An Investigation into the Mobilised Bearing Capacity and Head Displacement of Energy Piles

Abstract

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Energy piles offer a promising new method of reducing CO2 emissions by utilising geothermal energy to heat and cool buildings. Despite an increase in implementation over recent years a lack of understanding of energy pile behaviour due to thermal effects remains, with current designs either based upon the structural requirements alone or exacerbated safety factors. Existing literature has demonstrated that thermal loading has a significant impact on pile strains. However, little investigation has been conducted into the effect of thermal loading on the mobilised bearing capacity, or pile head displacements which are imperative to the design integrity of the pile and founded superstructure.

This dissertation aimed to assess if varying material properties and increasing thermal loads affect the pile factor of safety and head displacements. A parametric study was conducted where a finite element model, validated against a known field experiment, tested varying values of pile length, pile diameter, soil shear modulus and soil strength under thermal loading. The results of the testing indicated that while the factor of safety showed little variation, pile head displacements were quite sensitive to thermal loads. It was further demonstrated that pile length was the most critical property, as results showed the most significant trend in this data.

It is clear from this research that further industry understanding and formalised design codes are required for the design of energy piles, as the current approach does not account for the substantial change in pile head displacements indicated by this study.

Contents

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1 Introduction

2 Literature Review

2.1 Energy Piles

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2.2 Framework

2.3 Field Testing

2.4 Numerical Modelling

3 Numerical Model

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3.1 Model Description

3.2 Validation

4 Parametric Study

4.1 Analysis Arrangement

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4.2 Results

4.3 Critical Evaluation

5 Conclusion

6 References

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List of Figures

Figure 1: Annual Relationship between Surface Air Temperature and Ground Temperature, (Preene & Prowrie, 2009)

Figure 2: UK Energy Pile Installations 2005-10, (Laloui & Donna, 2011)

Figure 3: Typical Energy Pile Arrangement, (Laloui & Donna, 2011)

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Figure 4: Thermal Behaviour Pile Profiles (a) unrestrained heating (b) unrestrained cooling      (c) fixed heating (d) fixed cooling, (Bourne-Webb, et al., 2012)

Figure 5: Thermal Behaviour Pile Profiles (a) shaft restraint heating (b) shaft restraint cooling (c) shaft and end restraint heating (d) shaft and end restraint cooling, (Bourne-Webb, et al., 2012)

Figure 6: Mechanical Behaviour Pile Profile

Figure 7: Thermomechanical Behaviour Pile Profiles (a) shaft restraint heating (b) shaft restraint cooling (c) shaft and end restraint heating (d) shaft and end restraint cooling, (Bourne-Webb, et al., 2012)

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Figure 8: Strain Profiles (a) Lambeth College (b) Lausanne

Figure 9: T-z Beam Spring Method

Figure 10: T-z Load Transfer Curve

Figure 11: Lambeth College Test Pile, (Bourne-Webb, et al., 2009)

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Figure 12: Lambeth College Test Temperature Variation

Figure 13: Verification Mechanical Loading Results

Figure 14: Verification Heating Results

Figure 15: Verification Cooling Results

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Figure 16: Finite Element Results for E=40MPa

Figure 17: Finite Element Model Varying Properties

Figure 18: Test A – Strain Profiles (a) Heating (b) Cooling

Figure 19: Test A – Mobilised Shaft Friction Profiles (a) Heating (b) Cooling

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Figure 20: Test A – Pile Head Displacements due to Thermal Loading only

Figure 21: Test A – Factor of Safety

Figure 22: Test B – Pile Head Displacement due to Thermal Loading only

Figure 23: Test B – Factor of Safety

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Figure 24: Test C – Pile Head Displacements due to Thermal Loading only

Figure 25: Test C – Factor of Safety

Figure 26: Test D – Pile Head Displacement due to Thermal Loading only

Figure 27: Test D – Factor of Safety

Figure 28: Test E – Pile Head Displacements due to Thermal Loading only

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Figure 29: Test E – Factor of Safety

Figure 30: Test F – Pile Head Displacement due to Thermal Loading only

Figure 31: Test F – Factor of Safety

Figure 32: Test G – Pile Head Displacements due to Thermal Loading only

Figure 33: Test G – Factor of Safety

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Figure 34: Test H – Pile Head Displacement due to Thermal Loading only

