Analytical Solutions for Ultimate Limit State Design of Thermal Piles

This work aimed at providing analytical closed-form solutions for the design of thermal piles. To this end, a model in which a cylindrical pile is attached along the shaft to a series of distributed vertical springs representing soil stiffness is proposed. The pile has constant section and elastic properties; the restraints provided by the superstructure and base stiffness are represented through concentrated springs. The model allows derivation of exact solutions for homogeneous, two-layer soil and soil with linearly increasing stiffness with depth. In addition, approximate energy solutions are derived via the principle of virtual work for more general subsoil conditions with spring stiffness calibrated through finite element results. Expressions for the axial force and shear stress at the pile–soil interface are provided for typical soil stiffness distributions. A successful comparison to literature studies, involving complex transient-coupled numerical analyses and two field tests, corroborate model reliability. The proposed analytical solutions provide insight into the behavior of thermally loaded piles and can be used as a simple tool for ultimate limit state design.