# Influence of Different Freezing Modes on the Base Slab Displacement of an Upper Structure
## 1 Introduction  
With the massive increase of the urban population, underground space has been utilized to tackle relevant problems like traffic congestion. Large-scale metro tunnels have been built in the city, underpassing roads, buildings and underground structures [1; 2; 3]. Specially, a lot of tunnels are placed in water-rich and soft soil layers, affecting the safety performance of buildings and road operations [4]. Thus, there has been a high-risk level of building damage and road settlement [5; 6]. Generally speaking, most of underpassing tunnels were constructed by tunnel boring, artificial ground freezing (AGF), and grouting. Among these methods, tunnel boring is one of the most common methods for tunneling, with a high excavation rate and a circular tunnel profile [7]. However, due to existing of continuous retaining walls and other auxiliary structures along an excavation layer, it is not suitable for a closely underpassing construction, which may damage tunnel boring machines and pose an uncertain accident. Grouting is a construction process by means of a highly erratic permeability and a homogenized deformability of soil [8], aiming to seal and stabilize strata. Whereas a grouting method can only reduce the natural permeability of soil, and solidification after grouting may not be homogeneous enough to be against groundwater [9], resulting in tunneling water inrush and mud gushing. In contrast, AGF is a safe technique that converts soil pore water to ice, creating a strong, impervious frozen soil wall which is used as temporary excavation support and groundwater control. AGF has the advantages of excellent impermeability, high strength, no pollution, and recyclability. Meanwhile, it can reduce the disturbance to soil in comparison with other consolidation methods. Thus, AGF has been widely used in underground engineering projects, for example, the tunnel construction [10; 11], cross-passage construction [12], recovering collapsed tunnels [13] and other projects [14]. AGF is also an attractive solution in the case of where a tunnel is built at a limited distance below or close to existing buildings [15; 16]. However, migration and freezing of water in soil cause expansion of the soil volume in a construction process [17; 18]. As a result, the strata deformation and ground heave may threaten the safety of upper structures. In recent years, there have been more underpassing projects with a shorter vertical underpass distance, which put forward a tremendous challenge on the freezing design and construction. It is tough and difficult to ensure both the serviceability of existing structures and the safety of new tunnels [19]. A significant amount of research has been conducted on the ground surface movements induced by AGF [20; 21; 22; 23; 24; 25]. Several empirical formulas of ground surface deformation were presented. However, it is worth noting that, to the best of our knowledge, there are few studies that focus on the deformation of an upper building during a tunnel underpassing project. For example, in a twin-tunnel underpassing metro station by AGF with zero distance up to a base slab, the upper base slab is easily damaged under the effect of frost heave. That is, it is necessary to strengthen upper structures [26], and some measures for reducing frost heave have been applied. A length of 60 m twin-tunnel was built in Germany, located 5 m below the foundation of a building. The measured maximum heave and settlement were 20 and 10 mm, respectively. In Vienna, two tunnels under-passed the foundation of a building with a 1.6 m cover at the minimum in a water-rich layer and a frost heave of 13 mm was measured. With the development of frozen soil excavated, the frost heave reduced to 3.0-8.5 mm. A metro station platform enlarged by AGF, located in the center of the city, is 10 m beneath a building, and the heave and settlement were measured with a total deformation of 12 mm [27]. Although these studies are instructive for the construction of underpassing projects, there are still some significant differences.