Cross-sectional thermo-mechanical responses of energy piles
Introduction
It is well established that ground source heat pumps used in tandem with energy piles result in variations in temperature, deformations, and stress in the energy pile and surrounding soil. Due to the transient changes in the circulating heat exchange fluid temperature, the temperature across an energy pile's cross-section will also vary (Abdelaziz and Ozudogru, 2016a, Abdelaziz and Ozudogru, 2016b, Caulk et al., 2016, Han and Yu, 2020, Liu et al., 2019). However, most field-scale studies on energy piles only measured their thermal response at a single location in the cross-section of the pile (e.g., Laloui et al., 2006, Bourne-Webb et al., 2009, Akrouch et al., 2014; Murphy et al., 2015; Murphy and McCartney, 2015, Sutman et al., 2015, Faizal et al., 2016, Faizal et al., 2018, Mimouni and Laloui, 2015, Rotta Loria and Laloui, 2017a, Rotta Loria and Laloui, 2017b, Rotta Loria and Laloui, 2018, Fang et al., 2020, Moradshahi et al., 2020a, Moradshahi et al., 2020b, Wu et al., 2020). Assuming the temperature measured at the single location is representative of the temperature across the cross-section of an energy pile has been shown to lead to errors in estimating thermal strains and stresses, mostly when heating and cooling occur (McCartney et al., 2015, Murphy and McCartney, 2015, Abdelaziz and Ozudogru, 2016a, Abdelaziz and Ozudogru, 2016b, Caulk et al., 2016).
Numerical studies showed that non-uniform temperature and stress variations occurred between the centre and edge of an energy pile (Abdelaziz and Ozudogru, 2016a, Abdelaziz and Ozudogru, 2016b, Caulk et al., 2016, Han and Yu, 2020, Liu et al., 2019), but fewer field studies have validated these observations (e.g. Faizal et al., 2019a, Faizal et al., 2019b). Although Faizal et al., 2019a, Faizal et al., 2019b reported temperatures and stresses calculated using sensors at similar radial distances, they did not measure temperatures or thermal axial stresses near the pile-soil interface. The pile temperature at the edge of the pile would be expected to be closer to the surrounding soil temperature, potentially leading to temperature and stress gradients across the pile's diameter.
The numerical studies mentioned above were conducted for a single energy pile with a given inlet fluid temperature and one set of soil properties. Thus, factors governing the distribution in temperature and stress across an energy pile's cross-section are not fully understood. Accordingly, there is a knowledge gap on the effects of inlet fluid temperatures, soil properties, and the presence of a nearby energy pile on the distribution of temperatures and stresses in the cross-section of energy piles.
The magnitudes of thermal stresses in energy piles depend on the magnitudes of inlet fluid temperatures (e.g. You et al., 2014, Mimouni and Laloui, 2015, Murphy and McCartney, 2015, Faizal et al., 2016, Han and Yu, 2020). A recent parametric study based on field investigations (Moradshahi et al., 2020b) showed that soil parameters (i.e. soil thermal conductivity, λsoil, thermal expansion coefficient, αsoil, and elastic modulus, Esoil) could affect the axial thermal stresses at the centre of the energy pile. Hence, it can be hypothesised that the parameters of the surrounding soil will also influence thermal stresses in the energy pile's cross-section. Variations of λsoil affect the heat transfer between the pile and the soil (Jeong et al., 2014, Salciarini et al., 2015, Salciarini et al., 2017, Guo et al., 2018, Sani et al., 2019, Moradshahi et al., 2020b), which can affect the pile-soil interface temperatures and hence the temperature and stress distribution in the cross-section. Variations in αsoil and Esoil affect the restrictions imposed by the soil on the thermal expansion and contraction of energy piles (Bodas Freitas et al., 2013; Bourne-Webb et al., 2015; Salciarini et al., 2015, Salciarini et al., 2017, Khosravi et al., 2016, Rotta Loria and Laloui, 2017b, Moradshahi et al., 2020b), which in turn could influence the magnitudes of stresses developed in the cross-section of the energy pile. Moreover, the presence of a nearby energy pile can also influence the cross-sectional temperature and stress distributions of an energy pile due to possible thermal interaction between the piles through the soil. Therefore, it is critical to develop numerical models that are validated with field data for performing coupled thermo-mechanical analysis across the cross-section of energy piles for various parameters.
