Response of unsaturated soils to heating of geothermal energy pile

Accepted Manuscript Response of unsaturated soils to heating of geothermal energy pile Abubakar Kawuwa Sani, Rao Martand Singh PII:

S0960-1481(18)31351-X

DOI:

https://doi.org/10.1016/j.renene.2018.11.032

Reference:

RENE 10795

To appear in:

Renewable Energy

Received Date: 30 June 2018 Revised Date:

21 September 2018

Accepted Date: 10 November 2018

Please cite this article as: Sani AK, Singh RM, Response of unsaturated soils to heating of geothermal energy pile, Renewable Energy (2018), doi: https://doi.org/10.1016/j.renene.2018.11.032. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Response of unsaturated soils to heating of geothermal energy pile

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Department of Civil and Environmental Engineering, Faculty of Engineering and Physical Sciences, University of Surrey, Guildford, GU2 7XH, UK.

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ABSTRACT: Geothermal energy piles (GEPs) are an environmentally friendly heat exchange technology that dualizes the role of structural foundation pile for load support and in meeting the building heating/cooling need. Energy loops made from high-density polyethylene which allow heat carrier fluid circulation, are fitted into the pile foundation elements to extract or inject and store heat energy in the soil surrounding the pile. This paper reports the results of a numerical study investigating the response of an energy pile embedded in unsaturated soils (sand, silt and clay) to natural thermal recovery, after heat injection process. It was found that the increase in soil saturation, duration of heating operation i.e. intermittent (8 or 16 hours heating) or continuous mode, magnitude of the heat injection rates influences the temperature changes in the soil surrounding the pile, consequently impacting on the system performance. Similarly, it was observed that temperature at all location approached initial state in a duration equal to about twice that of the heating time. In addition, it was found that imposing excessive heat flux on the pile results in the drying up of the surrounding soil leading to lower thermal conductivity thus decreasing the overall GEP system performance.

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KEYWORDS: ground heat exchanger, heat flux, numerical modelling, ground thermal recovery, transient heating process.

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Geothermal energy piles (GEPs) also known as thermal piles or heat exchanging piles are an innovative way of incorporating the concrete pile foundation element of a building with closed-circuit heat exchanging loops, and coupled with a heat pump system, to exchange the heat energy present within the shallow earth surface [1,2]. These systems, when effectively designed and properly installed, could fully or partially meet the space heating and/or cooling demand of the superstructure. Thus, making the coupled GEP system one of the most energy efficient means to achieve sustainable thermal energy demand of the building.

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The first structural pile to be successfully incorporated with an energy loop took place about 4 decades ago [2]. Since then, the use of such structural elements to serve dual purpose: buildings’ structural integrity and its thermal need, has been on the rise. This is clearly evident particularly in Europe where the European Union is inclined towards meeting its 2020 emission target i.e. to lower greenhouse gas emissions by 20% compared to the 1990 levels [3]. In the UK alone, about 5891 energy piles were installed by December, 2016, providing an annual carbon dioxide savings of around 7545 tonnes [4].

Abubakar Kawuwa Sani and Rao Martand Singh

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INTRODUCTION

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Corresponding author’s email: [email protected]

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ACCEPTED MANUSCRIPT The advantage of utilising these foundation elements compared with other vertical closed loop heat source elements (i.e. conventional borehole heat exchangers) is that the heat transfer efficiency between the foundation piles and the surrounding soil is notably higher because of the higher thermal conductivity and heat storage capabilities of the concrete pile [5–8]. Similarly, the piles possess larger surface area, which allow more energy loops to be incorporated and permit higher energy exchange with the surrounding soil. Additionally, the dual role of piles for primarily providing structural stability to the superstructure and as a source of energy in meeting the building thermal comfort requirement, thus negating the need for drilling cost associated with vertical boreholes.

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Over the years, numerous studies have been performed which provided an invaluable insight into the geotechnical and thermodynamic behaviour of energy piles under working conditions. Of all these studies e.g. [9–13], they all reported that imposing cyclic heating and cooling operations on a structural pile alter its mechanical behaviour. This results in the development of additional stresses and strains in the pile and its surrounding soil. Similarly, the distribution of the axial load induced in a pile could be uniformly or non-uniformly distributed along the pile depth depending on the restraint at the pile head and its toe. Nonetheless, they showed that the imposed thermal changes behave in a thermoelastic manner, which are reversible in nature.

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While on the other hand, studies conducted on the energy pile performance e.g. [14–16], reported that improving the heat transfer efficiency of the pile could significantly improve the thermal extraction or injection rate of the pile heat exchanger system. In addition, studies reported on unsaturated soils indicates that increase in soil saturation has positive significance on the distribution of temperature and degree of saturation in the soil surrounding the pile [17], and on the amount of energy to be extracted/injected [18,19], which could increase by up to 40% as the soil approaches full saturation [20]. In addition, Thomas and Rees [21] studied the heat transfer through unsaturated soil beneath a floor slab. They concluded that influences heat transfer by about 20% and 35% when analysed in 2D and 1D respectively.

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Furthermore, maintaining near initial temperature in the soil surrounding the pile, either through natural [3] or forced [22] recovery methods, have long-term positive implication on the system performance. However, despite the attractiveness of implementing the latter in alleviating the heat build-up or deficit in the soil, it should be noted that it comes at an additional cost thus increasing the initial capital investment. Notwithstanding, it is advisable that accurate estimate of the possibility of natural thermal recovery should firstly be considered before employing any other alternative e.g. solar collectors or cooling towers.

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Singh et al. [3] carried out a field scale test on an instrumented energy pile located at Monash University, Australia. The study investigated the response of the energy pile embedded in almost dry sand under thermal and mechanical loading. It was observed that heat predominantly flows radially in the pile, and that natural heat recovery takes more than twice the heating injection time. In addition, Kawuwa et al. [23] investigated the behaviour of saturated London clay to natural recovery. They found out that the duration of the heat injection rate directly influences the time to achieve natural recovery. Similarly, they showed

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ACCEPTED MANUSCRIPT that it took about four times the heating time for the soil to naturally approach near initial state.

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Although, the findings of Singh et al. [3] and Kawuwa et al. [23] have provided an understanding about the natural thermal recovery of soils in dry/saturated state subjected to thermal load, there still exists a lack of knowledge regarding the behaviour of soils to natural recovery in unsaturated conditions. In addition, it is vital to know that the soil physical properties (i.e. grain size, soil type) and its thermal properties (including thermal conductivity, degree of saturation, geological condition and geographical location), which are location dependent, could significantly influence their natural thermal recovery. Thus, there still exists the need to investigate the natural thermal recovery of individual unsaturated soils found at different locations after thermal injection or extraction.

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This paper presents the results of a numerical study aimed at investigating the response of unsaturated soils: sand, silt and clay, towards natural thermal recovery when subjected to transient heating operation. The numerical study conducted was carried out using a finite element method (FEM).

