# Stability Index of Surrounding Rock during Deep Rock Excavation Considering Energy Release Speed
## 2 Local Energy Release Effectiveness  
### Local Energy Release Rate  
Rockburst is a result of the release of elastic strain energy stored in the rock mass, and its manifestation is rock failure. The strain energy release of brittle hard rock is extensive during the excavation of a deep rock mass. In the construction of hydropower projects in China, most of the rockburst induced by the excavation of a deep rock mass is strain-type rockburst, which is mainly in the form of local deformation or a small mass ejection. Most rockbursts are caused by the change in the stress state of the surrounding rock during excavation, leading to a reduction in the energy storage limit of the rock mass, as well as the accumulation and dissipation of the energy of the surrounding rock. When the energy exceeds the energy storage limit of the rock mass, the rock mass will be destroyed and the strain energy stored in the rock mass will be released. The energy released by the rock failure will lead to the failure of the adjacent rock mass. Furthermore, the failure of the rock mass and the release of energy will cause stress waves, which will become the trigger to break the equilibrium state of the rock mass in the far field. At present, there is insufficient research on the detailed energy release process during rockburst. However, it is widely accepted that energy release is the basic feature of rockburst, and the more energy released by the rock mass, the greater the tendency toward rockburst.  
Based on the above consideration, [PERSON] et al. [8] developed the local energy release rate index and conducted a quantitative analysis of the intensity of rockburst. The index represents the energy released when the strain energy stored in the surrounding rock exceeds the energy storage limit. The strain energy density of the elements before and after the excavation of a rock mass can be obtained via a numerical method. The local energy release rate can be calculated using the change in strain energy density before and after the failure of each element, as shown in Equation (1):  
\[LERR_{i}=U_{\text{imax}}-U_{\text{imin}} \tag{1}\]  
where \(LERR_{i}\) represents the local energy release rate of the element numbered \(i\), \(U_{i\text{max}}\) represents the peak value of elastic strain energy density before the brittle failure of element numbered \(i\), and \(U_{i\text{min}}\) is the residual value of elastic strain energy density after the brittle failure of element numbered \(i\). The elastic strain energy density can be calculated using Equation (2):  
\[Ui=\left[\sigma_{1}^{2}+\sigma_{2}^{2}+\sigma_{3}^{2}-2v(\sigma_{1}\sigma_{2} +\sigma_{2}\sigma_{3}+\sigma_{1}\sigma_{3})\right]/2E_{0} \tag{2}\]  
where \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\) are the major, intermediate, and minor principal stresses; \(v\) is Poisson's ratio; and \(E_{0}\) is the elastic modulus of rock.  
The local energy release rate index takes into account the influence of the stress path on the energy release of surrounding rock during excavation. It can reflect the energy release caused by excavation disturbance under complex stress states to a certain extent and demonstrate the potential intensity of rockburst. However, this index only accounts for the peak and residual values of energy in the energy evolution process of surrounding rock under excavation disturbance, and the detailed evolution process of energy from the peak to the residual value is not considered, that is, it does not consider the influence of the speed of energy release.