- What are the heating and cooling energy demand and loads for buildings? - What is the effect of the thermal mass on the energy performance of buildings? - What is the effect of freezing/thawing cycles and energy balance on the energy performance of buildings? - What is the thermo-hydro-mechanical behavior of thermal piles? - What is the result of excessive heat extraction from the geothermal piles?

1. Dr. Pooneh Maghoul, P.Eng., M.ASCE
Assistant Professor,
University of Manitoba,
Department of Civil Engineering
Application of Thermal Piles and Energy
Efficiency of Basements

2. Thermal Piles in Buildings

3. Thermal Piles in Buildings
• What is the heating and cooling energy
demand and loads for buildings?
• What is the effect of the thermal mass on the
energy performance of buildings?
• What is the effect of freezing/thawing cycles
and energy balance on the energy performance
of buildings?
• What is the thermo-hydro-mechanical
behavior of thermal piles?
• What is the result of an excessive heat
extraction from the geothermal piles?

4. Thermal Piles in Buildings
A Thermo-Hydro-Mechanical Modeling of Soils:
• Saturated and Unsaturated
• Considering Freezing/Thawing &
• Energy Balance at the Ground Surface

5. Problem
NRC. 2011. Energy Efficiency Trends in Canada 1990 to 2009, Canada.
Distribution of residential energy use by end-use in Canada, 2007

6. Problem
• Foundation heat losses can no longer be
considered a less important part in the
total building heat loss.
• According to NRC, foundation heat losses
can count for 20 to 35 percent of a
home's heat losses.

7. Problem
• To reduce the heating energy demand and
loads for buildings, it is of great
importance to take into account the effect
of the thermal mass on the energy
performance of buildings.
• Most commonly used building models
consider constant thermal properties for
soils surrounding foundations throughout
the year!
• The thermal properties of soil, varying
during the year, depend mainly on the
temperature, water content and phase
change.
* http://foundationhandbook.ornl.gov/handbook/section3-1.shtml

8. Case Study: Laboratory of Energy Technologies, QC
• The “Twin Houses” located in a
hemiboreal (Dfb) climate.
• Close to 1000 data points
sampled at 15 minute intervals.
* https://meeb.ca

9. Objective
• The influence of the simultaneous fully
coupled heat and moisture within the
soil surrounding building foundations
by considering the effect of seasonal
frost.
• As a complementary to those obtained
by the multi-zone building models that
are not really good in soil modeling.
* http://www.ncfoundationrepair.com/

10. Complexity of Taking into Account the Effect of
Freeze/Thaw
• Insulating effect of the snow cover:
good insulating properties & high albedo
• Phase change in the ground:
freezing-thawing cycles & latent heat
• Change of thermo-hydraulic properties:
thermal & hydraulic conductivities

11. Unsaturated Soil: Multiphase Porous Medium
An unsaturated porous medium as a three-phase system:
• Solid skeleton
• Water
• Air

12. Scheme of Unsaturated Soils
Soil
Particles
Water
Air
T
Air
Liquid Water
Ice
Soil Particles
Water Vapour
• Phase change
• Coupled transfer of mass (liquid and vapour) and heat

13. “Freezing = Drying” Assumption
• The ice in the capillary pores behaves like air.
• Both air and ice phases are assumed to be at atmospheric
pressure.
• The relationship between unfrozen
water content and soil freezing
temperatures can be expressed by
a function named “soil freezing
characteristic curve (SFC)”.

14. Soil Freezing Characteristic Curve
• The total water content Θ (water & ice) :
Θ = fVG ψw0 = θr + θs − θr 1 + αψw0
n −m
where Θ − is the dimensionless volumetric water content, Θs − and Θr –
are the volumetric water content at saturation (equal to porosity) and at
residual state, respectively, and α m−1
, n − are m − are fitting parameters.
• The liquid water content 𝜃 𝑤 :
θw = fVG ψw1 = θr + θs − θr 1 + αψw1
n −m
• The ice content 𝜃𝑖 :
𝜃𝑖 = Θ − θw

15. Freezing Point Depression
• At 𝑝 𝑤 = 𝑝 𝑎 = 1 𝑎𝑡𝑚, the melting temperature is 273.15 𝐾.
• When interfacial forces are present (e.g. in a capillary tube), the
melting temperature decreases, due to a combination of surface
energy and interface curvature:
𝑇∗ = 𝑇0 +
𝑔𝑇0
𝐿 𝑓
𝛹𝑤0
where 𝑇∗is the temperature of phase change under unsaturated
conditions, due to interfacial forces; 𝐿 𝑓 (𝐽/𝑘𝑔) is the latent heat of
fusion; 𝛹𝑤0
is matric potential corresponding to the total water
content (liquid and ice).

