The newly constructed Xi’an-Yan’an high-speed railway line is located in Guanzhong and northern Shaanxi. This double-track high-speed railway is designed to operate at a design speed of 350 km/h. It has a total length of 287.059 km and a newly-built line length of 281.968 km. The railway features 43 new tunnels along the main line, which collectively extend 165.751 km, accounting for 58.8% of the newly constructed line. The route traverses several geographical areas, including Weihe River alluvial plain area, loess tableland area, loess ridge gully area, and Ziwuling low mountain area. The Quaternary strata along the line predominantly consist of Holocene alluvium, diluvium, landslide accumulation layer, and artificial accumulation layer, as well as upper and Middle Pleistocene alluvium and aeolian deposits. The primary lithology includes clay (sandy) loess, with local occurrences of filled soil, silty clay, sandy soil, and gravel soil. The underlying bedrock is mainly composed of Paleogene, Jurassic, Triassic, Permian, Carboniferous, and Ordovician periods. The lithology is mainly shale, sandstone, mudstone, limestone, and conglomerate. The rock stratum exhibits a slight inclination.

The Luochuan Tunnel is located in Houzitou Township, Luochuan County, Yan 'an City, Shaanxi Province. It extends from DK194 + 759.57 to DK198 + 900, with a total length of 4140.43 m. It is a double-track medium-long tunnel. The tunnel’s entrance is situated on the slope of Huangtuliang, with the trajectory from the entrance to the exit being uphill. The burial depth of the tunnel decreases from the starting point to the endpoint. It ranges from a maximum depth of 64 m to a minimum depth of 8 m, indicating that the entire tunnel is relatively shallow. The tunnel excavation section measures 15.6 m in width, 13.18 m in height, and a cross-sectional area of 167.3 m², as illustrated in Figure 1.

The surrounding rocks of the tunnel are classified into Grade IV, Grade V, and Grade VI. Their respective lengths are 1240 m, 2531 m, and 331 m. Notably, 3,412 m of the tunnel consist of loess geological material in a soft plastic state. This soft plastic loess distributed throughout the tunnel, with concentrations primarily located at the top, body, and bottom. Specifically, in the section between DK194 + 800 and DK195 + 700, the soft-plastic loess is mainly found in the body and upper part of the tunnel, while in the section between DK197 + 560 and DK198 + 470, it is found in the body and lower part of the tunnel. The water content of the loess ranges from a minimum of 14.4% to a maximum of 27.4%. During construction, it is crucial to reinforce vault support and treatment of the tunnel base, monitor the water content of the loess, implement waterproofing and drainage measures, and ensure timely closure of the supports. These precautions are essential to prevent hazards such as soil deformation and collapse, which may result from prolonged exposure of the tunnel face to seepage and soaking.

The strata at the tunnel site are mainly Quaternary Holocene upper and middle Pleistocene aeolian deposits. The Quaternary Upper Pleistocene features clayey loess on the surface of loess beam, with thicknesses ranging from 5 to 20 m. Paleosols are often found at the bottom of loess beams, and their thicknesses range from 2 to 4 m. The Quaternary Middle Pleistocene consists of clayey loess within the loess beams, with thicknesses of 10–30 m; numerous paleosols are also present within this layer, generally measuring 3–8 m in thickness.

The geological structure in this area is relatively undeveloped. At the entrance site, the soil condition is classified as self-weight collapsible loess with a medium collapsible grade (Grade II) and a thickness of 15–25 m. Conversely, the exit site is categorized as self-weight collapsible loess with a serious collapsible grade (Grade IV) and a thickness of 25–30 m. Paleosol is the weakly expansive soil.

The tunnel traverses the loess plateau, with the Xiangu River at the entrance and Heimugou and Qujia River flowing on either side. The exit is located on the plateau, and the adjacent gullies exhibit year-round flow, which varies seasonally. During the dry season, the flow rate in the gully is approximately 5626 m³/d, located about 1650 m to the right of tunnel DK195 + 682, and 4166 m³/d, situated roughly 380 m to the left of tunnel DK195 + 075. Groundwater in the tunnel area is primarily pore phreatic water in the Quaternary unconsolidated layer. The groundwater level is significantly controlled by the rainfall, the size of loess plateau, and the thickness of loess layer. The tunnel is located above the groundwater level, and the available water supply is generally poor, leading to potential seepage and dripping during construction in the rainy season.

In this study, numerical analyses are performed using MIDAS-GTS finite element software. The selection of material parameters is based on the equivalent stiffness method, which considers the material properties of surrounding rock in each layer as well as the physical and mechanical parameters of the supporting structures utilized in the modeling process. Typically, the elastic modulus and bulk density of the steel arch frame are converted into those of concrete while ensuring the equivalence of compressive stiffness. The relationship expression is shown in Equation 1: E = E 0 + S g + E g S c (1) where E 0 is the elastic modulus of shotcrete; S g is the cross-sectional area of the steel arch frame; E g is the elastic modulus of the steel arch frame; S c is the cross-sectional area of shotcrete.

