# Calibration of Model Parameters for Soda Saline Soil-Subsoiling Component Interaction Based on DEM
## 3 Results and Discussion
### Contact Model and Parameter Correction  
To enhance the validation's reliability, we employed two distinct validation methods: the angle of repose (AoR) test and the direct shear (DS) test. During the verification process, it became evident that employing the same set of simulation parameters yielded different outcomes for these two tests. After that, we modified the relevant model parameters. Equation (11) is the calculation formula of model-related parameters. \[\left\{ \begin{array}{l}\Delta F_{n}=-v_{n}S_{n}A_{b}\Delta t\\ \Delta F_{\tau}=-v_{\tau}S_{\tau}A_{b}\Delta t\\ \Delta M_{n}=-\omega_{n}S_{n}\rfloor\Delta t\\ \Delta M_{\tau}=-\omega_{\tau}S_{\tau}\frac{t}{2}\Delta t\\ A_{b}=\pi R_{b}^{2}\\ J=\frac{1}{2}\pi R_{b}^{4}\end{array} \right. \tag{11}\]  
In Equation (11), \(A_{b}\) is the contact area between soil particles, m\({}^{2}\); \(R_{b}\) is the bond radius between soil particles, m; \(J\) is the cross-sectional polar moment of inertia of soil particles, m\({}^{4}\); \(S_{n}\) is the normal stiffness of bonded particles, N/m\({}^{3}\); \(S_{\tau}\) is the tangential stiffness of bonded particles, N/m\({}^{3}\); \(v_{n}\) and \(v_{\tau}\) are the normal and tangential components of particle velocity, m/s; \(\omega_{n}\) and \(\omega_{\tau}\) are the normal and tangential components of particle angular velocity, rad/s; and \(\Delta t\) is the time step, s.  
When the external force exceeds a preset value, the bond is destroyed. The normal critical stress, \(\sigma_{max}\), and the tangential critical stress, \(\tau_{max}\), are defined as follows:  
\[\sigma_{max}=\frac{-F_{n}}{A}+\frac{2M_{\tau}}{J}R_{b} \tag{12}\]  
\[\tau_{\max}=\frac{-F_{\tau}}{A}+\frac{M_{n}}{J}R_{b} \tag{13}\]  
The bond parameters in the HMB contact model mainly include the normal stiffness, \(S_{n}\); tangential stiffness, \(S_{\tau}\); critical normal stress, \(\sigma_{max}\); critical tangential stress, \(\tau_{max}\); and bond radius, \(R_{b}\). Previous studies have shown that the particle behavior is not sensitive to the change of bond stiffness parameters under this model [6]. After multiple pre-tests, the normal stiffness per unit area is taken as \(1\times 10^{5}\) N/m\({}^{3}\), the tangential stiffness per unit area is taken as \(1\times 10^{5}\) N/m\({}^{3}\), and \(\sigma_{max}=\tau_{max}\) is \(8\times 10^{3}\) Pa. The particle contact radius is 1.1 times the particle radius [12]. Meanwhile, the shear modulus affects the time step variation of the DEM solution [36]; the larger the shear modulus is, the smaller the Rayleigh time step, according to Equation (13). In general, the smaller the time step is, the more time the calculation will take, and the higher the calculation accuracy will be [37]. To obtain an accurate combination of simulation parameters, we adjusted the shear modulus and Rayleigh time step to obtain more accurate calculation results for subsequent simulations. In the direct shear simulation test, the Rayleigh time step is \(4.76\times 10^{-5}\) s, and the shear modulus is \(3\times 10^{7}\) Pa.  
\[T_{r}=\frac{\pi R\sqrt{\frac{\rho}{\rho}}}{0.1631v+0.8766} \tag{14}\]  
In Equation (14), \(T_{r}\) is the Rayleigh time step, \(R\) is the particle radius, \(\rho\) is the particle density, \(v\) is Poisson's ratio, and \(G\) is the shear modulus. After modifying the model parameters and conducting the DS simulation again (Figure 17), was is obvious that the bonds between soil particles were constantly broken during the DS test process. Because the bonds between soil particles have a certain strength, the simulated shear strength is improved compared with the single JKR model.