# Heat Transfer Analysis of Warm Guss Asphalt Concrete for Mini-Trench Overlaying

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Laboratory Testing

#### 2.1.1. Modified Asphalt Binder

#### 2.1.2. Binder Modified by Sasobit

^{3}at 25 °C, and a melting point of 81.5 °C, and a flash point of 280 °C [11,13]. Regarding the binder mixing process, an adequate quantity of asphalt was preheated in the mixer equipment to 160 °C and it was then mixed for 30 min. Afterward, the proper Sasobit contents were then applied, and the combination was stirred for an additional 15 min to create the initial form of guss asphalt mixture. Consequently, a mixer stirred the combined asphalt binder for 30 min at a speed of 3000 rpm while keeping the mixing temperature at 160 °C to produce the homogenous binder [11,12,13,21].

#### 2.1.3. Thermal Conductivity Test

#### 2.2. Heat Transfer Analysis

#### 2.2.1. Finite element Method of Heat Transfer

#### Heat Conduction Governing Equation

^{3}), C is specific heat (J/kgK), T is the temperature at each location over time, t is the time, $\left\{L\right\}=\left\{\begin{array}{c}\begin{array}{c}\raisebox{1ex}{$\partial $}\!\left/ \!\raisebox{-1ex}{$\partial x$}\right.\\ \raisebox{1ex}{$\partial $}\!\left/ \!\raisebox{-1ex}{$\partial y$}\right.\end{array}\\ \raisebox{1ex}{$\partial $}\!\left/ \!\raisebox{-1ex}{$\partial z$}\right.\end{array}\right\}$ is a vector operator, and $\left\{q\right\}$ is the heat flux vector.

#### 2.2.2. Boundary Conditions

#### 2.3. Composition and Elements of Analytical Model

#### 2.4. Physical Properties of Materials

^{3}to 2450 kg/m

^{3}, and the generated thermal conductivity ranged from 1.6 W/mK to 2.1 W/mK. Besides, the specific heat of the material ranged from 1475 J/kgK to 1853 J/kgK. Considering the granular material, Côté et al. [32] tested the thermal conductivity of granular material with a general density of 1545 kg/m

^{3}to 2405 kg/m

^{3}, and the result was distributed from 1.8 W/mK to 3.2 W/mK. Regarding the granular layer, Ižvolt et al. tested the specific heat of the granular material, and the extracted results ranged from 918 J/kgK to 1,091 J/kgK [33,34]. Regarding the subgrade layer, Xu et al. [35] showed that the thermal conductivity of subgrade materials varied from 0.7 W/mK to 2.2 W/mK under various moisture content and temperature conditions of the subgrade materials (densities ranging from 1769 kg/m

^{3}to 2027 kg/m

^{3}). Finally, Kay et al. [36] investigated the specific heat of the subbase material, and the results show the result was distributed from 875 J/kgK to 1968 J/kgK. Besides, according to ACI-122R-02, the specific heat of concrete backfill is 838 J/kgK~1088 J/kgK.

^{3}to 2400 kg/m

^{3}, and a value 1.25 times larger can be assumed in the wet state. The flexible buried pipe was assumed to be made of PVC material, and the density was determined to be 1380 kg/m

^{3}, the thermal conductivity to be 0.2 W/mK, and the specific heat to be 880 J/kgK [28].

_{c}is thermal conductivity as a function of the perfect dry density of concrete (W/mK) and d is the perfect dry density (kg/m

^{3}).

#### 2.5. Initial and Boundary Conditions

#### 2.5.1. Initial Conditions

#### 2.5.2. Thermal Load Case

#### 2.5.3. Boundary Conditions

^{2}was applied to the external inflow of radiant heat by solar radiation. Considering the convective boundary conditions shown in Equation (6), the convection coefficient model of Branco et al. [38] was applied as shown in Equation (9) with the assumed air temperature of 30 °C and the wind speed of 2 m/s. In addition, based on Equation (7) and the atmospheric radiation boundary condition, the effective emission coefficient ($\epsilon $) of asphalt was determined to be 0.93 and the Stefan Boltzmann constant was 5.67 × 10

^{−8}W/m

^{2}K

^{4}.

