# A Numerical Study of the Behavior of Micropile Foundations under Cyclic Thermal Loading
###### Abstract
Furthermore, numerical analysis of TA micropiles has been reported by [26; 27; 28; 25] where driven micropiles in fine-grained soils were modeled, and [29] who modeled a bored (wished-in-place) micropile in frictional media. The thermal response of TA piles of all types was reviewed by [30], and more recently by [31]. For micropiles, including those referred to above, thermal tests have yielded heat transfer rates in the range of 15 to 70 W/m. This is a rather wide range which is probably due to a multitude of factors such as ground and groundwater conditions, pile construction method and materials, the configuration of heat exchange pipes in the piles and the thermal load parameters (inlet temperatures, flow rates and duration). Heat transfer rates from intermittent tests, where the thermal loads are applied for only a few hours, lie at the upper end of the above range and those rates from long-term tests that approach steady state tend towards the lower end. Building upon this, a comprehensive understanding of heat transfer in micropiles was further developed by [32] who employed Taguchi statistical experimental design techniques to methodically establish and conduct analyses that were instrumental in identifying the pivotal factors that influence heat transfer within micropiles. The results showed that different design criteria to those for large diameter TA piles should be used for TA micropiles. In addition to pile length and thermal conductivity, the diameter of the heat exchanger pipes emerged as one of the key parameters for optimizing heat exchange efficiency in micropiles, while being the easiest parameter to engineer. On the other hand, while maximizing the number of U-pipes and pile diameter was crucial for large diameter TA piles, it did not impact the energy performance of TA micropiles, due to geometry constraints and the expected occurrence of thermal interference. Some field investigations on the thermal behavior of TA micropiles were carried out by [23] who performed thermal testing on a 180 mm diameter, 12 m long micropile installed into layered clayey and sandy silt, and reported heat transfer of 30 to 40 W/m with an inlet temperature, \(\mathrm{T_{in}}\), of about 34 \({}^{\circ}\)C and a fluid flow rate of 0.82 m/s (0.1 kg/s). [PERSON] et al. (2020) [24] and [PERSON] et al. (2021) [25] undertook heating and cooling tests on a group of eight 160 mm diameter, 13 m long micropiles in clayey soil underpinning an existing foundation, and reported heat transfer increasing from 20 to 70 W/m, as the inlet temperature was increased from 30 \({}^{\circ}\)C to 50 \({}^{\circ}\)C, at a flow rate of 0.51 m/s (0.113 kg/s). Modeling balanced seasonal heat exchange through an isolated 150 mm diameter, 15 m long micropile using the finite element method, [29] obtained peak heat exchange values of about 45 W/m for both heating (T\({}_{\text{in}}\) = 0 \({}^{\circ}\)C) and cooling (T\({}_{\text{in}}\) = 30 \({}^{\circ}\)C) modes with flow rates between 0.5 and 1.5 m/s (0.09-0.27 kg/s), during the first annual cycle of thermal loading. The authors are not aware of any long-term performance data from micropile-based TA pile foundation systems. [PERSON] et al. (2014) [17] tested two 180 mm diameter, 5.5 m long Type A micropiles constructed in a very stiff, high plasticity clay, and reinforced with a single 25 mm diameter steel reinforcement bar. Non-TA piles of the same dimensions were also tested, to provide a measure of pile creep and capacity under tensile mechanical load. A number of thermal tests were carried out under tensile mechanical loads that increased progressively from 40 kN up to 256 kN, about 9% to 56% of the ultimate tensile resistance. The results suggested that the thermal axial load generated during heating was very small (around 20 kN) which implied little shaft restraint was mobilized. Drawing upon the insights garnered from previous studies, particularly the examination of TA micropiles by [17], it becomes evident that the influence of mechanical load on thermal behavior is a crucial factor.