# Horizontal Distribution of Temperature Effect in Rubberized Concrete Pavement: A Case Study

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## Abstract

**:**

^{−1}greater than the temperature gradient at the center. The negative temperature gradient at the corner of the concrete pavement exacerbates the bottom deformation at the center and edge of the pavement, especially in the X-axis direction at the center and in the Y-axis and Z-axis directions at the edge. The relationships between temperature and horizontal strain at the center and edge of the RCP have a significant hysteresis effect and are markedly stronger than those at the corner. Moreover, when the temperature gradient is less than −23.4 °C·m

^{−1}or greater than 14.5 °C·m

^{−1}, the curling effect at the edge of the RCP is more obvious.

## 1. Introduction

## 2. Experiment Procedure

#### 2.1. Pavement Structures and Materials

#### 2.2. Sensor Parameters and Layout Scheme

#### 2.3. Data Collection and Processing

_{T}is the temperature sensitivity coefficient of the sensor, which was provided by the sensor manufacturer in °C/nm; P

_{t}is the test wavelength, nm; P

_{0}is the initial wavelength, nm; and T

_{0}is the constant of the sensor, which was provided by the sensor manufacturer.

_{S}is the strain sensitivity coefficient, με/nm; ${K}_{T}^{\prime}$ is the temperature compensation coefficient, P

_{S}is the measuring wavelength of the strain grating, nm; P

_{0}is the initial wavelength of the strain grating, nm; P

_{T}is the measuring wavelength of the temperature grating, nm; and P

_{T0}is the initial wavelength of the temperature grating, nm. K

_{S}and ${K}_{T}^{\prime}$ are fixed parameters of the sensor, which was provided by the manufacturer.

## 3. Results and Discussion

#### 3.1. Horizontal Distribution of Temperature of RCP

#### 3.1.1. Temperature

#### 3.1.2. Temperature Gradient

_{2}) caused by the corner of the RCP. This increased curling displacement is more severe in ordinary concrete pavements [32,42]. If the assumption of uniformity in the plane is used in the calculation of the temperature curling stress of the RCP, the obtained temperature curling stress will be smaller than the actual value. This should be highly regarded in the design and evaluation of RCP.

^{−1}, respectively. The percentages of negative temperature gradients in the center, edge and corner of the pavement were 70%, 75% and 100%, respectively. This further indicates that RCPs are mostly subject to negative, temperature-induced curling at the corners in the winter.

#### 3.2. Horizontal Distribution of Strain of RCP

#### 3.2.1. Horizontal Strain

#### 3.2.2. Vertical Strain

#### 3.3. Temperature–Strain Effect of RCP

#### 3.3.1. Temperature–Strain Hysteresis Effect

#### 3.3.2. Temperature Curling Effect

^{−1}or the positive temperature gradient is greater than 14.5 °C·m

^{−1}, the vertical strain at the edge of the pavement will be greater than the strain at the center and corner of the pavement, indicating that the curling effect at the edge of the RCP will be more obvious when the temperature gradient is outside the range of −23.4 to 14.5 °C·m

^{−1}[43]. Therefore, when the RCP is set up with tie bars for the longitudinal joints and no dowel bars for the transverse joints, the deformation caused by the temperature gradient at the edge of the pavement is the most obvious. This should be focused on during the RCP design.

## 4. Conclusions

- (1)
- The horizontal distribution of the temperature and temperature gradient of the RCP exhibited obvious inhomogeneity, resulting in the deviation of the theoretical calculation of the temperature characteristics from the actual situation. In particular, the larger negative temperature gradient at the corner will intensify the upward curling of the RCP caused by the negative temperature gradient, making the theoretical value smaller than the actual value when using the plane uniformity assumption. This should be highly regarded in the design and evaluation of the RCP;
- (2)
- The negative temperature gradient at the corner of the pavement aggravates the deformation of the pavement bottom at the center and edge, especially along the X-axis at the center and along the Y-axis and the Z-axis at the edge, resulting in the uneven distribution of the deformation. This leads to greater curling strain on the RCP at these locations;
- (3)
- The temperature-strain effects indicate that the deformation at the corner of the RCP is affected only by the temperature change, while the deformations at the center and edge are affected not only by the temperature change but also by the deformation at the corner. The coefficients of temperature gradient and strain at the center, edge and corner of the pavement were 0.13, 0.37 and 0.25, respectively, which indicates that the edge of the pavement is the most sensitive to changes in temperature gradient. When the temperature gradient is less than −23.4 °C·m
^{−1}or greater that 14.5 °C·m^{−1}, the curling effect at the edge of the RCP is more obvious; - (4)
- In this study, the horizontal distribution characteristics of the temperature effect on the RCP were analyzed based on the field monitoring data. In the subsequent study, numerical simulations will be carried out to further reveal the mechanism of the differences in the horizontal distribution of the RCP.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Cement | Water | Rubber Powder | Sand | Aggregate (5–10 mm) | Aggregate (10–19 mm) | Aggregate (19–37.5 mm) | Water Reducing Agent |
---|---|---|---|---|---|---|---|

405 | 162 | 110 | 358 | 410 | 410 | 546 | 5.7 |

Properties | Specification |
---|---|

Organic matter (%) | 67.21 |

Inorganic content (%) | 32.79 |

Rubber powder size (mesh) | 30–60 |

Contact angle (°) | 0 |

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**MDPI and ACS Style**

Zhang, G.; Zhang, J.; Yuan, J.; Ye, S.
Horizontal Distribution of Temperature Effect in Rubberized Concrete Pavement: A Case Study. *Buildings* **2023**, *13*, 686.
https://doi.org/10.3390/buildings13030686

**AMA Style**

Zhang G, Zhang J, Yuan J, Ye S.
Horizontal Distribution of Temperature Effect in Rubberized Concrete Pavement: A Case Study. *Buildings*. 2023; 13(3):686.
https://doi.org/10.3390/buildings13030686

**Chicago/Turabian Style**

Zhang, Gaowang, Jiake Zhang, Jie Yuan, and Shijiang Ye.
2023. "Horizontal Distribution of Temperature Effect in Rubberized Concrete Pavement: A Case Study" *Buildings* 13, no. 3: 686.
https://doi.org/10.3390/buildings13030686