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An Analytical Microcrack-Based Rock Model with Implications for Earthquake Mechanisms Induced by Stress Changes

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Abstract

Shear fracture triggered by subcritical crack extension in intact brittle rocks under long-term compressive loading plays a significant role in the evaluation of earthquake mechanisms. Changes in external loading strongly influence the subcritical crack growth of intact rocks during earthquake nucleation. An important conundrum is how to establish the relationship between shear fracture induced by subcritical crack growth and external loading path in brittle rocks under lithospheric conditions. A novel micromechanical method that introduces shear fracture behavior is proposed to predict the time-dependent shear properties induced by the subcritical cracking of brittle rocks when the initial state of rocks starts from the peak point of the stress–strain curve measured by the conventional triaxial compressive test. This approach is developed on the basis of the wing crack model, subcritical crack growth law, and Mohr–Coulomb strain-softening model. The effect of loading and unloading paths on the evolution of shear properties of rocks under lithospheric conditions is analyzed by drawing a function of historical stress. The corresponding evolution of strain, shear strength, cohesion, and internal friction angle caused by subcritical crack growth under different stress paths is studied. Cohesion and shear strength continuously undergo a weakening process, and the internal friction angle initially undergoes a strengthening and, finally, a weakening process during subcritical crack growth under constant compressive loadings. The effect of the sudden change in axial stress on shear strength is smaller than that of the sudden change in confining pressure. A sudden decrease in confining pressure causes a rapid drop in shear strength, leading to a dramatic rise and drop in the rate of shear strength. Implications for evaluating earthquake mechanisms triggered by stress changes from the evolution of shear properties caused by subcritical crack growth in brittle rocks are also proposed.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51708016), the Key Program for Shaanxi Key Laboratory of Geotechnical and Underground Space Engineering (Grant No. YT201902), the Fundamental Research funds for Beijing Universities (Grant Nos. X19006 and X19013), and the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT-17R06).

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Authors and Affiliations

  1. School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China

    Xiaozhao Li, Chengzhi Qi & Liren Ban

  2. Beijing Advanced Innovation Center for Future Urban Design, Beijing, 100044, China

    Xiaozhao Li, Chengzhi Qi & Liren Ban

  3. Shaanxi Key Laboratory of Geotechnical and Underground Space Engineering, Xi’an University of Architecture and Technology, Xi’an, 710055, Shaanxi, China

    Xiaozhao Li & Zhushan Shao

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  1. Xiaozhao Li
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Correspondence to Xiaozhao Li.

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Li, X., Qi, C., Ban, L. et al. An Analytical Microcrack-Based Rock Model with Implications for Earthquake Mechanisms Induced by Stress Changes. Math Geosci 53, 689–710 (2021). https://doi.org/10.1007/s11004-020-09857-2

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