Environmental Earth Sciences

, 78:650 | Cite as

Research on non-linear characteristics of rock energy evolution under uniaxial cyclic loading and unloading conditions

  • Qingbin Meng
  • Mingwei ZhangEmail author
  • Zhizheng Zhang
  • Lijun Han
  • Hai Pu
Original Article


Most of the existing researches on energy evolution in the process of rock deformation and failure mainly revolve around a specific stage (before or after the peak). However, there are few studies involving the impacts of lithology and loading rate on the energy evolution in the whole process from deformation to failure, especially the studies on non-linear characteristics of rock energy, which is the frontier of study on the mechanism of rock failure. In this context, this study further explores the influencing rule of lithology and loading rate on the energy evolution process of loaded rock. By employing the MTS 815 rock mechanics test system and conducting 18 groups of tests on yellow sandstone, limestone and marble, the research reveals the evolution process and distribution law of elastic energy resilience density along with the stress. Then the micro-mechanism of accumulation and dissipation of rock energy are analyzed. A non-linear evolution model (Logistic equation) is proposed that demonstrates how the energy density of loaded rock changes with axial stress. This model can also explore the bifurcation and chaos characteristics of rock energy evolution, and further reveals the rule that the iterative growth factor of energy density changes with lithology, stress level and loading rate. The results are conducive to deepening the understanding on the differences in engineering characteristics of rocks with different lithologies, and play a guiding role in the prevention and control against dynamic disasters of rocks in the engineering field.


  • Evolution rules of rock elastic and dissipated energy densities were revealed.

  • Microscopic mechanism of rock energy accumulation and dissipation was analyzed.

  • Nonlinear evolution model of rock energy density vs. axial stress was established.

  • Bifurcation and chaos characteristics of the rock energy evolution were analyzed.


Cyclic loading and unloading tests Lithology and loading rate Energy non-linear characteristics Energy evolution and distribution laws Bifurcation and chaos characteristics 



The financial and general support for this research, provided by the Fundamental Research Funds for the Central Universities (No. 2019QNA26), is gratefully acknowledged.


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Copyright information

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

Authors and Affiliations

  1. 1.State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil EngineeringChina University of Mining and TechnologyXuzhouChina

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