Abstract
Seismic disturbances frequently trigger or induce violent strainbursts, threatening regular operations and personnel safety in deep underground excavation. We reproduce the cyclic disturbance-induced strainburst, i.e., the strainburst under combined high static stress and cyclic disturbance conditions in the laboratory using a true triaxial testing system with a relatively low stiffness, where the seismic disturbance is simulated by a low-frequency cyclic load. A damage evolution model that enhances the residual strain method is established to quantify the effects of various factors on the damage evolution of this type of strainburst. The energy budget over the development of the cyclic disturbance-induced strainburst is studied, and its energy criterion and magnitude of the kinetic energy release are also discussed. The damage evolution curve of the cyclic disturbance-induced strainburst is typically inverted S-shaped that is well represented by the inverse logistic function with three stages, i.e., initial stage, constant speed stage, and acceleration stage. It is found that the cyclic disturbance can significantly activate and accelerate rock damage, thus inducing a strainburst. The unique underlying reason is that most of the energy input by the cyclic disturbance is dissipated, which degrades the energy storage capacity and strength of the rock. This energy-based failure mechanism is collectively explained as the ‘rock degradation through energy dissipation’ due to the cyclic disturbance.
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Abbreviations
- \(\alpha ,\,\beta \;{\text{and}}\;\gamma\) :
-
Three factors that control the damage accumulation rates in different stages
- \(c_{s}\) :
-
Velocity of shear stress wave
- \(D\) :
-
Damage variable
- \(D_{0}\) :
-
Initial damage caused by static loading
- \(D_{{\text{C}}}\) :
-
Damage variable of the cyclic disturbance-induced strainburst
- \(\Delta \sigma\) :
-
Amplitude of the cyclic disturbance
- \(\Delta \sigma_{\max }^{{\text{d}}}\) :
-
Dynamic stress increment caused by a shear stress wave
- \(\varepsilon_{r}^{0}\) :
-
Residual strain caused by static loading
- \(\varepsilon_{r}^{n} \;{\text{and}}\;\varepsilon^{n}\) :
-
Residual and total strains after \(n\) cycles, respectively
- \(\varepsilon_{r}^{N} \;{\text{and}}\;\varepsilon^{N}\) :
-
Residual and total strains when a strainburst occurs, respectively
- \(E\) :
-
Young’s modulus of the rock
- \(E^{\prime}_{1}\) :
-
Unloading stiffness of the rock during cyclic disturbance
- \(E^{\prime}_{2}\) :
-
Unloading stiffness of the rock when a strainburst occurs
- \(f\) :
-
Frequency of the cyclic disturbance
- \(\rho\) :
-
Density of the rock
- \(p\) :
-
A parameter relating to cyclic disturbance frequency and amplitude
- \(PGV_{s}\) :
-
Peak ground velocity induced by a seismic event
- \(\sigma_{1} ,\;\sigma_{2} \;{\text{and}}\;\sigma_{3}\) :
-
The maximum, intermediate, and minimum principal stresses in a rock element
- \(\sigma_{x} ,\;\sigma_{y} ,\;{\text{and}}\;\sigma_{z}\) :
-
The intermediate, minimum, and maximum stresses acting on a rock element in potential rockburst volume in three coordinate directions
- \(\sigma_{d}\) :
-
The stress increment caused by seismic disturbance
- \(\sigma_{f}\) :
-
The stress at failure of a cyclic disturbance-induced strainburst
- \(\sigma_{\min }\) :
-
The lower limit stress of the cyclic disturbance
- \(\tau_{xy} ,\;\tau_{yz} \;{\text{and}}\;\tau_{zx}\) :
-
Shear stresses acting on a rock element in potential rockburst volume, respectively
- \(U_{{\text{D}}}\) :
-
Energy input by cyclic disturbance, and \(U_{{\text{D}}} \left( n \right)\) means energy input by cyclic disturbance after \(n\) cycles
- \(U_{{\text{E}}}\) :
-
Elastic strain energy stored in the sample, and there are other forms of \(U_{{\text{E}}} \left( \varepsilon \right)\), \({\kern 1pt} U_{{\text{E}}} \left( n \right){\kern 1pt} {\kern 1pt} {\kern 1pt}\), \(U_{{\text{E}}}^{{{\text{Post}}}}\), and \({\kern 1pt} {\kern 1pt} {\kern 1pt} {\kern 1pt} U_{{\text{E}}}^{{\text{r}}}\) when refers to specific states
- \(U_{{\text{F}}}\) :
-
Work done by the contact force between the machine and rock sample
- \(U_{{\text{K}}}\) :
-
Released kinetic energy of the ejected rock fragments
- \(U_{{\text{M}}}\) :
-
Elastic strain energy released by the experimental system
- \(U_{{\text{P}}}\) :
-
Dissipated energy, and there are other forms of \(U_{{\text{P}}} \left( \varepsilon \right)\), \(U_{{\text{P}}} \left( n \right)\), \({\kern 1pt} U_{{\text{P}}}^{{{\text{Post}}}}\), \(U_{{\text{P}}}^{1}\), and \(U_{{\text{P}}}^{2}\) when refers to specific states
- \(U_{{\text{S}}}\) :
-
Energy input by static loading
- \(U_{{{\text{SD}}}}\) :
-
Energy input by static loading and cyclic disturbance, and there are two other forms of \(U_{{{\text{SD}}}} \left( n \right)\) and \(U_{{{\text{SD}}}}^{{{\text{Post}}}}\)
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Acknowledgements
The authors thank the financial supports from the National Natural Science Foundation (Grant No. 51809033), the National Key Research and Development Plan (Grant No. 2018YFC1505301), and the Fundamental Research Funds for the Central Universities (Grant No. DUT20LK15).
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Hu, L., Li, Y., Liang, X. et al. Rock Damage and Energy Balance of Strainbursts Induced by Low Frequency Seismic Disturbance at High Static Stress. Rock Mech Rock Eng 53, 4857–4872 (2020). https://doi.org/10.1007/s00603-020-02197-x
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DOI: https://doi.org/10.1007/s00603-020-02197-x