#### 2.5.4. Analysis Method

## 3. Results

#### 3.1. Thermal Conductivity Test Results

#### 3.2. Overlaying Surface Temperature

#### 3.3. Temperature around Buried Pipes

#### 3.4. Verification of FEM Model

## 4. Conclusions

- Based on the laboratory test results, the thermal conductivity of the WGA mixture was relatively equivalent to the conventional mixture, and adding a proper content of Sasobit (1%) resulted in a low viscosity for warm application purposes.
- WGA was found to be superior in terms of traffic opening time compared to conventional HGA materials, as it could shorten the opening time from 30 min to 1 h and 25 min.
- The study found that the time required to open traffic increased as the depth of the WGA mixture overlay increased. Therefore, an overlaying depth of 100 mm was deemed reasonable for practical construction purposes, as it is difficult to conduct traffic blocks for more than 4 h at the site.
- The investigation of the minimum cover thickness of the backfill concrete that protects the buried pipe from the heat source from the above 100 mm guss asphalt layer found that WGA could be used to construct thinner backfill concrete surrounding the landfill pipe, resulting in a cost-effective effect. Additionally, it was found that a conventional HGA mixture must be designed with a concrete thickness of 150 mm to achieve proper covering purposes.
- The accuracy of the simulation is supported by the testbed measurement, as both processes exhibit a comparable trend in the reduction of temperature over time. Nevertheless, the temperature in the measured section was slightly higher than that of the simulated work, particularly during the initial two-hour period, potentially due to fluctuations in temperature in the hot climate of southern Vietnam.
- In summary, the study found that the WGA mixture is a viable option for the mini-trench method due to its low production and compaction temperatures and shorter traffic opening time. However, future research is needed to further evaluate the developed WGA mixture for practical construction purposes, and further adjustments are required to refine the simulation’s thermal regulation capabilities in the field.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Illustration of laboratory test. (

**a**) absolute viscosity; (

**b**) Test specimen fabrication of Guss mastic asphalt mixtures; (

**c**) Thermal conductivity test.

**Figure 4.**Initial and boundary conditions. (

**a**) The transmitting of heat source; (

**b**) the relationship between temperature and depth.

**Figure 8.**Pavements surface temperatures of FEA results. (

**a**) Hot Mix Guss Mastic Asphalt; (

**b**) Warm Mix Guss Mastic Asphalt.

**Figure 9.**The temperature at the Top of the Conduit of FEA results. (

**a**) Hot Mix Guss Mastic Asphalt; (

**b**) Warm Mix Guss Mastic Asphalt.

**Figure 10.**FE Analysis Results of Pavement Temperature Distribution. (

**a**) Concrete Cover 50 mm (Warm Mix Guss Mastic Asphalt); (

**b**) Concrete Cover 50 mm (Hot Mix Guss Mastic Asphalt); (

**c**) Concrete Cover 100 mm (Hot Mix Guss Mastic Asphalt).

**Figure 11.**(

**a**) Field testbed section, measurement of the WGA surface by using instrument (

**b**) and thermal meter (

**c**).

Properties | Value | Standard Value |
---|---|---|

Penetration (1/10 mm) 25 °C | 87.2 | |

Softening point (°C) | 68.6 | |

Ductility at 5 °C (cm/min) | 105 | |

Thin film oven (160 °C, 300 min) | ||

Mass loss (%) | 0.05 | |

Penetration loss | 72 | |

G*/sinδ; at 76 °C (Original) | 1.72 kPa | Min. 1.0 kPa |

G*/sinδ at 76 °C (after RTFO) | 2.41 kPa | Min. 2.2 kPa |

G* × sinδ at 76 °C (after PAV) | 1527 kPa | Max. 5000 kPa |

Stiffness at −22 °C | 186 MPa | Max. 300 MPa |

m-value at −22 °C | 0.32 | Min. 0.3 |

Properties | Properties | Value |
---|---|---|

Aggregate | Relative apparent density | 2.67 |

Water absorption | 0.18% | |

Aggregate crushed value | 19.5% | |

Los Angeles abrasion value | 25.8% | |

Flakiness and elongation index | 12.5% | |

Mineral Filler | Relative apparent density | 2.36 |

Moisture content | 0.09% |

Sieve size (mm) | 16 | 13.2 | 9.5 | 4.75 | 2.36 | 1.18 | 0.6 | 0.3 | 0.15 | 0.075 |

Gradation (%) | 100 | 100 | 97.6 | 62.5 | 9.1 | 5.1 | 3.3 | 2.7 | 2.0 | 0.8 |

Properties | Result Value | Standard Value |
---|---|---|

Stability (N) | 11,789 | ≥5000 |

Flow value (1/100 cm) | 29 | 20~40 |

Warm Case | Content | Hot-Case | Content |
---|---|---|---|

50 mm–160 °C | Warm Guss mastic asphalt concrete & a depth of 50 mm | 50 mm–200 °C | Hot Guss mastic asphalt concrete & a depth of 50 mm |

