# Long-Term Thermo-Hydraulic Numerical Assessment of Thermo-Active Piles--A Case of Tropical Soils
## 2 Numerical, Modeling of the Long-Term Performance of Thermo-Active Piles
### Energy Demand Assessment
#### 2.2.2 Thermal Solicitations  
Based on the real external air temperature variations in the three selected cities, three different types of thermal solicitations imposed on the piles can be derived: T1--Brasilia; T2--Porto Alegre; T3--Manaus. As shown in Table 1, about one-third of the time in a year in Brasilia, buildings need to be heated. Since the peak cooling power requirements can be considerably higher than the peak heating power requirements, a smaller amplitude was adopted for the heating phase [30]. The energy injected and extracted during the year is proportional to the duration of cooling and heating and maintains a balance of respectively 37 and 63%. In Porto Alegre, it is almost half for heating and half for cooling, while in Manaus the energy demand is 100 % for cooling.  
The heat exchangers (absorber tubes) are modeled by finite line heat sources (FLS) instead of applying heat flux boundaries in the pile to simulate the energy exchange. For feasibility studies and pre-design of energy foundations, the decision tree coming from the Swiss Society for Engineers and Architects (SIA) is used to define the FLS intensity of thermo-active pile foundations (Figure 3). It considers the operation mode of the  
Figure 2: Locations (**a**) and the monitored monthly average temperature (**b**) of the three cities ([[https://www.123](https://www.123) rf.com]([https://www.123](https://www.123) rf.com)) (accessed on 9 July 2022).  
geothermal system as well as the ground conditions where the heat exchangers are installed, in particular the groundwater flow presence. In addition, the comfort air temperature threshold known from the Passivhaus standard (international energy performance standard for buildings) is assumed to be 20 \({}^{\circ}\)C. Therefore, when the temperature is above 20 \({}^{\circ}\)C, heat source power is positive, which means heat is injected into the ground to meet the cooling demand of buildings; while it is below 20 \({}^{\circ}\)C, the heat source power value is negative, allowing the pile to extract heat from the soil to meet the heating demand. Considering these factors, transient line heat source intensities of the whole energy pile for 1 year (1 cycle) are implemented in relation to the temperature and can be defined in Figure 4. As shown in this figure, three various typical tropical climate conditions are selected in this study: Manaus in the Amazonas state of Brazil with a constant high temperature of 27.4 \({}^{\circ}\)C, Brasilia with a mild climate zone with a temperature range of 18.9-22.5 \({}^{\circ}\)C. Porto Alegre in the south of the South American Plate with a temperature range of 14.4-24.7 \({}^{\circ}\)C. The magnitudes of their temperature variations are 0 \({}^{\circ}\)C, 3.6 \({}^{\circ}\)C, and 10 \({}^{\circ}\)C respectively.  
The transient thermal power of T1 and T2 fall in the ranges of [\(-\)30, 45] W/m and [\(-\)45, 45] W/m, respectively (pile diameter is 1 m), with a negative sign representing heat reaction. For T3 the power is fixed at 45 W/m. Depending on the temperature variation, the energy injection or extraction of the pile will also change. The heating peak and cooling peak of the pile are donated by HP and CP, respectively. In real practice, energy injection and extraction will not very likely be proportional to the cooling and heating demands, however, to quantify and compare the impact of imbalanced thermal demands, the simplified design of thermal solicitations described above is adopted.