Numerical Method for Optimizing Soil Distribution Using DEM Simulation and Empirical Validation by Chemical Properties

Abstract

Manure distribution in soil creates a ground environment that is conducive to crop cultivation. However, the lumping and concentration of manure in the field can occur, hindering the fertilization of the soil for plant growth, and the randomization of nutrients under different soil depths accelerates it. To overcome the challenges associated with agricultural testing, such as high cost, inclement weather, and other constraints, computational analysis is often used. In this study, rotary operations are performed using the discrete element method (DEM) to ensure the uniform distribution of manure and four soil layers. DEM analysis was conducted with three experimental factors, and simulation sets were designed using the Box-Behnken central combination method. The DEM results were evaluated using the uniformity index (UI), and the field test of the rotary operation was performed with the set showing the most uniform distribution among the results. Due to undistinguishable particles in reality, the uniformity was validated by a comparison of the chemical characteristics of the L₁ and L₅ in terms of before and after the rotary operation. The DEM parameter of the soil was determined by performing field measurements at different soil depths (0–20 cm), and this parameter was calibrated by conducting a penetration test. The Box–Behnken central combination method was implemented using the following factors: tillage depth (X₁), PTO revolution speed (X₂), and forward machine velocity (X₃). These factors were obtained using the UI regression model and the response surface method. In the results, it was indicated that the UI was affected by the factors in the following order: X₁ > X₂ > X₃. The optimized factor values were X₁ = 25 cm, X₂ = 800 RPM, and X₃ = 1.8 km/h, leading to a UI of 6.07, which was consistent with the analysis results. The operating parameters were maintained throughout the field test, and the acquired data were input into the measurement system. The lowest UI value of 6.07 had the strongest effect on decreasing the disparity between L₁ and L₅, especially in terms of pH, organic matter, P, Ca, and Mg. In summary, the results indicated that soil distribution can be controlled by adjusting mechanical parameters to ensure uniform chemical characteristics across various soil depths.

1. Introduction

Rotary operation is one of the fundamental steps in field cultivation, involving the mixing of soil, chemical fertilizers, and compost. Creating rich soil with depth is beneficial for farming because well-mixed soil with natural nutrients improves field productivity and significantly increases farmer income. Furthermore, deep fertilizer placement has a remarkable effect on soil quality [1,2]. To produce an abundance of nutrient-rich soil, it is important to ensure uniform nutrient distribution across soil depth. In fact, different nutrients reside at different soil depths, such as organic and microbial biomass carbon [3]. Field studies on nutrient abundance with soil depth have revealed that more nutrients are present at deeper soil depths at sites in Europe [4,5], Asia [6,7], and the USA [8,9,10]. However, contrasting results pertaining to the nutrient content level and soil depth have been reported at other sites [11,12]. The nutrient levels in shallow and deep soils appear to be nonuniform, and it is difficult for crops to uptake all available nutrients owing to this nonuniformity of nutrient distribution in soil, leading to reduced yield and inviting research into this problem [13,14]. In addition, studies have demonstrated that similar root uptake is a function of soil depth [15,16], and significant levels of soil microbial communities exist with increasing soil depth [17]. In previous studies, the distinct requirements to rearrange the soil layers and create a uniform distribution should be satisfied, and the machinery operation is implicated in this. For instance, a study aiming to optimize the rotary operation can lead to uniform nutrient distribution, resulting in the provision of sufficient nutrients for plant growth and an increase in farm productivity.

To optimize field operations, repeat field testing is the most direct method. However, repeating the rotary operation is time-consuming and cost-intensive when constructing a nutrient-abundant and uniformly distributed field environment [18]. Therefore, computational and numerical simulations are often implemented using the discrete element method (DEM) [19]. Many soil–tool interaction models, along with calibration measures, have been developed for investigating forces and soil disturbances [20]. To obtain accurate results, the following three steps must be implemented: (1) define the contact model, (2) investigate the input parameters, and (3) calibrate soil properties by referring to previous studies.

Setting up an appropriate contact model requires an understanding of the humid soil environment and soil conditions. Most shallow, intermediate, and deep soil regions are wet and easily become clods of clay, even when the soil surface is dry. Therefore, a suitable contact model for DEM should consider soil cohesiveness, such as the Edinburgh elastoplastic adhesion (EEPA) model and the linear parallel bond model [21,22]. Asaf et al. (2007) used cohesion in their DEM study of soil tillage [23], and Aikins et al. (2021) considered adopting cohesion in their model [24]. However, few soils have small cohesion values that have little influence on the results. Nevertheless, to validate measured and simulated data, soil cohesiveness should be considered when creating the desired soil environment [25,26]. Therefore, it is suitable to take plastic deformation into account for soil interaction, especially considering an agricultural operation such as tillage or rotavating.

