## 4 Numerical Simulation of Tunnel Excavation  
The application of the gradient-enhanced transversely isotropic RDP model is demonstrated by predicting the formation of the complex pattern of shear bands due to the excavation of a deep tunnel. To this end, two-dimensional simulations of the excavation of a stretch of the Brenner Base Tunnel, constructed by the drill and blast method, are performed. In a previous publication [12], the respective stretch was already the subject of a mesh study for investigating the capabilities of the gradient-enhanced regularization of the isotropic version of the rock damage-plasticity model ensuring mesh-independent response. Compared to the results of the latter, the impact of different orientations of the principal material directions of foliated rock mass will be demonstrated. The finite element mesh together with the initial and boundary conditions is illustrated in Figure 8. The tunnel profile is characterized by a circular cross section with a diameter of \(8.5\,\mathrm{m}\) and an overburden of \(950\,\mathrm{m}\) at the tunnel axis. To ensure a negligible influence of the boundary conditions (cf. Figure 8 left) on the stress distribution in the vicinity of the tunnel, the considered area of the surrounding rock mass is chosen as \(200\,\mathrm{m}\,\times\,200\,\mathrm{m}\)  
Figure 7: Computedfailure modes for \(\sigma_{0}=12.5\,\mathrm{MPa}\) for the three inclination angles of the foliation planes \(\beta=0^{\circ}\), \(60^{\circ}\) and \(90^{\circ}\) compared to the experimentally determined failure modes according to [PERSON] [51] (Images of experiments reprinted with permission from Ref. [51], 2014, [PERSON]). The model is discretized by 48,980 8-node finite elements with quadratic shape functions and reduced integration, resulting in 589,508 degrees of freedom. For triggering localized behavior, randomly chosen 20% of the elements in the near field of the tunnel cross section are weakened by reducing the uniaxial compressive strength \(f_{\rm cu}^{(1)}\) and the uniaxial yield strength \(f_{\rm cy}^{(1)}\) perpendicular to the foliation planes by 5%. For obtaining a high resolution of the localized shear bands in the vicinity of the tunnel, a finer mesh (cf. Figure 8) with a typical element size of \(\sim\)0.05 m is chosen in this region. Due to the high overburden, a spatially uniform distribution of the geostatic stress state, characterized by the hydrostatic pressure of \(p_{\rm i}^{(0)}=25.5\) MPa is assumed. It is determined from the density of _Innsbruck quartz-phyllite_ of \(2739\,\rm kg/m^{3}\). For the same reason, gravity is not active in the numerical model. For obtaining the most unfavorable excavation conditions, full-face excavation is assumed. At the beginning of the simulation, the initial stress state is represented by applying the hydrostatic pressure as initial stress in the discretized domain and the surface pressure \(p_{\rm i}=p_{\rm i}^{(0)}\) at the excavation boundary as shown in Figure 8 right. The latter is released continuously for modeling the excavation process in the 2D numerical simulation of tunneling. The excavation is completed upon full release of the surface pressure. Failure of the rock mass in the vicinity of the tunnel is indicated, if full release of the surface pressure is not possible in the numerical simulation. Since the focus of this contribution is on the influence of directional-dependent behavior of rock mass on the stress redistribution during the excavation process, supporting measures, such as a shotcrete shell or rock anchors, are neglected. The material parameters for _Innsbruck quartz-phyllite_ are adopted from the calibrated parameters for intact rock as listed in Table 1. For considering the effects of present joints and discontinuities in the rock mass, the geological strength index is set to \(\rm GSI=40\) as reported in [12]. In contrast to Table 1, the internal length parameter is increased to \(l=50\) mm in view of the considerably larger dimensions of the tunnel model.