Historical earthquake-induced damage and studies have shown that the impact of vertical earthquake motions on sand liquefaction cannot be ignored in liquefiable sites with underground structures. Therefore, this study performed a finite element-finite difference (FE-FD) coupling numerical method to compare the influence of different seismic component excitations (vertical, horizontal, and bidirectional) on sand liquefaction with and without subway stations and to further explore the uplift mechanism of the subway station under vertical earthquake motion. The results revealed that the liquefaction response of the foundation soil is much different in the model with and without the subway station. In a liquefiable site with a subway station, the vertical seismic component may also trigger soil liquefaction due to soil structure interaction, while in the unstructured site, it cannot trigger liquefaction. The vertical seismic component will aggravate the degree of liquefaction and horizontal acceleration response of soil near subway stations, and the extent of this influence decreases with the increase of horizontal distance between the soil and the side wall of the subway station. In addition, the influence of vertical earthquake motions on the uplift of subway stations is related to seismic wave characteristics and the value of Arias intensity. The mechanism of the effect of vertical earthquake motion on the uplift of subway stations is to reduce friction between structure and soil and increase the flow deformation of the soil.

A mathematical model is proposed to investigate the dynamic behavior of an end-bearing pile under vertical seismic loading in a water-pile-saturated soil system. The model is based on the Euler-Bernoulli beam theory and takes into account the stress balance between pile sections, representing the pile as a one-dimensional rod. The overall response of site is divided into two components: the free-field response and the scattered-field response. The pile and soil are considered as linearly viscoelastic materials with hysteresis-based damping, while water is modeled as a linear acoustic medium. By accounting for boundary conditions involving force equilibrium and displacement continuity at the pile-soil and water-soil interfaces, an analytical solution for the system response is derived. Analytical expressions of pore water pressure and displacements are obtained, on the basis of considering water-soil interaction in both fields. A parameterization study is then conducted to evaluate the impact of key parameters on the vibration characteristics of piles in a water-pile-saturated soil system.

To research the effect of vertical earthquakes on rectangular underground structures in inclined liquefied foundations, and explore the seismic response characteristics of the structure with bidirectional earthquake, the finite element-finite difference coupled numerical method is used. The results revealed that the vertical earthquake will increase the degree of soil liquefaction in the vicinity of the structure and the dynamic response of the structure. The influence is related to the type and amplitude of the seismic wave. The displacement of the subway station will increase gradually as the compactness of the sand decreases or the angle of inclination of the ground increases. The lateral displacement of the subway station mainly occurs during the earthquake, and the vertical displacement mainly occurs after the earthquake. In addition, in the inclined site, the vertical displacement and internal force of the left and right sides of the underground structure and the excess pore water pressure ratio of the soil are not symmetrically distributed along the central column, and the closer to the bottom at the slope, the larger the settlements of the structure produce to make the whole structure rotate. The study can provide some seismic strengthening suggestions for underground structures in the inclined liquefiable site with bidirectional earthquakes. The seismic design of underground structures also needs to take into account the effects of the structure rotation during an earthquake in the inclined liquefiable site.

The behavior of center columns in shallow-buried underground subway station structures resembles that of high-rise buildings. In both cases, these columns experience significant vertical loads during earthquake events and are susceptible to brittle failure due to inadequate deformation capacity. In this study, the design concept of split columns, commonly employed in high-rise structures, is adapted for application in a two-story, two-span subway station. Initially, a comparative analysis was conducted using quasi-static pushover analysis to assess the horizontal deformation characteristics of traditional and split columns under high axial loads. Subsequently, a comprehensive quasi-static pushover analysis model encompassing the soil-structure interaction was formulated. This model was employed to investigate differences in seismic performance between traditional and innovative underground structures, considering internal forces, deformation capacity, and plastic damage of crucial elements. The analysis results demonstrate that the incorporation of split columns in a two-story, two-span subway station enhances the overall seismic performance of the structure. This enhancement arises from the fact that split columns mitigate excessive shear forces while effectively utilizing their vertical support and horizontal deformation capacities.