# Microscopic Numerical Analysis of Sand Liquefaction Under Subway Train Load
## 1 Introduction  
With the accelerating urban construction and growing urban population, traffic congestion has become a common issue. However, the development of above-ground space is limited, prompting efforts to expand underground space. Consequently, many Chinese cities have embarked on subway construction. Nevertheless, in water-rich sandy strata, the vibration loads from subway trains can induce sand liquefaction, leading to issues such as track unevenness, mud pumping, and structural cracking [1, 2, 3], which pose significant safety hazards to subway operations [4]. Cities like Harbin, Tianjin, Guangzhou, Shenzhen, Foshan, and Wuhan have identified sand liquefaction as a key geological risk to mitigate during subway operation [5]. Current research on sand liquefaction predominantly focuses on seismic loads [6, 7, 8], with relatively limited studies on liquefaction induced by subway train vibrations. The liquefaction process is defined as the transition of saturated sand or silt from a solid-like toa flowable liquid state under dynamic shear forces, which can be triggered by earthquakes or mechanical vibrations. Sand liquefaction has long been a critical and challenging topic in geotechnical earthquake engineering. In the 1960s-1970s, scholars such as [PERSON] [9], [PERSON] [10], and [PERSON] [11] investigated the mechanisms of sand liquefaction through laboratory tests. [PERSON] [12] et al. conducted cyclic shear tests on liquefied soils from the Turkish Kocaeli earthquake and found that the type and content of clay particles are key factors determining liquefaction potential. [PERSON] [13] et al. demonstrated through dynamic triaxial tests on silty sand that the initial stress state significantly influences liquefaction likelihood. Compared to seismic loads, subway train vibrations involve more complex vibration sources and transmission mechanisms, with multiple influencing factors and excitation types. As a result, the theoretical framework for sand liquefaction induced by subway vibrations remains underdeveloped, and most existing studies rely on numerical simulation methods. Studying the mechanical behavior between sand particles at the mesoscopic scale--by analyzing force chain strength, force chain distribution, particle contact states, and movement patterns--helps reveal the internal mechanisms underlying the macro-mechanical evolution of sand liquefaction, particularly under subway vibration loads. Scholars such as [PERSON] et al. [14], [PERSON] et al. [15], [PERSON]. [16], [PERSON]. [17], and [PERSON] et al. [18] have conducted laboratory triaxial tests on the dynamic response and long-term deformation characteristics of various soil types (e.g., silty sand, soft clay, saturated silty soil, loess) under subway vibration loads, aiming to uncover relevant deformation laws and mechanisms. With the deepening understanding of sand particle properties, pore structures, and movement laws, it has become evident that changes in the mesoscopic structure of sand significantly influence its macro-mechanical behavior, making macro-experimental results alone insufficient to explain the underlying mechanisms. Although some scholars have initiated mesoscopic-scale studies in rail transit dynamics, comprehensive research remains scarce. Therefore, it is necessary to integrate macro-mechanical experiments, mesoscopic observations, and DEM analysis to further investigate the internal mechanisms linking macro-mechanical behavior to mesoscopic fabric changes. Many domestic and foreign researchers have employed the discrete element method (DEM) to investigate sand liquefaction at the microscopic level. For example, [PERSON] [19], [PERSON] [20], [PERSON] [21], [PERSON] [22], and others used DEM to study the evolution of microparameters (e.g., force chains, fabric tensors, coordination numbers, porosity) during vibration-induced liquefaction, further clarifying the solid-to-liquid transition behavior. [PERSON] et al.