**Parameter calibration for simulation of**,"

*Gentiana*seedling substrate based on discrete element method*BioResources*18(1), 1999-2010.

#### Abstract

The physical and mechanical parameters of the rotten rice straw (RRS), rice husk biochar (RHB), and the mixture of the two materials (the substrate) were calibrated by Plackett-Burman and Box-Behnken experiments to obtain the parameters for simulation of the forming of the *Gentiana* seedling substrate mat (GSSM). The particle contact parameters were calibrated, and the repose angle was taken as the response value based on the Hertz-Mindlin approach with the JKR contact model of discrete element method (DEM). A quadratic regression model was established and optimized using Design-Expert software. The parameters that most affected the substrate repose angle were the restitution coefficient of RRS of 0.20, the rolling friction coefficient of RRS of 0.04, the surface energy of RRS for JKR of 0.53, and the surface energy of RHB-RRS for JKR of 2.11. The simulated repose angle of the substrate and the bending strength of GSSM were compared with that of the verified experimental values respectively based on the optimal parameters. The relative errors of repose angles and bending strengths between the values of the simulation and the measurement were 0.71% and 1.39% respectively, indicating that the parameters obtained in this study can provide a reliable reference for the forming of GSSM.

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**Parameter Calibration for Simulation of Gentiana Seedling Substrate Based on Discrete Element Method**

Hongguang Cui,^{a} Tian Li,^{a }Tianyou Chen,^{a} Liyan Wu,^{a} Hongbo Li,^{b} Cuihong Liu,^{a} Mingjin Xin,^{a} and Yuqiu Song^{ a,}*

The physical and mechanical parameters of the rotten rice straw (RRS), rice husk biochar (RHB), and the mixture of the two materials (the substrate) were calibrated by Plackett-Burman and Box-Behnken experiments to obtain the parameters for simulation of the forming of the *Gentiana* seedling substrate mat (GSSM). The particle contact parameters were calibrated, and the repose angle was taken as the response value based on the Hertz-Mindlin approach with the JKR contact model of discrete element method (DEM). A quadratic regression model was established and optimized using Design-Expert software. The parameters that most affected the substrate repose angle were the restitution coefficient of RRS of 0.20, the rolling friction coefficient of RRS of 0.04, the surface energy of RRS for JKR of 0.53, and the surface energy of RHB-RRS for JKR of 2.11. The simulated repose angle of the substrate and the bending strength of GSSM were compared with that of the verified experimental values respectively based on the optimal parameters. The relative errors of repose angles and bending strengths between the values of the simulation and the measurement were 0.71% and 1.39% respectively, indicating that the parameters obtained in this study can provide a reliable reference for the forming of GSSM.

*DOI: 10.15376/biores.18.1.1999-2010*

*Keywords: Rotten rice straw; Biochar; Repose angle; Parameter calibration; Gentiana seedling substrate mat*

*Contact information: a: College of Engineering, Shenyang Agricultural University, Shenyang 110866 China; b: College of Horticultural, Shenyang Agricultural University, Shenyang 110866 China;*

** Corresponding author: songyuqiu@syau.edu.cn*

**INTRODUCTION**

The genus *Gentiana* is the source of a Chinese herbal medicine that has been applied for medicinal uses such as anti-rheumatic, anti-inflammatory, analgesic, antipyretic, hypoglycemic, and diuretic purposes (Rodrigues *et al*. 2019). However, the germination rate of traditionally distributed *Gentiana* is low, and the weeds are hard to control. Transplanting seedlings together with the substrate block remarkably increases the emergence proportion of crops and reduces the weeds. Biochar promotes the growth and development of traditional Chinese medicine (Zhang *et al*. 2010; Liu *et al*. 2015), inhibits the absorption of heavy metals and pesticides (Scortichini and Rossi 1991), prevents diseases, pests, and weeds (Yang *et al*. 2020), shortens the growth period, improves the physical and chemical properties of soil (Tang 2019), and avoids continuous cropping obstacles (Saha *et al*. 2019). Rotten rice straw (RRS) can be employed as crop growing substrate (Wang and Hou 2010) to increase the fertility of the soil (Guo* et al*. 2011; Chen *et al*. 2021; Qin 2021). Therefore, RRS and rice husk biochar (RHB) might be mixed as a substrate for Gentiana seedlings and compressed into a mat (GSSM), for planting.

