Issue 29

L. Contrafatto et alii, Frattura ed Integrità Strutturale, 29 (2014) 196-208; DOI: 10.3221/IGF-ESIS.29.17 201 The following symbols enter the theoretical formulas in Table 2: N u pull-out force d 0 hole diameter d anchor diameter  0 uniform bond stress  max maximum bond stress for adhesive anchor h ef anchor embedment length  b modification factor for bond area  c modification factor for concrete strength h cone depth of cone, depending on  0 , d 0 , h ef , f’ as in [2] f’ concrete compressive strength measured with standard cylinders ' 4 G tE   experimentally determined elastic constant that is dependent on shear stiffness G of the adhesive/concrete system , on the axial stiffness E of the threaded rod and on the thickness t of the adhesive layer Theoretical models from 1 to 9 have been applied merely considering the stones material parameters in place of concrete parameters and the anchor embedment length and diameters in previous section. The maximum bond stress  max was taken equal to the tensile strength of the stone (assumed equal to one tenth of compressive strength in Table 1), the uniform bond stress  0 equal to 0.85  max ,  b =  c =1.0. Data in Fig. 7, 8 and 9 show the predictions for fixed stone type, by varying the rod diameter and the embedment length. In the columns labeled N u all the predicted values exceeding the theoretical yield force (equal to 35,3 kN, 69,3 kN and 141,4 kN for steel rods with nominal diameter equal to 10 mm, 14 mm and 20 mm, respectively) are meaningless, because the yielding precedes the mechanism. The corresponding cells in the tables are highlighted. Columns labeled as “error” report the relative error w.r.t. the experimental data. Rows “Experimental” report, on the right of the pull-out force value, the crisis mode, so that it can be compared with the crisis mode defined by each theoretical model. Generally, three main mechanism were experimentally observed: 1) formation of a shallow stone cone with sliding at the stone/resin interface below the cone (Fig. 3(a)); 2) stone cone (Fig. 3(b,c)); 3) yielding of the steel rod (Fig. 2). More details are given in [7]. The only suitable model for basalt anchor results Model 6, combining an elastic bond-stress model with a concrete cone failure model. On the basis of the error value, in the case of limestone and sandstone the suitable model is Model 7 for L=3  and  =10-14 mm. However, it considers the sliding at the resin/stone interface, while the experimental crisis appeared as stone cone. Model 7 is the only adequate for sandstone in the case L=5  ,  =20mm, but no sliding generally appeared in the experimental tests. In the case L=5  and L=10  a uniform trend cannot be recovered for sandstone and limestone. As a general comment, from the analysis of data in Fig. 7-9, it is evident that a single Model able to predict the behavior either for a selected material or for an assigned rod diameter and specific embedment depth, cannot be identified. Moreover, the comparison of the results obtained by means of the application of theoretical models from 1 to 9 and the experimental data shows that the theoretical formulas can be applied to natural stones only if the mechanical characteristics of the stone are quite similar to the ones of a normal concrete for construction, with values of the rupture stress in compression between 20.0-50.0 MPa, as in the case of sandstone. On the contrary, they became useless and meaningless when the breakage of the steel bar precedes the other mechanisms 1-9. In this case the theoretical prediction of the rod rupture value can be considered exact when compared with the experimental one. Figure 7 : Etna basalt. Percentage error on the theoretical pull-out force estimation.