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A 75 m long experimental arch with a 1.6 m diameter was constructed in Tibet for a one-year test to determine the most unfavourable vertical temperature difference for a single pipe in the main arch of a concrete-filled steel tube arch bridge. Actual temperature observation data were used to analyse the vertical temperature difference in the single circular pipe arch rib using statistical methods. The standard value for the vertical temperature difference in the single pipe under a return period of 50 years was calculated. The results showed that the influence range of the vertical gradient temperature was 25 cm. The vertical temperature difference followed a lognormal distribution, and the standard values of the positive temperature difference at the upper and lower ends of the single pipe were 16 and 10°C, respectively; the standard values of the negative temperature difference at the upper and lower ends of the single pipe were both -8°C under a return period of 50 years. These results are considerably different from the values specified in the current Chinese code. These could serve as references for calculations involving arch bridges in Tibet with single circular pipes in the main arches.

Advancements in the construction technology of concrete-filled steel tube (CFST) arch bridges support their economic advantages over a certain period [

The bridge temperature problem has been studied extensively and results are reported. Some scholars have studied the gradient temperature difference in steel box girders. Wang et al. [

Some experts have studied the gradient temperature difference in concrete box girders. Leanne et al. [

Most of the above-mentioned studies focused on the vertical and horizontal temperature differences in box girders, and there is no systematic study on the gradient temperature difference in the main arch rib of a CFST arch bridge. Further, most research methods employed the extreme temperature differences obtained experimentally or through simulations and compared them with the corresponding specifications, and only some of them employed probability-statistical methods. Therefore, this study aimed to determine the temperature gradient in a single circular pipe of a CFST arch bridge on the Tibet Plateau in China. Long-term temperature observation tests using a large test arch will be performed; based on the large volumes of test data, we expect that probability-statistical analysis methods would help obtain the temperature difference estimates that satisfy the probability-statistical theory. This is the first study of its kind to study the temperature gradient in a CFST arch bridge with a single circular pipe main arch in a plateau area using probability-statistical methods. The findings of this study can serve as references for determining the temperature difference values of CFST arch bridges in Tibet, China.

A large experimental arch was built in the Shannan area of Tibet. The axial shape of the test arch was similar to the flat setting of the arch crown in the real bridge. The test arch was 75 m long and 11.25 m high; the diameter of the steel pipe was 1.6 m, and the wall thickness was 20 mm. The material used for the steel tube was Q235, and the concrete design grade was C60. The concrete mix proportions are listed in Table

Mix proportions of test concrete (kg/m^{3}).

Materials | Dosage |
---|---|

Cement | 400 |

Water | 157 |

Fly ash | 45 |

Expansion agent | 50 |

Mineral powder | 25 |

Silica powder | 10 |

Sand | 711 |

Stone | 1052 |

Water reducer | 10.60 |

Dimensions of test arch (mm).

Layout of measuring points in section A-A (mm).

Actual photograph of test arch.

A thermistor-type thermometer was used, and it was bound with a cross-fixed high-strength insulated steel wire rope. A wireless acquisition system was selected for automatic data acquisition at intervals of 10 min. Concrete was poured into the test arch in June 2018. The test period was from June 2018 to June 2019. The temperature sensor and acquisition instrument are shown in Figure

(a) Temperature sensor and (b) wireless data acquisition instrument.

Owing to the influence of sunshine, the temperature field in the main arch section of the CFST arch bridge presents a nonlinear temperature distribution. When the main arch is exposed to sunlight, the temperature at the edge of the main arch section is high and that at the centre is low. Therefore, a temperature gradient occurs in the main arch section.

The vertical temperature gradient curve for a single pipe main arch specified in Chinese code [

Gradient temperature difference curve as per the Chinese code.

Temperature differences _{1} and _{2} specified in the Chinese code (°C).