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The finite element code used in this study is known as COMPASS (Code for Modelling PArtially Saturated Soils). The code was developed at Cardiff University, and is based on mechanistic approach and its details can be found in [24–27]. It is capable of numerically solving a Thermo-Hydraulic-Mechanical and Chemical (THM-C) analyses in an unsaturated porous media.

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In the current study, the TH capability of the COMPASS code was used to determine the behaviour of unsaturated soil towards natural recovery after subjecting it to transient heating load. The governing equations of the code, written in the form of primary variables for solving the TH problem in an unsaturated porous media are reported here. The equations are solved for the coupled heat and moisture transfer processes via the use of pore water pressure (ul), pore air pressure (ua) and temperature (T), respectively as primary variables. The numerical solution to the TH problem is solved using finite element approach to achieve spatial discretisation, whilst the temporal discretisation is achieved by the use of implicit finite difference algorithm. The detailed equations are reported in [27–29].

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2.1

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The transfer of moisture in an unsaturated soil occurs in two forms: liquid and vapour form. According to the law of conservation of mass, it can be expressed mathematically as:

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FINITE ELEMENT MODELLING

Soil moisture transfer

ρl

∂ ( nS r ) ∂ ( ρv S a n ) + + ρ l ∇.v l + ρl ∇.v v + ∇. ( ρ v v a ) = 0 ∂t ∂t

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Where n is the porosity, Sa and Sr are the degree of saturation of pore air and pore water, respectively. The terms vl, vv and va are the velocities of liquid, vapour and air, respectively. The terms ρv and ρl represent the densities of water vapour and liquid water, respectively. ∇ is the gradient operator and t is the time. 3

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The flow of liquid water through an unsaturated media is given by Darcy’s law and mathematically expressed as:

vl = −

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kl   ul ∇ µ l   γ l

  u   + ∇z  = − K l ∇ l    γl

   + ∇z   

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Where kl is the intrinsic permeability, µl is the absolute viscosity of pore liquid, Kl is the unsaturated hydraulic conductivity, γl is the unit weight of liquid and z is the elevation.

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The vapour transfer occurs due to diffusive and pressure flows. The diffusive flow may be solved using the expression proposed by [29,30] and extended by [31,32], given as:

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D atms v v n  D atms v v n (∇ T )a  ∂ρ 0 ∂h  h  ρ0 ∇ u l − ∇ T  ∂T ρl ∂s  ρl  D atms v v n  ∂h  ∂h  + ρ0 ∇ T −  ρ0 ∇ u a ∂T  ρl ∂s   vv =

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Where Datms is the molecular diffusivity of vapour through air, vv is a mass flow factor. (∇Τ)a/∇Τ is the microscopic pore temperature gradient factor, h is the relative humidity, s is the suction and ρo is the saturated vapour density.

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The dry air present in an unsaturated porous soil media can be expressed as bulk and dissolved air. The former is driven by the gradient of air pressure, and can be determined using Darcy’s law. While, dissolved air is transported advectively with the pore liquid. The proportion of dry air contained within the pore liquid can be defined using Henry’s law.

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In addition, the law of conservation of mass dictates that the temporal derivative of the dry air content is equal to the spatial derivative of the dry air flux, mathematically defined as:

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Dry air transfer

∂ [θ a + H sθ l ]ρ da ∂V = −∂V ⋅ ∇.[ρ da ( v a + H s v l )] ∂t

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Where θa and θl are the volumetric air and liquid content, respectively, Hs is Henry’s volumetric coefficient of solubility, ρda is the density of dry air and ∂V is the incremental volume.

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2.3 Soil heat transfer The transfer of heat in soils occurs via conduction, convection, and radiation. Equally, heat is added due to phase change from liquid to vapour as latent heat of vaporization. However, the contribution of heat transfer via radiation in soils with smaller grain size is insignificant [33,34]. Thus, its effect is neglected in this study.

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The law of conservation of energy for heat flow dictates that the temporal derivative of the heat content, Ω, is equal to the spatial derivative of the heat flux, Q. This is mathematically defined as: ∂ (Ω∂V ) = −∇.Q(∂V ) (5) ∂t

The heat flux per unit area, Q, is defined as: 4

ACCEPTED MANUSCRIPT Q = −λT ∇T + (v v ρ v + v a ρ v )L + (C pl v l ρ l

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+ C pv v v ρ l + C pv v a ρ v + C pda v a ρ da )(T − To )

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Numerical model development

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Geometry description

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Where, λT is the coefficient of thermal conductivity of unsaturated soil, Cps, Cpl, Cpv and Cpda are the specific heat capacities of solid particles, liquid, vapour and dry air respectively, L is the latent heat of vaporisation, ρs is the density of solid particles, To and T are the initial and final temperature.

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A pseudo 2D axisymmetric geometry of a GEP shown in Figure 1 was set up in COMPASS. The model comprises a pile of 600 mm in diameter, with a length of 30 m chosen as a representative of a full scale energy pile. The model was restricted to only the soil domain because the study is aimed at investigating the processes happening in the soil surrounding the pile. Similarly, the heat transfer in the concrete pile is a steady state problem and the resultant heat flux at the GEP surface can be easily computed, which is the case in this study. This also reduces the total number of elements in the model, thus minimising the computation time. Figure 1 Geometry with the structured triangular element mesh

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A large domain size, with a radius of 20 m and a length of 50 m, was chosen to ensure that the geometry is sufficiently large enough to reduce the boundary effects on the soil close to the pile. The soil domain was discretised using 3 noded triangular mesh elements, with a minimum element size of 50 mm at the PHE surface and was allowed to expand to 1 m at the farthest boundary, as shown in Figure 1.

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The initial temperature (To) adopted corresponds to the typical temperature value that is found in the UK at a shallow depth within which an energy pile foundation is installed. A value of 286.4 K (13.4°C) was adopted in all the analyses. This agree with a To value measured by [35] during a thermal response test at East London.

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In addition, the initial degree of saturation (Sr) was varied across all the analyses carried out. The Sr value ranges from 0, 20, 60 and 100% saturation, respectively. The initial suction (s) corresponding to the respective Sr percentages were determined using the soil water characteristic curves. The values for the initial conditions are given in Table 1.

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Table 1 Initial conditions for the sand, silt and clay soils

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Initial conditions

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Initial Temperature, To (K)

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Saturation, Sr (%)

Soil suction, s, (MPa) Sand 103 4.3x10-3 2x10-3 0

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Silt 103 0.33 0.124 0

Clay 103 3.9 0.86 0

ACCEPTED MANUSCRIPT 2.4.3 Boundary conditions A heat flux boundary condition of 25 (W/m2) was applied at the GEP surface. This corresponds to a radial distance of 0.3 m from the axis of symmetry. The heat flux, q was determined based on the heat injection rate data reported by [7]. The q value was backcalculated for the GEP geometry used in this study. In addition, the sides, top and bottom of the model were considered as impermeable and adiabatic boundaries to ensure that no moisture and heat loss occurs to the environment.