The simulation of the substrate compression may provide a reference for actual production, and the accurate parameters will improve the precision of the DEM simulation. Therefore, it is necessary to calibrate the parameters of the materials before compressing. The rheological characteristics of the materials are important for the compression. Li *et al*. (2019) studied the rheological properties of the particle of clayey black soil. On the basis of the Hertz-Mindlin approach with the JKR contact model, the simulation parameters of the viscous powder mixture were calibrated (Mohammadreza *et al*. 2018; Tian *et al*. 2021), and Wang *et al*. (2021) obtained the discrete element parameters of corn stalk powder for compression molding. Na Risue *et al*. (2022) simulated the compression molding process of compound corn stalk powder feed using the Hysteretic Spring contact model, tracked the flow of the particles, and verified the accuracy and feasibility of simulation.

The rheological characteristics of the materials is highly complicated between particles of RRS and RHB due to cohesion (Li *et al*. 2015); therefore, the calibration of the parameters of the materials was carried out in this study.

**EXPERIMENTAL**

**Materials**

The rotten rice straw (RRS), ground and sieved to 2 mm, the rice husk biochar (RHB), and the substrate (the mixture of the two materials) were the study materials. The densities of RRS and RHB were 1.13×10^{3} kg/m^{3} and 0.50×10^{3} kg/m^{3}, respectively, and the moisture contents were 7% and 5%, respectively.

The adjustment of moisture content of the materials was based on the method of Xin *et al*. (2017). According to the preliminary test, the substrate was prepared by mixing RRS with RHB at a volume ratio of 7:1, and the moisture content of the mixture was adjusted to 35%.

**Method and Equipment**

*Parameters determination*

Intrinsic parameters and contact mechanical parameters are necessary for discrete element simulation, including Young’s modulus and Poisson’s ratio (Fan *et al*. 2022), which were collected by the universal material tester (Instron 5944, Bingyang Technology, China). The Young’s moduli of RRS and RHB were 30 and 140 MPa, respectively; the Poisson’s ratios were 0.3 and 0.4, respectively. The contact mechanical parameters include coefficient of restitution, coefficient of static friction and coefficient of rolling friction. The coefficient of restitution was tested using the freefall collision method (Bai *et al*. 2022) with the high-speed camera (PL2-C40C, Wuhan Kat Lite Technology Co., Ltd., China). The static friction coefficient and rolling friction coefficient are calculated using Eq. 1 with the frictional angles αmeasured with the incline method, at which most of the particles starting to slide and to roll respectively (Mi *et al.* 2022).

*f *= tan *α *(1)

*Substrate repose angle determination*

The cylinder lifting method (Qiu *et al*. 2022) was employed to measure the repose angle of the substrate. During the test, the sample was put into the cylinder, and then the cylinder was lifted slowly at a speed of 100 mm/min until all the particles formed a stable pile. The front-view image of the pile was taken with the high-resolution camera. Then it was binarized and the edge contour curve was extracted using MATLAB (V. 2020a, MathWorks, USA) software. The repose angle can be obtained by extracting the contour pixels and linear fitting by Origin (V. 2021, Origin Lab, USA). The measurement was repeated for 5 times, and the average repose angle of the substrate was 37.36°.

*Substrate mat compression process *

The compression of the substrate mat was conducted with a self-made mold equipped on a WDW-200 microcomputer-controlled electronic universal testing machine (Jinan Gold Testing Group Co., Ltd., China). The process includes feeding the prepared materials into the container, loading at preset pressure and speed, holding the pressure at preset displacement of the ram, unloading, and taking out the formed mat. The parameters of the automatic control program for the compression were set according to the trial experiment, and the key parameter settings for the compression were the ram speed of 100 mm/min, the pressure of 20 kN, and the retention time of 60 s.

**Placket-Burman Experiment Design**

The Hertz-Mindlin with JKR contact model was employed to investigate the surface energy of the particles, since there was bonding between the particles due to the wet substrate sample. Taking the repose angle of the substrate as the response value, the difference between the two levels of each factor was compared to determine the more significant factor through the Plackett-Burman test. The test parameters are shown in Table 1. The density of steel used in the simulation was 7850 kg/m^{3} with a shear modulus of 7.9 × 10^{9} MPa and Poisson’s ratio of 0.3.

**Table 1. **Test Parameters of Plackett-Burman

**Simulation Test**

The single sphere model was employed to present the ground RRS particles (Fig. 1a); according to the shape and dimensions, a modified straight four spheres model was used to stand for the RHB particles, in which the coordinates of each of the four spheres were adjusted (Fig. 1b) in this study. The simulation test is shown in Fig. 2.

