# Mechanisms of Tunnel Rockburst Development Under Complex Geostress Conditions in Plateau Regions
## 3 FLAC3D Secondary Development and Validation
### Calculation and Visualization of Tunnel Tangential Stress and the Russense Rockburst Criterion  
The Russense rockburst criterion is a stress-strength ratio-based method for determining the occurrence of rockbursts, which directly reflects the relationship between the tangential stress of the surrounding rock and the rock's strength, indicating the level of rockburst that may occur when the stress reaches a certain proportion of the strength. It is simple to calculate, highly applicable, and has been widely used in tunnel rockburst prediction [16; 19]. Compared to energy-based or other complex criteria, its fundamental principle lies in the recognition that stress conditions are a necessary prerequisite for rockburst. Moreover, the Russenes criterion requires fewer rock parameters, making it more suitable for rapid assessment in engineering practice. Therefore, the Russense criterion was selected in this study as the standard for rockburst risk determination. As a stress-strength index criterion, the Russense criterion allows tunnel-related stress indicators to intuitively reflect the geostress field of the surrounding rock, while the compressive strength of the rock directly indicates the hardness and stability of the tunnel surrounding rock. Both key factors in the stress-strength ratio are important influencing factors for the development and occurrence of rockbursts and have long been favored and widely applied by experts and scholars in the field of rockburst research. The standard of the Russenes criterion is derived from Reference [30], and the specific classification follows Equation (2). \[\left\{ \begin{array}{l}\sigma_{\theta}/\sigma_{\mathrm{c}}<0.2\ (\mathrm{No\ rockburst})\\ \sigma_{\theta}/\sigma_{\mathrm{c}}=0.2\sim 0.3\ (\mathrm{Low\-intensity\ rockburst})\\ \sigma_{\theta}/\sigma_{\mathrm{c}}=0.3\sim 0.55\ (\mathrm{Moderate\-intensity\ rockburst})\\ \sigma_{\theta}/\sigma_{\mathrm{c}}>0.55\ (\mathrm{Severe\ rockburst})\end{array} \right. \tag{2}\]  
where \(\sigma_{\theta}\) represents the tunnel tangential stress, and \(\sigma_{\mathrm{c}}\) denotes the uniaxial compressive strength of the rock. Although the Russenes criterion, based on the ratio of tangential stress to uniaxial compressive strength \(\sigma_{\theta}/\sigma_{c}\), has certain practical applicability, it still exhibits the following limitations:  
1. Neglect of rock type and brittleness differences. The criterion assumes that rockburst will occur once the threshold is exceeded. However, only hard and brittle rocks are prone to rockbursts under high stress, while soft rocks typically undergo plastic deformation. 2. Exclusion of elastic strain energy considerations. The occurrence of rockbursts depends on sufficient energy accumulation; high stress alone is not sufficient to trigger failure. The Russenes criterion fails to reflect this fundamental energy-based mechanism. 3. Lack of structural factors such as rock mass integrity. Factors like freshness of the rock, joint development, and fracturing significantly influence rockburst tendency but are not considered in the criterion. 4. Neglect of temperature and time effects. In high-altitude or deep-buried environments, temperature, excavation rate, and time-dependent behavior can affect rockburst occurrence, which the Russenes criterion does not account for. In FLAC3D, tunnel tangential stress cannot be directly called and must be implemented through secondary development using the FISH language. After each excavation step is completed, all surrounding rock zone elements are traversed to calculate the stresses in the xx, zz, and xz directions for each element, as well as the distance between the element node coordinates and the tunnel axis coordinates. The angular radian between each element and the tunnel axis is then calculated, and the resulting value is substituted into Equation (3) to obtain the tunnel tangential stress. Once the tangential stress is calculated, it is incorporated into the Russense criterion formula, and finally, the Russense criterion contour map is generated.