In terms of determining the proper DEM parameters, Kim et al. (2021) reported the variation of various soil properties with soil depths to analyze the draft force as a function of the tillage depth [27]. In addition, Du et al. (2022) discussed various soil parameters as a function of depth to improve the reliability of the DEM results [28]. Similarly, soil parameters have been measured by taking several soil samples [29,30,31,32]. According to previous DEM analyses pertaining to outdoor soil operations, soil has a random and heterogeneous nature, and it exhibits a nonlinear behavior that differs between different sites [33]. Thus, direct measurements of input parameters, such as the bulk density, the frictional coefficient, the angle of repose, and water content, are essential, and the manner in which the particle parameter is defined significantly affects the results. Furthermore, the separate properties of the different soil layers have to be defined, and field measurements are essential for the DEM analysis.

To obtain accurate and reliable DEM results, parameter details and bulk calibration should be determined [34]. In solving the complex motion of a particle based on Newton’s law, the solution accuracy mainly depends on the shape and size of the created particle, and these factors are compensated for by adjusting the characteristics of the bulk soil through calibration [35,36]. For an adhesive particle, calibration should be performed considering the interaction force between the material and bonded particle [37,38]. Meanwhile, the performance of agricultural operations, such as tillage, subsoiling, and traction, can be determined by conducting a penetration test [39,40,41,42]. Bulk compensation can be performed considering the soil depth, and the individual DEM parameters of each layer can be applied to improve simulation accuracy [43,44,45,46,47,48].

Using classical methods and trial-and-error to optimize agricultural operations is time-consuming [49] and the existing potential dangers that are present while performing the agricultural operation should be avoided, but the data to be obtained are still required for greater understanding. To improve our understanding, various experimental design methods can be used to shorten the experiment times and demonstrate the reliability of prediction models [50,51,52]. The response surface method (RSM) is an appropriate method for use in this experimental design because it optimizes machine performance by employing various factors [53] during the calibration of the DEM parameters [54,55].

In this study, a numerical granular study based on the cohesive contact model is conducted using DEM software (V4.4.1, Rockwell Automation Inc., Pittsburgh, NJ, USA). A rotary operation is designed using the Box–Behnken design method, and the uniformity index (UI) of particle layers and the reaction force against the machine are evaluated. Finally, optimization is performed using the response surface method (RSM), and a set of rotary operations for achieving uniform nutrient distribution in soil is obtained.

2. Materials and Methods

2.1. Measurement of Soil and Manure Properties

Soil properties were measured directly in an open field located at 18, Myeong-ri, Seohu-myeon, Andong-si, Gyeongsangbuk-do, Republic of Korea (36°36′10.4″ N, 128°39′41.03″ E). The field was divided into 10 sites by using the uniform grid SAMPLING method [56], and one soil sample from each of the four layers (1st layer (L₂): 5–10 cm; 2nd layer (L₃): 10–15 cm; 3rd layer (L₄): 15–20 cm; and 4th layer (L₅): 20–25 cm) was taken from each site, as illustrated in Figure 1a, by using a sampling apparatus (4.7 cm in diameter and 15 cm in height) (SL09112, Shinill Science Inc., Paju, Republic of Korea). The soil sample from each depth was taken, maintaining its structure in the cylinder by removing the apparatus. Soil density was computed using the weight (PAG4102, OHAUS Co., Ltd., Parsippany, NJ, USA) and volume of each sample (referenced volume of soil sampling apparatus), and the Young’s modulus of the samples was determined using a universal testing machine (LTCM-100, Chatillon, New York, NY, USA) and force gauges (DFX 2, AMETEK. Inc., Pennsylvania, NJ, USA) (Figure 1b). The measured parameters of the soil samples were interactively utilized to determine the DEM input parameters. Finally, the soil samples obtained from each layer were dried in an oven (SN-110, Shinnong Co., Ltd., Gimcheon, Republic of Korea) at 110 °C for 24 h to determine their moisture contents [57,58].

The cone index of the samples was measured by conducting a cone penetration test [59] using a cone penetrometer (HJ-4500, Heungjin, Gimpo, Republic of Korea) based on the soil cone penetration test suggested by ASABE Standards [60,61]. The test was performed ten times, and the average cone index was computed to compensate for the high standard deviation [62]. An angle of repose test was performed using a soil-filled cylinder, and the inclination angle was measured after removing the cylinder, with the remaining soil forming a heap [63,64].

