# Study on the Influence of Clogging on the Cooling Performance of Permeable Pavement

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Objective

## 3. Pavement Temperature Field with Green’s Function Method

#### 3.1. Heat Conduction Model of Multilayer Pavement Structure

_{0}= 0. The surface is considered as a mixed boundary where the pavement receives the solar radiation, radiates part of the heat into the atmosphere and exchanges heat with the air. When the depth is infinitely deep, the temperature can be considered as a constant.

_{r}is the heat flux when convective heat transfer occurs, W·m

^{−2}·s

^{−1}; h

_{r}is convective heat transfer coefficient, W/(m

^{2}·K). T

_{surf}is the temperature of the surface, K; and T

_{air}is the temperature of the air, K.

_{L}is the amount of long wave radiation energy, W·m

^{−2}·s

^{−1}; σ

_{sb}is Stefan–Boltzmann constant, 5.67 × 10

^{−8}W·m

^{−2}·K

^{−4}; and ε

_{a}is atmospheric long wave emissivity.

_{L}is the outward amount of pavement radiation, W·m

^{−2}·s

^{−1}; and ε is pavement emissivity.

_{g}is the total solar shortwave radiation, W·m

^{−2}·s

^{−1}; ε

_{e}is the absorptivity of solar shortwave radiation; and ε

_{f}is the absorptivity of atmospheric long wave radiation.

#### 3.2. Model of Temperature Field in Asphalt Pavement Based on Green’s Function

_{i}(z,t) is the distribution of temperature in i-th layer, K; z is the depth, m; and α

_{i}is the thermal diffusivity of i-th layer, m

^{2}·s

^{−1}.

_{i}is the thermal conductivity of i-th layer, W·m

^{−1}·K

^{−1}; f

_{1}(t) is the heat flux into the pavement; f

_{2}(t) is the distribution of temperature as z = z

_{m}.

_{i}(z,t) as the form as follows:

_{i}(z) and ψ

_{i}(z) are functions of z; f

_{1}(t) and f

_{2}(t) are functions of t; and θ

_{i}(z,t) is function of z and t.

_{i}(z) should satisfy the steady state heat conduction problem given as Equation (12):

_{i}(z) should satisfy the steady state heat conduction problem given as Equation (17), subjected to the boundary conditions Equations (18)–(21).

_{i}(z,t) should satisfy the transient state heat conduction problem given as Equations (22) and (23), subjected to the boundary conditions Equations (24)–(28).

_{i}(z) and ψ

_{i}(z) can be constructed as Equations (29) and (30):

_{i}(z,t) can be constructed as θ

_{i}(z,t) = Z(z) Γ(t); Equations (31) and (32) can be obtained as θ

_{i}(z,t) substituted into Equations (22) and (23).

_{n}is the eigenvalue, which can be determined by Equations (22) and (23). Equations (33) and (34) can be obtained by equations above.

_{i}(z,t) can be expressed as follows:

## 4. Test Process

#### 4.1. High Viscosity Modified Asphalt

#### 4.2. Mix and Structure Design

#### 4.2.1. Mix Design

_{4.75}) and 2.36 mm (P

_{2.36}) [20]. So the porosity of PAC13 mixture was mainly adjusted by controlling P

_{4.75}and P

_{2.36}. The gradation is shown in Table 4 and the gradation curves are shown in Figure 2.

#### 4.2.2. Structure Design

#### 4.2.3. Specimen Preparation

#### 4.3. Determination of Thermal Properties

_{c}is the specific heat of asphalt mixtures; A

_{i}is the specific heat of the i-th component; B

_{i}is mass fraction of the i-th component.

_{a}, k

_{b}, k

_{v}and k

_{w}are the thermal conductivity of the aggregate, asphalt, mineral powder and air respectively. G, h, i and j are volume fraction of each component. The thermal conductivities [23] of the components were listed in Table 9.

#### 4.4. Test Method

#### 4.5. Data Comparison

- (1)
- The heating power on the infrared light remained constant during the test;
- (2)
- The sides and the bottom of the specimen were adiabatic boundaries, and the upper surface of the specimen is a mixed boundary of fluid and solid;
- (3)
- Each layer of asphalt mixture was isotropic materials;
- (4)
- The thermal properties of asphalt mixture remained constant during the test;
- (5)
- There was no thermal resistance between two linked layers.

^{2}. Then the thermal properties of the remaining specimens were also plugged into Equation (40). The results of theoretical calculation and tests are shown in the following figures.

## 5. The Cooling Performance of the Temperature Field with Different Porosities

_{0}is the maximum radiation intensity at midday, q

_{0}= 0.131 mQ, m = 12/c; Q is the total amount of solar radiation in the day, J/m

^{2}; c is the actual effective sunshine time, h; and ω is angular frequency, ω = 2π/24, rad.

