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A coupled thermo-mechanical bond-based peridynamics for simulating thermal cracking in rocks

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Abstract

A coupled thermo-mechanical bond-based peridynamical (TM-BB-PD) method is developed to simulate thermal cracking processes in rocks. The coupled thermo-mechanical model consists of two parts. In the first part, temperature distribution of the system is modeled based on the heat conduction equation. In the second part, the mechanical deformation caused by temperature change is calculated to investigate thermal fracture problems. The multi-rate explicit time integration scheme is proposed to overcome the multi-scale time problem in coupled thermo-mechanical systems. Two benchmark examples, i.e., steady-state heat conduction and transient heat conduction with deformation problem, are performed to illustrate the correctness and accuracy of the proposed coupled numerical method in dealing with thermo-mechanical problems. Moreover, two kinds of numerical convergence for peridynamics, i.e., m- and \(\delta \)-convergences, are tested. The thermal cracking behaviors in rocks are also investigated using the proposed coupled numerical method. The present numerical results are in good agreement with the previous numerical and experimental data. Effects of PD material point distributions and nonlocal ratios on thermal cracking patterns are also studied. It can be found from the numerical results that thermal crack growth paths do not increases with changes of PD material point spacing when the nonlocal ratio is larger than 4. The present numerical results also indicate that thermal crack growth paths are slightly affected by the arrangements of PD material points. Moreover, influences of thermal expansion coefficients and inhomogeneous properties on thermal cracking patterns are investigated, and the corresponding thermal fracture mechanism is analyzed in simulations. Finally, a LdB granite specimen with a borehole in the heated experiment is taken as an application example to examine applicability and usefulness of the proposed numerical method. Numerical results are in good agreement with the previous experimental and numerical results. Meanwhile, it can be found from the numerical results that the coupled TM-BB-PD has the capacity to capture phenomena of temperature jumps across cracks, which cannot be captured in the previous numerical simulations.

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Acknowledgements

Authors would like to thank Dr. Shujun Peng from School of Naval Architecture, Ocean and Civil Engineering in Shanghai Jiao Tong University for helpful discussions. The present work is partially carried out with financial support from the National Natural Science Foundation of China (Grant Nos. 51325903 and 51679017), Natural Basic Research Program 973 of China (Grant No. 2014CB046903).

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  1. State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing, 400045, People’s Republic of China

    Xiaoping Zhou

  2. Institute of Geology and Underground Engineering, School of Civil Engineering, Chongqing University, Chongqing, 400045, People’s Republic of China

    Yunteng Wang, Xiaoping Zhou & Miaomiao Kou

  3. Key Laboratory of New Technology for Construction of Cities in Mountain Area, Chongqing University, Chongqing, 400045, People’s Republic of China

    Yunteng Wang, Xiaoping Zhou & Miaomiao Kou

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Wang, Y., Zhou, X. & Kou, M. A coupled thermo-mechanical bond-based peridynamics for simulating thermal cracking in rocks. Int J Fract 211, 13–42 (2018). https://doi.org/10.1007/s10704-018-0273-z

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