SCIENCE CHINA Technological Sciences, Volume 63 , Issue 5 : 809-818(2020) https://doi.org/10.1007/s11431-019-1441-7

Boundary-effect and scale-heating rate equivalence effect of cracking behavior in the rock models subjected to heating from the central borehole

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  • ReceivedMay 29, 2019
  • AcceptedSep 2, 2019
  • PublishedJan 2, 2020


Thermal cracking is broadly observed in rock engineering. A finite element numerical model which considers the heterogeneity of rock materials and the damage evolution process was used to simulate the thermal cracking behavior of square rock samples heated from the central borehole. The thermal and mechanical behaviors of two cases, i.e., the case with large size but low heating rate and the case with small size but high heating rate were compared to study the crack initiation location in the models with different model sizes and heating rates. The simulated stress and temperature fields, as well as the failure pattern, were in good agreement with the experimental observations. The temperature and thermal stress distribution during the heating process in both cases indicated that high tensile stress was concentrated around the thermal gradient front, which resulted in the cracks initiating at the location with a certain distance away from the borehole. The results show that under the same heating rate, crack initiation location moves outwards with the increment of the model size then remains approximately at one location, which reflects the boundary-effect. Furthermore, the results indicate that the relative crack initiation locations in two cases are nearly the same if the ratio between the heating rate in two cases (T˙x/T˙y) nearly equal to the square of the inverse ratio of corresponding model side lengths ((ay/ax)2). This concept is named the scale-heating rate equivalence effect in this study. It is beneficial for studying thermal cracking of rock both numerically and experimentally since the model size can be significantly decreased.

Funded by

the National Natural Science Foundation of China(Grant,No.,51874065)

and the National Major Scientific Instruments Development Project(Grant,No.,51627804)


This work was supported by the National Natural Science Foundation of China (Grant No. 51874065), and the National Major Scientific Instruments Development Project (Grant No. 51627804).


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