## 3 Parameter Calibration  
In the following, the material parameters of the TI-RDP model are calibrated for _Innsbruck quartz-phyllite_ based on experimental results of triaxial compression tests performed by [PERSON] [51] on specimens sampled from a construction site of the Brenner Base Tunnel. The eccentricity parameter \(e\) in (9) cannot be calibrated by triaxial compression tests. It is assumed as \(e=0.51\) as recommended in [50]. In the experimental study, tests with three different confining pressures \(\sigma_{0}=12.5\) MPa, \(25\) MPa and \(37.5\) MPa and three different directions of axial loading with respect to the inclination of the foliation planes, i.e., \(\beta=0^{\circ}\), \(60^{\circ}\) and \(90^{\circ}\), were carried out. The cylindrical specimens with a height of \(70\,\mathrm{mm}\) and a diameter of \(35\,\mathrm{mm}\) were tested in a displacement controlled manner by monotonically increasing the axial displacement at the top surface of the specimens. For the parameter calibration, a three-dimensional finite element model of the triaxial compression tests is employed. Compared to commonly used single-element tests for this purpose, by the 3D simulations, also the structural effects, such as non-uniform strain distributions associated with the formation of shear bands, are captured. In Figure 4, the geometry and boundary conditions of the finite element model are illustrated. To reduce the number of degrees of freedom, symmetry is exploited. The specimen is discretized by 20-node quadrilateral finite elements with quadratic shape functions, reduced integration and a characteristic element size of \(2.5\,\mathrm{mm}\), resulting in 53,582 degrees of freedom in total. For triggering strain localization, in a small zone at the center of the specimen, elements with slightly reduced values for \(f_{\mathrm{cu}}^{(1)}\) and \(f_{\mathrm{cy}}^{(1)}\) by \(5\%\) are considered, cf. Figure 4.  
The material parameters \(E_{1}\), \(E_{2}\), \(\
u_{12}\), \(\
u_{23}\), \(G_{12}\), \(f_{\mathrm{cu}}^{(1)}\), \(f_{\mathrm{cy}}^{(1)}\), \(m_{0}^{*}\), \(m_{g1}^{*}\), \(A_{\mathrm{h}}\), \(B_{\mathrm{h}}\), \(\gamma\), \(\delta\) and \(H_{\mathrm{h}}\) of the TI-RDP model are calibrated such that a best fit with the experimentally determined deviatoric stress-strain curves is obtained from tests with identical values of \(\sigma_{0}\) and \(\beta\). For this purpose, the sum of nonlinear least-squares is minimized by using the _trust-region constrained algorithm_ available within the framework of the scipy.optimize module [52] of Python. The calibrated material parameters are constrained to positive values, i.e., the lower bounds are set to zero. In addition, \(f_{\mathrm{cu}}^{(1)}\) is restricted to an upper bound of 200 MPa and \(f_{\mathrm{cy}}^{(1)}<f_{\mathrm{cu}}^{(1)}\) is applied as a linear constraint. This way, a unique local minimum could be found within the prescribed physically meaningful range of the material parametersfor _Innsbruck quartz-phyllite_. The _axial strain_ is taken as the top displacement divided by the initial length of the specimens. The hardening parameters \(C_{h}\), \(D_{h}\), and \(G_{h}\), the softening parameters \(A_{s}\) and \(B_{s}\) and the eccentricity parameter \(e\) are chosen as recommended by [PERSON] et al. [50]. The softening modulus \(e_{\mathrm{f}}^{(1)}\) perpendicular to the foliation planes and the internal length parameter \(l\) are chosen such that a characteristic value of the specific mode I fracture energy \(G_{\mathrm{f}}^{(1)}\) for uniaxial tension perpendicular to the foliation planes of \(0.15\,\mathrm{N/mm}\), as suggested by [PERSON] et al. [39], is obtained. The calibrated parameters and the hardening and softening parameters are listed in Table 1.