Considering the properties of manure, pig manure was used in this study (Figure 2). The particle shape was assumed to be spherical, and the particle size was categorized based on four classes of lump sizes (A: 50 mm, B: 40 mm, C: 30 mm, D: remained). Then, the distribution of the four classes was applied in the DEM analysis. Bulk density was determined by filling the cylinder to 150 mL [65] with manure and weighing it on a scale (PAG4102, OHAUS Co., Ltd., Parsippany, NJ, USA). Finally, the manure was oven-dried at 103 °C for 24 h to determine its moisture content [66].

The soil sample was loam with 39.63% sand, 37.51% silt, and 21.8% clay. The measured soil properties according to soil depth were as follows. The bulk densities of layers L₂, L₃, L₄, and L₅ were 1235.7 kg/m³, 1481.2 kg/m³, 1725.1 kg/m³, and 2118.9 kg/m³, respectively (

Table 1. Soil and manure parameters obtained in Rocky-DEM simulation.

Property	L1	L2	L3	L4	L5
Bulk density, kg/m3	676.9	1235.7	1481.2	1725.1	2118.9
Moisture content, %	25.4	21.0	21.1	20.6	19.4
Young’s Modulus, Pa	2.0 × 106	28.1 × 106	37.5 × 106	64.4 × 106	163.4 × 106
Cone Index, kPa	-	156.1	247.4	366.9	539.3
Poisson’s ratio	0.3	0.3	0.3	0.3	0.3

). A comparison of these bulk densities revealed that the deeper layers had higher densities, and the bulk density of soil increased by 19.72% on average as the soil depth increased by 5 cm. The cone indexes at L₂, L₃, L₄, and L₅ were 156.1 kPa, 247.4 kPa, 366.9 kPa, and 539.3 kPa, respectively. Both measured and represented DEM input parameter values were selected [67], and similar soil modeling results [27] and soil properties with manure [68] have been reported in other studies.

2.2. Agricultural Vehicle Used for the Field Experiment

The rotary implement (BG600, Bulls Co., Ltd., Sungju-gun, Republic of Korea) used in this work was a general agricultural machine used for tilling, and its specifications are listed in

Table 2. Specifications of rotary implement.

Specifications	Value
Model	BG600
Company	Bulls Co., Ltd.
Width × Length × Height, cm	120 × 140 × 72
Weight, kg	350
Rotary width, cm	120
Rotary depth, cm	23–25
PTO revolution speed, RPM	440–800
Required power, hp (kW)	20 (14)
Number of furrows, ea	6

. The operating width was 120 cm, the suggested operating depth was 23–25 cm, and the PTO (Power Take-off) revolution speed was 440–800 RPM. This implement was used in the DEM simulation and the field experiment to validate the power required for rotary operation and to compare the soil distribution after rotary operation. The vehicle used in the field test was a 14-kW agricultural cultivator (KM-2000, TYM Co., Ltd., Iksan, Republic of Korea) with dimensions of 2650 mm × 1400 mm × 1900 mm (length × width × height) and a rated power of 14 kW.

2.3. DEM Simulation Environment

DEM analysis was performed using Rocky-DEM software (V4.4.1, Rockwell Automation Inc., Pittsburgh, NJ, USA) on a computer equipped with an AMD Ryzen^TM Threadripper^TM PRO 3975 WX CPU @ 3.5 GHz and 256 GB RAM. To ensure accurate DEM simulation, it is necessary to select the most appropriate contact model. Kim et al. (2021) considered compressibility, adhesiveness, and stickiness by using the EEPA contact model available in EDEM software (Academic 2021) for the DEM of the soil [27]. Studies have already determined the moisture content of soil and reviewed its effect on the physical properties of soil [69,70]. Considering the existing DEM analysis methods and the environmental setup of our simulation, we accounted for soil–soil interaction by combining the adhesive force and hysteretic linear spring models in the simulation (Figure 3).

