## 1 Introduction  
The freezing method is commonly used to prevent the disaster of water innuls in underground excavation in China. This method uses artificial refrigeration technology to form a frozen wall around the underground space in the topsoil section, completely blocking the hydraulic connection between the topsoil aquifer and the excavation space. During freezing method construction, buildings are often on the surface. Freezing method construction has great influence on the stability of a building's foundation and its structural safety. The process of freezing method construction includes three stages: drilling, frost heaving and thaw settlement. In the drilling stage, the flushing fluid carries rock powder and sediment away from the formation, which may trigger the settlement of the building foundation. In the freezing stage, the frost heave of rock and soil cause the uplift of the building foundation. In the melting stage, uneven settlement of the foundation makes the shaft tower tilt. In a word, freezing method construction incurs frost heaving and thaw settlement of the soil, and, in turn, the heave or settlement of the building foundation. A significant amount of research has been conducted on the ground surface movement that is induced by freezing method construction [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14]. Among them, [PERSON] et al. considered the effect of the freezing margin and established a frost-heaving mode to calculate the frost heave deformation of roadbed by a semi-analytical numerical method [1]. [PERSON] et al. analyzed the influence of horizontal-freezing frost heave on the pile foundation of adjacent buildings in a railway tunnel through a finite element calculation and obtained the influence radius of horizontal-freezing frost heave [2]. [PERSON] et al. analyzed the displacement of upper structures under simultaneous and sequential freezing modes. The results are instructive to the construction of under-passing projects in a water-rich layer [3]. [PERSON] proposed a mathematical model for the variation and interaction of stress-strain, temperature and humidity fields in the structure and soil layer system in the permafrost region [4]. [PERSON] et al. proposed that the surface frost-heaving amount was the superposition of the frost-heaving rate along the whole freezing depth. According to their research, the normal frost-heave force was the integral of the frost-heaving stress on the frozen front along the influence range of the foundation, which had no direct relation with the surface frost-heaving amount [5]. [PERSON] systematically studied the frost-heaving deformation and its mechanical properties under unloading in freezing envelope engineering. He contended that frost heaving was closely related to the restriction conditions of soil properties, freezing time and degree, and the thickness of frozen soil wall. On this basis, he proposed that the effect of frost-heaving deformation could be alleviated through the pressure relief hole [6]. [PERSON] and [PERSON] focused on multiphase flow and coupled thermo-hydro-mechanical problems in saturated and unsaturated soils [15; 16; 17]. They offered numerical solutions to soil deformation during fluid flow. The inclination of the buildings under freezing construction certainly generate the variation of the internal structural stress. At present, finite element numerical calculation is an important method to study the structural stress of buildings. Conventionally, the deformation of a building's foundation is small, so most numerical simulation uses a linear elastic model [18]. Finite element method (FEM) models of buildings are often created based on experimental data. [PERSON] et al. established the finite element model of a telecommunication tower structure, according to the actual site conditions. The model carefully analyzed the specific wind velocity-time function, and then, first-order and second-order reliability methods were used to judge the reliability of two particular tower joints [19]. [PERSON] et al.