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Size-dependent Mohr–Coulomb failure criterion

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Abstract

Numerous experimental results show the compressive strength of rock decreases with the increase of rock size. Researchers have developed different empirical failure criteria to correlate the decreasing size effect of compressive strength. For the first time, this research theoretically derived the size-dependent Mohr–Coulomb failure criterion based on the Griffith theory. The failure criterion contains three parameters: the cohesion, the friction angle, and the scaling exponent, which can be determined based on the uniaxial compression test of different-sized specimens and the triaxial compression test of standard-sized specimens. The determined failure criterion can be used to predict the compressive strength of different-sized rocks at different compressive stress conditions. This failure criterion demonstrates that the cracks inside rock cause the size effect, and the crack length distribution affects the size effect. Next, this research developed the bonded-particle model of rock to verify the failure criterion. The rock model consists of matrix and cracks that are modeled by bonded particles and discrete fractures, respectively. The modeling result shows that the strength of matrix model is size independent, and the introduction of cracks causes the size effect of rock model. The parametric analysis verified the influence of crack length distribution on the size effect according to the failure criterion. At last, this research summarized the experimental data of uniaxial and triaxial compressive strength in previous size effect research to check the applicability of the failure criterion. The fitting result shows the failure criterion fits well with the experimental data. Moreover, this research found experimental evidence to support the failure criterion.

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Data Availability

The data that support the findings of this study are available in Zhao (2022).

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Authors and Affiliations

  1. West Virginia University, Morgantown, WV, USA

    Yun Zhao, Qingwen Shi & Gaobo Zhao

  2. The University of Utah, Salt Lake City, UT, USA

    Brijes Mishra

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  1. Yun Zhao
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  2. Brijes Mishra
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  4. Gaobo Zhao
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Correspondence to Yun Zhao.

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Zhao, Y., Mishra, B., Shi, Q. et al. Size-dependent Mohr–Coulomb failure criterion. Bull Eng Geol Environ 82, 218 (2023). https://doi.org/10.1007/s10064-023-03243-y

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