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A theoretical derivation of the dilatancy equation for brittle rocks based on Maxwell model

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Abstract

In this paper, the micro-cracks in the brittle rocks are assumed to be penny shaped and evenly distributed; the damage and dilatancy of the brittle rocks is attributed to the growth and expansion of numerous micro-cracks under the local tensile stress. A single crack’s behaviour under the local tensile stress is generalized to all cracks based on the distributed damage mechanics. The relationship between the local tensile stress and the external loading is derived based on the Maxwell model. The damage factor corresponding to the external loading is represented using the p–alpha (p–α) model. A dilatancy equation that can build up a link between the external loading and the rock dilatancy is established. A test of dilatancy of a brittle rock under triaxial compression is conducted; the comparison between experimental results and our theoretical results shows good consistency.

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Acknowledgements

The authors would like to acknowledge the financial support from the National Basic Research Program of China (973 Program, No. 2013CB036005) and the National Natural Science Foundation of China (Grant No. 51527810, No. 51679249, No. 51309233), which is greatly appreciated by the authors.

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Authors and Affiliations

  1. State Key Laboratory of Disaster Prevention and Mitigation of Explosion and Impact, PLA University of Science and Technology, Nanjing, China

    Jie Li, Houxu Huang & Mingyang Wang

  2. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, China

    Jie Li & Mingyang Wang

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  1. Jie Li
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  2. Houxu Huang
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  3. Mingyang Wang
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Correspondence to Jie Li.

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Li, J., Huang, H. & Wang, M. A theoretical derivation of the dilatancy equation for brittle rocks based on Maxwell model. Acta Geophys. 65, 55–64 (2017). https://doi.org/10.1007/s11600-017-0006-0

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