# 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

## References

- Yang, S.; Ceylan, H.; Gopalakrishnan, K.; Kim, S.; Taylor, P.C.; Alhasan, A. Characterization of environmental loads related concrete pavement deflection behavior using Light Detection and Ranging technology. Int. J. Pavement Res. Technol.
**2018**, 11, 470–480. [Google Scholar] [CrossRef] - Qiao, S.; Xiong, Z.; Li, Y.; Ye, Z.; He, S.; Li, L.; Zeng, Y. Mechanical properties of seawater sea-sand concrete exposed to daily temperature variations. Buildings
**2022**, 12, 517. [Google Scholar] [CrossRef] - Ioannides, A.M.; Davis, C.M.; Weber, C.M. Westergaard curling solution reconsidered. Transp. Res. Rec.
**1999**, 1684, 61–70. [Google Scholar] [CrossRef] - Mohamed, A.R.; Hansen, W. Effect of nonlinear temperature gradient on curling stress in concrete pavements. Transp. Res. Rec.
**1997**, 1568, 65–71. [Google Scholar] [CrossRef] - Hiller, J.E.; Roesler, J.R. Simplified nonlinear temperature curling analysis for jointed concrete pavements. J. Transp. Eng.
**2010**, 136, 654–663. [Google Scholar] [CrossRef] - Chen, J.; Wang, H.; Xie, P. Pavement temperature prediction: Theoretical models and critical affecting factors. Appl. Therm. Eng.
**2019**, 158, 113755. [Google Scholar] [CrossRef] - Liao, W.; Zhuang, Y.; Zeng, C.; Deng, W.; Huang, J.; Ma, H. Fiber optic sensors enabled monitoring of thermal curling of concrete pavement slab: Temperature, strain and inclination. Measurement
**2020**, 165, 108203. [Google Scholar] [CrossRef] - Sharifi, N.P.; Mahboub, K.C. Application of a PCM-rich concrete overlay to control thermal induced curling stresses in concrete pavements. Constr. Build. Mater.
**2018**, 183, 502–512. [Google Scholar] [CrossRef] - Nam, B.H.; Yeon, J.H.; Behring, Z. Effect of daily temperature variations on the continuous deflection profiles of airfield jointed concrete pavements. Constr. Build. Mater.
**2014**, 73, 261–270. [Google Scholar] [CrossRef] - Zhou, Y.; Tan, Z.; Liu, S.; Niu, K. Analysis of near-corner stresses in concrete pavement structure. Eng. Mech.
**2010**, 27, 205–211. [Google Scholar] - Shao, J.; Lister, P.J. An automated nowcasting model of road surface temperature and state for winter road maintenance. J. Appl. Meteorol. Climatol.
**1996**, 35, 1352–1361. [Google Scholar] [CrossRef] - AASHTO. Mechanistic-Empirical Pavement Design Guide: A Manual of Practice; AASHTO: Washington, DC, USA, 2008. [Google Scholar]
- Westergaard, H.M. Analysis of stresses in concrete pavements due to variations of temperature. In Highway Research Board Proceedings; National Research Council: Washington, DC, USA, 2 December 1926. [Google Scholar]
- Thomlinson, J. Temperature variations and consequent stresses produced by daily and seasonal temperature cycles in concrete slabs. Concr. Constr. Eng.
**1940**, 36, 298–307. [Google Scholar] - Huang, B.; Shu, X.; Li, G. Laboratory investigation of Portland cement concrete containing recycled asphalt pavements. Cem. Concr. Res.
**2005**, 35, 2008–2013. [Google Scholar] [CrossRef] - Choubane, B.; Tia, M. Nonlinear temperature gradient effect on maximum warping stresses in rigid pavements. Transp. Res. Rec.
**1992**, 1370, 11. [Google Scholar] - Liang, R.Y.; Niu, Y.Z. Temperature and curling stress in concrete pavements: Analytical solutions. J. Transp. Eng.
**1998**, 124, 91–100. [Google Scholar] [CrossRef] - Kim, S.M.; Nam, J.H. Measurements and experimental analysis of temperature variations in Portland cement concrete pavement systems. Road Mater. Pavement Des.
**2010**, 11, 745–771. [Google Scholar] [CrossRef] - Tian, B.; Quan, L.; Niu, K. Structural experiment and theoretical analysis of thermal curling in JPCP with different base types. China J. Highw. Transp.
**2014**, 27, 17–26. [Google Scholar] - Quan, L.; Tian, B.; Chen, L. Experimental Investigation of built-in curling evolution in full scale concrete pavement. J. Highw. Transp. Res. Dev.
**2017**, 34, 1–8. [Google Scholar] - Guo, S.; Dai, Q.; Si, R.; Sun, X.; Lu, C. Evaluation of properties and performance of rubber-modified concrete for recycling of waste scrap tire. J. Clean. Prod.
**2017**, 148, 681–689. [Google Scholar] [CrossRef] - Roychand, R.; Gravina, R.J.; Zhuge, Y.; Ma, X.; Youssf, O.; Mills, J.E. A comprehensive review on the mechanical properties of waste tire rubber concrete. Constr. Build. Mater.
