the simulated contact parameter values or ranges of the substrate were determined based on the characteristics of the seedling substrate, with reference to the GEMM database of EDEM software and the discrete element parameter values of elastoplastic particles studied by Wang et al. [13], Liu Jinkai [30], Yan et al. [15], and Zhao et al. [14]. That is, the recovery coefficient of interparticle collision ranges from 0.2 to 0.8, the static-friction coefficient ranges from 0.3 to 1.0, and the dynamic-friction coefficient ranges from 0.1 to 0.9. The collision-recovery coefficient between the particle and the geometric model is between 0.1 and 0.6, the static-friction coefficient is between 0.2 and 0.9, and the dynamic-friction coefficient is between 0 and 0.3. In the EEPA contact model, the constant initial bond strength is set at 0 N, with a surface energy ranging from 4 to 30 J/m², a plastic deformation ratio ranging from 0.3 to 0.8, a loading branch index of 1.5, a binding branch index ranging from −5 to 5, and a tangential stiffness factor ranging from 0.2 to 0.7.

The simulation process of the uniaxial closed-compression test refers to the physical test [31], and the test process is shown in Figure 6a–f. Among them, the diameter of the die is 50 mm, the height is 90 mm, and the chassis diameter is 160 mm. The simulation settings are as follows: First, 0.1 kg of growing media particles are generated statically, and the particles are gradually settled into the concave mold (Figure 6a,b). After 0.19 s, the scraper moves horizontally along the upper surface of the die at a speed of 5 m/s to remove excess growing media particles (Figure 6c). Then, the punch is moved directly above the punch, and the bottom surface of the punch is flush with the upper surface of the growing media particles (Figure 6d). Finally, the punch moves down 72.2 mm at a constant speed of 50 mm/s, so that the growing media-compression ratio is consistent with the physical test (Figure 6e,f). The fixed time step is set to 2% of the Rayleigh time step, the total simulation time is 2 s, and the simulation mesh size is set to 2R; that is, 1.8 mm. After the simulation, the maximum axial load of the punch in the simulation process is derived by EDEM software.

2.2.6. PB Screening Test

PB screening test was conducted to preliminarily screen the parameters that had a significant impact due to the numerous and imprecise simulation parameters of the growing media. The experimental parameter columns and levels are shown in

Table 1. Parameters and levels of PB screening test.

Code	Parameter	Level
		−1	0	1
X1	Interparticle collision-recovery coefficient	0.2	0.5	0.8
X2	Static-friction coefficient between particles	0.3	0.65	1
X3	Dynamic-friction coefficient between particles	0.1	0.5	0.9
X4	Collision-recovery coefficient between particles and geometric models	0.1	0.35	0.6
X5	Static-friction coefficient between particles and geometric models	0.2	0.55	0.9
X6	Dynamic-friction coefficient between particles and geometric models	0	0.15	0.3
X7	Surface energy (J/m2)	4	17	30
X8	Plastic deformation ratio	0.3	0.55	0.8
X9	Adhesion branching index	1.5	3.5	5.5
X10	Tangential stiffness factor	0.2	0.45	0.7
X11	Virtual parameters	/	/	/

, where X₁–X₁₀ is the real test parameter and X₁₁ is the virtual test parameter. According to the reference range of each parameter, the high and low levels were selected for the experimental design. The simulation repose angle of growing media particles was used as the response value, and the total number of experiments was 12 [13].

3. Results and Discussion

3.1. PB Screening Test Results and Significance Analysis

The method and results of the PB screening test are shown in

Table 2. Design and results of PB screening test.

