Issue 29

L. Contrafatto et alii, Frattura ed Integrità Strutturale, 29 (2014) 196-208; DOI: 10.3221/IGF-ESIS.29.17 204 Figure 12 : Sandstone failure prediction  mm  and  mm  L=10  . Despite the inaccurate determination of the limit strength, the limit value of the embedment depth, separating the rock failure from the steel failure is correctly identified. Therefore the determination of the necessary embedment length to obtain the road breakage can even be made by using professional software. On the contrary, only appropriate numerical simulations can reproduce the crisis mechanism for each embedment length, provided that the materials properties are correctly identified. Therefore, a second set of simulations was built with two different advanced numerical codes, able to reproduce the complete evolution of the cracking process. The same material parameters utilised in previous simulations were adopted. In the first case the study of the post-critic behaviour of the stone was made by means of a numerical model based on the Strong Discontinuity Approach (SDA) and proposed in [18-20]. Cracks are numerically simulated by a jump in the displacement field, that can be physically identified with the discontinuity surface that arises, for instance, in the failure mechanism previously described with development of a cone in the rock. The opening of cracks is ruled by the bilinear cohesive fracture activation function in Fig. 13, defined by the activation traction of the rock f 0 , the softening moduli H S,1 and H S,2 and the limit crack opening w cr . Interface f 0 =20 MPa H S,1 =-66.6 MPa/mm H S,2 =-6.0 MPa/mm w cr =0.45 mm Bulk E=50000 MPa  =0.2 Steel rod E= 206000 MPa f y =400 MPa  =0.3 Figure 13 : Cohesive fracture criterion. The continuum behaves linearly elastic. The steel rod constitutive model is the elastic- plastic one with yield stress f y . The values of the parameters are given in the picture. The numerical algorithm falls in the context of the Finite Elements with Embedded Discontinuity. It was implemented in the original code FracSDA8 developed in [21]. The model has been applied to the analysis of the post-installed adhesive anchors under investigation. The simulation of test B-10-3, that always gave bad results by using standard software, was performed, under the hypothesis of plane stress. In fact, in the test in question, the embedment depth is equal to 3 times the diameter, i.e. 3 cm. Therefore, the anchoring is so near the surface of the stone block that the confinement characterising axis-symmetric stress states is negligible and the plane stress state hypothesis is admissible [7]. The model accurately predicts the initial activation of the failure, that starts for detachment of the bottom end of the bar, under a preponderant tensile stress state in that area. Then, failure progresses and develops along a shear band, with angle equal about to the friction angle of the stone. The peak load given by the numerical analysis is in good agreement with the experimental one, as it is shown in Fig. 14. In the second case, the simulations were built by using the commercial software Midas FEA [22]. Unlike the previously analysed commercial software [14-16], it implements seven different interface models. Specifically, the bond-slip model was used in the simulations, coupled to a Mohr-Coulomb criterion for the description of the stone behavior. Once again the steel bar was modelled according to a bilinear constitutive law with hardening. The bond-slip constitutive law was used for modeling the behavior at the resin-stone interface, while a perfect adhesion between the resin and the rod was