** (a) (b)**

**Fig. 1. **Particle model: (a) RRS, (b) RHB

**Fig. 2. **Simulation test of repose angle. (a) The simulated pile of the substrate, (b) original graph, (c) binarization graph, (d) contour extraction curve of the pile and (e) Fitting line

**RESULTS AND DISCUSSION**

** Factor Significance Analysis of the Plackett-Burman Test**

The simulation result of the repose angle of the Plackett-Burman test is shown in Table 2, and the significance analysis is given in Table 3. The factors that significantly affected the repose angle were the restitution coefficient of RRS *X*_{4}, the rolling friction coefficient of RRS *X*_{6}, the rolling friction coefficient of RRS-steel *X*_{8}, the surface energy of RRS for JKR *X*_{9}, and the surface energy RHB-RRS for JKR *X*_{10}. The other parameters were not highly significant. The rolling friction of RRS-steel was ignored in the regression test because it was imperceptible in the actual test.

**Table 2. **Design and Results of Plackett-Burman Test

**Table 3. **Significance Analysis of Plackett-Burman Test Parameters

** Box-Behnken Test and Regression Model**

The Box-Behnken experiment of four-factor with three-level was designed to obtain the optimal parameter combination of significant factors (*X*_{4}, *X*_{6},* X*_{9}, *X*_{10) }in the simulation test. The repose angle *θ* was taken as the response value while the other parameters took the intermediate value. A total of 29 experiments were conducted. The coding of test factors is shown in Table 4.

**Table 4. **Factors and Codes of Box-Behnken Test

*Regression analysis*

The test protocol and the simulation results are given in Table 5. The multiple regression fitting analysis was performed using Design-Expert (V. 8.0.6, STAS-EASE Inc., Minneapolis, MN, USA), and the regression equation for repose angle was represented by Eq. 2,

*θ = *42.50 – 0.37*X*_{4} + 1.98*X*_{6} + 3.72*X*_{9} + 2.55*X*_{10} – 0.39*X*_{4}*X*_{6} + 0.11*X*_{4}*X*_{9} – 1.08*X*_{4}*X*_{10} – 2.16*X*_{6}*X*_{9} – 2.20*X*_{6}*X*_{10} – 2.14*X*_{9}*X*_{10} – 0.27*X*_{4}^{2} – 1.43*X*_{6}^{2} – 1.60*X*_{9}^{2 }– 3.06*X*_{10}^{2}*
*(2)

**Table 5. **Test Plan and Results of Box-Behnken

The variance analysis results of the experiment are shown in Table 6. It can be observed that the P-value of the regression model was less than 0.01(*P* < 0.01), the* Lack of Fit* = 0.0894 was less than 0.05, the determination coefficient *R*^{2} was 0.8999, and the adjusted coefficient of determination *R*_{adj}^{2} was 0.7998. It can be concluded that the model was well able to express the relationship between the repose angle and the significant factors. The variation coefficient *CV*= 4.62%, indicated that the test reliability is relatively high. The adequate precision *A*_{p} = 11.450, indicated that the model could reasonably predict the substrate repose angle. The significance order of the four factors on the repose angle were *X*_{10} > *X*_{6} > *X*_{9} > *X*_{4}, and the interactions of *X*_{6 }and *X*_{9}, *X*_{6 }and* X*_{10}, *X*_{9 }and* X*_{10}, *X*_{9}^{2} had significant effects on the repose angle while the other factors and interactions were not insignificant.

The model was represented as Eq. 3 after eliminating the insignificant items *X*_{4}, *X*_{4}*X*_{6}, *X*_{4}*X*_{9}, *X*_{4}*X*_{10}, *X*_{4}^{2}, and *X*_{6}^{2} on the basis of the original model. Variance analysis of regression models is shown in Table 7, and it can be observed that the test accuracy increased to 14.720, indicating that the model can be used to predict the relations between the substrate repose angle and the four significant factors. The optimized quadratic regression equation was developed as Eq. 3:

*θ *= 41.57 + 1.98*X*_{6 }+ 3.72*X*_{9 }+ 2.55*X*_{10 }– 2.16*X*_{6}*X*_{9 }– 2.20*X*_{6}*X*_{10 }

– 2.14*X*_{9}*X*_{10 }– 1.33*X*_{9}^{2 }– 2.79*X*_{10}^{2 }(3)

**Table 6 **Variance Analysis of Quadratic Model

**Table 7. **Variance Analysis of Regression Model Optimization

*Interaction effects analysis *

Design-Expert software was employed to draw the 3D response surface of the interaction between the factors. It can be observed from Fig. 3a that the trend of the surface energy of RRS for JKR *X*_{9} was slightly steeper than that of rolling friction coefficient *X*_{6} of RRS, indicating that the surface energy of RRS for JKR had a more highly significant effect on repose angle. It can be obtained from Fig. 3b that the curve trend of the surface energy of RHB-RRS for JKR *X*_{10} gradually became flatter with the increase of the factor value, compared with the curve trend in the direction of rolling friction coefficient of RRS* X*_{6}, indicating that the surface energy of RHB-RRS for JKR *X*_{10} had a more significant impact on the repose angle. According to Fig. 3c, the curve in the direction of the surface energy of RHB-RRS for JKR *X*_{10} was similar to that of the surface energy of RRS for JKR *X*_{9}, indicating that the effects of the two factors on the repose angle are similar.