Number	Experimental Factors 1										Repose Angle (°)
	X1	X2	X3	X4	X5	X6	X7 (J/m2)	X8	X9	X10
1	0.8	1	0.9	0.1	0.2	0	30	0.3	5.5	0.7	88.35
2	0.2	0.3	0.1	0.1	0.2	0	4	0.3	1.5	0.2	50.64
3	0.2	1	0.1	0.6	0.9	0	30	0.8	5.5	0.2	25.03
4	0.8	0.3	0.1	0.1	0.9	0	30	0.8	1.5	0.7	89.43
5	0.8	0.3	0.9	0.6	0.9	0	4	0.3	5.5	0.2	89.19
6	0.2	0.3	0.9	0.1	0.9	0.3	4	0.8	5.5	0.7	2.18
7	0.8	0.3	0.9	0.6	0.2	0.3	30	0.8	1.5	0.2	56.26
8	0.2	1	0.9	0.6	0.2	0	4	0.8	1.5	0.7	23.36
9	0.2	0.3	0.1	0.6	0.2	0.3	30	0.3	5.5	0.7	3.08
10	0.8	1	0.1	0.1	0.2	0.3	4	0.8	5.5	0.2	89.91
11	0.2	1	0.9	0.1	0.9	0.3	30	0.3	1.5	0.2	24.04
12	0.8	1	0.1	0.6	0.9	0.3	4	0.3	1.5	0.7	46.97

¹ X₁–X₁₀ are inter-particle collision-recovery coefficient, static-friction factor, and dynamic-friction factor, respectively, collision-recovery coefficient, static-friction factor, and dynamic-friction factor between particle and geometric model, surface energy, plastic deformation ratio, adhesion branch index, and tangential stiffness factor.

.

Sensitivity analysis was conducted by Design Expert software, and the results are shown in

Table 3. The results of sensitivity analysis.

Parameter 1	Standardization Effect	Mean Sum of Squares	Contribution Degree (%)
X1	55.30	9672.83	73.32
X2	1.15	3.94	0.03
X3	−3.61	39.09	0.31
X4	−16.78	844.60	6.75
X5	−5.79	100.65	0.80
X6	−23.92	1717.07	13.72
X7	−2.68	21.51	0.17
X8	−2.68	21.60	0.17
X9	1.18	4.14	0.003
X10	−13.62	566.16	4.45

¹ X₁–X₁₀ are inter-particle collision-recovery coefficient, static-friction factor, and dynamic-friction factor, respectively, collision-recovery coefficient, static-friction factor, and dynamic-friction factor between particle and geometric model, surface energy, plastic deformation ratio, adhesion branch index, and tangential stiffness factor.

.

The contributions of these 10 simulation parameters to the repose angle of growing media particles are as follows: X₁ (collision-recovery coefficient between particles), X₆ (dynamic-friction coefficient between particles and geometric models), X₄ (collision-recovery coefficient between particles and geometric models), X₁₀ (tangential stiffness factor), X₅ (static-friction coefficient between particles and geometric models), X₃ (dynamic-friction coefficient between particles), X₈ (plastic deformation ratio), X₇ (surface energy), X₂ (static-friction coefficient between particles), and X₉ (adhesion branching index). In addition, the analysis of variance results showed that the p-values of the collision-recovery coefficient between particles, the collision-recovery coefficient between particles and geometric models, and the dynamic-friction coefficient between particles and geometric models were <0.0001, 0.0062, and 0.0009, respectively, which had a significant impact on the repose angle of growing media particles. The p-value of the tangential stiffness factor is 0.0164, which has a significant impact on the repose angle of growing media particles. Other parameters have no significant impact (p ≥ 0.05).

Among the four significant parameters, the collision-recovery coefficient between particles is positively correlated with the repose angle of growing media particles, while the other three are negatively correlated. Chen et al. [9] and Wang et al. [13] found that the inter-particle collision-recovery coefficient had a significant influence on the depth of compression settlement when establishing the discrete element model of wheat soil planted after rice in the lower reaches of the Yangtze River based on the EEPA model and when no tillage soil was used. Lin et al. [32] and Wang et al. [33] found that, compared with the static-friction coefficient, the rolling-friction coefficient had a more significant effect on the repose angle of earthworm manure and pig manure, which was consistent with the results of this study. Wan et al. [34] also found the significant influence of tangential stiffness factor on the repose angle when using the EEPA model to conduct the parameter calibration of the soil discrete-element model.

3.2. BB Experiment Design and Analysis

On the basis of the PB screening test, the BB experiment was conducted with significance parameters X₁, X₄, X₆, and X₁₀ as experimental parameters to seek the optimal combination of growing media particle parameters, as shown in

Table 4. The BB experimental design.

Level	Experimental Factors 1
	X1	X4	X6	X10
−1	0.3	0.2	0.1	0.3
0	0.5	0.4	0.2	0.5
1	0.7	0.6	0.3	0.7

¹ X₁, X₄, X₆, and X₁₀, respectively, represent the collision-recovery coefficient between particles, the collision-recovery coefficient between particles and geometric models, the dynamic-friction coefficient, and the tangential stiffness factor.