The characteristic particle overlap graph of this combination is similar to that of the EEPA contact model available in EDEM software (Academic 2021). Moreover, the normal force between particles can be calculated using the following equations [71].

$$\mathrm{N}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l} \mathrm{f}\mathrm{o}\mathrm{r}\mathrm{c}\mathrm{e}=\left\{\begin{array}{c}-K_{nu}{s}_n+{\displaystyle \frac{10}{9}}{F}_{ce}, from A to B\\ \begin{array}{c}{K}_{nu}{s}_n+{\displaystyle \frac{8}{9}}{F}_{ce}, from B to C\\ K_{nl}\left(s_n-s_o\right), from C to D\\ K_{nu}\left(s_n-s_p\right), from D to E\end{array}\\ -K_{nu}\left(s_n+s_p-2s_{cp}\right), from E to F\end{array}\right.$$

(1)

where F_ce (N) is the pull-off force, K_nl (Nm) is the contact loading stiffness, K_nu (Nm) is the contact unloading stiffness, and s_o, s_p, and s_cp (%) are the overlap limits.

$$F_{ce}=-{\displaystyle \frac{3}{2}}\pi RT$$

(2)

$$s_o=-{\displaystyle \frac{8}{9}}({\displaystyle \frac{F_{ce}}{K_{nu}}})$$

(3)

$$s_p=s_{max}-{\displaystyle \frac{K_{nl}}{K_{nu}}}\left(s_{max}-s_0\right)$$

(4)

$$s_{cp}=s_p-\sqrt{{\displaystyle \frac{162}{137}}{\displaystyle \frac{\pi T}{K_{nu}}}(s_p-s_0)(2R-s_p+s_0)}$$

(5)

where R (mm) is the effective radius, T (mJ/m²) is the surface energy, and s_max (%) is the maximum overlap.

Spherical soil particles were obtained using a soil bin with a radius of 0.7 cm, which was selected considering the simulation accuracy and time [34]. Moreover, manure particles with the same shape were created with the abovementioned size distribution (0.7, 3, 4, and 5 cm). The total number of particles in the soil bin was 1,159,534. The soil bin was created virtually with a width of 200 cm, a length of 600 cm, and a depth of 25 cm. The soil particles were placed in the bin in order of depth, and manure was sprayed on the top layer (Figure 4). Then, rotary simulation was conducted using different tillage depths (23–25 cm), PTO revolution speeds (440–800 RPM), and forward velocities of the machine (1.2–2.4 km/h) by referring to the literature.

Table 3. Key parameters used in simulation.

Parameter		Value	Source
Soil particles	Density, kg·m−3	Listed in Table 1	Field measurements
	Young’s modulus, Pa	Listed in Table 1	Field measurements
	Poisson’s ratio	Listed in Table 1	Field measurements
Manure particles	Density, kg·m−3	Listed in Table 1	Field measurements
	Young’s modulus, Pa	Listed in Table 1	Field measurements
	Poisson’s ratio	Listed in Table 1	Field measurements
Steel	Density, kg·m−3	7850	[72]
	Young’s modulus, Pa	2.054 × 1011	[27]
	Poisson’s ratio	0.28	[70]
Particle–particle	Restitution coefficient	0.21	[73]
	Static friction coefficient	0.68	[73]
	Rolling friction coefficient	0.27	[73]
Particle–steel	Restitution coefficient	0.54	[73]
	Static friction coefficient	0.31	[73]
	Rolling friction coefficient	0.13	[73]

lists the key parameters input into the Rocky-DEM software program (V4.4.1, Rockwell Automation Inc., Pittsburgh, NJ, USA). The accuracy of the DEM result hinges on the key parameters, and therefore these parameters must be calibrated. In this study, the penetration test, which yields the properties of various soil layers, was considered appropriate for calibrating soil particles.

2.4. Measurement of UI

To determine the UI, the proportions of the particle numbers belonging to different layers in a unit volume were computed. The unit volume of cubes in the 125 × 10⁻⁶ m³ was used to count the number of particles; the process was simultaneously conducted at 22 different locations with double layers. The 1st and 2nd layers were placed at depths of 0–12.5 cm and 12.5–25 cm, respectively (Figure 5). The average proportion was taken as the UI, according to the following equation:

$$R_L={\displaystyle \frac{P_L}{P_T}}\times 100$$

(6)

where R_L (%) is the average proportion of each layer, P_L is the number of each particle in each layer, and P_T is the total number of particles (L₁: 0–5 cm, L₂: 5–10 cm, L₃: 10–15 cm, L₄: 15–20 cm, L₅: 20–25 cm).

Then, five different soil layers were created in the bin and were considered equally distributed when the R_L of each layer was 20% as a median. The R_L deviated from 20%, root-mean-square (RMS) UI in relation to the deviation from the uniform particle distribution, as follows:

$$\mathrm{U}\mathrm{I}=\sqrt{{\sum }_{L=1}^5{(20-R_L)}^2}$$

(7)

where UI (%) is the percentage of distribution in each particle layer (L₁: 0–5 cm, L₂: 5–10 cm, L₃: 10–15 cm, L₄: 15–20 cm, and L₅: 20–25 cm) within the cube.

