## 3 Results and Discussion  
### Time-Dependent Temperature Variation During the Whole Testing Process  
The temperature variations were monitored in the whole testing process including two periods: the fluid circulation period (i.e., GSHP operation time from the starting of tests to the end of fluid circulation and recovery period, i.e., from the termination of GSHP running to the end of tests). They were divided by a red arrow line, shown in Figure 5a,b. All TSs temperature variations of 50 \({}^{\circ}\)C in summer case and \(-10\)\({}^{\circ}\)C in winter case are addressed respectively. Specifically, from the whole process, the time-dependent temperature curves advance in three states: temperature ascending, stable state, and recovery stage. From the concept of heat-energy in soils, it can also be regarded as heat storage (temperature increasing) and heat-release (temperature decreasing), all the curves can also be divided into three stages including heat-storing, heat equilibrium, and heat-releasing, irrespective of summer (Figure 5a) or winter (Figure 5b). From the aspect of time, the fluid circulation period includes the time of the previous two stages and the recovery period equal to the time of the recovery stage. It is surprising to notice that both figures show that after recovery time, the stable temperatures are a little bit elevated than the initial starting temperature. They were numbered in array number connected with elevation number (such as 5-1 means the one in the fifth TS array at the first elevation). To better understand the radial heat influence on the temperature in soils to the U-tube, temperature variations of temperature sensors (TSs) in the same elevation number (such as 2-2, 3-2, 4-2, and 5-2) are selected, shown in Figures 6 and 7. They are located at a same depth in model soil but different distances to U-tubes. Specifically, they are arranged in a row seen from the model elevation of Figure 4b and labeled as No.1 TSs, No.2 TSs, No.3 TSs, and No.4 TSs (such as No.1 TSs includes TS 2-1, TS 3-1, TS 4-1, and TS 5-1). Curves in Figure 6 note that the visible temperature influence exhibited in almost all No.1 TSs, No.2 TSs, No.3 TSs, and No.4 TSs along various distances to the U-tube. They show \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Elevation No.** & **TS Series** & **1** & **2** & **3** & **4** & **5** \\ \hline \multirow{3}{*}{
\begin{tabular}{c} **Initial** \\ **temperature** \\ **(\({}^{\circ}\)C)** \\ \end{tabular} } & 1 & 16.78 & 16.8 & 16.47 & 16.37 & 16.84 \\  & 2 & 16.83 & 16.98 & 16.67 & 16.44 & 16.03 \\  & 3 & 16.91 & 16.61 & 17.27 & 16.91 & 16.4 \\  & 4 & 17.45 & 17.23 & 16.63 & 17.12 & 16.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Soil temperatures measured by TSs before circulation. Figure 5: Temperature variations with time of No.3 TSs under a certain temperature fluid circulation: (a) 50 \({}^{\circ}\)C; (b) \(-10\)\({}^{\circ}\)C.  
an asymptotic behavior, being fast at the start and then slowing down subsequently. This reflects characteristics of heat conduction within soils. This heat conduction is continuously induced by the heat exchange between U-tube and the surrounding soils under a constant rate (the same q), while the temperature could not increase all the time. It increased very fast firstly and then got into a stable stage. The internal motivation is the thermal gradient for temperature variation. With time advance, the difference of temperatures within the adjacent soils became smaller until a heat equilibrium state approached. At this circumstance, the temperatures could not change even GSHP kept running. The heat conduction within soils also stopped. Figure 6: Time-dependent temperature curves of TSs of different distances to UT along each row in the fluid circulation of 50 \({}^{\circ}\)C: (**a**) No.1 TSs; (**b**) No.2 TSs; (**c**) No.3 TSs; (**d**) No.4 TSs.