**Fig. 3. **Response surface of significant factors’ interaction. (a) Interaction between *X*_{6} and *X*_{9}, (b) interaction between *X*_{6} and *X*_{10 }and (c) interaction between *X*_{9} and *X*_{10}

**Verification Testing**

*Repose angle verification test*

The repose angle, as illustrated in Fig. 4, was tested. To verify the accuracy of the calibration parameters, the real measured repose angle 37.36° was taken as the target value, and the combination of the factors was obtained based on the optimization function of Design-expert. The optimal combination is the restitution coefficient of RRS *X*_{4} of 0.20, the rolling friction coefficient of RRS *x*_{6} of 0.04, the surface energy of RRS for JKR *X*_{9} of 0.53 and the surface energy of RHB-RRS for JKR *X*_{10} of 2.11.

**Fig. 4. **Comparative verification test of repose angle. (a) Real repose angle test: (1) TMS-pro texture analyzer, (2) Automatic control system, (3) Steel plane, (4) Material pile and (5) cylinder; (b) The actual pile of the substrate; (c) The simulated pile of the substrate

The values of *X*_{4}, *X*_{6}, *X*_{9} and *X*_{10} in EDEM were set as the optimal values in the regression model, and the other parameters taking the intermediate level of each factor to obtain the discrete element model of the substrate. The experiment was repeated five times, and the average simulated repose angle was 37.63°. The relative error of repose angles between simulation and experiment values was 0.71 %, indicating that the simulation parameters were reasonable. The results of the verification test and the simulation showed that there were a few local angles exceeded 90°. This might have resulted from the lumps of the substrate materials for the cohesion among them.

*Bending strength verification test*

To further verify the accuracy of the parameters obtained from the regression model and the discrete element model, the bending strength of the compressed substrate mat of the actual experiment, measured with the electronic universal testing machine, was compared with that of the simulated mat which derived from the EDEM post-processing, as shown in Fig. 5.

**Fig. 5. **The bending strength verification test. (a) real destruction, (b) simulated destruction

**Fig. 6. **Comparative analysis of bending strength test

The bending stress-displacement curves of the real experiment and simulation test are shown in Fig. 6. The bending strength (the peak of the bending stress curve) obtained from the simulation test was 50,300 Pa, which was close to the measured value of 51,009 Pa. The relative error of the real experimental bending strength was 1.39%, which was larger than that of the accumulation verification (0.71%). The reason is that RHB particles are special-shape particles, and the cohesion will change after compression deformation (Zhang and Shu 2009), resulting in greater error. It can be concluded from Fig. 6 that the determination coefficient *R*^{2} of the two curves obtained by fitting was 0.97609, which is close to 1, indicating that the two curves fit well. In conclusion, the discrete element simulation model of gentian substrate block is accurate and reasonable.

**CONCLUSIONS**

- The highly significant factors affecting the substrate repose angle were determined through the Placket-Burman method. The restitution coefficient of rotten rice straw (RRS), the rolling friction coefficient of RRS, the surface energy of RRS for the Johnson-Kendall-Roberts (JKR) model, and the surface energy of RHB-RRS for JKR were determined.
- The optimal discrete parameter combination for repose angle was obtained by Design-Expert as the restitution coefficient of RRS of 0.20, the rolling friction coefficient of RRS of 0.04, the surface energy of RRS for JKR of 0.53, and the surface energy of RHB-RRS for JKR of 2.11.
- The relative errors of repose angle and bending strength, based on the combination of optimal parameters, between the simulation and the real measurement were 0.71% and 1.39%, respectively, indicating that the simulation parameters of the substrate dispersion element calibration based on the JKR model were reasonable and reliable.

**ACKNOWLEDGMENTS**

The authors are grateful for the support of the Shenyang Bureau of Science and Technology, Grant No.22-317-2-05; the support of the Educational Department of Liaoning Province, Grant No. LJKMZ20220998；the support of the Ecological Planting and Quality Assurance Project of Authentic Medicinal Materials.

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Article submitted: October 5, 2022; Peer review completed: December 31, 2022; Revised version received and accepted: January 19, 2023; Published: January 25, 2023.

DOI: 10.15376/biores.18.1.1999-2010