2.5. Design of Experiment

To perform the rotary operation, Dai et al. (2020) identified the following as key working factors: the tillage depth, the PTO revolution speed, and the machine forward velocity [1]. The level of tillage depth should be greater than 0.5 cm, starting at 24 cm, and the forward velocity should be 1.8 km/h. In view of these constraints, we set three levels for each factor in the DEM simulation. The experimental set was designed using the Box–Behnken central (BBC) combination theory, and the factors are listed in

Table 4. Experimental set created using Box–Behnken central (BBC) combination theory.

Level	Tillage Depth, cm (X1)	PTO Revolution Speed, rpm (X2)	Forward Machine Velocity, km/h (X3)
−1	23	440	1.2
0	24	600	1.8
1	25	800	2.4

. Three factors, namely tillage depth, PTO revolution speed, and forward machine velocity, were used in the DEM simulation, and their ranges were 23–25 cm, 440–800 RPM, and 1.2–2.4 km/h, respectively.

2.6. Field Measurement System

The rotary operation for experimentally studying the effects of the suggested operating parameters on soil distribution was performed with the data acquisition system (Figure 6). A torque measurement system was constructed to measure the torque acting on the PTO shaft and the revolution speed of the shaft by using a strain gauge equipped with a transmitter (V3-BNN-1CH, SMART C&S, Daejeon, Republic of Korea) and a photosensor (BRQT3M-PDTA, Autonics, Busan, Republic of Korea). This torque measurement system was installed on the surface of the PTO shaft, and an RPM measurement system was installed on the PTO frame box by using a magnetic support jig to ensure that the system could not detach or fall off during data acquisition. The field test was conducted with a travel distance of 10 m, and the operating soil depth was measured at intervals of 1 m, including the start point.

2.7. Chemical Analysis of the Soil Sample

A low UI value indicates a well-mixed soil with a constant nutrient value in different soil layers. To validate the effect of UI, the chemical compositions of L₁ and L₅ before and after rotary operation were compared. The general chemical properties of the soil (including pH, EC, organic, phosphate, potassium, calcium, and magnesium) were analyzed based on the specific standard method [74] (Figure 7).

2.8. Statistical Analysis

The UI and the selected variables were statistically analyzed using the RSM and prediction models. Analysis of variance of each variable was performed using Minitab 22 and built on the published results. Please note that the publication of your manuscript that provided approval and the corresponding ethical approval code.

3. Results and Discussion

3.1. Properties of the Soil Model

The DEM particle was calibrated by performing a penetration test. In the Rocky-DEM simulation, each particle layer was created in the cylinder (10 cm in diameter and 25 cm in height), and the cone tip was pushed into the cylinder at a velocity of 0.3 m/s [74,75]. The corresponding cone index with soil depth (D_n) is depicted in Figure 8. The cone index values of D₁, D₂, D₃, and D₄ were 151.1 kPa, 252.5 kPa, 375.0 kPa, and 549.4 kPa, respectively, and the differences between the measured and simulated values were 3.2%, 2.1%, 2.2%, and 1.9%. The cone index of the site was smaller than 600 kPa, indicating the presence of soft soil that had been tilled recently. Moreover, in the validation test, the cone index values at each depth in the field site were 78.6 kPa, 247.7 kPa, 349.3 kPa, and 524.8 kPa, which were similar to the values at D₂, D₃, and D₄; however, the value at D₁ was smaller than that obtained from the soil sample (Figure 8).

3.2. Effects of Each of the Parameters on UI Value

The experimental results are listed in

Table 5. Results of Box–Behnken design.

No.	Experiment Factors			Uniformity Index
	Tillage Depth, X1	PTO Revolution Speed, X2	Forward Velocity, X3
1	−1	0	−1	15.89
2	1	0	1	10.09
3	0	−1	−1	17.78
4	1	−1	0	10.87
5	1	1	0	6.07
6	−1	1	0	18.27
7	−1	0	1	20.83
8	0	−1	1	16.99
9	0	1	1	16.00
10	0	0	0	13.33
11	0	0	0	13.78
12	0	0	0	13.15
13	1	0	−1	7.85
14	0	1	−1	10.49
15	−1	−1	0	19.59

. The lowest UI was found for design #5 (X₁: 25 cm, X₂: 800 RPM, and X₃: 1.8 km/h), while design #7 (X₁: 23 cm, X₂: 600 RPM, and X₃: 2.4 km/h) had the highest UI. The BBC design results generally indicated that greater depths, higher PTO revolution speeds, and smaller forward machine velocities led to more uniform nutrient distribution in the soil field with low UI.

