# Simulation of Track-Soft Soil Interactions Using a Discrete Element Method
## 2 Material and Methods
### Parameters Calibration of Scaled-Up Particles
#### 2.1.2 Calibration of the JKR Model Parameters  
Riverbed surface soil is a complex sediment with a high moisture content. With the increase in moisture content, the soil presents a plastic state, fluid plastic state and flow state. The different content of sand in the soil will also change the soil characteristics. In this paper, the clay and sand were collected from the Huai River, a representative river in northern China, used as the in situ data for tests and simulations. As a supplement, three kinds of clay and sand mixed soil, 1# (75:25 wt.%), 2# (50:50 wt.%) and 3# (25:75 wt.%),  
Figure 1: Schematic of the JKR contact model. (**a**) Particle–particle contact model; (**b**) particle–particle force/torque interactions.  
were applied to soil shear tests and DEM simulations. The wet densities of mixed soil 1\(\#\), 2\(\#\) and 3\(\#\) were 1.54 g cm\({}^{-3}\), 1.65 g cm\({}^{-3}\) and 1.74 g cm\({}^{-3}\), respectively.  
The discretization of DEM particle sizes and their distribution which comprises particle sizes of natural soils is very complex and computationally prohibitive. The main particle size composition of soil can be screened by standard assays. Based on the main particle size of the soil, soil particles are assumed to be uniformly distributed. Under the assumed condition, the scaled-up particle is set to 1 mm in the DEM simulation, which can simplify and accelerate the calculation [25].  
In this paper, standard screening and drying experiments were applied to test the physical properties of soil. First, the standard screening of 300 mesh and 200 mesh was used to identify clay particles of sizes 0.05-0.075 mm. Meanwhile, the standard screening of 35 mesh and 18 mesh was used to identify soil particles of sizes 0.5-1 mm. Second, the collected soil was placed in a graphite crucible and warmed in the incubator at 100 \({}^{\circ}\)C. The weight of the crucible was measured every 24 h until the error of two measurements was less than 1%. The wet density, dry density and moisture content (water mass fraction) of the soil could be obtained through calculations, with the results shown in Table 1.  
As shown in Table 1, particle sizes of clay and sand were less than 0.075 mm and 1 mm, respectively, and modeling soil based on actual particle sizes requires a significant amount of computing resources. The optimal method is to increase the size of soil particles proportionally and derive the same mechanical properties as the actual soil particles by setting appropriate parameters. In this study, for comprehensive consideration of the actual particle size and the calculation ability of computer, the clay and sand particles were set as spherical particles 1 mm in size in the DEM simulation [26]. The characteristic coefficients of particle interactions were determined by comparing the real experiment with the simulation [15,16].  
Three types of parameters were indispensable in the JKR contact model [14]:  
1. The intrinsic parameters of particles, including wet density, Poisson ratio, shear modulus and particle size, are basic parameters and can be measured by the test. The parameters are shown in Table 2;
2. The contact parameters of particles, including the static friction coefficient and rolling friction coefficient, are friction characteristic parameters and can be measured by tests or calibrated by simulations. The friction between particles is calculated according to the friction characteristic parameters, and the specific calculation method refers to the Hertz-Mindlin model [20,21];
3. The JKR models specific particle parameters, i.e., surface energy, which is a cohesive characteristic parameter and is difficult to measure. However, it can be calibrated by DEM simulation. The cohesive force between particles is calculated according to the cohesive characteristic parameters, as shown in Equation (1).