# Large Deformation Settlement Series Solution and Numerical Simulation for Underpass Project Track
## 1 Introduction  
In recent years, with the rapid development of traffic construction, the traffic safety problems of road and railroad level crossings have become more and more prominent. Therefore, the level crossing of the railroad and road can be changed into an interchange, and the underpass railroad frame culvert (also called box culvert) becomes the main solution to this problem [1; 2; 3; 4]. The process of box culvert jacking or subway tunnel shield construction will inevitably cause disturbance of the surrounding soil, which in turn leads to different degrees of ground displacement and deformation [5; 6; 7], causing loss of the existing equilibrium, and then triggering the settlement of soil, track or pipeline. However, in practical engineering, for beam type structures such as tracks or pipelines, the settlement cannot be measured directly due to the on-site construction, therefore, the soil settlement under the beam is measured to predict the settlement of the beam in the underpass project. This settlement of the beam becomes a practical and effective method. The main research methods for the displacement of soil and adjacent track pipeline caused by jacking or shield construction are as follows: (1) the formula method [8; 9; 10; 11]; (2) the numerical analysis method [12; 13; 14; 15; 16]. For the settlement analysis of the track, the elastic foundation beam model is usually used. In recent years, many scholars have conducted in-depth research on the calculation theory and method of the foundation beam [17; 18; 19], among which the Winkler model is widely used by the engineering community because of its simplicity and practicality. The Winkler foundation model assumes that the pressure at a point on the foundation is proportional to the displacement at that point. The frictional resistance between the foundation and the beam is neglected. However, in actual engineering, when the foundation soil is hard and the contact between the beam and thefoundation is rough, there is obvious frictional resistance between the two. Second, this effect of frictional resistance between beams and soils is often not directly neglected because the deformation moduli of beams and soils usually have significant differences, which also make the contact mode between them more complicated. [PERSON] et al. [20] investigated the effect of interfacial friction between the beam and the foundation with numerical examples, and also studied the mechanical behavior due to the tension-free properties of the foundation. The numerical results show that the effects of the tension-free characteristics of the foundation and the interfacial friction have significant effects on the mechanical behavior of the beam-foundation system. [PERSON] et al. [21] proposed an embedded beam formulation for discrete independent finite element (FE) analysis of pile foundations or rock anchors interacting with the surrounding soil in geotechnical and tunnelling engineering. [PERSON] et al. [22] derived that the lateral deflection of the generalized foundation Timoshenko beam is more sensitive to the compressive stiffness of the Winkler foundation than to the stiffness of the shear layer and rotating springs of the foundation. Horizontal interfacial friction due to foundation adhesion has the same effect as foundation cohesion. It is reasonable to incorporate horizontal interfacial friction into elastic foundations. [PERSON] and [PERSON] [23; 24] investigated the effects of pipe-soil geometric defect amplitudes and friction on critical loads and post-bending structures. The above research shows that the theoretical solution considering the effect of friction is more accurate, therefore, the effect of the friction effect should be considered in the analysis of the elastic foundation beam. In addition, the traditional elastic foundation beam model is based on the assumption of small deformation, which does not consider the axial elongation of the beam and the effect of additional axial force generated by the deformation of the beam.