Figure 35: Test H – Factor of Safety

Figure 36: Test I – Pile Head Displacement due to Thermal Loading only

Figure 37: Test I – Factor of Safety

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Figure 38: Test J – Pile Displacement due to Thermal Loading only

Figure 39: Test J – Factor of Safety

Figure 40: Test K – Pile Head Displacement due to Thermal Loading only

Figure 41: Test K – Factor of Safety

Figure 42: Test L – Pile Head Displacement due to Thermal Loading

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Figure 43: Test L – Factor of Safety

Figure 44: Test M – Pile Displacement due to Thermal Loading only

Figure 45: Test M – Factor of Safety

Figure 46: Test N – Pile Displacement due to Thermal Loading only

Figure 47: Test N – Factor of Safety

Figure 48: Test O – Pile Displacement due to Thermal Loading only

Figure 49: Test O – Factor of Safety

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Figure 50: Test P – Pile Head Displacement due to Thermal Loading only

Figure 51: Test P – Factor of Safety

Figure 52: Factor of Safety Change for Increasing Loading

Figure 53: Pile Head Displacement Change for Increasing Loading (a) 80% (b) 90%

Figure 54: Factor of Safety for Varied Pile Lengths

Figure 55: Pile Head Displacement under Thermal Loading Only for Varied Pile Lengths

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Figure 56: Factor of Safety for Varied Pile Diameters

Figure 57: Pile Head Displacement under Thermal Loading Only for Varied Pile Diameters

Figure 58: Factor of Safety for Varied Soil Shear Modulus

Figure 59: Pile Head Displacement under Thermal Loading Only for Varied Soil Shear Modulus

Figure 60: Factor of Safety for Varied Soil Strength

Figure 61: Pile Head Displacement under Thermal Loading Only for Varied Soil Strength

List of Tables

Table 1: Verification Model Loading

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Table 2: Verification Model Pile Properties

Table 3: Verification Model Soil Properties

Table 4: Model Varying Properties Values

Table 5: Parametric Study Constant Properties

Table 6: Test A – Input Values

Table 7: Test B – Input Values

Table 8: Test C – Input Values

Table 9: Test D – Input Values

Table 10: Test E – Input Values

Table 11: Test F – Input Values

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Table 12: Test G – Input Values

Table 13: Test H – Input Values

Table 14: Test I – Input Values

Table 15: Test J – Input Values

Table 16: Test K – Input Values

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Table 17: Test L – Input Values

Table 18: Test M – Input Values

Table 19: Test N – Input Values

Table 20: Test O – Input Values

Table 21: Test P – Input Values

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Table 22: Summary of Results

List of Symbols

GSHP	Ground Source Heat Pump
αc	Coefficient of thermal expansion
ΔT	Temperature Change
εT-Free	Unrestrained pile strains
εT-Fixed	Fixed pile strains
εT-Obs	Observed pile strains
εT-Rest	Restrained pile strains
PT	Thermal loading
E	Young’s Modulus
A	Pile cross-sectional area
kEL	Local beam element stiffness matrix
kspring	Local spring element stiffness matrix
t	Shaft friction
z	Pile displacements (t-z model)
tm,undrained	Maximum shaft friction undrained soil
tm,drained	Maximum shaft friction drained soil
α	Soil adhesion factor
Su	Soil undrained shear strength
As	Area of pile in contact with soil
k0	Coefficient of earth pressure
ϕ’	Soil friction angle
σ’v	Effective vertical soil stress
km	Maximum stiffness for displacement
G	Soil shear modulus
r	Pile radius
L	Pile length
ν	Poisson’s Ratio
γ	Unit weight of soil
h	Hardening parameter
d	Degradation parameter (t-z model)
k	Global stiffness matrix
kp	Global pile stiffness matrix
ks	Global soil stiffness matrix
P	Mechanical load
u	Displacements
c’	Soil cohesion factor
d	Pile diameter
Nc	Empirical factor
Qult	Ultimate pile bearing capacity
Qmob	Mobilised pile bearing capacity
Ab	Area of pile base

1                Introduction

Geothermal energy is heat which is stored within the ground. It is considered a good source of renewable energy and is receiving increasing interest with the ever-growing pressures regarding carbon reductions. One method of accessing this energy is with a ground source heat pump system (GSHP). The GSHP involves laying a series of tubes below the ground surface, which allow for the circulation of a fluid. As the ground remains at a constant temperature throughout the year, as shown in Figure 1, a transfer of heat energy takes place with the fluid heated or cooled depending on the seasonal surface temperature. This energy can be exchanged using a heat pump to meet the heating requirements of buildings.

