Environmental Earth Sciences

, 78:629 | Cite as

Complete stress–strain constitutive model considering crack model of brittle rock

  • Handong Liu
  • Liangdong LiEmail author
  • Shunli Zhao
  • Shaohua Hu
Original Article


The microcrack propagation-coalescence mechanism and stress–strain constitutive model of brittle rock is of great significance for prediction of mechanical properties. To establish a more applicable constitutive model of brittle rock, the crack model based on fracture mechanics was introduced. First, based on the crack slip model and maximum circumferential stress theory, a theoretical equation for crack propagation length was established. The microcrack propagation-coalescence mechanism of brittle rock material under loading was studied. On this basis, a macro-coalescence zone model was proposed. Through the relationship between the deformation characteristics of stress–strain curves at different crack growth stages and the behavior of microcracks, a complete stress–strain constitutive model of brittle rock based on the crack model was theoretically deduced. The constitutive model was verified by the results of a coupling hydro-mechanical test of granite carried out after different heat treatment temperatures. The advanced intelligent algorithm, genetic algorithm, was adopted to simulate experimental data. The research results showed that: (1) The derived stress–strain constitutive model of brittle rock is not only high in accuracy of stress–strain simulation, but also can simulate both the axial and circumferential stress–strain curves. Moreover, the dilatancy and crack initiation stresses can be obtained directly. (2) The parameters of the stress–strain constitutive model not only have clear physical meaning, but the mechanisms of rock mechanical properties, such as dilatancy, acoustic emission, and stress fluctuation, can be explained.


Brittle rock Crack model Propagation-coalescence mechanism Stress–strain constitutive model 



This work was funded by the National Natural Science Foundation of China (Grant no. U1704243).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Handong Liu
    • 1
  • Liangdong Li
    • 1
    Email author
  • Shunli Zhao
    • 2
  • Shaohua Hu
    • 3
  1. 1.College of Geosciences and EngineeringNorth China University of Water Resources and Electric PowerZhengzhouChina
  2. 2.Yellow River Engineering Consulting Co., LtdZhengzhouChina
  3. 3.School of Safety Science and Emergency ManagementWuhan University of TechnologyWuhanChina

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