## 1 Introduction  
In soft-soil areas, the shield method has become the primary method for constructing subway tunnels. Its advantages of high efficiency, advanced technology, and broad applicability significantly enhance the construction efficiency of subway lines. The number of subway lines is increasing, and the underground pipelines in the city are intricate, which will inevitably produce a situation in which the subway lines and the underground pipelines cross or become very close. Pipeline stiffness is generally small; a shield tunnel in the construction of the boring process will cause the surrounding soil body to produce a large deformation and additional stress [1, 2], which in turn affects the pipeline, resulting in pipeline deformation or even cracking, affecting the normal use of the pipeline. In the shield tunnel construction design, not only do we need to carry out a large number of necessary geological explorations, but they also need to be predicted in advance of the construction process, which may lead to the vertical deformation of the pipeline, to ensure that the construction will not affect the normal use of the pipeline and to verify the feasibility of the project. Scholars in this country and abroad have conducted a lot of research on this problem. [PERSON] et al. [3] introduced a calculation method for pipeline deformation caused by tunnel excavation based on the Winkler foundation model by using the theoretical solution method. [PERSON] et al. [4] combined the Pasternak foundation model and the soil movement model to derive a formula for calculating the pipeline settlement caused by single- and double-line shield tunnel excavation. [PERSON] et al. [5] carried out an indoor model test on the impact of shield construction on neighboring pipeline groups in sandy soil stratum, as well as studying the effect of the vertical settlement of pipelines when the tunnel shield vertically undermines multiple existing pipelines. [PERSON] et al. [6] also conducted indoor modeling tests on the effects of tunnel construction on pipeline deformation in sandy soil stratum to investigate the impacts of different pipelines, tunnel depths, and pipeline-tunnel intersection angles on pipeline deformation. [PERSON] et al. [7] started from the finite element method and established several models using the finite-difference software Abaqus to simulate the effects of shield tunneling on the settlement of parallel pipelines under different working conditions. [PERSON] et al. [8] used FLAC3D finite element software for numerical simulation, and combined with the measured values, it was concluded that the deformation of the pipeline conformed to a Gauss distribution after the construction of the left and right lines of the shield tunnel. [PERSON] et al. [9] conducted a series of three-dimensional finite element analyses that revealed the influence of tunnel excavation on the vertical deformation of existing tunnels. The above studies have investigated the influence of shield tunnels on the vertical deformation of pipelines under the conditions of vertical intersections of pipe tunnels in different ways, while there are fewer studies on pipe tunnels in parallel conditions, and according to a large number of engineering practices, the relative positions of pipe tunnels are not only perpendicularly intersecting but also parallel to each other. Therefore, it is necessary to study the vertical deformation of pipelines parallel to shield tunnels. In this paper, the impacts of double-lane shield tunnel boring on adjacent pipelines under parallel conditions are investigated. Compared with numerical simulation and model test methods, which often require a lot of time and effort and a lot of preliminary preparation, the theoretical solution method is universal and efficient and can provide designers with a timely reference for the preliminary construction design.