To predict the UI, the following constants and coefficients were used: X₁, X₂, X₃, X₂², X₃², X_1×2, and X_2×3; the factor X₁² and the coefficient X_1×3 were not significant in the regression equation. The single factors X₁, X₂, and X₃ affected the UI significantly, with p-values smaller than 0.01. However, among the interaction factors, only X_1×2 and X_2×3 affected the UI significantly, with confidence intervals greater than 95% (p < 0.05). Moreover, the multiple factors X₂² and X₃² significantly affected the UI with significance levels of less than 0.01 (p < 0.01). The factors with negative coefficients strongly influenced the uniform construction of the environment with reduced UI, while the factors with positive coefficients increased the UI. For instance, if X₁ (negative coefficient, −4.962) increased, a low UI value was returned as the result. The regression model of the UI in terms of the dependent variable is as follows:

$$\mathrm{U}\mathrm{I}=-13.42-4.962{\mathrm{X}}_1-1.8{\mathrm{X}}_2+1.487{\mathrm{X}}_3+0.965X_2^2+0.93X_3^2-0.8.7X_1{X}_2+1.575X_2{X}_3$$

(8)

The statistical analysis results indicated that the order of influence on UI was X₁ > X₂ > X₃, and the lack-of-fit p-value of the regression model (0.145) indicated that no other factors affected the index significantly. Furthermore, the coefficient of determination R² and the adjusted coefficient of determination R_adj² were 99.2% and 97.7%, respectively. However, the predicted coefficient of determination R_pre² was 88.3%, which was smaller than R². Nevertheless, considering that the predicted objective is an environmental factor, the value is reasonable, and the difference between R_adj² and R_pre² is less than 0.2% (

Table 6. Variance analysis of uniformity.

Source	Uniformity Sum of Squares	df	F Value	p Value
Module	264.076	9	69.11	0.000 **
X1	197.011	1	464.06	0.000 **
X2	25.92	1	61.05	0.001 **
X3	17.701	1	41.70	0.001 **
X1 X2	3.028	1	7.13	0.044 *
X1 X3	1.823	1	4.29	0.093
X2 X3	9.923	1	23.37	0.005 **
X12	1.733	1	4.08	0.099
X22	3.438	1	8.10	0.036 *
X32	3.193	1	7.52	0.041 *
Residual	2.123	5
Lack of Fit	1.912	3	6.05	0.145
Pure Error	0.211	2
Sum	266.199	14

Note: * significant (p < 0.05). ** extremely significant (p < 0.01).

).

3.3. Effect of UI Value on Soil Distribution

For the UI value obtained using design #5, a comparison between the initial particle distribution in each cube within the bin and that after rotary operation is presented in Figure 9. Additionally, the design sets that yielded the lowest and highest UI values (6.07 and 20.83, respectively) were compared. Initially, each layer was clearly separated, with L₄ and L₅ in the bottom cubes (a depth of 12.5–25 cm), L₁ and L₂ in the top cubes (a depth of 0–12.5 cm), and L₃ being invisible. Then, the particles of all layers were identified in every cube after rotary operation, but the ratios of each of the layers were different in terms of the UI value. When the UI value was 20.83, the ratios of layers L₁, L₂, L₃, L₄, and L₅ were 17.1 ± 9.5%, 14.1 ± 2.7%, 38.2 ± 3.1%, 18.1 ± 5.5%, and 12.6 ± 6.1%, respectively. While design #5 afforded higher uniformity with a UI value of 6.07, the ratios of layers L₁, L₂, L₃, L₄, and L₅ were 18.2 ± 3.8%, 18.3 ± 5.6%, 25.1 ± 3.6%, 20.3 ± 5.2% and 17.9 ± 5.1%, respectively. The particle ratio of L₁, L₂ in the bottom layer and L₄, and L₅ in the top layer had the highest disparity on soil distribution, which indicated that the deeper the rotary blades penetrated the soil, the greater the soil feed ability was (Figure 9).