_{a}is the air temperature, °C; $\overline{T}$

_{a}is the average value of the temperature in a day, $\overline{T}$

_{a}= (T

_{max}+ T

_{min})/2, °C; T

_{m}is the daily temperature variation, T

_{m}= (T

_{max}− T

_{min})/2, °C; t

_{0}is the initial phase; and T

_{max}= 40 °C, T

_{min}= 26 °C, t

_{0}= 3.

## 6. Conclusions

- (1)
- The prediction model of the temperature field of permeable pavement was obtained based on Green’s function, and the model was verified by the experimental results. The values of theoretical calculation were close to the experimental results. This indicated that the model had a wide applicability, which could be applied to the theoretical analysis of heat conduction problem for asphalt pavement.
- (2)
- The linear fitted model was proposed based on the Williamson formula and the results of the test. The model could explain the relationship between thermal conductivity of the mixture and that of the components well.
- (3)
- According to the results of test, the cooling performance of pavement became worse with the attenuation of porosity. When the porosity of permeable asphalt pavement reaches 23.05%, the cooling performance at the depth of 10 cm could reach 1.18 °C. When the porosity reached 16.68%, the cooling effect declined to 0.29 °C.
- (4)
- Void clogging has a great influence on the cooling effect of drainage pavement. At present, the porosity of single layered drainage pavement is about 20%. The cooling effect of the pavement under this porosity was about 0.63 °C. If the porosity declined by about three percent, the cooling performance would be less than half of the original.
- (5)
- Through the regression analysis of the relationship between cooling performance and porosity in the permeable pavement, a linear model was set up. The model could be used as a reference for rapid judgment of pavement cooling performance in the field, so as to determine the cleaning cycle of permeable pavement.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 8.**(

**a**) Results of theoretical calculation and tests of S1; (

**b**) Results of theoretical calculation and tests of S2; (

**c**) Results of theoretical calculation and tests of S3; (

**d**) Results of theoretical calculation and tests of S4; (

**e**) Results of theoretical calculation and tests of S5.

**Figure 9.**Structure of the pavement. CTB: cement treated base; LS: lime-stabilized soil; SG: subgrade.

Test | Value | Specification Limits |
---|---|---|

Penetration 25 °C, 100 g, 5 s (0.1 mm) | 54 | 40–60 |

Softening point (°C) | 88.0 | ≥75 |

Ductility, 5 °C, 5 cm/min (cm) | 28 | ≥20 |

Density, 25 °C (g/cm^{3}) | 1.031 | |

After aging in rolling thin film oven | ||

Mass change (%) | +0.045 | ±1.0 |

Retained penetration, 25 °C (%) | 83 | ≥65 |

Retained ductility, 5 °C (cm) | 19 | ≥15 |

Index | Value | Specification Limits |
---|---|---|

Mass of single particle (g) | 0.022 | ≤0.03 |

Density (g/cm^{3}) | 0.978 | 0.90–1.00 |

Appearance | Granular, uniform and plump | - |

Index | Value | Specification Limits |
---|---|---|

Penetration 25 °C, 100 g, 5 s (0.1 mm) | 44 | 40–60 |

Softening point (°C) | 98.0 | ≥90 |

Ductility, 5 °C, 5 cm/min (cm) | 35 | ≥30 |

Dynamic viscosity, 60 °C(Pa·s) | 440,806 | ≥400,000 |

Density, 25 °C | 1.027 | - |

After aging in rolling thin film oven | ||

Mass change (%) | −0.023 | ±0.6 |

Retained penetration, 25 °C (%) | 82.4 | ≥65 |

Retained ductility, 5 °C (cm) | 25 | ≥20 |

Sieve Size | 16 | 13.2 | 9.5 | 4.75 | 2.36 | 1.18 | 0.6 | 0.3 | 0.15 | 0.075 | Porosity | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Upper limit | 100 | 100 | 71 | 30 | 22 | 18 | 14.0 | 12 | 9 | 7 | ||

Lower limit | 100 | 90 | 40 | 10 | 8 | 6 | 4 | 3 | 3 | 3 | ||

Gradation | 1 | 100 | 92.7 | 56.8 | 16.7 | 10.4 | 7.9 | 6.6 | 5.2 | 4.5 | 3.8 | 20.79% |

2 | 100 | 95.0 | 65.0 | 25.0 | 16 | 14.0 | 11.0 | 9.0 | 6.0 | 4.0 | 19.66% | |

3 | 100 | 95.0 | 67.5 | 26.5 | 18.5 | 14.3 | 10.0 | 8.0 | 6.0 | 4.0 | 18.11% | |

4 | 100 | 95.0 | 70.0 | 28.0 | 21 | 14.5 | 10.5 | 9.0 | 6.0 | 4.0 | 16.36% | |

5 | 100 | 95.0 | 45.0 | 10.0 | 8.0 | 7.0 | 6.0 | 5.0 | 4.0 | 3.0 | 23.05% |

Sieve Size | 16 | 13.2 | 9.5 | 4.75 | 2.36 | 1.18 | 0.6 | 0.3 | 0.15 | 0.075 |
---|---|---|---|---|---|---|---|---|---|---|

