# Microscopic Numerical Analysis of Sand Liquefaction Under Subway Train Load
## 6 Conclusions  
A combined numerical-experimental methodology was employed to investigate the micromechanical mechanisms of sand liquefaction induced by varying dynamic stresses (10-200 kPa) and frequencies (5-40 Hz) under simulated train loading conditions. Critical insights were derived through systematic analysis of pore pressure evolution, coordination number (4.2 \(\pm\) 0.3), mechanical coordination number (3.8 \(\pm\) 0.2), porosity variation (0.38-0.42), contact force chain networks, fabric anisotropy (0.15-0.32), and energy dissipation patterns (0.8-1.6 J/m3/cycle), with the principal findings summarized as follows:  
(1) Pore pressure increases with vibration frequency, with higher dynamic stress amplitudes or lower frequencies accelerating its accumulation rate. Critically, train vibrations induce progressive porosity reduction (volumetric contraction), whereas seismic loading may exhibit initial dilation followed by contraction. This fundamental difference explains why subway vibrations are more likely to trigger cumulative settlements in saturated silty sands--even without full liquefaction. Although particle geometry simplifications cause simulated values to deviate from experimental measurements, the observed trends remain consistent. (2) The coordination number and mechanical coordination number decrease with the increase in vibration frequency due to the presence of suspended particles, the coordination number curve is always higher than the mechanical coordination number curve. Increasing the amplitude of dynamic stress or decreasing the frequency will cause a sharp decrease in coordination number and mechanical coordination number with fewer vibrations. (3) At the beginning of loading, the porosity inside the sample gradually decreases with the increase in vibration frequency. The sample gradually becomes denser under cyclic loading; after reaching a certain critical number of vibrations, the porosity rapidly decreases and the sample is destroyed. (4) The number of force chains decreases with the increase in vibration frequency. The number of weak chains is always higher than the number of strong chains due to the fact that the load-bearing capacity of the sample is mainly provided by strong chains, the rate of reduction in strong chains is significantly lower than that of weak chains. Increasing the amplitude of dynamic stress or decreasing the frequency will accelerate the trend of force chain reduction. (5) The anisotropy gradually increases with the increase in vibration frequency. The anisotropy change curve in the early stage of vibration is relatively gentle. When the number of vibrations exceeds the critical value, anisotropy rapidly increases. Under lower dynamic stress amplitudes and higher loading frequencies, the anisotropy generated after liquefaction failure of the specimen is greater. (6) The sliding energy, damping energy, and boundary energy increase at an approximately constant rate with the increase in vibration frequency. When the critical number of vibrations is reached, the three energies increase sharply, while the strain energy is the opposite. As the amplitude of dynamic stress increases, the damping energy and boundary energy generated decrease, and the anti-liquefaction ability of the sample weakens, resulting in a decrease in the number of vibrations required for liquefaction. However, under the action of seismic loads, more microscopic energy is generated. (7) Anti-liquefaction design for subway projects cannot directly apply seismic liquefaction mitigation experience. For train-induced vibrations, particular attention must be paid to soil compression characteristics under low-amplitude, high-frequency cyclic loading with long-term accumulation effects.