Based on a review of geological exploration reports and relevant literature, and by disregarding soil layers with minimal thickness, the strata are ultimately divided into four layers: Q₃ loess, Q₂ loess (I), Q₂ loess (II), and Q₂ soft-plastic loess. The parameters for the soil strata and supporting structures selected for the modeling process are presented in Tables 1 and 2.

According to the Saint-Venant principle, the excavation disturbance range of the tunnel is estimated to be 3 to 5 times the tunnel’s diameter. To eliminate the influence of the boundary effect on the numerical results and to accommodate the requirements of the working conditions, the overall dimensions of the model are established at 100 m × 80 m×60 m (X × Y × Z), as illustrated in Figure 2.

The actual thickness of the soft-plastic loess layer in the Luochuan Tunnel ranges from 0.8m to 6.4 m. A uniform layer thickness of 5 m is selected to establish calculation models of soft-plastic loess layers distributed at different locations, as shown in Figure 3. Numerical models of soft-plastic loess layers with different thicknesses,as shown in Figure 4.

The side and bottom boundaries are fixed, while the top surface is designated as a free boundary. The Mohr-Coulomb constitutive model is chosen for calculation. The tectonic stress is excluded from the modeling, while the effect of self-weight stress is incorporated as the initial geostress.

The model tunnel excavation adopts a three-bench reserved core soil method. During the simulation process, the construction stages are organized according to the actual site conditions. The tunnel excavation and the construction of the supporting structures are simulated using the 'activation’ and 'passivation’ commands in the software. Additionally, advanced support is simulated by adjusting the soil parameters in the reinforcement area.

A comprehensive analysis of numerous construction cases involving loess tunnels reveals that the pipe roof advanced support method is effective in controlling tunnel face collapse and stratum deformation. The inherent stiffness of the pipe roof, coupled with its pronounced support capabilities, rapid construction process, and high safety profile, make it a preferred choice for preventing tunnel vault collapse and roof fall. However, with the increasing prevalence of shallow excavation projects in recent years, the efficacy of short-distance pipe-shed advanced support has proven insufficient for the current demands of deformation control construction. Consequently, the technology associated with pipe roof support has evolved towards the implementation of medium and long pipe roofs.

In the section of the Luochuan Tunnel from DK195 + 000 to DK195 + 100, a soft-plastic loess layer with a thickness of 3 m is situated above the vault. A three-bench reserved core soil method is employed for tunnel excavation. Given the specific construction environment, φ89 mm pipe roofs and advanced small conduits are used for support. The circumferential spacing of the pipe roofs is 60 cm, and the external insertion angle ranges from 6° to 8°. Each ring measures 6 m in length. The horizontal overlap between adjacent rings is maintained at a minimum of 3 m. Ф42 advanced small conduits with a length of 3.5 m are placed between the pipe roofs, with a circumferential spacing of 0.6 m, an external insertion angle of 10°–15°, and a longitudinal loop of 2.4 m. When the advanced small conduits are used in conjunction with the steel frame, the horizontal lap length between two adjacent rows of small catheters is required to be no less than 1 m. The overall model and details of pipe roof advanced support are presented in Figure 9, the displacement nephograms of the surrounding rock are presented in Figure 10.

In contrast to the scenario of an invert covered with a 3-m thick soft-plastic loess layer without pipe roof reinforcement (illustrated in Figures 7, 8), the application of pipe roof significantly controls the deformation of surrounding rock. Figure 10 reveals that the vertical and horizontal displacements of the surrounding rock are improved under the action of advanced pipe roof compared to the situation without such support. Specifically, the maximum horizontal displacement of the surrounding rock is 7.29 mm on the left side and 7.21 mm on the right side. The maximum horizontal displacement is mainly concentrated in the left and right arches. The maximum vertical settlement of the surrounding rock is 23.91 mm, which reflcts a reduction rate of 63.46% compared to the scenario without pipe roof support. Additionally, the maximum uplift is 22.05 mm, which corresponds to a reduction rate of 54.41%. These findings indicate that the use of pipe roof support during the construction of the soft-plastic loess layer covering the tunnel vault is an effective method for controlling deformation.

The loose surrounding rock and the poor self-stability of shallow soft-plastic loess sections make tunnel excavation susceptible to the collapse of surrounding rock, excessive deformation, and significant surface settlement. Therefore, it is crucial to implement monitoring sections to monitor the stress and deformation of surrounding rock and supporting structures during tunnel excavation. This monitoring allows for the assessment and verification of the stability of the tunnel section, thereby ensuring the safety of the construction process. To facilitate effective construction management based on real-time deformation monitoring of surrounding rock and supporting structures, the typical sections DK195 + 000 and DK195 + 050 of the Luochuan tunnel, along with their monitoring point layouts, are illustrated in Figure 11.