## 4 Discussion
### Calibration of Soil Contact Parameters  
The Hertz-Mindlin and JKR contact models have been commonly utilized as soil contact models in the literature when performing DEM simulations [29]. The Hertz-Mindlin contact model is suitable for non-cohesive materials, while the JKR contact model is more suitable for adhesive materials. The soil with water content that we calibrated is a typical cohesive material. In the combined Hertz-Mindlin and JKR contact model, the tangential contact force, normal damping force, and tangential damping force can be calculated similarly to the Hertz-Mindlin model. The normal contact force employs JKR theory to account for cohesion [30]. Therefore, in this paper, the Hertz-Mindlin with JKR contact model was used to simulate soil.  
The contact parameters used in the simulation are the material-to-material friction coefficient, the recovery coefficient, and the JKR surface energy coefficient. In order to obtain these contact parameters for bulk sandy soil with different water content, we conducted a calibration test with the rest angle error as an indicator. We screened the three most significant factors from the seven factors as soil-soil recovery coefficient, soil-soil rolling friction coefficient, and JKR surface energy coefficient using the Plackett-Burman test, which is similar to the results obtained in numerous studies. For example, in [31], it was found that the static friction coefficient, rolling friction coefficient, and surface energy were the key parameters for wet bulk coal. Similarly, [PERSON] et al. [32] found that the most significant parameters for wheat flour were surface energy and rolling friction coefficient. [PERSON] et al. [33] presented a calibration method and found that the dominant parameters of wet sand were rolling friction and surface energy. Finally, [PERSON] et al. [34] calibrated the DEM parameters of rice and found that AoR was strongly influenced by rolling friction and restitution. It is noteworthy that they all used tiny spherical particles instead of irregularly shaped particles for the parameter calibration, so that rolling friction was a highly significant factor in all cases. In contrast, [PERSON] [15] et al. used the EDEM multi-sphere approach, which treats soil particles as miniature irregularly shaped particles for simulation, and the rolling friction is less significant compared to soil-soil static friction.  
After the factors with significant effects were found, they were subjected to Box-Behnken response surface analysis. The Box-Behnken design (BBD) is an effective technique for parameter calibration [34, 35]. It suggests how to select points from the three-level factorial arrangement, which allows efficient estimation of the first- and second-order coefficients of the mathematical model [36, 37]. The BBD consists of a central point and several middle points located at the edges of a cube superimposed on a sphere [38]. The design is more efficient and economical because it greatly reduces the number of experiments. The experimental results revealed that the soil-soil recovery factor, which was significant in the Plackett-Burman test, became insignificant in the Box-Behnken test. The analysis revealed that the reason for this was the change in the horizontal range, for which a smaller interval was chosen in the Box-Behnken test, resulting in a smaller interval in the range of inquiry for the soil-soil recovery factor to have little influence on the test results. We conducted one Box-Behnken test, but the error rate of the rest angle for different water content conditions could be obtained. Using the error rate as an index for the test analysis and response surface analysis, the parameters of sandy soil with different water content conditions could be directly obtained. This method simplifies the experimental process, and the parameters can be solved directly for soil with certain water content collected in the future without the need for re-simulation.