The number of particles belonging to each layer was analyzed using the cubes located at different soil depths. Initially, each particle layer was separated into five layers in the forward direction, and during DEM analysis, these layers were mixed and displaced in the cube located in the back section of the soil bin. Based on the selected experimental factors, the most well-mixed soil distribution was obtained when the UI value was 6.07 (Figure 10). This UI value represented small RMS differences between the layers and reflected the uniform distribution of soil particles within the bin. The effects of X₁ and X₂ on UI seemed intuitive; as the penetration depth of the implement into the soil and the rotating frequency increased, the interchangeability between each of the particle layers increased. Interestingly, level 0 of X₃ yielded the lowest UI, which was counterintuitive because neither the longer nor shorter operating time resulted in a well-mixed field site. Considering the operation factors, similar results of the distribution tendency were found with the slower forward velocity through five different soil depths [28].

Furthermore, the selected method for the formula for calculating the distribution of soil, UI, based on analyzing significant variation from the mean value, seems to have been adopted in general agricultural data analysis [59]. Compared to other DEM literature results using an adhesive soil model, the selected operation condition in this study can be a more effective method by which to create a uniform soil environment in which a similar level of the distribution index was found at each soil depth in this study, while increasing significant variations were observed [75]. However, Song et al. (2023) discussed influencing factors that make soil cultivation more complex and decrease simulation accuracy [75]. Similarly, the validation test in this study was performed through an open field test, while some of the instances in the literature used an indoor schematic system [19,21,46]. The aim of this study was to create a soil environment containing uniform nutrients at each depth. Therefore, performing the outdoor validation test can be a suitable method, taking the natural nutrient itself rather than using second-treated soil for making the soil bin.

To validate the DEM results, a field test of the rotary operation based on design #5 (X₁: 25 cm, X₂: 800 RPM, X₃: 1.8 km/h) was performed, and the resulting state of the field site was compared to the initial state of the field site. To validate the counterintuitive aspect of X₃, a comparative design set with a changing X₃ was used.

3.4. Validation of Soil Distribution through Chemical Characteristics

Based on the DEM result of design #5, a rotary operation was performed in the field to measure the required power. In addition, a comparative test in which X₃ was increased to a higher level (2.4 km/h) was performed to analyze the counter-intuitive effect of this design factor on the UI value. The results of the field test for measuring the power, the sustained PTO revolution speed, and the soil depth at a forward machine speed of 1.8 km/h are presented in Figure 11a. While fluctuating power and RPM curves were observed in the latter part of the test owing to an adjustment of the machine to the travel environment, the average power was 2.4 kW, and the sustained PTO revolution speed was 800 RPM within the actual operating period; for the same design set, the required power according to the DEM result was 2.2 kW. Compared to the target depth of 25 cm, the minimum and maximum operated depths were 23 and 27 cm, respectively, and the average soil depth of 11 points was 25.6 cm (Figure 11a).

For comparison, the measured power and sustained PTO revolution speed obtained by varying the forward machine speed to 2.4 km/h are presented in Figure 11b. While the operation time decreased owing to an increase in forward machine speed, the average power of the comparison set was 1.7 kW, and the PTO revolution speed was maintained at 800 RPM. However, in the field test with the comparison set, the target soil depth was not achieved. The average soil depth was 24.9 cm, and this deficiency was observed at four different points among the eleven measurement points (Figure 11b).

The validation results of soil distribution were obtained by performing the rotary operation with design #5, and the chemical characteristics of L₁ and L₅ were compared, as illustrated in Figure 12. Design #5 yielded the lowest UI value, which indicated the uniformity of chemical characteristics across soil depths. In terms of pH, the overall value in both L₁ and L₅ was 6.0–6.4, but the difference between these two layers decreased after rotary operation. Moreover, the EC values of the two layers were 0.1–0.2 dS/m, and no significant difference was found, indicating that the ability to provide nutrients was maintained during field operation. However, nutrients such as organic potassium (K), phosphate (P), calcium (Ca), and magnesium (Mg) were transferred to other soil layers relative to the initial status. The organic disparity of L₁ and L₅ before operation was 8.33 ± 0.5 g/kg (14.3 ± 0.5 and 6.0 g/kg, respectively), but it decreased to 4.3 ± 0.3 g/kg (18.0 ± 4.3 and 13.6 ± 4.0 g/kg, respectively) after the rotary operation. A similar decrease in nutrient disparity was observed: The initial disparity value of K was 0.12 ± 0.03 cmol⁺/kg (0.23 ± 0.04 cmol⁺/kg for L₁ and 0.11 ± 0.01 cmol⁺/kg for L₅), that of P was 46.34 ±0.04 cmol⁺/kg (55.67 ± 28.36 cmol⁺/kg for L₁ and 9.33 ± 4.04 cmol⁺/kg for L₅), that of Ca was 1.83 ± 0.6 cmol⁺/kg (5.07 ± 0.12 cmol⁺/kg for L₁ and 6.9 ± 0.72 cmol⁺/kg for L₅), and that of Mg was 1.13 ± 0.2 cmol⁺/kg (1.67 ± 0.06 cmol⁺/kg for L₁ and 2.8 ± 0.26 cmol⁺/kg for L₅); these values decreased to 0.04 ± 0.03 cmol⁺/kg, 0.0 ± 4.62 cmol⁺/kg, 0.27 ± 0.47 cmol⁺/kg, and 0.03 ± 0.04 cmol⁺/kg, respectively, after the rotary operation (Figure 12).

