67 Figure 5.21: Soil stresses and displacement along the z-direction for different cycles under combined loads (a)-(c) for pile design #3. 73 Figure 5.28: Soil stresses and displacement along z-direction for different cycles under combined loads (a)-(c) for pile design #4. 78 Figure 5.35: Soil stresses and displacement along z-direction for different cycles under combined loads (a)-(c) for pile design #5.

## Introduction

*Overview**Research hypothesis**Thesis problem statement**Objectives**Outline of the thesis*

The second is to evaluate the structural responses of the pile foundations under combined loads. First, the temperature distributions within the concrete portion of the pile foundation were studied by non-stationary heat transfer analyses. Investigation of structural responses of the pile foundation under both temperature changes and internal air pressure.

## Background Information

*Applications of CAES technology**Studies on thermal induced response on the energy piles**Thermodynamic cycles of CAES**Compression process**Cooling process**Heating process**Expansion process**Stresses in the pile foundations*

It showed higher voltages near the bottom of the pile at the end of cooling. When it is compressed, the pressure and temperature of the compressed air increases dramatically. They will gradually decrease as it approaches the outside of the pile.

## Description of the Study

*Variable parameters**Temperature and pressure loadings**Model for thermal analyses**Model for thermal mechanical analyses**Yield surface function*

The temperature change from the compressed air was applied to the inner surface of the pile foundation. Internal pressure changes were applied using the surface pressure at the internal surface of the pile foundation. The pressure was applied to the inner surface of the pile while the temperature was applied at a particular set of nodes.

## Thermal Analyses

*Pile design #1**Pile design #2**Pile design #3**Pile design #4**Pile design #5**Summary of thermal analyses*

The temperature changing with time at different points of the pile is shown in Figure 4.7a. The temperature changing with time at different points of the pile can also be seen in Figure 4.10a. The temperature changing with time at different points of the pile can also be seen in Figure 4.13a.

## Thermal Mechanical Analyses

### Pile design #1

At the end of the cycle, a negligible effect of the internal air pressure can be observed. Mid-cycle radial stresses induce compressive stresses under three load cases. It is interesting to note that circumferential stresses at mid-cycle under internal air pressure generate tensile stresses.

On the inner surface of the pile, circumferential stresses under compression generate high tensile stresses. However, vertical and circumferential stresses on the outside of the pile decrease as time passes. However, tensile stresses at the outer surface are also reduced due to the residual stress effect.

However, at the end of the cycles, it generates compressive stresses only in the first cycle. Tensile stresses continue to increase with cycling on the inner surface of the pile and decrease closer to the outer surface. However, starting from the 10th cycle, tensile stresses can be observed on the inner surface of the column.

The same description can also be applied to circumferential stresses at the end of the cycle.

### Pile design #2

The combination of temperature changes and internal air pressure results in approximately 3.3 MPa of tensile stresses at mid-cycle for γ=1%. Stress distribution along the radial direction under combined loadings at the middle and end of the cycle is presented in Figure 5.9 below for pile design #2. At the end of the cycle, radial stresses generate compression with the lowest of -1.2 MPa at the inner surface of the pile.

The same can be applied to the vertical tension in the middle of the cycle. Peripheral stresses in the middle of the cycle start with -4 MPa of compressive stresses on the inside, slowly progressing to about 4 MPa of tensile stresses closer to the outside. At the outer surface of the pile, for γ=1% vertical and circumferential stresses respectively induce approx. 2 and 3.5 MPa tensile stresses.

While vertical and circumferential stress on the outside of the pile decreases as time passes. Stress distribution along the radial direction at the middle and end of the different cycles for pile design #2 is shown in Figure 5.12. However, from the 13th cycle, tensile stresses can be noticed at the inner surface of the pole.

Vertical and circumferential stresses reach a maximum of 4 and 6 MPa tensile stresses, respectively, at the end of the 365th cycle.

### Pile design #3

The same trend is followed by the vertical tension in the middle of the cycle. An exception is a pole with din=400 mm, where stress can also be observed on the inner surface of the pole. Circumferential stresses in the middle of the cycle start with -4 MPa of compressive stresses for γ=1% and -8 MPa for γ=1.5% on the inside.

