Issue 29

L. Contrafatto et alii, Frattura ed Integrità Strutturale, 29 (2014) 196-208; DOI: 10.3221/IGF-ESIS.29.17 203 one tenth of compressive strength. The mechanical properties of the rocks in Table 1 were used with Poisson ratio equal to 0.25. The parameters characterising the Microplane Concrete Model were accordingly calculated. The steel bar was modelled according to a bilinear constitutive law with hardening (Young Modulus 206000 MPa, yield stress 400 MPa, hardening modulus 100 MPa, Poisson ratio 0.3). The resin was hypothesised as linear elastic with the material properties specified by the manufacturer. The analyses provided a reliable value of the ultimate strength, except in the case of test B-10-3 for which a rod failure was predicted by the numerical simulation, while the effective crisis was characterized by a stone cone mechanism. However, a stiffer behavior of the model affects the simulations of pull-out tests with the lower embedment length L=3  , as it can be seen for instance in Fig. 10 for all the three models. The Microplane Concrete Model was often affected by the loss of convergence well before the peak load. It has been observed that the pathologic behavior of the models, when considering the shorter embedment length L=3  , can be ascribed to the hypothesis of axis-symmetric regime. (a) (b) Figure 10 : Basalt (a) and Limestone (b) predictions for  mm  L=3  . This conclusion was confirmed by two additional simulations of test B-10-3. The first, in plain strain regime, gave the same inaccuracy on the initial stiffness; the second, carried out in plane stress, using for simplicity the Von Mises constitutive model under the hypothesis of elastic-plastic behaviour without hardening, showed the right prediction of the initial stiffness (see Fig. 11). That is, in the case of very short embedment length, a stress state accounting for confinement actions is not adequate in reproducing the physical behavior, in agreement with what observed in [9]. For basalt and limestone the peak load prediction was really accurate for L=5  and L=10  , the crisis being related to the yielding of the steel bar. In this situation the bilinear elastic-plastic criterion of the steel rod rules the problem. Therefore, the error on the solution is very low. For sandstone the stone cone crisis was almost correctly predicted, as well as the pull-out strength and stiffness of the system, as it can be observed in Fig. 12. A uniform trend in the reliability of the numerical prediction was not recovered. The reason can be ascribed to mixed failure mechanisms, due to unpredictable physical and mechanical phenomena arising during the physical cracking process and also caused by imperfect bonding, whose prediction by means of numerical simulation is not feasible. Figure 11 : Von Mises plane stress elastic-plastic simulation of test B-10-3.