A constitutive model for rock based on energy dissipation and transformation principles

  • Tianbai ZhouEmail author
  • Yueping Qin
  • Qiufeng Ma
  • Jia Liu
Original Paper


The study on constitutive relations is of great significance to the understanding of the complex mechanical properties and failure criteria of rock. The establishment of a scientific rock constitutive model can provide theoretical support for engineering safety and geological disaster prevention. From the view point of energy, a new rock constitutive model under triaxial compression was developed by connecting the law of energy transformation with the mechanical properties of rock in the paper. First, the concepts of elastic energy conversion rate and elastic energy conversion function were proposed to describe principles of energy dissipation and energy transformation in the whole stress-strain process of rock. And, a mathematical description was made of the work of external force transforming into elastic energy. Second, assumptions were proposed to describe the evolution laws of some important mechanical parameters. Finally, the quasi-static constitutive model for rock under triaxial compression based on conservation of energy was established, combining theories of damage mechanics and thermodynamic, and the fitted results of this constitutive model were compared to experimental data of sandstone under triaxial cyclic loading tests. The rationality of the constitutive model for rock was proved by describing the whole stress-strain process of triaxial compression under different confining pressures. And, the model can describe the initial compaction stage and residual stress of stress-strain curve, which can reflect the nonlinear characteristics of rock.


Energy dissipation and energy transformation Elastic energy conversion rate Law of energy conservation Constitutive model for rock under triaxial compression 


Funding information

The authors gratefully acknowledge the financial support from the project supported by the National Natural Science Foundation of China (Nos. 50174055 and 51274207) and the National Natural Science Foundation for Young Scientists of China (No. 50904071).


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Copyright information

© Saudi Society for Geosciences 2019

Authors and Affiliations

  • Tianbai Zhou
    • 1
    Email author
  • Yueping Qin
    • 1
  • Qiufeng Ma
    • 1
  • Jia Liu
    • 1
  1. 1.College of Resources & Safety EngineeringChina University of Mining & TechnologyBeijingChina

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