Issue 29

L. Contrafatto et alii, Frattura ed Integrità Strutturale, 29 (2014) 196-208; DOI: 10.3221/IGF-ESIS.29.17 202 Figure 8 : Floresta limestone. Percentage error on the theoretical pull-out force estimation. Figure 9 : Palagonia sandstone. Percentage error on the theoretical pull-out force estimation. N UMERICAL PREDICTION OF THE PULL - OUT STRENGTH he comparison between the theoretical results obtained by means of the application of concrete models and the experimental data suggests that two way may be covered. The development of new theoretical formulations, whose formulas fit the experimental results, or the prediction of the pull-out strength by means of numerical analysis. The task at hand, beyond the scientific interest due to the possible application of a lot of advanced models to achieve the failure prediction of the rupture mechanism and of the bearing capacity, is especially a practical problem encountered by technicians and engineers. They denounce the lack of information about the necessary embedment depth for the considered materials. Only the suggestion of the resin producer is available and there isn’t any normative recommendation. The design and usage of embedment depth different from the one suggested by the resin producer, that results oversized for those materials having low compressive strength, must be widely justified to the competent authority. For this purpose the engineers usually make use of software for structural analysis, in which only few constitutive model are implemented for modeling brittle materials like rocks. Very often just geotechnical material models are the possible choice, sometimes limited to specific stress states. Three widespread professional software for structural analysis [14-16] were studied to understand the possible way for modeling the experiments. When present, the possible inelastic constitutive models available for the stone behaviour were Drucker Prager and Mohr-Coulomb criteria. No specific capability for modeling the stone-resin and rod-resin interface behavior was found. With the aim of understanding the reliability of these numerical simulations, provided the exact material parameters have been assigned, the experimental tests described in the previous section were numerically reproduced. A first set of simulations was built with the commercial software Adina (version 8.8), because this software implements in addition to Mohr-Coulomb and Drucker-Prager models available in [14-16], the Microplane Concrete model [16]. All the eighty-one experimental tests previously described were numerically reproduced. Thanks to the polar symmetry of the geometrical and mechanical characteristics of the problem, the numerical simulations were carried out under the axis- symmetric stress regime. Therefore, just a 1 radian central angle portion of the system was discretised. Roller supports allowing vertical displacements were entered along the bar axis and roller supports allowing horizontal displacements were entered along the base of the model. The loading condition consisted in the self weight and in imposed vertical displacement at the top end of the steel bar. The friction angle and the cohesion coefficient, entering the Mohr-Coulomb and Drucker-Prager models of the rock, were evaluated in terms of the tensile and compressive strength of the materials. Tensile strength was assumed equal to T