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2.5 Material parameters The materials used in this study comprised three different soil types adopted from literature. These soil types include sandy soil with its properties obtained from the work of [28,29,36], silty soil from [17] and a clay (Speswhite kaolin clay) soil from [37], respectively. The different respective parameters required for carrying out the numerical investigation in this study are given in Table 2.

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Table 2 material parameters Parameter

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Silt

Clay

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Hydraulic parameters Saturated hydraulic conductivity, ksat (m/s) Unsaturated hydraulic conductivity, Kl (m/s) Degree of saturation, (%) van Genuchten [38] fitting parameters

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Thermal parameters Thermal conductivity, λ (W/m K) Soil specific heat capacity, Cps (J/kg K) Vapour specific heat capacity, Cpv (J/kg K) Specific heat capacity of water, Cpw (J/kg K)

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Other parameters Density, ρd (Kg/m3) Porosity, n Latent heat of vaporisation, L (J/kg) Henry's volumetric coefficient of solubility, Hs

1.24x10 -7 1.02x10 -10 Kl = (Sr)δ ksat ; δ=3 ranges from 0 – 100% α= 0.095 α= 0.09 α= 0.015 a=4.162 a=2.71 a=1.9 θlr =0.0025 θlr =0.03 θlr =0.0001 θls = 0.389 θls = 0.47 θls= 0.38

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λT= f (Sr) 1200 1870 4200

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2.5.1

Thermal conductivity

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The coefficient of thermal conductivity (λT) is an important parameter for determining the thermal properties of soils. It relates the rate at which heat is conducted through a material per unit time. An accurate estimate of the λT does have a significant influence on the amount of heat to be extracted or injected into the soil. The λT of an unsaturated soil is expressed as a function of the degree of soil saturation. Thus, it increases with an increase in water content. It is mathematically expressed as: 6

ACCEPTED MANUSCRIPT λT = f (Sr)

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In addition to the soil saturation, porosity, soil particle shape, granularity distribution, and mineralogy also influence the λT. Different mathematical expressions have been proposed to capture the granularity and/or fineness depending on soil type. In this study, the expression proposed by Ewan and Thomas [29], shown in Equation 8, was used for the sandy soil type.


 = 0.256 + 2.548 1 − −22.94

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Where M is the volumetric moisture content.

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However for the fine grained soils, i.e. clay and silt, the expression proposed by Melhuish [39], based on the linear interpolation of the laboratory experimental data of Borgesson and Hernelind [40] was adopted and used here. The mathematical expression is given in Equation 9

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 =
 + 
 −
 

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(9)

The variation in thermal conductivity of the three soils against the degree of saturation is shown in Figure 2. The thermal conductivity at different Sr values were obtained from the work of Ewen and Thomas [36], for sands and McCartney and Baser [17] for the silty soil, respectively. In addition, the λT values for the clay were back calculated from the suction data provided by Singh [37].

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Figure 2 Thermal conductivity & degree of saturation relationships for clay, silt and sand (after [17,36,37])

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2.5.2

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The soil water characteristic curve (SWCC), also known as water retention curve, provides a relationship between the volumetric/gravimetric water content of soils and suction or water potential. The water retention curve over the entire soil moisture range, i.e. 0 to 100% saturation, is often plotted on a logarithmic scale [41]. In the current work, van Genuchten curve fitting technique, given in Equation 7, was used to establish the SWCC of the soils.

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Soil water characteristic curve (SWCC) and unsaturated hydraulic conductivity (Kl)

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 1  1−  a

θ l − θ lr  1   =  θ ls − θ lr  1 + (αs )a 

(8)

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Where θl is the volumetric liquid water content, θlr is the residual volumetric liquid water content, θls is the saturated volumetric liquid water content (i.e. taken equal to porosity), s is the matric suction, α and a are constant fitting parameters. The SWCC parameters for the respective soils are given in Table 1. The relationship between the matric suction and the degree of saturation for the different soils is shown in Figure 3, adopted from the work of Singh [37], McCartney and Baser [17] and Fredlund and Xing [41].

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Figure 3 Soil water characteristic curves (SWCC) for clay, silt and sand (after [17,37,41]) 7

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In addition, Melhuish [39] reported that the unsaturated hydraulic conductivity, Kl, is a function of the void ratio (e), degree of saturation (Sr) and the temperature (T), mathematically expressed as: Kl = (Sr)δ ksat

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Where ksat is the saturated hydraulic conductivity (m/s), δ is a parameter ranging between 3 and 10 Bӧrgesson and Hernelind [40].

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NUMERICAL SIMULATIONS

Thermo-hydraulic numerical analyses were carried out by applying a heating load at the pile surface to investigate the soil response to natural recovery. The total duration of the heating cycle was 3 months, i.e. 90 days heat application followed by 6 months of resting period. In total, three sets of numerical analyses were carried out investigating the effects of different factors towards soil natural recovery, including:

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3.1 Effect of different soil types. A transient heat flux, q = 25 (W/m2) was applied at the pile surface in a stepwise manner, comprising 8 hours of heating followed by 16 hours resting period per each 24 hours, as shown in Figure 4.

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3.2 Influence of Intermittent and continuous heating modes The hours of operating a GEP could vary from several hours per day, termed as intermittent heating, or may run continuously for 24 hours. The former mode of operation is commonly found in residential buildings, whereas the latter is an operational mode exhibited in public buildings: industries, hospitals etc. In addition, it should be noted that the duration of the heating and/or cooling cycle are weather dependent, i.e. on the variation of air temperature, which varies by location. For example, Figure 5 depicts the average daily and monthly air temperature in Guildford, measured at the University of Surrey. A heat flux, q = 25 (W/m2) was applied at the pile surface, for both the intermittent and continuous operating modes. The intermittent operation comprises 8 hours of heating followed by 16 hours resting period, and 16 hours of heating followed by 8 hours resting period, per day (Figure 4). The continuous operating mode runs continuously through the test duration.

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An intermittent operation (comprising 8 of hours heating and 16 of hours resting), was used by applying three sets of heat flux values, i.e. 12.5, 25 and 37.5 (W/m2), for this investigation. The value of q = 12.5 and 37.5 (W/m2) corresponds to 50% reduction and increase to the 25 (W/m2) heating load, back calculated from literature. In addition, q = 100 W/m2 was adopted from McCartney & Baser [17] and used in this study.

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Figure 4 Intermittent cyclic heating operation

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Effect of increasing or decreasing the heat injection rate

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ACCEPTED MANUSCRIPT Figure 5 Annual air temperature of Guildford town, Surrey (October, 2016 – October, 2017).

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The results were obtained at the pile mid-depth, at several radial distances away from the pile surface: i.e. R=0 (pile surface), 0.5 and 1 m, respectively. Similarly, the results of radial temperature distribution were obtained at the pile mid-depth. In addition, results of Sr variation with depth at ½-pile diameter from the pile were obtained and discussed.