. In this simulation experiment, the steps and analysis of the repose angle test are the same as those of the PB test. The parameters that do not have a significant impact on the repose angle are taken as the median of the interval, which means that the static-friction coefficient and dynamic-friction coefficient between particles are 0.65 and 0.5; the static-friction coefficient between particles and geometric models is 0.55; the surface energy, plastic deformation ratio, and adhesion branching index are 17 J/m², 0.55, and 3.5, respectively.

The design scheme and results of the BB experiment are shown in

Table 5. Design scheme and results of the BB test.

Number	Experimental Factors 1				Repose Angle (°)
	X1	X4	X6	X10
1	0.3	0.4	0.1	0.5	3.89
2	0.5	0.4	0.1	0.3	89.57
3	0.7	0.4	0.1	0.5	88.65
4	0.5	0.4	0.1	0.7	5.53
5	0.5	0.4	0.2	0.5	11.94
6	0.5	0.2	0.3	0.5	14.58
7	0.5	0.6	0.3	0.5	8.94
8	0.7	0.4	0.3	0.5	89.21
9	0.5	0.4	0.2	0.5	14.20
10	0.5	0.4	0.3	0.3	88.39
11	0.5	0.2	0.2	0.7	7.05
12	0.3	0.4	0.3	0.5	2.14
13	0.5	0.2	0.1	0.5	6.81
14	0.5	0.4	0.2	0.5	6.30
15	0.7	0.2	0.2	0.5	87.12
16	0.7	0.4	0.2	0.3	88.68
17	0.5	0.4	0.3	0.7	2.29
18	0.5	0.4	0.2	0.5	8.26
19	0.3	0.6	0.2	0.5	2.96
20	0.5	0.6	0.1	0.5	6.42
21	0.3	0.4	0.2	0.7	1.19
22	0.7	0.6	0.2	0.5	87.22
23	0.5	0.6	0.2	0.7	2.86
24	0.7	0.4	0.2	0.7	86.04
25	0.5	0.4	0.2	0.5	7.02
26	0.5	0.6	0.2	0.3	88.97
27	0.3	0.2	0.2	0.5	3.02
28	0.5	0.2	0.2	0.3	87.41
29	0.3	0.4	0.2	0.3	1.11

¹ X₁, X₄, X₆, and X_10, respectively, represent the collision-recovery coefficient between particles, the collision-recovery coefficient between particles and geometric models, the dynamic-friction coefficient, and the tangential stiffness factor.

, and the results of variance analysis are listed in

Table 6. Analysis of variance of the BB test.

Source of Variance	Sum of Squares	Degree of Freedom	Mean Square	F	p-Value
Model	37709.65	14	2693.55	5.67	0.0013 **
X1	21897.40	1	21897.40	46.10	<0.0001 **
X4	6.19	1	6.19	0.013	0.9107
X6	1.83	1	1.83	3.86 × 10−3	0.9514
X10	9586.57	1	9586.57	20.18	0.0005 **
X1X4	6.40 × 10−3	1	6.40 × 10−3	1.35 × 10−5	0.9971
X1X6	1.34	1	1.34	2.81 × 10−3	0.9585
X1X10	1.85	1	1.85	3.89 × 10−3	0.9511
X4X6	6.88	1	6.88	0.014	0.9059
X4X10	8.27	1	8.27	0.017	0.8969
X6X10	1.06	1	1.06	2.22 × 10−3	0.9631
X12	3520.34	1	3520.34	7.41	0.0165 *
X42	238.24	1	238.24	0.50	0.4905
X62	269.34	1	269.34	0.57	0.4639
X102	3823.38	1	3823.38	8.05	0.0132 *
Residual error	6650.37	14	475.03
Pure error	45.97	4	11.49
Sum total	44360.02	28

Note: X₁, X₄, X₆, and X₁₀ represent the collision-recovery coefficient between particles, the collision-recovery coefficient between particles and geometric models, the dynamic-friction coefficient, and the tangential stiffness factor, respectively; ** is extremely significant (p < 0.01), * is significant (p < 0.05).

.

