## 1 Introduction  
With the acceleration of urbanization, the development and utilization of underground space are becoming more and more extensive, and the construction of subway tunnels and their affiliated communication channels has become an important part of urban infrastructure [1; 2]. However, in the construction process of tunnels and communication channels, especially when freezing technology is used for geotechnical reinforcement [3; 4], its impact on the existing upper buildings has become a key problem to be solved urgently. Although freezing technology can effectively control the groundwater flow and enhance the formation stability, the temperature field change caused by it, the frost-heaving effect of soil, and the deformation in the subsequent thawing process may cause adverse effects on the upper buildings, such as foundation settlement and structural cracking [5; 6]. Therefore, it is of great significance to deeply study the influence law of freezing of contact channels on the existing upper buildings to ensure the construction safety of underground engineering and protect the structural stability of existing buildings [7; 8]. In the research field of tunnel-soil-building interaction, scholars at home and abroad have carried out a lot of work, especially on the influence of tunnel construction on underground pipelines, and have made remarkable progress [9; 10]. These research results provide valuable references and enlightenment for this paper to study the effect of freezing of contact channels on the upper existing buildings [11; 12]. In recent years, soil deformation caused by tunnel construction and its influence on underground structures has become a research focus. The free displacement field theory based on Gaussian distribution has been proposed, which lays a theoretical foundation for evaluating the influence of tunnel construction on underground pipelines [13; 14]. On this basis, the continuous medium elastic solution of pipeline longitudinal deformation has been further derived, and the nonlinear change of soil stiffness has been considered, which makes the evaluation method more perfect [15; 16]. Scholars have not only paid attention to the soil deformation caused by tunnel construction but also deeply studied the interaction mechanism between pipelines and soil. Considering the influence of soil stiffness weakening on pipeline bending stress, it has been found through model tests and numerical simulation that the longitudinal deformation of the pipeline can be more accurately predicted by considering the out-of-plane shear caused by pipe-soil interaction. In addition, there is more and more research on the discontinuous interface pipeline, and the calculation methods of pipeline deflection considering the interface effect have been proposed with respect to this, so that the simulation results are more close to the actual situation. To simulate the deformation characteristics of the foundation more accurately, scholars have improved the foundation model. The traditional Winkler foundation model neglects the continuity of foundation deformation, while new models, such as the Pasternak foundation model, can better reflect the actual deformation of the foundation. Based on the Pasternak foundation model, the finite difference decomposition of discontinuous interface pipeline deflection has been constructed, which provides a new tool for evaluating the influence of freezing of the contact channel on superstructure. With the wide application of freezing technology in underground engineering, the changes of soil temperature field, seepage field, and stress field caused by freezing technology have been deeply studied by scholars at home and abroad. Remarkable achievements have been made in analytical solutions, the frost heave model, and experimental device development, which provide theoretical support for the application of freezing technology in the construction of subway connection passage.