Abstract
To investigate the quantification of the extent of damage by considering the energy during rock failure, the pattern of energy dissipation and energy conversion, and the stress–energy mechanism for induced rock failure were analysed under cyclic loading/unloading. Based on damage mechanics, rock mechanics, and energy conservation theory, the test data were analysed. The results showed that the characteristics of hard rock compression are small deformation, high energy, and sudden failure; an elastic–plastic damage constitutive model and a stress–energy–rigidity–damage multi-criteria model for rock failure were established for hard rock. We compared the numerical curves and the experimental curves and found that they coincide. Rock failure is a combination of the results of elastic strain accumulation and dissipation by stress propagation. The key to inducing the energy storage capacity of rock before failure is closely related to the rock damage evolution. The pattern of energy release and dissipation through stress during rock failure was revealed from the perspective of energy using the constitutive model and multi-criteria model established for rock failure; these theoretical studies are very helpful in elucidating the mechanism of rock failure.
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Abbreviations
- \(W\) :
-
The positive work done on the rock samples by the loading system
- \(E_{\text{b}}\) :
-
The absorbed energy
- \(E_{\text{e}}\) :
-
The stored elastic strain energy
- \(E_{\text{p}}\) :
-
The positive work of the plastic deformation
- \(E_{\text{d}}\) :
-
Dissipation energy
- \({\text{d}}D\) :
-
The differential of the damage variable
- \({\text{d}}\varepsilon\) :
-
The differential of the strain
- \(\phi (\varepsilon )\) :
-
The probability distribution function of the strain
- \(\sigma\) :
-
Stress
- \(D\) :
-
Damage variable
- \(E\) :
-
Elastic modulus
- \(\varepsilon\) :
-
Strain
- \(\varepsilon_{\text{max} }\) :
-
Rock strain at the uniaxial compression strength point
- \(m,\alpha\) :
-
Basic parameters of the rock
- \(E_{0}\) :
-
Initial elastic modulus
- \(\dot{\sigma }_{1}\) :
-
Rate of the maximum principal stress
- \(\sigma_{2}\) :
-
Intermediate principal stress
- \(k_{1}\) :
-
Elastic coefficient
- \(\eta_{2}\) :
-
Viscous coefficient
- \(\dot{\varepsilon }\) :
-
Strain rate of model I
- \(\mathop {\dot{\varepsilon }}\nolimits_{{_{1} }}\) :
-
The strain rate in the elastic body of model I
- \(\dot{\varepsilon }_{2}\) :
-
The strain rate in the cohesive body of model I
- \(E_{1}\) :
-
Elastic modulus of part I in Fig. 11
- \(t\) :
-
Time interval
- \(E_{j}^{{(\text{s})}}\) :
-
Static energy
- \(E_{j}^{{({\text{d}})}}\) :
-
Dynamic energy
- \(p_{\text{s}}\) :
-
The vertical component of the static loading
- \(P_{\text{d}}\) :
-
The vertical component of the dynamic loading
- \(f(z)\) :
-
The load of the rock mass
- \(k^{\prime }\) :
-
The rigidity of the roof
- \(f^{\prime } (z)\) :
-
The rigidity of the rock mass
- \(\sigma_{{b{\kern 1pt} \text{min} }}\) :
-
The minimum stress of the rock failure
- \(u\) :
-
The displacement of the rock
- \(D_{\text{c}}\) :
-
The critical value of damage to the rock unit
- \(G_{\text{c}}\) :
-
The critical value of the damage energy dissipation rate of the rock unit
- \(G\) :
-
The energy release rate
- \(\sigma_{\text{c}}\) :
-
The uniaxial compressive strength
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Acknowledgements
This work was jointly supported by the National Natural Science Foundation of China (Grant No. 51574246), the National Key Research and Development Project (No. 2017YFC0804201), the Yue Qi Distinguished Scholar Project, China University of Mining & Technology, Beijing (No. 800015Z1138), and the Fundamental Research Funds for the Central Universities (No. 2011QZ01). We thank Dr. Zefeng Liao and Dr. Changfeng Li for improving the revised manuscript.
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Wang, C., He, B., Hou, X. et al. Stress–Energy Mechanism for Rock Failure Evolution Based on Damage Mechanics in Hard Rock. Rock Mech Rock Eng 53, 1021–1037 (2020). https://doi.org/10.1007/s00603-019-01953-y
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DOI: https://doi.org/10.1007/s00603-019-01953-y