Figure 1: Annual Relationship between Surface Air Temperature and Ground Temperature, (Preene & Prowrie, 2009)

A more recent innovation the integration of the GSHP with foundation piles. This system is termed ‘energy pile’ and, in theory, is an excellent idea as it utilises an element which is already structurally required, resulting in a significant reduction in construction costs.  This has led to an increase in energy pile installations in recent years, as shown in Figure 2.

Figure 2: UK Energy Pile Installations 2005-10, (Laloui & Donna, 2011)

However, concerns have been raised as to the effects of the heating and cooling cycles on the pile structure. Without a comprehensive understanding of the energy pile behaviour, it is hypothesised that the structure expansion and contraction associated with the temperature cycles may have a detrimental effect on the pile-soil interaction and the overall bearing capacity of the foundation.

This project aims to expand the current understanding of energy pile behaviour, specifically the effect of varied properties and temperature cycles on the mobilised bearing capacity and head displacements.  The objectives are detailed below:

• Research current understanding of energy pile behaviour

• Validate a finite element model against existing field data

• Perform a parametric study using a finite element model in order to simulate energy pile behaviour under different parameters

• Analyse produced results in order to form an understanding of the energy pile behaviour throughout testing

2                Literature Review

This section aims to explain current understanding of energy piles and identify gaps in the knowledge which require further study.

2.1          Energy Piles

Energy pile installation involves the incorporation of U-shaped tubes into the pile structure which is usually achieved by attaching them to the reinforcement, as shown in Figure 3Error! Not a valid bookmark self-reference..

This simple system has shown to produce 20-100W per m of pile of renewable heating energy, which is popular with developers as it assists in meeting the 10% on site renewable energy obligation enforced for medium and large scale developments in the UK (Laloui & Donna, 2011; Boennec, 2008). Despite a significant increase in the number of energy piles installed around the world, concerns remain regarding their structural integrity (Laloui & Donna, 2011). This stems predominantly from a lack of understanding in the behaviour of the piles during the heating and cooling cycles associated with their geothermal applications (Laloui & Donna, 2011). Furthermore, few design codes exist with those that do based upon limited field testing (Laloui & Donna, 2011). Today most energy piles are either designed based purely upon their structural requirements, or with significantly increased safety factors (Ouyang, et al., 2011; Abuel-Naga, et al., 2015). Neither approach specifically addresses thermal behaviour, leading to potentially dangerous or over conservative designs. Therefore, the development of standardised design practices and wider industry understanding is crucial for the successful widespread usage of energy piles.

2.2          Framework

A framework for the behaviour of energy piles was first suggested by Bourne-Webb et al. (2009) which was further developed by Bourne-Webb et al. (2012) and Amatya et al. (2012). Energy piles are subjected to two loads; mechanical and thermal. Mechanical loading is specified by the above ground superstructure, the traditional application of piles. Thermal loading induced by the heating or cooling effects associated with the geothermal applications. Each load has a specific effect on the behaviour of a pile and each will now be analyses separately before their combined effects are considered.

2.2.1         Thermal Loading

First, the pile response under thermal loading only is considered. If the pile is unrestrained it will expand or contract in proportion to the coefficient of thermal expansion (α_c) and temperature change (ΔT):

εT-Free=αc∆T

           (1)

Thus, when the pile is heated (+ΔT) it expands and contracts when cooled (-ΔT). Similarly, under fully fixed conditions, where movement is restricted in all directions, thermal strains will be induced within the pile (ε_T-Fixed). Under heating conditions, where the pile wants to expand compressive strains will be induced and tensile strains will be induced where the pile wishes to contract under cooling, as illustrated in Figure 4.