# Thermal Properties of Hydrated Lime-Modified Asphalt Concrete and Modelling Evaluation for Their Effect on the Constructed Pavements in Service

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## Abstract

**:**

## 1. Introduction

## 2. Experiment

#### 2.1. Raw Materials and Mixtures

#### 2.2. Specimen Preparation and Thermal Property Test

#### 2.3. The Experimental Results

## 3. Modelling Evaluation for the Pavement Constructed Using HL Asphalt Concrete

- Motion equation

_{x}; u

_{y}; u

_{z}), f is a body force per unit volume, E is modulus, $v$ is the Poisson ratio, and ρ is density. The strain and stress of the solid material are shown in Equations (2) and (3), respectively.

- Energy equation

_{p}is the specific heat, k is the thermal conductivity, and r is the heat source per unit mass. For the pavement challenge, the heat source r and the thermal energy, due to the deformation strain rate ($\frac{d{\epsilon}_{kk}}{dt}$), are neglected in this study.

^{−2}m

^{2}[7], was deliberately increased for this study in terms to compare with the thermal effect. The Equations (1)–(4) were solved using the partial differential equation module of a commercial FEA software (COMSOL Multiphysics).

## 4. Modelling Results and Discussion

#### 4.1. Temperature Profile and Thermal Strain & Stress Distribution

#### 4.2. The Coupled Thermomechanical Effect

## 5. Conclusions

- 2.5% addition of HL to replace the equivalent weight of limestone dust filler enhances the thermal properties of the modified asphalt concrete of increased magnitudes of thermal conductivity (27% for wearing mix, 7% for leveling mix, 0.17% for base mix) and specific heat (25% for wearing mix, 6% for leveling mix, 0.16% for base mix). For the HL modified mix there is no correlation between the thermal properties and either the optimum asphalt cement or the mineral filler content.
- Between pavement using HL concrete and that not using HL concrete, there is a very small difference between the local temperature profiles within the structural layers. Correspondingly, the difference of the thermal strain and stress profiles with in the two pavements is very small as well.
- The thermal effect is pronounced under the coupled thermomechanical conditions for pavement exposed to both traffic and climatic impacts because of the temperature effect on the mechanical properties, such as the modulus and deformation coefficient, of the mixes.
- The modelling analysis shows that the HL pavement has about 1.5% less deformation than the control pavement at the place under the direct traffic loading. The result highlights the benefit of HL on long-term fatigue and rutting resistance.
- The modelling results indicate that the benefit of the HL on traffic-only stress reduction is about 39%, but the thermal effect increases that maximum total internal tensile stress level by 26% in the HL pavement in the winter season. It explains why there is an optimum HL content for asphalt concrete modification when exposed to temperature variation.
- The modelling results have showed that for HL pavement asphalt concrete, the local maximum tensile stress predominates in the surface region, i.e., wearing layer. It will help reduce the workload in crack repairing and in the long term help on saving costs and efforts of maintenance.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Table A1.**Traffic load information for estimating the 80-kN ESAL [7] (Al-Tameemi et al., 2019).

Vehicle Type | Percentage of ith Vehicles P_{i} (%) | Number of Vehicles/Lane per Year N_{i} | Equivalent Axle Load Factor (EALF) | Growth Factor G _{f} | ESALs |
---|---|---|---|---|---|

Passenger car unit (PCU) | 55 | 250,937.50 | 0.0008 | 20.02 | 4019.02 |

Single-unit trucks | |||||

2 axles, 4 tires | 10 | 45,625 | 0.003 | 20.02 | 2740.24 |

2 axles, 6 tires | 10 | 45,625 | 0.21 | 20.02 | 191,816.60 |

3 axles or more | 5 | 22,812.58 | 0.61 | 20.02 | 278,590.80 |

Tractor semitrailers and combinations | |||||

4 axles or fewer | 5 | 22,812.50 | 0.62 | 20.02 | 283,157.90 |

5 axles | 10 | 45,625 | 1.09 | 20.02 | 995,619.60 |

6 axles or more | 5 | 22,812.50 | 1.23 | 20.02 | 561,748.70 |

Total | 100 | 456,250 | 2,317,693 |

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**Figure 3.**Comparison of the thermal properties between the control mix and the mix of 2.5% hydrated lime.