Upper limit | 100 | 100 | 85 | 68 | 50 | 38 | 28 | 20 | 15 | 8 |

Lower limit | 100 | 90 | 68 | 38 | 24 | 15 | 10 | 7 | 5 | 4 |

Gradation | 100 | 96.9 | 70.2 | 41.8 | 29.1 | 19.9 | 14.4 | 10.5 | 8.2 | 5 |

Sieve Size | 26.5 | 19.0 | 16.0 | 13.2 | 9.5 | 4.75 | 2.36 | 1.18 | 0.6 | 0.3 | 0.15 | 0.075 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Upper limit | 100 | 100 | 95 | 86 | 70 | 48 | 33 | 23 | 16 | 11 | 9 | 6 |

Lower limit | 100 | 90 | 83 | 73 | 56 | 35 | 22 | 15 | 10 | 6 | 5 | 4 |

Gradation | 100 | 96.8 | 89.4 | 78.9 | 60.9 | 42.8 | 29.3 | 21.1 | 14.6 | 10.7 | 8.3 | 5.5 |

Type | Porosity/Material (Upper Layer) | Porosity/Material (Lower Layer) | Label |
---|---|---|---|

Traditional | AC13 | AC20 | AC |

Permeable | 16.68%/PAC13 | AC20 | S1 |

18.11%/PAC13 | AC20 | S2 | |

19.66%/PAC13 | AC20 | S3 | |

20.79%/PAC13 | AC20 | S4 | |

23.05%/PAC13 | AC20 | S5 |

Numbering | Porosity (%) | Specific Heat (J/(kg·K)) | Density (kg/m³) |
---|---|---|---|

PAC13-1 | 16.68 | 926.88 | 2229.52 |

PAC13-2 | 18.11 | 926.09 | 2194.62 |

PAC13-3 | 19.66 | 926.09 | 2142.77 |

PAC13-4 | 20.79 | 925.30 | 2116.84 |

PAC13-5 | 23.05 | 915.82 | 2090.92 |

AC13 | - | 922.51 | 2420.96 |

AC20 | - | 920.60 | 2381.07 |

Index | Aggregate | Asphalt | Mineral Powder | Air |
---|---|---|---|---|

Thermal conductivity (W/(m·K)) | 2.18 | 0.66 | 0.2 | 0.026 |

Numbering | Porosity (%) | Thermal Conductivity (W/(m·K)) | |
---|---|---|---|

Williamson’s Formula | Test | ||

PAC13-1 | 16.68 | 0.82 | 1.03 |

PAC13-2 | 18.11 | 0.78 | 0.97 |

PAC13-3 | 19.66 | 0.73 | 0.93 |

PAC13-4 | 20.79 | 0.70 | 0.88 |

PAC13-5 | 23.05 | 0.67 | 0.8 |

AC13 | - | 1.07 | 1.15 |

AC20 | - | 1.16 | 1.38 |

Specimen | Porosity/Material (Upper) | Porosity/Material (Lower) | Temperature in 4 cm (°C) | Temperature in 10 cm (°C) |
---|---|---|---|---|

AC | AC13 | AC20 | 42.4 | 31.4 |

S1 | 16.68%/PAC13 | AC20 | 42.0 | 31.2 |

S2 | 18.11%/PAC13 | AC20 | 41.4 | 30.3 |

S3 | 19.66%/PAC13 | AC20 | 40.8 | 29.5 |

S4 | 20.79%/PAC13 | AC20 | 40.5 | 29.4 |

S5 | 23.05%/PAC13 | AC20 | 40.0 | 28.9 |

Layer | Density (kg/m³) | Specific Heat (J·kg^{−1}·K^{−1}) | Conductivity (J·m^{−1}·h^{−1}·K^{−1}) |
---|---|---|---|

AC25 | 2300 | 924.9 | 1.3 |

CTB | 2200 | 911.7 | 1.56 |

LS | 2100 | 942.9 | 1.43 |

SG | 1800 | 1040 | 1.56 |

Type | Maximum Temperature (°C) | Reduced Temperature (°C) |
---|---|---|

AC | 43.00 | 0.00 |

S1 | 42.71 | 0.29 |

S2 | 42.51 | 0.49 |

S3 | 42.37 | 0.63 |

S4 | 42.18 | 0.82 |

S5 | 41.82 | 1.18 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xie, J.; Jia, S.; Li, H.; Gao, L.
Study on the Influence of Clogging on the Cooling Performance of Permeable Pavement. *Water* **2018**, *10*, 299.
https://doi.org/10.3390/w10030299

**AMA Style**

Xie J, Jia S, Li H, Gao L.
Study on the Influence of Clogging on the Cooling Performance of Permeable Pavement. *Water*. 2018; 10(3):299.
https://doi.org/10.3390/w10030299

**Chicago/Turabian Style**

Xie, Jianguang, Sicheng Jia, Hua Li, and Lei Gao.
2018. "Study on the Influence of Clogging on the Cooling Performance of Permeable Pavement" *Water* 10, no. 3: 299.
https://doi.org/10.3390/w10030299