# Microscopic Numerical Analysis of Sand Liquefaction Under Subway Train Load
## 4 Microscopic Mechanism of Sand Liquefaction
### Pore Pressure  
Due to the use of a linear contact model in the simulation process, this model does not withstand bending moments and the particles are simplified to spherical shapes in the simulation. Compared to the actual situation, this simplification cannot accurately  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Particle** & **Normal Contact** & **Tangential Contact** & **Frictional** & **Local** \\
**Density/(kg/m\({}^{3}\))** & **Stiffness/(N/m)** & **Stiffness/(N/m)** & **Coefficient** & **Damping** \\ \hline
2640 & \(3\times 10^{8}\) & \(3\times 10^{8}\) & 0.5 & 0.7 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Model microscopic parameter values.  
Figure 7: Comparison of stress–strain relationship curves between indoor experiments and discrete element numerical simulations.  
simulate the contribution of particle shape to shear strength, which may result in lower pore pressure simulation results.  
Figure 8 shows the relationship curves of the variation in pore water pressure with the number of vibrations caused by different dynamic stress amplitudes and frequencies under a confining pressure of 100 kPa. It can be seen from the figures that the numerical samples generated instantaneous pore pressures of 9.25 kPa, 9.27 kPa, and 9.30 kPa, respectively, due to the application of a static deviatoric stress of 30 kPa. The overpressure gradually increases with the increase in vibration frequency, and the higher the amplitude or frequency of dynamic stress, the faster the accumulation rate of overpressure, When the amplitude of dynamic stress is 10 kPa, 15 kPa, 20 kPa, and 60 kPa, the sample needs to be vibrated 65, 170, 103, and 13 times, respectively, to undergo liquefaction failure; When the loading frequency is 0.5 Hz, 1.0 Hz, and 2.5 Hz, the sample reaches liquefaction failure after 59, 170, and 425 vibrations, respectively. This means that greater dynamic stress and lower frequency amplitudes will accelerate the occurrence of liquefaction phenomena. The simulation results are consistent with the laws obtained from indoor experiments. Due to the continuous dynamic load, the bearing capacity of the specimen gradually decreases with the increase in vibration frequency. When a critical vibration frequency is reached, the collapse type failure phenomenon of rapid increase in pore pressure occurs. The high excess pore water pressure causes the specimen to suddenly lose strength and stiffness, resulting in the inability of the specimen to continue bearing dynamic load and uncontrollable large deformation, which in turn leads to a sharp increase in pore pressure.  
As shown in Table 5, a systematic comparison of key parameters such as liquefaction cycles and peak pore pressure ratios reveals quantitative discrepancies between the discrete element model and laboratory tests. Under the working condition of dynamic stress amplitude 10 kPa and frequency 0.5 Hz, the experimental liquefaction cycles are 59, while the simulation result is 65, with a relative error of +10.2%. When the dynamic stress  
Figure 8: The pressure vibration relationship curve of the super hole under different dynamic stress amplitudes and frequencies: (**a**) super pore pressure vibration relationship curve (experimental); (**b**) super pore pressure vibration relationship curve (simulation); (**c**) super pore pressure vibration relationship curve (experimental); (**d**) super pore pressure vibration relationship curve (simulation).  
increases to 20 kPa, the error between the experimental value (103 cycles) and the simulated value (92 cycles) expands to \(-\)10.7%. Peak pore pressure ratios also exhibit systematic deviations: experimental values stabilize in the range of 0.99-1.02, while simulated values only reach 0.94-0.97, with an average underestimation of 3.5%.