Thermomechanical Framework for Settlement Calculation of Geothermal Energy Piles in Multilayered Soil

Abstract

In this study, a continuum-based analytical model of the geothermal energy pile subjected to an axial mechanical load and undergoing temperature change is presented, in which soil displacements are assumed considering the kinematic compatibility between the pile and the soil. Stresses caused by the temperature change are explicitly taken into account by relating it to the restrained thermal strain. The principle of minimum potential energy and calculus of variations are used to obtain the differential equations of the pile and soil displacements. The differential equations are solved using an iterative algorithm. Verification and validation studies with equivalent finite-element analysis and experimental/field studies show that the analysis produces accurate pile responses in terms of vertical displacement, strain, and stress and can produce field pile response with reasonable accuracy. The novelty of the developed framework lies in its ability to incorporate the effect of soil temperature change on the thermomechanical pile–soil interaction, a feature missing in all other existing analytical frameworks. The effect of soil temperature change on the mechanical response of the pile is examined and is found to have negligible effects on energy piles. Subsequently, closed-form solutions for vertical displacement, strain, and stress are developed for energy piles under mechanical and thermal loads embedded in different soil profiles that can be directly used by designers. Another novel feature of this framework is that the soil spring parameters representing elastic soil compression and shear resistances are obtained iteratively as part of the solution without requiring ad hoc empirical equations. Fitted equations for these parameters are developed after a thorough parametric study that eliminates the need for iterations in obtaining the pile responses analytically.