Through analysis of variance (Table 6), it can be seen that experimental parameters X₁ (particle-to-particle collision-recovery coefficient) and X₁₀ (tangential stiffness factor) have a significant impact on the repose angle of growing media particles, X₁² and X₁₀² have a significant impact on the repose angle of growing media particles, while other parameters and their interactions have no significant impact on the repose angle.

3.3. Parameter Optimization and Simulation Verification

The Design Expert software takes the actual repose angle (44.64°) as the target value and performs parameter optimization within the range of the simulation test. The optimal solution combination is as follows: The interparticle collision-recovery coefficient X₁ is 0.5066, the collision-recovery coefficient X₄ between particle and geometric model is 0.714, the dynamic-friction coefficient X₆ between particle and geometric model is 0.381, and the tangential stiffness factor X₁₀ is 0.375.

The optimized discrete-element simulation parameters of growing media particles (significance parameters X₁, X₄, X_6, and X₁₀ are taken as optimized parameters, and the rest of the parameters are taken as the median value of the interval) are substituted into the simulation test of the growing media repose angle. Using the same analytical method as in the actual experiment to collect accumulation test-image data, the average simulated repose angle for the growing media particles was determined to be 46.30° (as shown in Figure 7a). The relative error compared to the actual repose angle (44.64°) is 3.72%, reflecting a high degree of fit.

In order to verify the accuracy and reliability of the calibrated growing media model, the simulation test of punch force in the process of growing media-block compression was conducted according to the discrete-element model of growing media. By substituting the optimized parameters of the growing media-particle model (collision-recovery coefficient, static-friction coefficient, and dynamic-friction coefficient between particles are 0.5066, 0.65, and 0.5, respectively; collision recovery coefficient, static-friction coefficient, and dynamic-friction coefficient between particles and geometric models are 0.714, 0.55, and 0.381, respectively; surface energy, plastic deformation ratio, adhesion branching index, and tangential stiffness factor are 17 J/m², 0.55, 3.5, and 0.375, respectively) into the uniaxial closed-compression simulation test, the maximum axial load borne by the convex mold during the growing media block-forming process is 2532.64 N, and the relative error with the actual maximum axial load of 2644.41 N is 4.23%, which is within an acceptable range (as shown in Figure 8). Through uniaxial closed-compression verification tests, it is known that the calibrated discrete-element model of growing media particles can be used for simulation analysis of growing media-compression molding and has high reliability.

4. Conclusions

In this study, a discrete-element model of the growing media was obtained through calibrating the contact parameters of the growing media based on accumulation tests and uniaxial closed-compression tests.

The measured density of growing media was 1080 kg/m³, and the geometric average particle size was 0.43 mm. The repose angle of the growing media was 44.64° by means of the cylinder-lifting method. The maximum axial load during growing media compression (compression ratio of 4:1) was 2644.41 N by the uniaxial closed-compression test.

According to the characteristics of the growing media, the EEPA model was selected to calibrate the contact model of the growing media of seedling nursery blocks. Based on the sensitivity analysis of the PB test results, it was found that the parameters that had significant effects on the growing media repose angle were the interparticle collision-recovery coefficient, the interparticle collision-recovery coefficient between the particle and geometric model, the dynamic-friction coefficient between the particle and geometric model, and the tangential stiffness factor. Then, the four parameters were optimized by the BB test, and the discrete-element parameters of the growing media were obtained as follows: interparticle collision-recovery coefficient, static-friction coefficient, and dynamic-friction coefficient were 0.5066, 0.65, and 0.5, respectively; the collision-recovery coefficient, static-friction coefficient, and dynamic-friction coefficient between the particle and geometric model were 0.714, 0.55, and 0.381, respectively. The surface energy, plastic deformation ratio, adhesion branch index, and tangential stiffness factor were 17 J/m², 0.55, 3.5 and 0.375, respectively.

The growing media model was used to conduct the simulation test of uniaxial closed compression, and the physical verification test was conducted. The results showed that the relative error between the maximum axial load on the punch and the measured value is 4.23%, which had high reliability and could provide a reference for the simulation of growing media. This study also verified that the discrete-element method could be employed to simulate the interaction between the growing media and the seedling machine, thereby supporting the design of the precise seedling machine and the enhancement of the operation precision of the facility horticulture.