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DISCUSSION OF RESULTS

Prior to utilising the COMPASS code for carrying out numerical analyses, it is a good practice to verify the capability of the code in numerically solving for the coupled TH problem in a porous media. To achieve this, an experimental study conducted by Singh [37] was reproduced. Figure 6 shows the results of temperature and Sr for the COMPASS code compared with that reported by him. It can be observed that the code was able to accurately capture and replicate the experimental results for both the temperature and Sr. In addition, the discrepancy of the Sr results at the farthest distance may be attributed to an error in measurement as reported by Singh.

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Figure 6 Results of Temperature (°C) and degree of saturation (Sr) versus distance (m)

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4.1

Effect of different soil types

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4.1.1

Results of temperature evolution for different soil types

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Figure 7 presents the results of temperature evolution against time, after transient thermal load application for the different soil types: i.e. sand, silt and clayey soils, respectively, at R=0, 0.5 and 1.0 m from the pile surface.

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Figure 7 Results of temperature evolution for sand, silt and clay soils, at R=0, 0.5 and 1.0 m from the pile surface.

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The average temperature at the pile surface increases uniformly to a maximum value of about 28, 26, and 43°C for the sand, silt and clay soils, respectively at the duration of the heating test. The maximum temperature build up occurred in the soils having 0% Sr value, with the temperature magnitude decreasing with increase in the degree of saturation. A temperature difference of about 13°C, 10°C and 27°C were observed as the soil saturation increases from 0% to 100%, for the sand, silt and clay soils, respectively.

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The reason for the decrease in temperature owing to the increase in soil saturation could be attributed to the contribution of moisture present within the soil voids towards heat dissipation, radially away from the pile surface. This was found to be more significant as the soil fineness increases from clay to silty and sandy soil, respectively. This, therefore, portray 9

ACCEPTED MANUSCRIPT the nature in which heat radiates away from the pile as a result of temperature gradient and its associated mass transfer.

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In addition, higher temperature magnitude was observed in the clay soil. This could be attributed to conduction being the dominant mode of heat transfer especially in the drier soils. Also, it could be due to low permeability of the clay soil to easily allow pore water to transfer heat away from the pile as demonstrated in the silty and sandy soil. The ability of the soil to retain heat in the soil surrounding the pile could be significantly important where the GEP system is required for heat storage. However, that is beyond the scope of this paper.

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Similar to the results obtained at the pile surface, the maximum temperature witnessed at 0.5 and 1 m radial distances occurred in soils with 0% Sr, and the temperature magnitude keep decreasing with increasing soil saturation in all the three soil types. At the beginning of the simulations, a time lag of about 2, 3 and 4 days were observed before heat could flow to a distance of 0.5 m away from the pile, for the sand, silt and clay soils, respectively. At this location, the maximum temperature monitored was about 20°C in the sand and silt soils, while a value of 25°C was observed in the clay soil, after 90 days intermittent heating operation. Consequently, the soil temperature decreases gradually with time towards initial state.

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Equally, at the radial distance of 1 m, the soil temperature remained at initial state until after 5, 8 and 9 days following the start of the heating operation for the sand, silt and clay soils, respectively. The magnitude of temperature increase observed at this point, for the three soils at the different soil saturation, ranges between 0.6–5.6°C above the initial soil temperature.

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Upon switching off the heating source, the temperature at all locations decreases rapidly with time in the first 10 days following the heating operation. Afterwards, the rate of temperature decrease reduces uniformly as the soil approach initial state, at duration equal to about twice that of the heating time, for the sand, silt and clay.

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4.1.2

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Additionally, results were obtained for the radial heat flow, and the associated contribution of the initial Sr, on the soil volume that could be influenced by the heating operation. This is especially important where the GEPs are installed in a group, following the structural spacing requirement as stipulated by the design engineer. Or where the piles are placed close to other existing energy geostructures such as boreholes, diaphragm walls or tunnels. This could potentially result in thermal interaction between the structures. Thus, could possibly lower the performance of the GEP system. On the other hand, citing the energy geostructures at an optimum distance to each other could be positively significant for the purpose of heat storage.

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Results of radial temperature distribution for the different soil types

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Figure 8 Results of radial temperature distribution for sand, silt and clay soils under transient heating mode

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Figure 8 presents the results of temperature (°C) with normalised distance (X/D: X radial distance; D-pile diameter) for the sand, silt and clay soils. The results were obtained, at the 10

ACCEPTED MANUSCRIPT pile mid-depth, at the end of the heating process i.e. 90 days of injecting heat into the surrounding soil.

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In the sandy soil, a maximum temperature of about 28°C was observed at the pile surface, when the soil is in a fully dry state. The magnitude of the maximum temperature reduces as the soil saturation increases from 0 to 100%. A significant reduction in temperature magnitude by about 5°C was observed as the soil saturation increases from 0 to 20% and from 20% to 40%. Beyond 40% saturation, the rate of temperature drop becomes less significant, as soil initial Sr increases from 60 to 100%. Conversely, in the case of silty soil, the maximum temperature (of about 26°C) observed at the pile surface decreases linearly at the rate of about 2°C with increasing soil Sr.

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Furthermore, in the clay soil, a maximum temperature of about 43°C was witnessed at the pile, and significantly decreases by about 10°C as the Sr increases from 0% to 20 and 40%, respectively. As the soil initial Sr increases from 60 to 100%, the reduction in the maximum temperature observed at the pile surface becomes negligible.

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In all the cases studied, i.e. sand, silt and clay soils with 0–100% initial Sr, the temperature decreases non-uniformly with distance away from the pile surface. The maximum radial distance of about 6 m from the pile surface was found to be influenced by the heating application, for the sandy soil. This could be attributed to the soil granularity which easily allow moisture to flow within the voids owing to temperature and pressure gradient. However, as the soil grain sizes becomes finer, i.e. in silt and clay soils, the area influenced by the heating operation decreases to about 5 and 4 m for the silt and clay, respectively. This could be because of the high pressure, also known as air entry value or air entry pressure, required to allow moisture to flow within the voids of fine soils (e.g. clay) as compared to that in sands. The results give an insight into the optimum energy pile spacing value between 4 to 6 m can be applied to different ground conditions (i.e. soil type and its saturation).

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Figure 9 presents the results of temperature versus depth, obtained at a distance of ½ pile diameter from the pile surface, for the sand, silt and clay soils, at the end of the heat injection period. It can be seen that the drier soils witnessed higher temperature build-up across the whole pile length, and the magnitude of the observed temperature decreases with the increase in soil saturation and soil granularity. This could be as a result of the contribution of heat transfer via convection, which becomes more pronounced with the increase in soil grain size distribution. In addition, about the same temperature was observed when the sand and silt soils were in a fully dry state. However, as the soil moisture increases to 20% and 60%, the heat dissipation in sand significantly increases due to its higher thermal conductivity as compared to silt and clay soils (refer to Figure 2 for the thermal conductivity curve). Thus, this highlights the usefulness of heat transfer via convection, in soils which should not be neglected during the design process, especially in granular soils.

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Figure 9 Results of temperature distribution with depth at the end of heating period for sand, silt and clay soils 11

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Results of saturation with depth for the different soil types

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Figure 10 presents the results of the initial soil Sr with depth, obtained at a distance of ½ pile diameter from the pile surface, at the end of the heating and recovery periods, for the sand, silt and clay soils, respectively.