Steel pipe surface coating | Single pipe main arch | |
---|---|---|

Dark (red, grey) | 12 | 6 |

Light (white, silver, etc.) | 8 | 6 |

A previous study [

We have the following assumptions for theoretical calculations: (1) The diameter of the CFST is infinite. (2) The ambient temperature changes as

To determine the internal temperature of concrete with depth

The boundary conditions are as follows:

Without considering the effect of the initial temperature, the solutions satisfying the above conditions are as follows:

According to formulae (

Formula (

To verify the accuracy of temperature difference influence range, relevant data from the measuring points in the test arch were statistically analysed. The temperature data from vertical measuring points 1, 2, 4, 6, and 7 were selected for the analysis, and these data are presented in Figure

Temperature data obtained from measuring points. (a) Summer, (b) winter, (c) one day in summer, and (d) one day in winter.

Cluster analysis results of temperature data from measuring points.

Statistical analysis results of temperature data (°C).

Measuring point | Summer | Winter | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 4 | 6 | 7 | 1 | 2 | 4 | 6 | 7 | |

Average | 19.4 | 20.6 | 19.5 | 18.3 | 19.0 | 3.0 | 2.4 | 3.0 | 1.7 | 2.5 |

Median | 18.2 | 20.7 | 19.7 | 18.4 | 18.4 | 2.5 | 3.2 | 2.4 | 1.2 | 2.4 |

Variance | 21.0 | 3.7 | 3.0 | 3.1 | 18.7 | 21.3 | 5.8 | 5.4 | 5.2 | 14.1 |

Minimum | 12.0 | 16.3 | 15.9 | 14.4 | 10.1 | −6.2 | −0.5 | −0.9 | −2.6 | −5.5 |

Maximum | 36.3 | 24.7 | 24.2 | 22.2 | 32.4 | 17.3 | 9.2 | 8.0 | 7.2 | 14.0 |

On comparing the temperature change curves corresponding to measuring points 2, 4, and 6, we found that the change trends for the three curves were similar in summer and in winter, and the temperature differences were small. The change ranges observed for the curves corresponding to measuring points 1 and 7 were obviously different from those corresponding to measuring points 2, 4, and 6.

As observed in Figure

On comparing the statistical data of each measuring point presented in Table

According to the results obtained from the temperature change curves, cluster analysis, and statistical analysis for the data at each measuring point, the temperature changes at measuring points 2, 4, and 6 were the same, and the vertical gradient temperature difference in the section was considered as the temperature difference between measuring points 1 and 2 and that between measuring points 6 and 7. Theoretical calculations and experimental temperature data analysis indicated that the influence range of the gradient temperature difference was 25 cm. When the influence range of gradient temperature difference is small, it is considered that the temperature changes rapidly in a small range, which has a great influence on the structure. So the smaller influence range of gradient temperature difference was safe for design calculation.

According to the Chinese code, the influence range of the gradient temperature in the test should be 40 cm, which is obviously different from the value obtained in the test. Moreover, the Chinese code is not applicable in this case. The maximum influence range of the gradient temperature difference in the single pipe was 0.25 m. When the diameter of steel pipe was greater than 0.5 m, the influence range of gradient temperature was 0.25 m; when the diameter of the steel pipe was less than 0.5 m, the influence range of gradient temperature was equal to the pipe radius.

To obtain the characteristic values of the temperature gradients in a single pipe, the measured temperature fields in the test arch under sunlight were analysed statistically. The temperature difference data for measuring points 1 and 2 (corresponding to

The temperature differences were obtained by comparing different probability density functions, and a lognormal distribution function was selected to fit the gradient temperature differences. The lognormal distribution function is expressed as

Figure

Estimated parameters of probability density statistical model.

