## 1 Introduction  
Subway tunnel excavation frequently traverses intricate subterranean environments and often necessitates the penetration of diverse surface structures, particularly the complex network of crisscrossing railways and high-speed railway embankments. The process of shield tunnel excavation inevitably exerts an impact on the overlying strata and the foundations of high-speed railways [1, 2]. Conversely, the passage of high-speed trains generates vibrational effects on the underlying strata and tunnel construction. In regions characterized by loess and other soft soil layers, the construction of tunnels encounters significant challenges due to the loose structure of these soils, which are highly susceptible to disturbance. The stability of the tunnel face during shield tunneling is of paramount importance, as it is a critical issue that demands meticulous attention and robust engineering solutions [3, 4, 5]. In recent years, many scholars have studied the stability of shield tunnel faces [6, 7, 8]. [PERSON] and [PERSON] [9] used a centrifugal model of a sandy foundation to test typical auxiliary anchorage methods, and the research results showed that each anchorage technique had its optimal anchorage length and anchorage arrangement; the failure state of a tunnel face under three anchorage positions was given. [PERSON], [PERSON] [10] used X-ray scanning technology to conduct a scanning study on the formation-deformationprocess during the failure of tunnel faces and obtained the failure mode of tunnel faces. The results showed that it was more reasonable to describe the failure surface of tunnel faces using a logarithmic spiral equation. [PERSON] [11] conducted a 1 g (gravity) small-scale model test to evaluate the supporting pressure model required for the face of a shallow buried tunnel and simulated the collapse of the face of the tunnel. The results showed that a chimney wedge collapse mechanism formed in the dense sand and spread to the soil surface. [PERSON], [PERSON] et al. [12] studied the failure behavior of tunnel faces under different buried depths in a sandy stratum of Ottendorf-Okrilla using a 1 g model test method and obtained the load-displacement curve of tunnel faces and the ultimate supporting force of tunnel faces under different working conditions. [PERSON], [PERSON] [13] used a small geocentrifuge to study the collapse mechanism of the face of non-cohesive soil tunnels under different soil pressures, surface settlements, stresses (acting on the face of the tunnel), and supporting forces required to ensure the safety of the face. [PERSON], [PERSON] [14] carried out indoor physical model tests on the influence of faults on tunnel stability, and the results showed that the influence range of tunnel excavation across faults increased significantly. [PERSON], [PERSON] [15] carried out a series of 1 g small-scale tunnel tests, taking into account the influence of excavation rate (unloading time) on system response and the change in displacement of the tunnel face with time due to a rapid reduction in horizontal stress imposed on the tunnel face. [PERSON] et al. [16] conducted dynamic model tests to study the dynamic characteristics of an inverted arch and its foundation soil regarding high-speed railway tunnels under different train speeds; they analyzed the acceleration, dynamic coefficient, and dynamic stress of the inverted arch and foundation soil and discussed their relationship with train speed in detail. They obtained an attenuation law of vibration propagating upward along the track, established the calculation formula of the speed influence coefficient of the tunnel inverted arch, and determined the depth of the stratum affected by vibration. [PERSON] et al. [17] used a combined method of centrifugal tests and 3D numerical simulation to study the dynamic response of shield tunnels passing under existing high-speed railway tunnels; they analyzed the influence of settlement joints and steel pipe pile reinforcement on the existing tunnels. [PERSON] et al.