**Figure 13.**The coupled thermomechanical stress, ${\sigma}_{max}+{\sigma}_{min}-\alpha \left(3\lambda +2\mu \right)\Delta T$, at 720 h.

Notation | Application | Hydrated Lime Content (%) | OAC% |
---|---|---|---|

CW | Wearing | 0 | 4.9 |

CL | Levelling | 0 | 4.6 |

CB | Base | 0 | 4.3 |

HL2.5W | Wearing | 2.5 | 5.3 |

HL2.5L | Levelling | 2.5 | 5 |

HL2.5B | Base | 2.5 | 4.6 |

Sieve Size | mm | Type I | Type II | Type IIIA |
---|---|---|---|---|

Base Course | Levelling Course | Wearing Course | ||

% Passing by Weight of Total Aggregate and Filler | ||||

1.5 in | 37.5 | 100 | ||

1 in | 25.0 | 95 | 100 | |

0.75 in | 19.0 | 83 | 95 | 100 |

0.5 in | 12.5 | 68 | 80 | 95 |

3/8 in | 9.5 | 61 | 68 | 83 |

No. 4 | 4.75 | 44 | 50 | 59 |

No. 8 | 2.36 | 32 | 36 | 43 |

No. 50 | 300 μm | 11 | 12 | 13 |

No. 200 | 75 μm | 5 | 6 | 7 |

Surface/Wearing | Binder/Levelling | Base | Subbase | Subgrade | Wheel | |
---|---|---|---|---|---|---|

Thickness (mm) | 50 | 70 | 90 | 300 | 2500 | - |

Width (mm) | 1800 | 1800 | 1800 | 1800 | 1800 | 250 |

Property | Mix | Wearing | Levelling | Base | Subbase | Subgrade |
---|---|---|---|---|---|---|

Modulus * E (MPa) | 0% HL | 0.28T^{2} − 41.53T + 2090 | 0.39T^{2} − 46.41T + 1929 | 0.34T^{2} − 40.41T + 1649 | 170 | 65 |

2.5% HL | 0.19T^{2} − 43.03T + 2623 | 0.52T^{2} − 63.3T + 2527 | 0.34T^{2} − 41.12T + 1803 | 170 | 65 | |

Poisson ratio ν | 0% HL | 0.35 | 0.4 | |||

2.5% HL | ||||||

Density ρ (g/cm^{3}) | 0% HL | 2.34 | 2.32 | 2.31 | 1.76 | 1.29 |

2.5 HL | 2.32 | 2.30 | 2.3 | |||

Thermal Conductivity k (W/m/K) | 0% HL | 0.71 | 0.73 | 0.75 | 1.3 | 0.28 |

2.5 HL | 0.90 | 0.78 | 0.88 | |||

Thermal Capacity c_{p} (J/kg/K) | 0% HL | 1062.6 | 1092.79 | 1121.12 | 837 | 800 |

2.5 HL | 1333.48 | 1155.49 | 1303.09 | |||

Thermal deformation coefficient * α | 0% HL | CTC—Equation (5a) CTE—Equation (5b) | 3.32 × 10^{−6} | 3.4 × 10^{−5} | ||

2.5 HL |

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**MDPI and ACS Style**

Al Ashaibi, A.; Wang, Y.; Albayati, A.; Byzyka, J.; Scholz, M.; Weekes, L.
Thermal Properties of Hydrated Lime-Modified Asphalt Concrete and Modelling Evaluation for Their Effect on the Constructed Pavements in Service. *Sustainability* **2022**, *14*, 7827.
https://doi.org/10.3390/su14137827

**AMA Style**

Al Ashaibi A, Wang Y, Albayati A, Byzyka J, Scholz M, Weekes L.
Thermal Properties of Hydrated Lime-Modified Asphalt Concrete and Modelling Evaluation for Their Effect on the Constructed Pavements in Service. *Sustainability*. 2022; 14(13):7827.
https://doi.org/10.3390/su14137827

**Chicago/Turabian Style**

Al Ashaibi, Azedin, Yu Wang, Amjad Albayati, Juliana Byzyka, Miklas Scholz, and Laurence Weekes.
2022. "Thermal Properties of Hydrated Lime-Modified Asphalt Concrete and Modelling Evaluation for Their Effect on the Constructed Pavements in Service" *Sustainability* 14, no. 13: 7827.
https://doi.org/10.3390/su14137827