Issue 47

E. Grande et alii, Frattura ed Integrità Strutturale, 47 (2019) 321-333; DOI: 10.3221/IGF-ESIS.47.24 322 I NTRODUCTION he reinforcement of existing structures has always been a relevant problem both in the technical and scientific civil engineering community. Lately, the study and design of new reinforcement materials is a challenging issue. In particular, fabric reinforced cementitious matrix (FRCM) is an emerging strengthening system obtained embedding a grid of the carbon, glass or aramid reinforcement in an inorganic matrix. In general, the matrix is applied as a double layer incorporating the reinforcement. Nowadays, FRCM systems are used in the current practice to reinforce concrete and masonry structures. Some experimental investigations [1-7] and theoretical/numerical studies ([2, 3, 8-16] on FRCM strengthening systems are available in the recent literature. They testify the efficacy and advantages of FRCM systems together with the need to investigate aspects specifically characterizing the bond behavior of this new family of strengthening systems. The experimental investigations are mainly shear-lap tests that analyze the local bond behavior of FRCMs. From the experimental evidence different failure mechanisms can occur, such as a cohesive failure of the substrate, de-bonding at the reinforcement/substrate interface, de-bonding at the reinforcement/matrix interface, sliding of the reinforcement, tensile failure of the reinforcement in the un-bonded portion and tensile failure of the reinforcement within the mortar. The above mechanism occurrence depends on the characteristics of the strengthening system as well as of the support, such as the mechanical properties of the materials, the thickness of the mortar layers and the configuration of the reinforcement. These mechanisms particularly underline the role of additional phenomena to be necessarily considered for the study and the development of theoretical models/design formulas specific for FRCMs. Regarding the theoretical and numerical studies, the approaches available in literature show particular interest to the derivation of simple laws able to simulate the de-bonding phenomenon and, moreover, models able to account for additional phenomena specific of FRCMs. In [2] the shear stress-slip law at the interface level was obtained throughout a procedure applied to steel and carbon FRCM strengthening systems externally embedded on masonry supports. The procedure was carried out by directly considering the experimental data and in particular the strain gauge measurements. A procedure for the derivation of the shear stress-slip law for FRCMs based on the experimental data was also proposed in [3]. In particular, the authors firstly estimated the fracture energy by using the well-known formula derived by the theory of linear fracture mechanics and, subsequently, they performed numerical FE analyses to detect the optimal values of the parameters of the cohesive shear stress-slip law. In[4] the bond behavior of FRCM-to-concrete was analytically examined by using a general approach applied to the case of FRP-materials. The results emerged from this study particularly emphasized the role of the pronounced descending branch of the calibrated laws in leading to large values of the effective anchorage length. In addition, lower values of bond shear stresses on the concrete surface with respect to those typically characterizing FRP strengthening systems were observed. A similar approach was also presented in [3] for the case of carbon-FRCM materials externally applied on masonry supports. In [13] two approaches for numerically studying the bond behavior of masonry specimens strengthened with FRCMs were proposed. The first one, consisted of an analytical-numerical approach specifically accounting for the interaction between the reinforcement and the mortar; the second approach consisted of a full 3D-FEM non-linear approach obtained as an extension of the procedure originally adopted in [13] and in [15]. A recent study presented in [9,16] was mainly devoted to investigate the influence of the upper mortar layer on the bond behavior of FRCM-strengthening systems applied on structural supports. In particular, the authors carried out a theoretical modeling approach based on the solution of a system of differential equations obtained by introducing equilibrium considerations. From the study emerged interesting aspects concerning the role of the upper mortar layer on the debonding process of FRCMs. Among these, it was observed that increasing the applied load after the occurrence of the de-bonding between the reinforcement and the upper interface it does not lead to further increases of the peak value of normal stresses of the upper mortar. On the other hand, after the occurrence of the first crack at the upper mortar, only the peak value of slips at the lower interface continues to increase whilst the peak value of slips at the upper interface does not significantly increase. In [10] it was proposed a simple approach for the study of the bond behavior of FRCM applied to concrete supports able to enable the use of a common interface modeling strategy by implicitly introducing the effect of the damage of the matrix into the shear behavior of the reinforcement/mortar interface layer. In this paper a one dimensional simple model, based on the one presented in [9] and in [16], is proposed for the study of the bond behavior of FRCM strengthening systems externally applied to masonry substrates. The model is mainly T