# Semi-Analytical Framework for Thermo-Mechanical Analysis of Energy Piles in Elastic and Elastoplastic Soils

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## Date

2024-10-29

## Authors

## Advisor

Basu, Dipanjan

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## Publisher

University of Waterloo

## Abstract

Energy piles or geothermal piles are used to reduce the energy demand of a building by helping in the heating/cooling of the building as required. The advantage of energy piles over other ground heat exchangers is that piles are an integrated part of the foundation of a building to carry the superstructure load. The same piles can be used to extract/inject heat from/to the ground and that heat can be used in the cooling/heating of the building. Thus, the energy demand of the building for heating/cooling is reduced. Energy piles are subjected to mechanical load that comes from the superstructure as well as thermal load (temperature change) caused by the heat exchange operation. The combined mechanical and thermal load changes the behavior of the pile foundation. Because the length of the pile is much higher compared to its diameter, the temperature change affects the axial behavior of the pile rather than its lateral response. The settlement of an energy pile is different than a conventional pile foundation as heating or cooling of the pile causes extension in some parts of the pile and compression in other parts of the pile. The axial response of an energy pile under mechanical and thermal loads in terms of vertical settlement, strain, and stress in the pile is calculated in the available literature where the pile-soil interaction has been considered by modeling the soil with equivalent linear and nonlinear soil springs. The representation of soil as springs does not take into account the effect of three-dimensional pile-structure interaction. Analysis of the energy pile considering the three-dimensional pile-structure interaction has been done in the literature using numerical methods which are computationally expensive. Apart from that, the thermo-mechanical behavior of soil needs to be considered in the energy pile analysis because of the temperature change of the pile and soil, and heat exchange between the pile and the soil. In this context, the thermo-mechanical soil constitutive model should satisfy the laws of thermodynamics. The analysis of the energy pile with a thermodynamically acceptable thermo-mechanical soil constitutive model is lacking in the available literature.
In this thesis, a continuum-based semi-analytical framework for the analysis of the energy pile that takes into account the three-dimensional pile-structure interaction is proposed. First, the semi-analytical framework for an energy pile that is embedded in multi-layered soil and subjected to mechanical axial load and thermal load is developed using the variational principle of mechanics by minimizing the potential energy of the pile-soil continuum where both the pile material and soil are considered to behave as a linear elastic material.
In the next part of the thesis, a semi-analytical framework for the same energy pile is developed where the soil is modeled as an elastoplastic material. The analysis framework for the energy pile in elastoplastic soil is developed from the laws of thermodynamics with the energy potential and dissipation function where the plastic behavior of soil is taken into account through the dissipation function. The derived analytical framework is used for elastoplastic soil response with the Drucker-Prager constitutive model. The results from the present analysis are verified with available results in the literature from experiments and numerical analysis. The Drucker-Prager constitutive model does not take into account the effect of temperature on the stress-strain response of the soil. So, this constitutive model is most suitable to model the thermo-mechanical behavior of sand as the effect of temperature on the thermo-mechanical response of sand is not significant. Therefore, energy piles in sand can be analyzed using the present framework with the Drucker-Prager constitutive model. Energy pile in clay needs to be represented with a soil constitutive model that can capture the effect of temperature on the thermo-mechanical response of clay. In the third part of the thesis, the present analytical framework for an energy pile in elastoplastic soil is used to analyze the pile in clay with a thermo-mechanical constitutive model that takes into account the change in the mechanical response of clay due to temperature change. The thermo-mechanical model used in the analysis was developed using the hyperplasticity formalism, which satisfies the laws of thermodynamics. The present framework in all cases predicts results with acceptable accuracy. The present analytical framework predicts the response of energy pile under different loads (mechanical and thermal) in terms of vertical displacement, stress (with <10% difference between the results from the present analysis and finite element analysis/field tests) with acceptable accuracy in less computational time. The run time for the present analysis is approximately 10 and 5 times faster than axisymmetric finite element analysis for elastic and elastoplastic cases, respectively.
In the final part of the thesis, the stresses developed in an energy pile under mechanical and thermal loads are observed for different soil properties. A parametric study is conducted on the developed stresses in an energy pile in single and two-layer soils under multiple loading conditions. A correlation between the applied mechanical and thermal load is established, and under these loading conditions, the effects of soil layering and material properties on the developed stresses are observed. The development of the tensile zone and its range in an energy pile for certain conditions are concluded from the parametric study.

## Description

## Keywords

energy pile, thermo-mechanical, thermodynamics, elastoplastic, settlement, geothermal