## 3 Active Bearing Concept of the FSP  
### FSP and Its Action Mechanism  
Due to the low bearing capacity and strong deformation capacity of surrounding rock, tunnels with weak surrounding rock such as water-rich loess are prone to large subsidence and even collapse [16]. FSP is a common method to control large settlement of tunnel. Its implementation scheme is as follows: during or after the primary lining construction of each step of the tunnel, steel pipes with larger diameter are driven horizontally or diagonally downward from the arch foot of the tunnel to the outside, and the steel pipe tail and the steel arch frame of the primary lining are firmly welded to achieve common deformation and bearing (Figure 6). Commonly used steel pipes have diameters of 42 mm, 50 mm, 89 mm, and 108 mm. Figure 4: Surface morphology of tunnel support structure at the initial stage. Figure 5: Water intrusion and surface collapse of Yulinzi Tunnel. Figure 6: Position of FSP under the three-benches and seven-steps excavation method. According to the related research [5], the supporting force of the FSP on the primary lining structure comes from three aspects: the normal pressure caused by relative extrusion between the surrounding rock and the steel pipe side wall, the friction resistance caused by relative slip between the surrounding rock and the steel pipe side wall, and the supporting force of the surrounding rock at the bottom of the steel pipe. The normal pressure caused by the relative extrusion between the surrounding rock and the steel pipe side wall is the main part. The FSP is driven in the surrounding rock on both sides of the tunnel, and its end bears the vertical load and bending moment transmitted by the arch frame. When the steel pipe has bending deformation, the surrounding soil will restrict the deformation of the steel pipe. Therefore, the steel pipe body will be supported by the uneven soil, and the supporting force is proportional to the deformation of the steel pipe. Therefore, when analyzing the internal force of the steel pipe bearing transverse load in the soil, the soil can be simplified into a spring only under compression. Based on the Winkle hypothesis, a semi-infinite length elastic foundation beam model can be established (Figure 7). Numerical methods can also be used for simulation analysis. Considering the size characteristics and large transverse deformation of the FSP, finite element simulation using ABAQUS software can better solve the problems of geometric nonlinearity and material nonlinearity and improve the accuracy of numerical simulation results. Taking a steel pipe with a diameter of 50 mm as an example, according to the Saint Venant principle, in order to prevent boundary effects from affecting the analysis accuracy, the surrounding rock that exceeds the range of five times the diameter of the steel pipe is taken as the research object. Since the steel pipe is a slender column and the surrounding rock area is a cylinder, better grid quality can be obtained. The length of the rock and soil mass is 3000 mm, and the bottom radius is 500 mm. The area occupied by the steel pipe is excavated in advance to form a hollow structure. The outer diameter of the FSP is 50 mm, the wall thickness is 5 mm, and the length is 2500 mm. According to the symmetry of the model structure and stress deformation, a calculation model is established by taking half of the surrounding rock mass and steel pipe, as shown in Figure 8.  
Figure 8: Simulation of deformation characteristics of vertical bearing capacity of foot steel pipe end. Figure 7: Elastic foundation beam model of foot steel pipe bearing. Under the influence of construction excavation, the stress state of the surrounding rock at the side of the tunnel is complex, but it can be determined that the density of surrounding rock along the longitudinal driving direction of the steel pipe is increasing, and the surface of surrounding rock exposed to the outside is unrestricted.