This paper presents a unique research approach for developing and validating a thermo-mechanical numerical model with cross-sectional temperatures and strains measured in an energy pile (diameter = 0.6 m and length = 10 m) installed under a six-storey building. The numerical model is further used to address knowledge gaps such as the influence of inlet fluid temperatures, soil properties (soil thermal conductivity, λsoil, thermal expansion coefficient, αsoil, and elastic modulus, Esoil) and the presence of a nearby energy pile on the temperature and stress distribution in the cross-section of an energy pile. Finally, a comparison between the investigated cross-sectional thermal results and existing conventional energy pile analysis based on average and single point thermal evaluations was performed for design applications.
Section snippets
Site description and experimental procedure
The experiments were conducted on two energy piles installed under a six-storey residential building. A schematic of the piles is shown in Fig. 1. The site's soil profile is Brighton Group of materials, consisting of dense to very dense clayey sands (Barry-Macaulay et al., 2013, Singh et al., 2015, Faizal et al., 2018, Faizal et al., 2019a, Faizal et al., 2019b, Wang et al., 2015). The piles' diameter and length were 0.6 m and 10 m, respectively. The average compressive strength and modulus of
Numerical modelling
A numerical study was performed to evaluate the cross-sectional behaviour of EP1 for varying inlet fluid temperatures and soil properties (i.e. soil elastic modulus, Esoil, thermal conductivity, λsoil, and thermal expansion coefficient, αsoil,) for single and dual pile experiments. A three-dimensional finite element model was developed and simulated using COMSOL Multiphysics software. The model was validated against field results. The 40 × 15 × 30 m3 model, shown in Fig. 3, consisted of 381,980
Field results and numerical validation
The distribution of EP1 temperatures and axial thermal strains were obtained from the axial VWSGs located in the planar cross-section of EP1. The locations of these axial VWSGs, shown in Fig. 1, were non-dimensionalised with respect to the radius of EP1. In this regard, the axial VWSG at location V5 (Fig. 1) corresponds to the centre of EP1, V1 and V2 correspond to the non-dimensional radius of −0.47, and V3 and V4 correspond to the non-dimensional radius of 0.47. The axial thermal stresses in
Numerical investigation
A parametric evaluation was performed using the validated numerical model to investigate the effect of varying fluid temperature and varying λsoil, Esoil, and αsoil on the cross-sectional thermal response of EP1. Two inlet fluid temperatures were studied for each heating and cooling experiment, as shown in Fig. 6. The fluid temperatures were varied by ±10 °C intervals for heating and cooling operations (i.e. |ΔTf| = 10 °C, and 20 °C, where ΔTf is the difference between the inlet fluid
Thermal responses across different diametrical axes
The cross-sectional thermal response of EP1 over the four different axes (i.e. X-axis, Y-axis, D1-axis, and D2-axis, as shown in Fig. 3e) at a depth of 2.5 m for |ΔTf| = 10 °C is shown in Fig. 7. The depth of 2.5 m had the highest stresses than other depths and is likely the null point's location. The magnitudes of temperatures and thermal strains/stresses were symmetrical between heating and cooling for a given axis. Higher values of temperature, thermal strains and stresses were observed at
Conclusions
This paper investigated the cross-sectional thermal response of one of two field-scale energy piles spaced at a centre-to-centre distance of 3.5 m under monotonic heating and cooling operations. A numerical model validated against field data was used to perform a parametric study to investigate the effects of varying inlet fluid temperatures, soil thermal conductivity, thermal expansion coefficient, and elastic modulus on the cross-sectional thermal response of the considered energy pile. The
CRediT authorship contribution statement
Aria Moradshahi: Conceptualization, Writing - original draft. Mohammed Faizal: Conceptualization, Writing - review & editing. Abdelmalek Bouazza: Conceptualization, Supervision, Writing - review & editing. John S. McCartney: Conceptualization, Writing - review & editing.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This research project was supported under the Australian Research Council’s Linkage Projects funding scheme (project number LP120200613). The support of all the sponsors (Geotechnical Engineering-Acciona, Golder Associates, Geoexchange Australia, Brookfield-Multiplex) is gratefully acknowledged. The authors also acknowledge the Australian Government Research Training Program Scholarship provided to the first author. The US National Science Foundation grant CMMI-0928159 supported the fourth
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