16. Energy Conservation
• The internal energy of the soil :
𝑈 = 𝐶 𝑇 𝑇 + 𝜃 𝑤 𝜌 𝑤 𝐿 𝑓
• The internal energy may be seen as
the sum of two components:
𝑪 𝑻 𝑻 : which is the sensible part
responsible of the temperature
variation of the volume.
𝜽 𝒘 𝝆 𝒘 𝑳 𝒇: which is the potential part
due to the phase change.

17. Energy Conservation and Heat Flow Equation
• Conservation of energy :
𝜕𝑈
𝜕𝑡
+ 𝛻 ∙ 𝐺 + 𝐽 = 0
 𝐺 is the conduction flux within the soil (Fourier’s law) :
𝐺 = −𝜆 𝑇 Ψ 𝑤0, 𝑇 𝛻𝑇
 𝐽 is the convection heat flux (heat transported by water flow) :
𝐽 = 𝜌 𝑤 𝑐 𝑤 𝐽 𝑤 Ψ 𝑤0, 𝑇 𝑇

18. Mass Conservation and Transfer Equations for Water
𝜌 𝑤
𝜕𝜃 𝑤
𝑓𝑙
𝜕𝑡
+ 𝜌 𝑤
𝜕𝜃 𝑤
𝑝ℎ
𝜕𝑡
+ 𝜌𝑖
𝜕𝜃𝑖
𝑝ℎ
𝜕𝑡
+ 𝜌 𝑤 𝛻 ∙ 𝐽 𝑤 = 0
in which 𝐽 𝑤 is the water flux within the soil and follows the Darcy-Buckingham
formulation:
𝐽 𝑤 = 𝐽 𝑤 Ψ 𝑤1 = −𝐾 𝐻 𝛻 Ψ 𝑤1 + 𝑧𝑓
where 𝐾 𝐻 is the hydraulic conductivity, and 𝑧𝑓 is the elevation with respect to
a reference elevation and represents the gravitational head.
= 0

19. Model Linearization
• This system of governing partial differential equations (PDEs) is solved
by using a finite element model builder FlexPDE 6.
• As the system of equations are highly non-linear, an adaptive mesh
refinement and dynamic time step control are used to precisely model
the phase change in the medium.
• A smooth hyperbolic tangent function is used to facilitate the transition
of the phase change around the melting point:
F T, ∆T =
1
2
tanh
𝑇 − 𝑎
𝛿
− tanh
𝑇 − b
𝛿
0
0.2
0.4
0.6
0.8
1
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
F(T,T)
Temperature (C)
http://www.pdesolutions.com/

20. Application
5m
14m
4m
1.5m 𝑇𝑒𝑥𝑡; 𝜓 𝑤0 = −10𝑚
Convection: ℎ = 6.0
𝑊
𝑚2°𝐶
Convection: ℎ = 6.0
𝑊
𝑚2°𝐶
Inside temperature = 20°𝐶
𝑞 𝑇 = 0
𝑞 𝑤 = 0
𝑞 𝑇 = 0
𝑞 𝑤 = 0
𝑇 = 2°𝐶; 𝜓 𝑤0 = −5𝑚
• 2D coupled heat and mass movement in unsaturated soil surrounding a
non-insulated basement of a building in a cold region.
• At the soil upper surface, a cosine function is fitted for the ambient air
daily temperature distribution.

21. Application: Soil Temperature Field Around a Non-
Insulated Basement Taken at Different Times
January March
May

22. Application: Ice Distribution Around a Non-
Insulated Basement Taken at Different Times
January
March May
February

23. • To show the effect of outside temperature changes on
foundation heat loss, heat flux was computed at the floor
slab and basement wall for months of a year-cycle.
Heat Loss 𝐖/𝐦
Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec
Slab 7.7 7.8 8.1 8.0 8.0 7.9 7.5 7.3 7.2 7.3 7.2 7.4
Wall 42.7 32.5 29.5 19.6 10.3 4.3 2.2 4.6 11.7 21.9 31.4 38.9
Application: Heat Loss

24. Heat loss/gain through an uninsulated basement during the 5th year
when the GWL is at 10 m below the ground surface.
• the heat loss shows an increase
of about 5% and 7% for the
buried basement wall and the
slab, respectively, in
comparison with the dry soil.
• Pore water (in both states, ice
and liquid) increases the heat
conductivity and the heat
capacity of the soil, which leads
to the higher heat flow in soils in
comparison with dry soils.

25. • Snow Melting & De-icing of Bridge Decks and Pavements Using
Thermal Piles
• THM Modeling of Energy Geo-Structures in Freezing Soils
• Effect of Excessive Heat Extraction on Thermo-Mechanical
Behavior of Energy Geo-Structures
On-Going Work

26. Thank you!