## 3 Triaxial Compression Calibration Test and Verification
### Test and Numerical Simulation of Triaxial Compression in Wet Sand
#### 3.2.2 Simulation of Triaxial Compression by DEM  
In discrete element studies, using spherical particles to represent sand is common [42; 43]. A total of 8238 particle units were generated, and a simulation model was established based on the experimental conditions. To ensure uniform force distribution in the granular system during simulation, a small load was applied for pre-compression and allowed to settle until the longitudinal force reached a stable value of 1.82 N. The process of loading and unloading through the piston is the critical stage in the DEM simulation. Due to the computational complexity of the DEM, it would be time-consuming to perform the simulation directly using the experimental loading and unloading velocities. To address this, a sensitivity analysis based on varying velocity gradients was performed to assess the dynamic response of wet sand to loading and unloading velocities. The sensitivity analysis results, depicted  
Figure 6: Sand triaxial compression test and its “load–displacement” curve. in Figure 7, include three experimental setups. The first setup utilized a loading speed of 50 mm/s for 0.04 s and an unloading speed of 20 mm/s from 0.04 to 0.06 s. The second setup featured a loading speed of 5 mm/s for 0.4 s and an unloading speed of 2 mm/s from 0.4 to 0.6 s. The third setup mirrored the actual experimental conditions with a loading speed of 0.5 mm/s for 4 s and an unloading speed of 0.2 mm/s from 4 to 6 s. The simulation times for these setups were 0.1714 h, 1.2985 h, and 6.467 h, respectively, with a notable increase in the computational time as the loading rate decreased. Despite the significant differences in the loading and unloading velocities, the load-displacement curves across all three setups exhibited similar nonlinear behavior with minimal variation. Consequently, to optimize simulation efficiency and enable the generation of a dataset through multiple simulation iterations, this study employed the loading and unloading velocities from the first setup for subsequent investigations. The other simulation conditions were consistent with the triaxial compression test. To accurately capture the data characteristics, we chose the sampling frequency as 2000 Hz, and each sequence of data was sampled 99 times. The entire simulation process is illustrated in Figure 8.  
Figure 8: An overall simulation diagram of the triaxial compression test based on EDEM 2022. (**a**) At the infancy of the experiment, the wet sand is subjected to uniform forces after the preloading treatment. (**b**) As the loading progresses, the upper part of the wet sand experiences higher stresses, and the stress is gradually propagated along the force chains in the longitudinal direction. (**c**) After the unloading process is completed, the system retains residual stresses, exhibiting certain plastic behavior, which complies with the fundamental constraints of the EEPA model. Figure 7: Sensitivity analysis of load–displacement curve of discrete element triaxial compression test on loading and unloading velocities. The DEM dynamics simulations in this research employ particles shaped as a dual sphere in EDEM 2022, where both spheres have a physical radius of 1 mm and are connected together by a contact zone. In the world coordinate system, the coordinates of these two spheres' centers are, respectively, (\(-\)0.405 mm, 0.000 mm, 0.000 mm) and (0.405 mm, 0.000 mm). The smoothing value of the particles was set to 5. In order to accurately simulate the triaxial compression experiment, a container made of Perspex was used to simulate the acrylic tube in the experiment, and the upper surface of the wet sand was loaded and unloaded using a steel piston. The experiment was simulated in EDEM 2022, and the input parameters used are shown in Table 2.  
In the dimensionality reduction experiment in Section 3.3, we found that \(f_{s-s}\), \(f_{s-a}\), and \(\lambda_{p}\) are significant parameters for EEPA.