**2020**, 237, 117651. [Google Scholar] [CrossRef] - Mubaraki, M.; Abd-Elhady, A.A.; Sallam, H.E.M. Mixed mode fracture toughness of recycled tire rubber-filled concrete for airfield rigid pavements. Int. J. Pavement Res. Technol.
**2013**, 6, 8–14. [Google Scholar] - Pham, P.N.; Zhuge, Y.; Turatsinze, A.; Toumi, A.; Siddique, R. Application of rubberized cement-based composites in pavements: Suitability and considerations. Constr. Build. Mater.
**2019**, 223, 1182–1195. [Google Scholar] [CrossRef] - Ho, A.C.; Turatsinze, A.; Hameed, R.; Vu, D.C. Effects of rubber aggregates from grinded used tyres on the concrete resistance to cracking. J. Clean. Prod.
**2012**, 23, 209–215. [Google Scholar] [CrossRef] - Sreedhar, S.; Biligiri, K.P. Comprehensive laboratory evaluation of thermophysical properties of pavement materials: Effects on urban heat island. J. Mater. Civ. Eng.
**2016**, 28, 04016026. [Google Scholar] [CrossRef] - Hall, M.R.; Dehdezi, P.K.; Dawson, A.R.; Grenfell, J.; Isola, R. Influence of the thermophysical properties of pavement materials on the evolution of temperature depth profiles in different climatic regions. J. Mater. Civ. Eng.
**2012**, 24, 32–47. [Google Scholar] [CrossRef] - Stempihar, J.J.; Pourshams-Manzouri, T.; Kaloush, K.E.; Rodezno, M.C. Porous asphalt pavement temperature effects for urban heat island analysis. Transp. Res. Rec.
**2012**, 2293, 123–130. [Google Scholar] [CrossRef] - Phelan, P.E.; Kaloush, K.; Miner, M.; Golden, J.; Phelan, B.; Silva III, H.; Taylor, R.A. Urban heat island: Mechanisms, implications, and possible remedies. Annu. Rev. Environ. Resour.
**2015**, 40, 285–307. [Google Scholar] [CrossRef] - Herrero, S.; Mayor, P.; Hernández-Olivares, F. Influence of proportion and particle size gradation of rubber from end-of-life tires on mechanical, thermal and acoustic properties of plaster–rubber mortars. Mater. Des.
**2013**, 47, 633–642. [Google Scholar] [CrossRef][Green Version] - Sukontasukkul, P. Use of crumb rubber to improve thermal and sound properties of pre-cast concrete panel. Constr. Build. Mater.
**2009**, 23, 1084–1092. [Google Scholar] [CrossRef] - Ocholi, A.; Ejeh, S.P.; Yinka, S.M. An investigation into the thermal performance of rubber-concrete. Acad. J. Interdiscip. Stud.
**2014**, 3, 29. [Google Scholar] [CrossRef] - Ferretti, E. Waste tire rubberized concrete plates for airport pavements: Stress and strain profiles in time and space domains. Comput. Mater. Contin.
**2012**, 27, 231–273. [Google Scholar] - Xu, G.; Sun, L.; Pei, Z. Analysis of structural mechanics response of rubber concrete pavement under temperature gradient. J. Inn. Mong. Univ. Sci. Technol.
**2019**, 38, 380–388. [Google Scholar] - Zhou, Z.; Liu, W.; Huang, Y.; Wang, H.; He, J.; Huang, M.; Ou, J. Optical fiber Bragg grating sensor assembly for 3D strain monitoring and its case study in highway pavement. Mech. Syst. Signal Process.
**2012**, 28, 36–49. [Google Scholar] [CrossRef] - Zhao, H.; Wu, C.; Wang, X.; Zheng, Y. Pavement condition monitoring system at shanghai Pudong international airport. In Pavement Materials, Structures, and Performance (GSP 239); ASCE: Reston, VA, USA, 2014; pp. 283–295. [Google Scholar] [CrossRef]
- JTG 3420-2020; Testing Methods of Cement and Concrete for Highway Engineering. China Ministry of Transport: Beijing, China, 2020.
- ASTM C78; Standard Test Method for Flexural Strength of Concrete (Using Simple Beam with Third-Point Loading). ASTM International: West Conshohocken, PA, USA, 2022.
- ASTM C469; Standard Test Method for Static Modulus of Elasticity and Poisson’s Ratio of Concrete in Compression. ASTM International: West Conshohocken, PA, USA, 2022.
- AASHTO T336; Standard Method of Test for Coefficient of Thermal Expansion of Hydraulic Cement Concrete. AASHTO: Washington, DC, USA, 2019.
- Wang, Z.; Zhang, W.; Gao, X.; Liu, H.; Böhlke, T. Stability analysis of soil slopes based on strain information. Acta Geotech.
**2020**, 15, 3121–3134. [Google Scholar] [CrossRef] - Armaghani, J.M.; Larsen, T.J.; Smith, L.L. Temperature response of concrete pavements. In Proceedings of the 66th Annual Meeting of the Transportation Board, Washington, DC, USA, 12 January 1987. [Google Scholar]
- Zhao, H.; Ma, L. Investigation into effects of temperature variations on airport cement pavements based on measured data. J. Tongji Univ. (Nat. Sci.)
**2019**, 47, 1764–1771. [Google Scholar] [CrossRef]

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