Empirical formulas for borehole thermal resistance of parallel U-type cast-in-place energy pile

The borehole thermal resistance (mK/W) is an essential design factor of a ground source heat pump system, which allows to predict changes in the circulating fluid temperature. However, there are no proven and/or practical solutions to the borehole thermal resistance of ground heat exchangers with large borehole diameters and multiple U-type pipes, such as a large-diameter cast-in-place energy pile. In this study, empirical formulas were provided to estimate the borehole thermal resistances of large-diameter cast-in-place energy piles equipped with multiple pairs of U-type heat exchange pipes. First, the borehole thermal resistances of parallel U-type energy piles were evaluated through a series of in-situ thermal performance tests. Then, a numerical model for parallel U-type energy piles was developed and verified using the field test results. With the developed numerical model, the effects of various influencing factors on the borehole thermal resistances of parallel U-type energy piles were identified. Finally, empirical formulas were developed and verified by comparing with the field tests and numerical simulations. Consequently, the empirical formulas could predict the borehole thermal resistance of parallel U-type energy piles with a difference of less than 0.23% compared to the numerical model and 6.4% compared to the field test results.