# Bridging Macro-Microscopic Parameters: Correspondence and Calibration Approaches
## 4 Bridging Macro-Micro Parameters
### Verification Approaches  
To further validate the results of macro parameter calibration, an indoor pile-up experiment was conducted and compared with the numerical simulation.  
Pile-up test numerical simulation was conducted using circular particles, with particle size distribution, coefficient of interparticle friction, density, and other parameters consistent with those of the sandy soil sample mentioned earlier. The calibrated \(k_{n}\) and \(k_{s}\) were used. The inclination angle of the ramp in the simulation device was consistent with the interparticle friction experiment, set at 65\({}^{\circ}\).  
The simulation process followed the interparticle friction test, with particles generated in small amounts multiple times at the midpoint of the ramp (particle size distribution consistent with the sandy soil sample) to avoid excessive impact on the ramp, which could cause particles to jump violently. The particles slid down the ramp, initially forming a pile, and additional particles were added to further pile up on the already formed slope. Eventually, a small-scale slope was formed, and additional particles were continuously poured onto the ramp's upper section using a small shovel. When the distance from the base of the slope to the ramp matched the interparticle friction test, it indicated the completion of the particle pile-up process. The angle of the slope was measured multiple times using relevant angle measurement software, and the height of the slope was recorded. The pile-up process was compared with the interparticle friction test (Figure 13). The slope length indicates the distance from the bottom of the plate to the leading edge of the slope body, while the slope height represents the distance from the bottom of the plate to the top of the slope body. Additionally, the slope angle denotes the measured angle in the middle of the slope body.  
Figure 12: Comparison between direct shear tests and simulation under compressive stress of 100 kPa.  
The particle pile-up length obtained from the particle accumulation experiment at the central axis of the slope was 25 cm, with a height of 26 cm and an angle of 37.3\({}^{\circ}\). This angle was measured at the middle part of the slope. The particle pile-up length obtained from the numerical simulation was 25 cm, with a height of 26 cm and an angle of 38.0\({}^{\circ}\). The two results showed highly consistent pile-up forms and ranges, further demonstrating the rationality of the calibration method.  
Previously, direct shear test numerical simulations were conducted for particle parameter calibration under a pressure of 100 kPa. We further conducted direct shear test numerical simulations under pressures of 200 kPa and 300 kPa using the same method as before. The obtained shear stress-shear displacement curves under different pressures were compared with the data obtained from direct shear tests (Figure 14).  
The direct shear effects under various pressures were good. Particularly, under pressures of 100 kPa and 200 kPa, the curves fit excellently, not only showing consistent shear strength but also well reflecting the bending of the experiment curve. Under a pressure of 300 kPa, although the curvature did not completely match, this was attributed to the increased difference between circular particles and actual particles under high pressure. However, the maximum strength still closely matched the experimental value, indicating a good effect of parameter calibration.  
Figure 14: Comparison between direct shear experiments and simulations.  
Figure 13: Comparison of pile-up experiment and numerical simulation. (a) Indoor pile-up experiment value, and (b) numerical simulation value.