Consequently, the effects of design #5 (UI value of 6.07) on soil distribution after rotary operation were as follows: the disparity between L₁ and L₅ decreased, which was consistent with the goal of creating a uniform environment with soil depth. The average disparity values of all chemical characteristics decreased, except that of EC, and decreased deviations were observed, except in the case of K. These results indicated that the rotary operation created a soil environment with uniform pH, organic matter, P, Ca, and Mg, but not uniform EC and K (

Table 7. Effect of UI value on decreasing disparity.

Chemical Characteristics	Unit	Disparity between L1 and L5				Comparison
		Before Operation		After Operation		Average	STD
		Average	STD.	Average	STD	in Percentage (%)
pH	-	0.17	0.17	0.07	0.06	−60.0	−66.7
EC	dS/m	0.03	0.10	0.07	0.06	+133.3	−42.3
Organic	g/kg	8.33	0.58	4.33	0.32	−48.0	−45.0
P	cmol+/kg	46.33	24.32	-	4.62	−100.0	−81.0
K	cmol+/kg	0.13	0.03	0.03	0.04	−73.7	+133.3
Ca	cmol+/kg	1.83	0.61	0.27	0.46	−85.5	−23.7
Mg	cmol+/kg	1.13	0.21	0.03	0.04	−97.1	−79.6

). Thus, the statistically identified UI value reflected significant differences in chemical value, which indicated that optimizing the rotary operation can help provide a uniform level of nutrients to the target crop across soil depths, thereby creating a sustainable environment.

4. Conclusions

In this study, a rotary operation to ensure uniform nutrient distribution across soil layers (L₁–L₅) was optimized, and a test was conducted to validate the resulting soil distribution by comparing the chemical characteristics of different soil layers in terms of before and after the target operation. The properties of soil and manure were measured at test sites and used as the DEM input parameters. The experiment set was designed using the BBC method, and 15 sets of DEM analysis were performed. The UI was calculated using the RMS error method and optimized using the RSM. The field test was performed using design #5, and the general chemical characteristics of soil were analyzed and compared to validate the resulting distribution. The conclusions are as follows:

For the UI value, the lowest result, 6.07, was observed with the experiment set of #5 (X₁ = 25 cm, X₂ = 800 RPM, X₃ = 1.8 km/h), and the UI was affected by the factors in order of X₁ > X₂ > X₃, while the multiple factor X₁² and the interaction factor X_1×3 did not significantly affect the objective, and the regression model was described using these factors. The predicted coefficient of determination (R_pre²) and its adjusted value (R_adj²) were 88.3% and 97.7%, respectively. A validation test was performed based on BBC design #5 (X₁: 25 cm, X₂: 800 RPM, and X₃: 1.8 km/h). Sustained operating conditions were provided through a data acquisition system, and soil samples were taken from L₁ and L₅ before and after the rotary operation. The disparity in the chemical characteristics of the two layers decreased, especially in terms of pH, organic matter, P, Ca, and Mg, resulting in L₁ and L₅ having similar chemical characteristics. The disparity values of 0.17 ± 0.17, 8.33 ± 0.58 g/kg, 46.33 ± 24.32 cmol⁺/kg, 1.83 ± 0.61 cmol⁺/kg, and 1.13 ± 0.21 cmol⁺/kg were decreased to 0.07 ± 0.06, 4.33 ± 0.32 g/kg, 0 ± 4.62 cmol⁺/kg, 0.27 ± 0.46 cmol⁺/kg, and 0.03 ± 0.04 cmol⁺/kg for pH, organic matter, P, Ca, and Mg, respectively.

However, the results were drawn from the empirical test validating the uniform distribution underground by analyzing the chemical characteristics. A further study to enhance findings would be to cultivate the crop on the field created with #5 and compare its growth and yield to those of the traditional method.