1. Introduction
With the large-scale development of western cities, rail transportation inevitably passes through wet collapsible loess areas. Considering the special engineering properties of the wet collapsible loess and the large number of traffic loads that the upper part of the tunnel bears, it is likely to cause a series of engineering disasters such as cracks, misalignments, and water and sand inrush in the tunnel after operations. Therefore, reasonable tunnel reinforcement measures are particularly necessary.
Currently, research on reinforcement measures for loess tunnels mainly focuses on tunnel surrounding rock pressure, lining structure calculations, and construction techniques. Most of these studies use theoretical analysis and numerical simulation methods. For example, Shao, S. et al. (2021) used numerical simulations to simulate the structural properties, strata, geological conditions, and excavation support effects of loess, analyzing and revealing the formation mechanisms of different types of failures during the construction process of loess tunnels [
1]. Qiu, J. et al. (2022) used a comprehensive method combining theoretical derivation and numerical simulation to study the response mechanism of loess subway tunnels under partial water environments [
2]. Cheng, X. et al. (2017) studied the influence of seepage on the seismic response of loess tunnels using ADINA to simulate the structural field and fluid field, compared and analyzed the maximum principal stress, minimum principal stress, lining maximum displacement, and internal forces of the tunnel structure, and further obtained the influence of rainwater seepage on the mechanical properties of LTSLS [
3]. Weng, X. et al. (2021) used numerical simulations to study the effects of different flooding methods on tunnel linings and further studied the stress and deformation of tunnel linings, strata, and surface subsidence after local soil collapse in the tunnel, as well as the mechanical mechanisms causing these effects [
4]. In order to investigate the potential damage of shallowly buried multi-support underground structures during earthquakes, Zucca, M. and Valente, M. (2020) conducted extensive numerical simulations and evaluated the seismic performance of various structural configurations [
5]. In addition, Xue, Y. et al. (2020) obtained a representative data sample set of total deformation in loess tunnels using numerical simulation methods and could effectively predict the total deformation of typical loess tunnels using a backpropagation neural network (BPNN) [
6]. Hongtao, N. et al. (2022) used the finite difference software FLAC3D to simulate and analyze three-dimensional modeling numerical calculations under the construction conditions of upper and lower step excavation for the technical problems of tunnel excavation under special stratum conditions of loess-covered soil–rock contact zones and analyzed the rock failure characteristics of the contact zone surrounding rock from multiple aspects [
7]. Moreover, in the machine learning applications in geomechanics, Savvides, A.-A. and Papadopoulos, L. (2022) have proposed a set of feed forward neural networks to estimate the stresses and strains at failure for cohesive soils subjected to loads from shallow foundations [
8]. Furthermore, Sun, Z. et al. (2022) comprehensively described the deformation characteristics of tunnels crossing through loess-bedrock strata through numerical simulations and discussed in detail the mechanical behavior and displacement effects of cyclic loads on tunnels and sliding surfaces [
9]. Mao, Z. et al. (2019) used the MIDAS geotechnical analysis system to simulate the construction process of a navigation tunnel and bilateral guide tunnels in a loess multi-arch tunnel, and studied the changes in surrounding rock stress and seepage fields during the construction process of the loess multi-arch tunnel [
10]. Liu, Y. et al. (2017) simulated the strain–stress behavior of loess using the Duncan–Zhang EB model and studied the deformation and mechanical properties of tunnel linings under different flooding conditions [
11].
Currently, there is still a lack of clear theoretical support for research on foundation stress and deformation in tunnel engineering, and design personnel mainly rely on subjective engineering experience to design reinforcement schemes for tunnel bottoms. In other soft rock tunnel foundation reinforcement designs, the processing methods used lack a rigorous theoretical basis. Therefore, it is necessary to conduct in-depth research on tunnel surrounding rock stability and support control to ensure the construction and excavation of tunnels in loess areas and safe operation in the later stages. However, due to the complexity of the tunnel surrounding rock structure and geological environment, traditional theoretical analytical solutions have difficulty handling these complex nonlinear deformation problems related to tunnel excavation. At the same time, considering that numerical analysis still faces difficulties in simulating underground engineering strength failure, geological model experiments have become a better choice. Geological model experiments can better simulate the excavation construction process of tunnels and the effects of load application and time effects and can reflect the complete process of engineering stress deformation more realistically.
Experts led by Fumagalli (2013) pioneered engineering geological model test technology at the Italian Structural Model Test Center, followed by extensive research by many scholars [
12]. Fan, H. et al. (2023) analyzed the mechanical properties and deformation characteristics of tunnel linings for reinforced jet grouting piles in loess tunnel foundations and the impact of changes in pile geometry on tunnel foundation stability using centrifugal model tests and numerical simulations [
13]. Cheng, X. et al. (2021) established a dynamic model and a rainwater infiltration model for loess two-lane tunnels considering the coupled effects of seismic activity, rainfall infiltration, and traffic movements. Using near-field pulse seismic excitation, the influence of loess tunnel seepage, traffic loads, and seismic activity on the driving dynamic response of loess tunnels was studied [
14]. Qiu, J. et al. (2020) designed model tests according to different water source locations and tunnel lining forms, studied the collapsibility of loess under a high-pressure water environment and the failure behavior of subway tunnels, and analyzed the distribution laws of tunnel water pressure field, displacement field, and stress field [
15]. Cheng, X. et al. (2020) established four different section tunnel models and combined them with fluid models to study rainwater leakage, earthquakes, and train-induced effects, further analyzing the displacement, stress, and pore water pressure of loess tunnel critical points, and obtained the dynamic response mode of loess tunnels under the action of earthquake, rainwater infiltration, and train loads [
16]. Lai, H. et al. (2019) first studied ground subsidence caused by loess tunnel construction through a uniquely designed centrifuge model test and proposed a new method that considers the special engineering characteristics of loess to evaluate the construction settlement of loess tunnels [
17]. Fan, H. et al. (2023) analyzed the settlement of tunnel bedrock and the structural mechanical response characteristics under the influence of jet grouting piles with different lengths and diameters in weak loess areas using centrifugal model tests, effectively reducing tunnel bottom settlement and significantly shortening the stress adjustment time of surrounding rocks [
18]. Yang, T. et al. (2020) established a precise grouting reinforcement test system, using the Yuhang Road tunnel with overlying loess as the injection medium, and conducted an orthogonal test based on slurry dry density, moisture content, water–cement ratio, and grouting pressure [
19].
Based on the #1 tunnel of the Lanzhou–Qinhuangdao Expressway on the north bank of the Yellow River in Lanzhou City, this paper conducts a model test for the reinforcement of loess tunnel foundations. Similarity theory is used to theoretically study the design of the model, aiming to obtain a more scientific and specific experimental plan for the project to ensure the safety of the reinforcement of loess tunnel foundations in engineering.