# Evaluation of the Implicit Gradient-Enhanced Regularization of a Damage-Plasticity Rock Model
## 4 Numerical Study
### Modeling of Mode I Failure, Demonstrated by Analyzing Wedge Splitting Tests on Indiana Limestone
The represented dependence of the inclination angle on the level of confining pressure is explained by the curvature of the compressive meridian of the yield surface and of the employed plastic potential function of the RDP model. Modeling of Shear Failure, Demonstrated by Analyzing Triaxial Extension Tests on Innsbruck Quartz Phyllite  
In a third step, the ability of the model for predicting shear failure under confined stress states attaining the tensile meridian of the yield surface is demonstrated. To this end, numerical simulations of triaxial extension tests on specimens with geometric and material properties identical to those of the previously presented triaxial compression tests are performed. Similar to the triaxial compression tests, confining pressures \(p^{(0)}\) of \(0\,\)MPa, \(12.5\,\)MPa, \(25\,\)MPa, and \(37.5\,\)MPa are investigated. The same finite element meshes are employed for investigating the influence of the discretization. In contrast to the triaxial compression tests, subsequent to the application of the initial hydrostatic stress state, generated by the confining pressure, a displacement in positive vertical direction is applied at the top surface of the specimens. Since for triaxial extension tests experimental results are not available, the present study focuses on the assessment of the influence of the finite element mesh on the obtained results and serves as further verification of the gradient-enhanced RDP model. The predicted load-displacement curves are shown in Figure 2:1 While nearly identical results are obtained for the medium mesh and the fine mesh, the load-displacement curves for the coarse mesh are somewhat more ductile. This discrepancy indicates the coarse mesh as insufficiently fine for the accurate resolution of the gradient of the nonlocal field. Compared to the results from the triaxial compression tests, a more brittle structural response is predicted, resulting in strong snapback behavior in the post-peak regime for all three confining pressures and, in particular, for the uniaxial tension test. In contrast to the triaxial compression tests, the structural response becomes increasingly brittle as confining pressure increases, and the peak load decreases gradually. This phenomenon was also observed in experiments on Berea sandstone in [53], and it is characteristic of brittle and quasi-brittle materials. Figure 13 shows the computed deformation of the specimen for an applied axial displacement of \(0.1\,\)mm and a confining pressure of \(37.5\,\)MPa. Compared to the triaxial compression tests, a smaller inclination angle of the shear band is predicted for the medium mesh and the fine mesh, whereas for the coarse mesh a considerably steeper inclination angle of the shear band is obtained. Again, this discrepancy indicates the insufficient representation of the gradient of the nonlocal field by the coarse mesh. Figure 2:2 Triaxial compression tests: distribution of the vertical displacement \(u_{z}\) in the symmetry plane for the four different levels of confining pressure.