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The change in soil Sr value as a result of the heat injection process remains relatively insignificant and ranges between 5 and 10% for the 20 and 60% soil saturation. Specifically for the 20% saturation (Figure 10a), the change in Sr is less pronounced in sand followed by that of silt and clay soils. This could be attributed to two coupled phenomena: temperature gradient and the soil permeability or hydraulic conductivity. During the heat injection, the imposed high temperature dissipates away from the pile to a lower temperature region within the soil via conduction and convection. Conduction is the dominant heat transfer particularly considering the particles are closely interlocked to each other, especially in finer soils e.g. clay and silt. Therefore, this affects the free movement of pore water: in the form of liquid water and vapour water, which is driven by temperature and pressure gradient. This phenomena was observed and has been reported by other researchers [17,31,42]. This results in the soils having lower hydraulic conductivity of 1.02x10-10 m/s and 1.24x10-7 m/s for the clay and silt, respectively. Hence, the lower hydraulic conductivity leads to lower contribution of heat transfer via convection thus resulting in high temperature build-up in the soil next to the pile and drier soil domain. However, in sand with larger grain size distribution, the high hydraulic conductivity of 1.1x10-3 m/s aids in allowing the pore water to easily flow within the voids. Thus, transport and dissipates heat away from the pile.

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Figure 10 Results of Sr with depth at the end of heating and recovery periods: (a) 20% saturation, (b) 60% saturation, for sand, silt and clay soils without gravity effect.

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In addition the effect of superimposing gravity on the model was also investigated in the simulations. Figure 11 shows the results of soil Sr versus depth for the sand, silt and clay with gravity effect, compared with Figure 10 without the effect of gravity superimposed. It can be seen that superimposing the effect of gravity on the model causes the pore water to percolate and settles at the bottom of the model i.e. 50 m depth, which was considered as an impermeable layer during the analyses. The level of water that settled at the bottom of the model increases with increasing initial Sr. The ease of water percolation within the soil voids is govern by the soil hydraulic conductivity which is higher in sand. However, the gravity effect becomes less significant in silt and clay soils. This could be attributed to the high water retention capacity, also defined as the ability to hold water within the soil voids at high pressure, for the silt and clay soils as compared to that of sand shown in Figure 3.

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Figure 11 Results of Sr with depth at the end of heating and recovery periods: (a) 20% saturation, (b) 60% saturation, for sand and silty soils, with gravity effect

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Figure 12 Results of temperature evolution for different heating modes, at R=0 m, for sand (1st column), silt (2nd column) and clay (3rd column).

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As shown in Figure 12, the duration of the heat injection period has significant effect on the temperature increase in the surrounding soil. In the sandy soil, the maximum temperature observed at 0%–Sr (27°C) increases by about 13°C and 24°C as the heating process increases to 16 hours and continuous heating modes respectively. Similar trends and temperature values were seen in silty soil. However, in the clay soil, a maximum temperature of about 43, 68 and 94°C were observed at the end of the heating process for the 8, 16 and 24 hours heating modes respectively, with 0% Sr value. The magnitude of the temperature witnessed in all the soils irrespective of the heating mode drastically decreases with Sr above 50%.

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Furthermore, the intermittent operation allow the heated soil to dissipate heat away, during the discontinuous heating cycle, i.e. 16 and 8 hours resting, for the 8 and 16 hours heat injection respectively. This is significantly important and ensures the GEP system longevity especially where the system is used for monotonic operation, i.e. heating or cooling only. However, that is not the case in systems that are operated continuously. Thus, such systems should be equipped with a comprehensive control management system to deliver and monitor the energy needed and prevent excessive temperature build-up in the soil. Moreover, the magnitude of temperature witnessed reduces with the increase in soil saturation for the three heating cases.

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After switching off the heating source, the temperature at all locations decreases and approach near initial state at the end of the recovery period. Higher residual temperatures were observed in the continuous heating mode followed by 16 and 8 hours heating operations. Also, the drier soils, 0 and 20% Sr, indicated higher magnitude of temperature residue, and decreases with increase in soil saturation.

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Figure 13 presents the results of Sr distribution for 8, 16 and 24 hours heating operations obtained at the end of the 90 days heat injection period. For the purpose of brevity, the results of 0 and 100% Sr were not reported because no changes were observed in the fully dry or saturated conditions. The results show a slight drying at the location of the pile, with the magnitude of the drying increasing with an increase in the duration of the heat injection process i.e. 8 hrs, 16 hrs and 24 hrs respectively. For the case with 20% saturation, higher drying was witnessed in the clay soil, followed by the silt and sandy soil. This could be as a result of the higher magnitude of temperature witnessed in the clay soil, which was caused by the low hydraulic conductivity and lower thermal conductivity at very low degree of saturation. This creates a region of soil with low thermal conductivity surrounding the pile and resulting in higher temperature build-up. However, in silt and sand, lower soil drying up was observed due to the contribution of heat transfer via conduction and convection, which led to a higher thermal conductivity of about 0.8 and 2.3 W/mK as compared to clay with a value of about 0.3 W/mK at 20% Sr. However, as the soil Sr increases to 60%, the drying becomes less significant due to the contribution of heat dissipation via convection.

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Figure 14 presents the results of temperature evolution at different heat injection rates i.e. 12.5, 25 and 37.5 W/m2, for the sand, silt and clay soils. The analyses were carried out to investigate the effect of decreasing or increasing the injection rate on soil natural recovery. It was observed that decreasing and/or increasing the heat injection rate, i.e. 12.5, and 37.5 W/m2 from the baseline value (25 W/m2), has influence on the magnitude of temperature development in the surrounding soil. Higher temperature magnitudes were witnessed in the drier soils, and increases with higher injection rates. At the higher Sr i.e. 60 & 100%, the rate of increase in temperature with increasing injection rate becomes negligible. This could be due to the contribution of pore liquid, in addition to conduction (being the dominant case in drier soils), towards heat dissipation away from the pile. Same exact phenomenon was observed across the different soil types.

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Thus, imposing excessive injection rates on the GEP system should be avoided especially where the system is working for longer durations, with no or insufficient intermittent recovery period. Furthermore, the soil temperature returns to near initial state with a value ranging between 0.15–3.35°C above its initial value, at the end of the recovery period, i.e. twice the heating time.

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Figure 14 Results of temperature evolution for different heat injection rates, at R=0 m, for sand (1st column), silt (2nd column) and clay (3rd column).

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Figure 15 presents the results of the soil saturation against depth for 12.5, 25, 37.5 and 100 W/m2 heating power, at initial Sr values of 20 and 60%, for the sand, silt and clay soils. The heat injection rate has significant influence on the drying up of the soil. A slight decrease in soil saturation was observed along the pile depth, and the drying increases with an increase in in the heat injection rate. i.e. 12.5, 25 and 37.5 W/m2 respectively. Furthermore, a heat flux value of 100 W/m2 reported by McCartney & Baser [17] was adopted and used here to investigate the effect of higher heating power on the soil initial Sr. It was observed that imposing excessive heat flux value on the pile results in higher drying up of the soil surrounding the pile. This has an influence on the overall system performance whereby the thermal conductivity value of the surrounding soil decreases due to the soil drying process. This creates a layer of dry soil next to the pile having lower heat exchanging properties especially in finer soils e.g. silt and clay.