100 mm–160 °C | Warm Guss mastic asphalt concrete & a depth of 100 mm | 100 mm–200 °C | Hot Guss mastic asphalt concrete & a depth of 100 mm |

150 mm–160 °C | Warm Guss mastic asphalt concrete & a depth of 150 mm | 150 mm–200 °C | Hot Guss mastic asphalt concrete & a depth of 150 mm |

200 mm–160 °C | Warm Guss mastic asphalt concrete & a depth of 200 mm | 200 mm–200 °C | Hot Guss mastic asphalt concrete & a depth of 200 mm |

250 mm–160 °C | Warm Guss mastic asphalt concrete & a depth of 250 mm | 250 mm–200 °C | Hot Guss mastic asphalt concrete & a depth of 250 mm |

Material | Properties | Value | Reference |
---|---|---|---|

Asphalt layer & Guss Mastic overlaying | Density, kg/m^{3} | 2373 | Laboratory experiment results (Section 3.1) and Luca and Mrawira (2005) [31] |

Thermal Conductivity, W/mK | 1872 | ||

Specific heat, J/kgK | 1664 | ||

Subgrade | Density, kg/m^{3} | 1975 | Côté et al. (2005) [32] Ižvolt et al. (2014) [33,34] |

Thermal Conductivity, W/mK | 2.5 | ||

Specific heat, J/kgK | 1005 | ||

Subbase | Density, kg/m^{3} | 1898 | Kay et al. (1975) [36] Xu et al.(2020) [35] |

Thermal Conductivity, W/mK | 1.5 | ||

Specific heat, J/kgK | 1422 | ||

Concrete backfills | Density, kg/m^{3} | 2300 | ACI-122R-02 [37] |

Thermal Conductivity, W/mK | 1.6 | ||

Specific heat, J/kgK | 963 | ||

PVC | Density, kg/m^{3} | 1380 | |

Thermal Conductivity, W/mK | 0.2 | ||

Specific heat, J/kgK | 880 |

Type | Min. Temp. for Storage and Transportation | Min. Temp. for Installation and Operation | Range of Operating Temp. |
---|---|---|---|

1 | −5 °C | −5 °C | −5 °C~60 °C |

2 | −25 °C | −25 °C | −15 °C~60 °C |

Overlaying Depth | Traffic Opening Time | |||
---|---|---|---|---|

Warm Mix Guss Mastic Asphalt | Hot Mix Guss Mastic Asphalt | |||

40 °C | 50 °C | 40 °C | 50 °C | |

50 mm | 4 h | 2 h | 4 h 40 min | 2 h 30 min |

100 mm | 6 h | 3 h 15 min | 7h | 4 h |

150 mm | 7 h 45 min | 4 h 5 min | 8 h 40 min | 4 h 40 min |

200 mm | 9 h | 4 h 55 min | 10 h | 6 h |

250 mm | 10 h 35 min | 5 h 15 min | 12 h 45 min | 6 h 40 min |

Concrete Cover | Warm Mix Guss Mastic Asphalt | Hot Mix Guss Mastic Asphalt | ||
---|---|---|---|---|

Max. Temp. (°C) | Operation Limit | Max. Temp. (°C) | Operation Limit | |

250 mm | 38.3 | Lower | 39.6 | Lower |

200 mm | 42.4 | Lower | 44.5 | Lower |

150 mm | 48.0 | Lower | 51.9 | Lower |

100 mm | 57.1 | Lower | 64.1 | Higher |

50 mm | 76.8 | Higher | 94.8 | Higher |

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## Share and Cite

**MDPI and ACS Style**

Kim, K.-N.; Kim, Y.-M.; Lee, S.-Y.; Le, T.H.M. Heat Transfer Analysis of Warm Guss Asphalt Concrete for Mini-Trench Overlaying. *Materials* **2023**, *16*, 2808.
https://doi.org/10.3390/ma16072808

**AMA Style**

Kim K-N, Kim Y-M, Lee S-Y, Le THM. Heat Transfer Analysis of Warm Guss Asphalt Concrete for Mini-Trench Overlaying. *Materials*. 2023; 16(7):2808.
https://doi.org/10.3390/ma16072808

**Chicago/Turabian Style**

Kim, Kyung-Nam, Yeong-Min Kim, Sang-Yum Lee, and Tri Ho Minh Le. 2023. "Heat Transfer Analysis of Warm Guss Asphalt Concrete for Mini-Trench Overlaying" *Materials* 16, no. 7: 2808.
https://doi.org/10.3390/ma16072808