On the inside of the pile, circumferential stresses produce compressive stresses of about -6 MPa and -10 MPa for γ=1% and γ=1.5%, respectively. At the outer surface of the pile, vertical and circumferential stresses induce approximately 3 and 3.5 MPa tensile stresses for γ=1% respectively. Stress changing with time for the first 10 cycles at the inner and outer surface of the pile for pile design #3 is illustrated in this Figure 5.18.

Stress distribution along the r-direction at the middle and end of the different cycles for pile design #3 is shown in Figure 5.18. Tensile stresses continue to increase with the cycle at the inner surface of the pile and decrease closer to the outer surface. Vertical and circumferential stresses reach a maximum of about 4 and 5 MPa of tensile stresses at the end of the 365th cycle, respectively.

Compressive stresses arise on the inside of the pile during the 1st cycle.

### Pile design #4

Radial stresses create compression with a minimum of -1.2 MPa on the inner surface of the pile at the end of the cycle. The mid-cycle circumferential stresses start with -4 MPa compressive stresses on the inside. Moderately passes up to about 4 MPa tensile stresses on the outer surface of the pile.

Circumferential stresses on the inside of the pile cause compressive stresses of around -6 MPa. On the outer surface of the pile, both stresses result in tensile stresses of approximately 3 and 3.6 MPa, respectively. The variation of stress with time for the first 10 cycles on the inner and outer surface of the pile for pile design #4 is shown in this Figure 5.25.

Tensile stress increases with the cycle at the inner skin of the pile and decreases closer to the outside. However, from the 11th cycle, tensile stresses can be observed at the inner surface of the pole. Vertical and circumferential stresses reach a maximum of about 4 and 6 MPa of tensile stresses at the end of the 365th cycle, respectively.

Compressive stresses are generated on the inner surface of the pile in the 1st cycle.

### Pile design #5

Radial stresses cause compressive stresses at the inner surface of the pile at the end of the cycle. Radial stresses in the middle of the cycle generate compressive stresses of -6 MPa at the inner skin and reach 0 MPa on the outer side. Circumferential stresses in the middle of the cycle begin with compressive stresses on the inside.

On the inside of the pile, circumferential stresses cause compressive stresses of approximately -6 MPa at the top and bottom of the pile. At the outer skin of the pile, both stresses generate approximately 3 and 3.6 MPa tensile stresses, respectively. Tensile stresses increase with cycle at the inner surface of the pile and decrease at the outer skin.

From the 11th cycle, however, tensile stresses can be observed at the inner surface of the pole. Circumferential stresses in the middle of the 1st cycle start from compressive stresses and gradually increase to tensile stresses. At the inner skin of the pile, compressive stresses are generated at the 1st cycle.

A minor increase in lateral and frictional stress can be observed at the bottom of the pile compared to the original stress profile.

## Discussions and Design Recommendations

### Parametric results

However, the magnitude of the voltage became almost the same closer to the outside, regardless of the noise. At the end of the cycle, radial stresses also follow a similar trend closer to the outer surface. While vertical and circumferential stresses show lower outer tensile stresses as the pile becomes thinner.

Maximum stresses and the yield function changing with cycles for different pile spacings are shown in the following Figure 6.3. As expected, the smaller distance between the piles results in higher stresses, as faster heat transfer can be observed between adjacent piles with smaller pile spacing. For radial stresses, the lowest coefficient results in higher stresses with a small deviation from other coefficients.

The minimum tensile stresses occur at 12×10-6/°C thermal expansion coefficient. The reason for this may be the compatibility of materials between the concrete and steel caps placed on the top and bottom of the pile. Thus, it produces lower stresses when the same coefficient of thermal expansion of concrete is used.

Using concrete with a higher coefficient of thermal expansion will thus give a slower transition to the pure transition zone.

### Design recommendations

Furthermore, Figure 6.8b shows that the transition from the compression and tension region to the pure tension region appears to be faster as the pile thins regardless of pile spacing. In summary, the maximum design temperatures (Td) to be stored in pile foundations for various pile thicknesses are given in the table below. In addition, it is suggested to de-energize and cool down the energy storage piles every N days, depending on the chosen pile design, to minimize the adverse effect on the structure.

## Conclusions

It is suggested that energy storage piles be switched off and cooled every N (ranging from 5-14) days, depending on the pile design chosen, to avoid a pure stress condition in the pile section. Structural responses of reinforced concrete pile foundations subjected to compressed air pressure for renewable energy storage. Preliminary analytical study on the feasibility of using reinforced concrete pile foundations for sustainable energy storage using compressed air energy storage technology.