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The magnitude of temperature rise in the soil surrounding the pile decreases with increasing soil saturation. In other words, increase in soil water content has positive significance on the longevity and performance of the GEP system, because it prevents excessive temperature build-up, which dissipates away from the pile surface due to temperature gradient and mass transfer associated with it. Thus, ensuring that near initial temperature is maintained in the soil domain surrounding the pile. Temperature changes at all locations significantly decreases in the first 10 days following the end of the transient heating operation. The rate of the decrease reduces uniformly as the soil approach near initial state in duration equal to twice that of the heating time. The soil grain size or granularity has a significant influence on the temperature distribution around the GEP. In sand, the soil porous nature allow moisture to easily flow in the voids, and in doing so transport heat away from the pile surface. It was observed that it took about 2 days for heat to flow to a distance of 0.5 m from the pile. The duration, increases to 3 and 4 days, as the soil fineness increases from silt to clay respectively. The thermally active region in the soil domain under the influence of the transient heating process, for the sand, silt and clay soils, was found to be at a radial distance of 6, 5 and 4 m, respectively. However, this could likely vary in situations where groundwater flow with high flow velocity exists, especially in large granular soils. Nonetheless, the results reveal an insight into the optimum spacing that should be allowed between energy piles installed in group under different ground conditions i.e. soil type and saturation. The 24 hours (continuous) mode imposes excessive temperature changes on the surrounding soil by about 51°C and 26°C when compared to the 8 and 16 hours intermittent heating operations. Equally, the temperature difference reduces with an increase in soil saturation. The heat injection/extraction rate has significant influence on the heat build-up in the surrounding soil. Increasing the injection rate results in greater temperature changes in the soil, for the sand, silt and clay soils, with the temperature magnitude decreasing with increasing soil saturation. This results in the drying of the soil next to the pile, thus lowering its thermal conductivity and consequently the overall GEP system performance. It is recommended that the soil moisture should be taken into consideration during the design process of the energy pile system. Because the pore water aid in preventing excessive temperature build-up in soil, which would render the system non-usable or less efficient. However, in situations where higher temperature are expected due to higher injection rate or very low soil Sr value, then an automated control management system should be installed to monitor the system and deliver the required energy needed in order to ensure the short-term and long-term efficiency of the GEP system.

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A.K. Sani, R.M. Singh, I. Cavarretta, S. Bhattacharya, Heat storage performance of a pile heat exchanger installed in partially saturated swelling clay, in: The 7th International Conference on Unsaturated Soils, Hong Kong, 2018. D. Banks, Introduction to Thermogeology : Ground Source Heating and Cooling, 2nd Editio, John Wiley & Sons, 2012. R.M. Singh, A. Bouazza, B. Wang, C.H. Haberfield, S. Baycan, Y. Carden, Thermal and ThermoMechanical Response of a Geothermal Energy Pile, World Geothermal Congress 2015. (2015) 7. A.K. Sani, R.M. Singh, T. Amis, I. Cavarretta, A review on the performance of geothermal energy pile foundation , its design process and applications, Renewable and Sustainable Energy Reviews. (2018). N. Batini, A.F. Rotta Loria, P. Conti, D. Testi, W. Grassi, L. Laloui, Energy and geotechnical behaviour of energy piles for different design solutions, Applied Thermal Engineering. 86 (2015) 199–213. doi:10.1016/j.applthermaleng.2015.04.050. T. Amis, P.J. Bourne-Webb, C. Davidson, B. Amatya, K. Soga, The effects of heating and cooling energy piles under working load at Lambeth College, UK, Proceedings of the 33rd Annual and 11th International Conference on Deep Foundations. (2008) 10. http://scholar.google.com/scholar?hl=en&btnG=Search&q=intitle:THE+EFFECTS+OF+HEATING+A ND+COOLING+ENERGY+PILES+UNDER+WORKING+LOAD+AT+LAMBETH+COLLEGE+,+U K#0%5Cn+. K.A. Gawecka, D.M.G. Taborda, D.M. Potts, W. Cui, L. Zdravkovic, Muhamad S. Haji Kasri MEng, Numerical modelling of thermo-active piles in London Clay, Proceedings of the Institution of Civil Engineers - Geotechnical Engineering. 170 (2016) 1–19. doi:10.1680/jgeen.16.00096. F. Loveridge, The Thermal Performance of Foundation Piles used as Heat Exchangers in Ground Energy Systems, (2012) 206. L. Laloui, M. Nuth, L. Vulliet, Experimental and numerical investigations of the behaviour of a heat exchanger pile, International Journal for Numerical and Analytical Methods in Geomechanics. 30 (2006) 763–781. doi:10.1002/nag.499. P.J. Bourne-Webb, B. Amatya, K. Soga, T. Amis, C. Davidson, P. Payne, Energy pile test at Lambeth College, London: geotechnical and thermodynamic aspects of pile response to heat cycles, Géotechnique. 59 (2009) 237–248. doi:10.1680/geot.2009.59.3.237. J.S. Mccartney, J.E. Rosenberg, Impact of Heat Exchange on Side Shear in Thermo-Active Foundations, in: Advances in Geotechnical Engineering, 2011: pp. 488–498. http://ascelibrary.org/doi/abs/10.1061/41165(397)51. R.M. Singh, A. Bouazza, B. Wang, Near-field ground thermal response to heating of a geothermal energy pile: Observations from a field test, Soils and Foundations. 55 (2015) 1412–1426. A. Di Donna, A.F. Rotta Loria, L. Laloui, Numerical study of the response of a group of energy piles under different combinations of thermo-mechanical loads, Computers and Geotechnics. 72 (2016) 126– 142. doi:10.1016/j.compgeo.2015.11.010. F. Cecinato, F. Loveridge, Influences on the thermal efficiency of energy piles, Energy. 82 (2015) 1021–1033. doi:10.1016/j.energy.2015.02.001. J. Gao, X. Zhang, J. Liu, K.S. Li, J. Yang, Thermal performance and ground temperature of vertical pile-foundation heat exchangers: A case study, Applied Thermal Engineering. 28 (2008) 2295–2304. doi:10.1016/j.applthermaleng.2008.01.013. Y. Hamada, H. Saitoh, M. Nakamura, H. Kubota, K. Ochifuji, Field performance of an energy pile system for space heating, Energy and Buildings. 39 (2007) 517–524. doi:10.1016/j.enbuild.2006.09.006. J.S. Mccartney, T. Baser, Role of coupled processes in thermal energy storage in the vadose zone, in: 2nd Symposium on Coupled Phenomena in Environmental Geotechnics (CPEG2), Leeds, UK, 2017: pp. 2–7. G.A. Akrouch, M. Sánchez, J.-L. Briaud, Effect of the Unsaturated Soil Condition on the Thermal Efficiency of Energy Piles, Ifcee. (2015) 1618–1627. doi:10.1061/9780784479087.146. G.A. Akrouch, M. Sánchez, J.-L. Briaud, An experimental, analytical and numerical study on the thermal efficiency of energy piles in unsaturated soils, Computers and Geotechnics. 71 (2016) 207–220. doi:10.1016/j.compgeo.2015.08.009. J.C. Choi, S.R. Lee, D.S. Lee, Numerical simulation of vertical ground heat exchangers: Intermittent operation in unsaturated soil conditions, Computers and Geotechnics. 38 (2011) 949–958. doi:10.1016/j.compgeo.2011.07.004. H.R. Thomas, S.W. Rees, Measured and simulated heat transfer to foundation soils, Geotechnique. 59 (2009) 365–375. doi:10.1680/geot.2008.59.4.365. M. Faizal, A. Bouazza, Effect of forced thermal recharging on the thermal behaviour of a field scale geothermal energy pile, in: Energy Geotechnics, 2016: pp. 557–568.

