## 3 Simulation Results and Analysis
### Microscopic Behaviour  
A detailed analysis of microscopic behaviour was conducted to further investigate the underlying causes behind the compression outcomes. This step included an examination of the simulation results related to pebble velocities, force chains, contact force distributions and contact force directions. (1) Pebble velocities  
The states of pebble velocities under various compressive displacement conditions are illustrated in Figure 11.  
Upon the downward application of the pressing plate, the particles initiate a descending motion, with the impacted range expanding as the plate continues to press down, as can be seen from the above-mentioned figure. A cross-sectional analysis at the centre reveals that initially only a few particles in direct contact with the pressing plate are stimulated. At a depth of 0-2 mm, particles begin to compress against each other, intensifying with further penetration. In the range of 3 mm to 5 mm, acceleration is observed on the sides, whilst the centre exhibits a slower velocity. This phenomenon indicates that initially only the surface particles are affected by the pressing force. However, the force  
Figure 11: Pebble velocities under various compressive displacement conditions. (**a**) 0 mm; (**b**) 1 mm; (**c**) 2 mm; (**d**) 3 mm; (**e**) 4 mm; (**f**) 5 mm. Figure 10: Simulation results. cles propagates as the plate penetrates deeper, causing those directly beneath the plate to descend synchronously and those around the periphery to accelerate. The central particles experience compression from the sides, resulting in less noticeable positional changes. The states of force chains under various compressive displacement conditions are illustrated in Figure 12.  
Overall, the force chain distribution exhibits a root-like pattern, as illustrated in the above-mentioned figure. The force chain continues to expand with the progressive increase in the displacement of the pressing plate, particularly noting that the central stress predominantly concentrates in the lower part of the pressing plate's centre. Contact force distributions  
During the simulation, the contact forces between all particles were quantified, with the corresponding probability density distribution illustrated in Figure 13.  
The average contact force between particles gradually increases with the continuous pressing of the plate, as illustrated in the above-mentioned figure. Under the same displacement, the probability distributions of the contact forces, normal contact forces and shear contact forces are essentially consistent. The force application process under varying displacements was categorised into three stages to further investigate the variations in the probability density distribution of the contact forces at different displacements. The results are depicted in Figure 14.  
Figure 12: Force chains under various compressive displacement conditions. (**a**) 0 mm; (**b**) 1 mm; (**c**) 2 mm; (**d**) 3 mm; (**e**) 4 mm; (**f**) 5 mm. Figure 13: Probability density distribution of the contact forces. (**a**) contact forces; (**b**) normal contact forces; (**c**) shear contact forces. In Stage 1 (0-2 mm), a significant intensification can be observed in the overall distribution of contact forces. This intensification is primarily due to the emergence of stronger contact forces, resulting in an elevated average contact force, whilst the majority of existing forces remain unchanged. In Stage 2 (2-3 mm), the dynamic change in contact forces experiences a slowdown attributed to the consistent displacement leading to stress being distributed amongst a larger number of particles. This extensive stress distribution ensures that the average contact force distribution remains relatively stable as the displacement progresses. In Stage 3 (3-5 mm), a notable shift occurs with a decrease in smaller forces, resulting in the establishment of a new equilibrium. The particles surrounding the pressing plate exhibit increased motion as compression progresses, forming a cyclic pattern.