## 3 Parameter Design Method of TBM Tunnel ASRBs
### Test Scheme Determination for ASRBs and Method for Evaluating Their Stress Release Effect
#### 3.3.4 Establishment of Test Scheme Indicators  
In the process of simulating the established ASRB arrangement scenarios, it is important to statistically measure the changes to compare the differences in stress release effects under the different test scenarios. This is especially true considering that in deep-buried TBM-constructed tunnels, the mechanical behavior of the rock mass is closely related to various factors, such as ground stress conditions, lithology, tectonics, the excavation method, and the support system. The above factors will ultimately determine the stress state and energy accumulation in the rock mass and create the breeding conditions for rockburst. At the same time, the numerical simulation process should make it easy to quantify the test scheme indicators, so the evaluation indexes used are usually developed in terms of stress and energy. These two test indicators serve two purposes. Firstly, they are used to investigate the effect of stress and energy release under different types of ASRBs. Secondly, they are utilized for the comparative analysis of conclusions. If the two conclusions match, it provides further proof of the reliability of the results. 1. Stress aspect  
From the viewpoint of stress, the change in the maximum principal stress can be taken as the embodiment of the ASRB stress release effect to compare the stress release effect under different ASRB arrangements. Therefore, the average stress release rate calculated by Equations (7) and (8) can be used as an evaluation index of the stress release effect of ASRBs under different schemes. \[\phi^{i}=\frac{\sigma_{before}^{i}-\sigma_{after}^{i}}{\sigma_{before}^{i}} \times 100\% \tag{7}\]  
\[\Phi=\frac{\sum_{i=1}^{n}\phi^{i}}{n} \tag{8}\]  
Within the equations above, \(\phi^{i}\) is the maximum principal stress release rate at the ith measuring point, \(\Phi\) is the average stress release rate at all measuring points, \(\sigma_{before}^{i}\) is the maximum principal stress value of the \(i\)th monitoring point before drilling (unit: Pa), \(\sigma_{after}^{i}\) is the maximum principal stress value of the ith monitoring point after drilling (unit: Pa), and \(n\) is the number of monitoring points. 2. Energy aspect  
From the viewpoint of energy, the unit elastic strain energy (Equation (9)) is used as the index of energy calculation in this study, and the change in elastic strain energy in the monitoring area before and after drilling the ASRBs is used as the embodiment of the ASRB energy dissipation effect. Note that because the calculation of energy is related to the total volume of the elements involved in the calculation, the reason for the large change in the elastic strain energy under a certain arrangement of ASRBs may be the large calculation area of the scheme. To circumvent inconsistencies in the calculation area size across different schemes and prevent errors, Equation (10) normalizes both energy change and volume by dividing them. The average volume release energy can be obtained to compare the release effect of energy under different arrangement schemes. \[\pi^{i}=\frac{\sigma_{1}^{2}+\sigma_{2}^{2}+\sigma_{3}^{2}-2\
u(\sigma_{1} \sigma_{2}+\sigma_{2}\sigma_{3}+\sigma_{1}\sigma_{3})}{2E} \tag{9}\]  
\[\Pi=\frac{\sum_{i=1}^{n}\Bigl{[}\Bigl{(}\pi_{before}^{i}-\pi_{after}^{i}\Bigr{)} \times V_{i}\Bigr{]}}{V} \tag{10}\]Above, \(\pi^{i}\) is the elastic strain energy under the average volume of the ith unit (unit: J/m\({}^{3}\)), \(\Pi\) is the average volume release energy in the energy calculation area (unit: J/m\({}^{3}\)), and \(\sigma_{1}\), \(\sigma_{2}\), and \(\sigma_{3}\) are the maximum principal stress (unit: Pa), intermediate principal stress (unit: Pa) and minimum principal stress (unit: Pa) at the centroid of the element, respectively.