## 1 Introduction
The passive soil pressure of cohesionless backfill and the active soil pressure of cohesive backfill in a narrow area were investigated under the RB mode [25; 26]. Considering the horizontal shear force, the idea of arc differentiation was introduced to explore the soil pressure in the nonlimited state in the RB mode [27]. The soil pressure calculation model of narrow backfill under the RT mode but rotating about the top of the retaining wall with the horizontal differential element method was studied [28]. The relationships between the finite width and the coefficient of active soil pressure and height of the action point under three displacement modes were studied. It is found that the point of application of three wall movement modes is generally higher than one-third of the wall base [29]. Soil-structure interaction has an important impact on the structure. The influence of soil-structure interaction in the yield system was evaluated [30; 31]. For practical engineering, nonlinear analysis was carried out considering the interaction between soil and the foundation system [32]. The excavation of the foundation pit will disturb the surrounding soil and change the stress in the original soil. The soil-structure interaction has a significant impact on the stress and deformation of the retaining structure. The retaining structure with different rough degrees and the soil with different strength parameters are also important factors that affect the soil pressure. The influence of interface friction angle on soil pressure is analyzed by pasting transparent adhesive tape and coarse sandpaper on the surface of the retaining structure [33]. The distribution of soil pressure under the sand with different water content is studied by laboratory tests [34]. Thus, studies of finite soil pressure have typically focused on the failure mode of finite soil. This approach is more applicable to new foundation pits near buildings with underground structures. With the further development of urban underground space, new foundation pits are often adjacent to existing underground structures. The failure mode of a finite amount of soil and the distribution of soil pressure lacks systematic research due to the soil overlying the existing underground structures. In this paper, a finite soil failure mode was proposed to help engineer a new foundation pit adjacent to an existing subway station. Considering the interface friction between the soil and the structure, formulas to calculate the finite soil pressure are derived with the horizontal differential element method, and the corresponding distribution was given. Then, a simplified calculation of the resultant force due to the finite soil pressure and its relative height was proposed based on the principle of area equivalence. The rationality of the proposed method was verified by combining calculation examples and model tests, and the influences of parameters on the resultant force and its relative height were analyzed. This study proposed a reasonable prediction method for the finite soil pressure in engineering projects in which a new foundation pit is adjacent to an existing subway station, providing a basis for the design of the braced structure in the foundation pit.