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Geomechanics and Engineering Volume 15, Number 5, August10 2018 , pages 1081-1089 DOI: https://doi.org/10.12989/gae.2018.15.5.1081 |
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Damage constitutive model of brittle rock considering the compaction of crack |
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Qingheng Gu, Jianguo Ning, Yunliang Tan, Xuesheng Liu, Qing Ma and Qiang Xu
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| Abstract | ||
| The deformation and strength of brittle rocks are significantly influenced by the crack closure behavior. The relationship between the strength and deformation of rocks under uniaxial loading is the foundation for design and assessment of such scenarios. The concept of relative crack closure strain was proposed to describe the influence of the crack closure behavior on the deformation and strength of rocks. Considering the crack compaction effect, a new damage constitutive model was developed based on accumulated AE counts. First, a damage variable based on the accumulated AE counts was introduced, and the damage evolution equations for the four types of brittle rocks were then derived. Second, a compaction coefficient was proposed to describe the compaction degree and a correction factor was proposed to correct the error in the effective elastic modulus instead of the elastic modulus of the rock without new damage. Finally, the compaction coefficient and correction factor were used to modify the damage constitutive model obtained using the Lemaitre strain equivalence hypothesis. The fitted results of the models were then compared with the experimental data. The results showed that the uniaxial compressive strength and effective elastic modulus decrease with an increase in the relative crack closure strain. The values of the damage variables increase exponentially with strains. The modified damage constitutive equation can be used to more accurately describe the compressive deformation (particularly the compaction stage) of the four types of brittle rocks, with a coefficient of determination greater than 0.9. | ||
| Key Words | ||
| uniaxial loading; constitutive equation; damage; acoustic emission; compaction coefficient; correction factor | ||
| Address | ||
| Qingheng Gu, Qing Ma and Qiang Xu: School of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao, Shandong 266590, PR China Jianguo Ning, Yunliang Tan and Xuesheng Liu: 1.) Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao, Shandong 266590, PR China 2.) School of Mining and Safety Engineering, Shandong University of Science and Technology, Qingdao, Shandong 266590, PR China | ||