## Materials and Methods
### Experimental System Design  
To acquire variations of temperature field and re-stabilization characteristics during the operation of the GSHP system in summer and winter cases in the laboratory, an experimental system should be specifically designed. One of the most important aspects considered in modeling design is scale law. The similarity ratios should be considered in many aspects to make the model and prototype consistent. In physics and engineering, the Fourier number is a dimensionless number that characterizes transient heat conduction; and the Reynolds number is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. Hence, the Fourier number and the Reynolds number are selected as similarity criterions since phenomena of heat transfer and fluid mechanics are mainly involved in this program. Firstly, the soil thickness in prototype layer is 30 m (The depth of soil in field mostly involving muddy silt clay, muddy clay, and silty clay in the shallow GSHP system is around 30 m). The model soil is filled to 1.0 m as a most appropriate size in the laboratory; then the geometry similarity ratio was calculated by \(C_{l}=1.0\) m/30 m \(=1/30\), i.e., 1:30. Considering the space of installing U-tube heat exchange, instruments and some insulation materials, the model box height is set to be 1.5 m. In addition, the influence range of 1.5 H (H is the thickness of soil) is considered according to the national standard of the Technical Code for Ground Source Heat Pump System (GB 50366-2005). Thus, the sectional model box dimension is set to be 170 cm (the aiming direction of temperature-sensor distribution) \(\times\) 120 cm. The heat exchanger of UT is directly related to the heat transfer between the soil surrounding and UT. It plays a very important role in the model experiment. Single U-shaped PE tube is selected in this model experiment. In practice, the diameter of the PE tube is about 20-40 mm. If the same geometry similarity ratio of 1:30 was utilized in UT, the diameter of UT can only be less than 1 mm, which is impossible in the manufactory product. In addition, to get enough heat exchange efficiency, a certain amount of heat flux is required. Comprehensively considering the above aspects and prior to ensure the consistent q (heat flux per surface area) with general prototype circumstance, the geometry  
Figure 2: Shanghai geology and hydrology profile. similarity ratios of UT can be set as 1:1 in cross section and 1:30 in depth (U-tube heat exchanger dimensions by such similarity ratios is 2 cm in diameter and 100 cm in height). According to the Fourier number (similarity criterion in heat transfer), there is a similarity criterion in ratio form as: \(\dfrac{C_{a}C_{t}}{C_{l}^{2}}=1\) where \(C_{a},C_{t},C_{l}\) is respectively similarity ratio of thermal diffusion, time and geometry. Moreover, \(C_{a}=1\) conspicuously due to the same model soil with the prototype, combined the above formula, the time similarity ratio can be yielded \(C_{t}=C_{l}^{2}=\left(1/30\right)^{2}=1/900\). The time similarity ratio is 1:900, i.e., a unity minute in the experiment is equivalent to 900 min in prototype and it is about 15 h. Therefore, the model experiment can greatly shorten the testing time (time similarity ratio is deduced by the Fourier number). Lastly, the crux in our model tests is the temperature conduction, which is directly related to the heat flux per surface area. To ensure \(C_{q}=1\), i.e., to guarantee the simulation quality, the heat flux used in the model tests should be calculated precisely to attain the same flux per surface area in the unit cylindrical heat source, and the heating power also should be controlled exactly to get the constant heat flux. The similarity ratio of the heat flux is relative to the geometry similarity ratio of UT, i.e., \(C_{V_{f}}=\left(C_{l_{1}}\right)^{2}\cdot C_{l_{2}}=1/30\).