Season | Temperature difference type | Estimation of the probability density parameters of the gradient temperature differences in the cross section of a single circular pipe | |||||
---|---|---|---|---|---|---|---|

Similarity | |||||||

Summer | 0.007 | 0.789 | 9 | 8.316 | 0.350 | 0.927 | |

0.0003 | 1.012 | 10 | 7.900 | 0.458 | 0.973 | ||

Winter | −0.0024 | 1.120 | 8 | 6.895 | 0.701 | 0.970 | |

−0.006 | 1.191 | 5 | 5.912 | 0.657 | 0.940 |

The method for calculating the standard values is not specified in the Chinese code [

Using formulae (

Standard values of gradient temperature differences in single tube (°C).

Season | Summer | Winter | Code | |||
---|---|---|---|---|---|---|

Temperature difference types | ||||||

Standard values of temperature differences | 16 | 10 | 10 | 8 | 12 | 6 |

On comparing the statistical analysis results with the standard values, it was found that the calculated standard value was 4°C higher than the standard value in Chinese standard. Based on the experimental and statistical analysis results and considering the low data count for the temperature sample and the influence of error, 16°C and 10°C were, respectively, considered the upper and lower gradient temperature differences.

The obtained values of the gradient temperature differences in single pipes and those specified in the Chinese code are all positive temperature gradients; that is, the analysis was conducted under conditions with a high external temperature and low internal temperature of main arch section. Therefore, Figures _{1} and _{2}, are negative. There are limited results and specifications available to quantitatively analyse the negative temperature gradient of single pipes. Therefore, in this study, the negative temperature gradient of the single tube was analysed based on the standards specified in the Chinese code and gradient curve, given in Table

Moreover, considering that the exceedance probability is 2%, the formula for calculating the exceedance probability of the negative gradient temperature difference is as follows:

Using formulae (

Standard values of negative gradient temperature differences in single tube (°C).

Season | Summer | Winter | ||
---|---|---|---|---|

Temperature difference type | ||||

Standard values of negative temperature differences | −8 | −7 | −7 | −4 |

Comparing the data in Tables _{1} and _{2} were close. To simplify the analysis when studying the influence of the negative gradient temperature difference on the bridge structure, both the negative gradient temperature differences, _{1} and _{2}, were set to −8°C.

In this study, a long-term continuous temperature observation experiment involving a large-scale test arch was conducted in Tibet. Large volumes of test data were statistically analysed to verify the influence range of the gradient temperature difference in a single circular pipe. The probability distribution function form of the gradient temperature difference was obtained in addition to the standard values of the temperature differences corresponding to a 50-year return period. The findings of this study can serve as references for determining the temperature load parameter values using the Chinese bridge design codes. The following conclusions can be drawn from the study:

The maximum influence range of the gradient temperature difference in a single pipe was 0.25 m. When the diameter of the steel pipe was greater than 0.5 m, the influence range of gradient temperature was 0.25 m; when the diameter was less than 0.5 m, the influence range of the gradient temperature was equal to the pipe radius.

The vertical temperature difference in the single pipe of the bridge in Tibet followed a lognormal distribution.

The vertical gradient temperature differences of the single pipe (positive _{1} = 16°C and _{2} = 10°C; negative _{1} = _{2} = −8°C) were obtained from the lognormal distribution function, for which the return period was 50 years.

These results are considerably different from the standards specified in the Chinese bridge design codes. Therefore, the gradient temperature differences calculated in this study must be used for the calculations involving arch bridges in Tibet with single circular pipes in the main arches.

The period of this study was only one year, and there were not enough temperature samples. We intend to conduct another study with more temperature samples spanning several years. Furthermore, as there are some differences between the test arch and actual CFST arch bridge, a long-term real bridge test is necessary to verify the results of this test.

The data used to support the findings of this study are included within the Supplementary Materials files.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This research was funded by the National Natural Science Foundation of China (Grants nos. 51738004, 51868006, and 51878186), by the Major Science and Technology Foundation of Guangxi (Grant no. AA18118029), and by Project of Science and Technology Research and Development Plan of China Railway Corporation (2017G006-B).

Supplementary Figures 8 and 9: single pipe gradient temperature difference analysis.