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A.S. Kawuwa, R.M. Singh, I. Cavarretta, Ground thermal response to a pile heat exchanger subjected to heating load, in: Symposium on Coupled Phenomena in Environmental Geotechnics (CPEG2), Leeds, UK, 2017. H.R. Thomas, Y. He, A coupled heat–moisture transfer theory for deformable unsaturated soil and its algorithmic implementation, International Journal for Numerical Methods in Engineering. 40 (1997) 3421–3441. doi:10.1002/(sici)1097-0207(19970930)40:18<3421::aid-nme220>3.0.co;2-c. H.R. Thomas, Y. He, M.R. Sansom, C.L.W. Li, On the development of a model of the thermomechanical-hydraulic behaviour of unsaturated soils, Engineering Geology. 41 (1996) 197–218. doi:10.1016/0013-7952(95)00033-X. H.R. Thomas, Y. He, C. Onofrei, An examination of the validation of a model of the hydro/thermo/mechanical behaviour of engineered clay barriers, International Journal for Numerical and Analytical Methods in Geomechanics. 22 (1998) 49–71. doi:10.1002/(SICI)10969853(199801)22:1<49::AID-NAG908>3.0.CO;2-I. H.R. Thomas, M.R. Sansom, Fully coupled analysis of heat moisture and air transfer in unsaturated soil, Journal of Engineering Mechanics. 121 (1995) 392–405. doi:10.1680/geot.1995.45.4.677. H.R. Thomas, C.L.W. Li, An assessment of a model of heat and moisture transfer in unsaturated soil, Geotechnique. 47 (1997) 113–131. J. Ewen, H.R. Thomas, Heating unsaturated medium sand, Geotechnique. 39 (1989) 455–470. J.R. Philip, D.A. De Vries, Moisture movement in porous materials under temperature gradients, Eos, Transactions American Geophysical Union. 38 (1957) 222–232. doi:10.1029/TR038i002p00222. P.J. Cleall, R.M. Singh, H.R. Thomas, Non-isothermal moisture movement in unsaturated kaolin: An experimental and theoretical investigation, ASTM Geotech. Test. Journal. 34 (2011) 514–524. P.J. Cleall, R.M. Singh, H.R. Thomas, Vapour transfer in unsaturated compacted bentonite, Géotechnique. 63 (2013) 957–964. doi:10.1680/geot.12.P.147. J.K. Mitchell, Fundamentals of soil behavior, J. Wiley and Sons, New York, N.Y., 1993. O.T. Farouki, Thermal Propeties of Soils, (1981) 136. F. Loveridge, G. Holmes, T. Roberts, W. Powrie, Thermal response testing through the Chalk aquifer in London, UK, Proceedings of the ICE - Geotechnical Engineering. 166 (2013) 197–210. doi:10.1680/geng.12.00037. J. Ewen, H.R. Thomas, The thermal probe-a new method and its use on an unsaturated sand, Geotechnique. 37 (1987) 91–105. R.M. Singh, An experimental and numerical investigation of heat and mass movement in unsaturated clays, Cardiff University, 2007. M.T. van Genuchten, A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils1, Soil Science Society of America Journal. 44 (1980) 892. doi:10.2136/sssaj1980.03615995004400050002x. T.A. Melhuish, An investigation of the three-dimensional thermo/hydro/mechanical behaviour of large scale in-situ experiments, Cardiff University, 2004. L. Bӧrgesson, J. Hernelind, Preparatory modelling for the backfill and plug test - Scoping calculations o f H-M processes, Sweden, 1998. D.G. Fredlund, A. Xing, Equations for the soil-water characteristic curve, Canadian Geotechnical Journal. 31 (1994) 1026–1026. doi:10.1139/t94-120. S. Olivella, A. Gens, Vapour transport in low permeability unsaturated soils with capillary effects, Transport in Porous Media. 40 (2000) 219–241. doi:10.1023/A:1006749505937.

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Temperature (°C)

50

10

0

2 4 6 8 Normalised distance, X/D, (m/m)

10

Figure 8 Results of radial temperature distribution for sand, silt and clay soils under transient heating mode

6

ACCEPTED MANUSCRIPT 10 0

10

10

20

20

Depth (m)

Depth (m)

0

30

30

40

50

50

Clay 10

Temperature (°C) 20 30

30

EP AC C

Depth (m)

20

TE D

0

10

M AN U

40

Temperature (°C) 20 30

RI PT

10

Silt

Temperature (°C) 20 30

SC

Sand

Trendline 0% - End of heating 20% - End of heating

40

60% - End of heating 100% - End of heating 50

Figure 9 Results of temperature distribution with depth at the end of heating period for sand, silt and clay soils

7

ACCEPTED MANUSCRIPT Saturation, (Sr)

0.594 0

0.202

10

10

20

20

30

0.602

M AN U

30

0.598

RI PT

0.192

Depth (m)

Depth (m)

0.182 0

Saturation, (Sr)

(b)

SC

(a)

40

40

50

50

60% - End of heating (Sand)

20% - End of recovery (Sand)

60% - End of recovery (Sand)

20% - End of heating (Silt)

60% - End of heating (Silt)

20% - End of recovery (Silt)

60% - End of recovery (Silt)

EP

TE D

20% - End of heating (Sand)

60% - End of heating (Clay)

20% - End of recovery (Clay)

60% - End of recovery (Clay)

AC C

20% - End of heating (Clay)

Figure 10 Results of Sr with depth at the end of heating and recovery periods: (a) 20% saturation, (b) 60% saturation, for sand, silt and clay soils without gravity effect.

8

ACCEPTED MANUSCRIPT Saturation, (Sr)

0

0.2 0

10

10

20

20

30

0.4

0.6

0.8

1

M AN U

30

0.2

RI PT

0.1

0

Depth (m)

Depth (m)

0

Saturation, (Sr)

(b)

SC

(a)

40

40

50

50

60% - End of heating (Sand)

20% - End of recovery (Sand)

60% - End of recovery (Sand)

20% - End of heating (Silt)

60% - End of heating (Silt)

20% - End of recovery (Silt)

60% - End of recovery (Silt)

20% - End of heating (Clay)

60% - End of heating (Clay)

AC C

EP

TE D

20% - End of heating (Sand)

20% - End of recovery (Clay)

60% - End of recovery (Clay)

Figure 11 Results of Sr with depth at the end of heating and recovery periods: (a) 20% saturation, (b) 60% saturation, for sand and silty soils, with gravity effect

9

ACCEPTED MANUSCRIPT

Sand

40 30 20

10

10 30 60 90 120 150 180 210 240 270

0

0

80 70 60 50 40 30 20 10

30 60 90 120 150 180 210 240 270

16 hours

0

Time (days) 0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

110

70 50 30

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

Continuous heating

90

AC C

90

10

70 50

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

30 10

0

30 60 90 120 150 180 210 240 270

Time (days)

0

30 60 90 120 150 180 210 240 270

Time (days) 80 70 60 50 40 30 20 10

30 60 90 120 150 180 210 240 270

EP

Continuous heating

10

16 hours heating

0

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

30 60 90 120 150 180 210 240 270

Time (days)

Time (days)

Temperature (°C)

Temperature (°C)

110

20

Temperature (°C)

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

TE D

16 hours heating

30

Time (days)

Temperature (°C)

Temperature (°C)

Time (days) 80 70 60 50 40 30 20 10

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

8 hours

40

30 60 90 120 150 180 210 240 270

M AN U

0

50

Temperature (°C)

20

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

8 hours

110 Continuous heating

Temperature (°C)

30

50

RI PT

40

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

Clay

SC

8 hours heating

Temperature (°C)

Temperature (°C)

50

Silt

90 70

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

50 30 10

0

30 60 90 120 150 180 210 240 270

Time (days)

0

30 60 90 120 150 180 210 240 270

Time (days)

Figure 12 Results of temperature evolution for different heating modes, at R=0 m, for sand (1st column), silt (2nd column) and clay (3rd column).

10

ACCEPTED MANUSCRIPT Saturation, (Sr)

Silt (20% Sr)

0.162 0.172 0.182 0.192 0

20

40

40

50

50

Sand (60% Sr) 0.58 0

Saturation, (Sr) 0.6

0.58 0

50

20

EP AC C

40

Depth (m)

20

30

Saturation, (Sr)

0.6

TE D

10

30

40

Silt (60% Sr)

0.62

10

Depth (m)

30

20

SC

30

RI PT

20

10

Depth (m)

10

Saturation, (Sr)

0.162 0.172 0.182 0.192 0

30

50

Clay (60% Sr)

0.62

0.58 0

Saturation, (Sr) 0.6

0.62

10

Depth (m)

10

Depth (m)

Depth (m)

0.162 0.172 0.182 0.192 0

Clay (20% Sr)

Saturation, (Sr)

M AN U

Sand (20% Sr)

20

30

40

40

50

50

Trendline 8 hrs - 20% -Sr

16 hrs - 20% -Sr

24 hrs - 20% -Sr

8 hrs - 60% -Sr

16 hrs - 60% -Sr

24 hrs - 60% -Sr

Figure 13 Results of Sr distribution with depth for sand, silt and clay soils having different heating modes

11

ACCEPTED MANUSCRIPT

20 15 10

10 0

20

M AN U

30

40 30 20 10

10 0

0

30 60 90 120 150 180 210 240 270

40 30 20 10

30 60 90 120 150 180 210 240 270

Time (days)

0

30 60 90 120 150 180 210 240 270

Time (days)

60

37.5 (W/m2)

50 40

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

30 20

0

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

25 (W/m2) 40 30 20 10

10

0

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

15

0

30 60 90 120 150 180 210 240 270

EP

Temperature (°C)

50

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

AC C

Temperature (°C)

37.5 (W/m2)

20

30 60 90 120 150 180 210 240 270

Time (days)

Time (days)

Time (days) 60

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

TE D

40

25 (W/m2)

Temperature (°C)

Temperature (°C)

Time (days)

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

25

30 60 90 120 150 180 210 240 270

Time (days) 25 (W/m2)

12.5 (W/m2)

30

10

0

30 60 90 120 150 180 210 240 270

Temperature (°C)

25

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

Temperature (°C)

15

12.5

Temperature (°C)

20

30

Clay

RI PT

25

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

(W/m2)

SC

12.5 (W/m2)

30

Silt Temperature (°C)

Temperature (°C)

Sand

37.5 (W/m2)

60 50 40

0% Sr 20% Sr 60% Sr 100% Sr Initial temperature

30 20 10

30 60 90 120 150 180 210 240 270

Time (days)

0

30 60 90 120 150 180 210 240 270

Time (days)

Figure 14 Results of temperature evolution for different heat injection rates, at R=0 m, for sand (1st column), silt (2nd column) and clay (3rd column). 12

Sand (20% Sr) 0.185 0

Saturation, (Sr) 0.195

ACCEPTED Saturation, (Sr) Clay (20% Sr) Silt (20% Sr) MANUSCRIPT 0.185 0

0.205

0.16 0.17 0.18 0.19 0

0.205

10

20

20

20

50

0.58 0

Saturation, (Sr) 0.6

0.58 0

10

40

50

0.6

Depth (m)

20

EP AC C

30

Saturation, (Sr)

TE D

10

20

RI PT

Silt (60% Sr)

0.62

30

SC

50

0.2

40

30

50

Clay (60% Sr)

0.62

Depth (m)

40

M AN U

Depth (m)

30

40

Sand (60% Sr)

Depth (m)

10

Depth (m)

10

30

Depth (m)

0.195

Saturation, (Sr)

0.58 0

Saturation, (Sr) 0.6

0.62

10

20

30

40

40

50

50

Trendline 12.5 W.per sq. m - 20% Sr

12.5 W.per sq. m - 60% Sr

25 W.per sq. m - 20% Sr

25 W.per sq. m - 60% Sr

37.5 W.per sq. m - 20% Sr

37.5 W.per sq. m - 60% Sr

100 W.per sq. m - 20% Sr

100 W.per sq. m - 60% Sr

Figure 15 Results of the distribution of Sr having different heat injection rates for the sand, silt and clay soils 13

ACCEPTED MANUSCRIPT HIGHLIGHTS

RI PT

SC M AN U

•

TE D

•

EP

•

Soil grain size has influence on the magnitude of heat build-up in the soil surrounding a geothermal energy pile. The increase in soil moisture content has positive significance on the efficiency of the geothermal energy pile system, because it prevent excessive heat build-up. The thermally active region in the soil domain surrounding an energy pile is dependent soil grain size, and soil type. Imposing greater heat injection rate results in the drying of the soil next to the pile, thus decreasing its thermal conductivity, and consequently lower the system performance.

AC C

•