Semi-analytical approach for curved masonry pillars reinforced with FRCM

Abstract

The paper presents a semi-analytical approach for the study of the debonding phenomenon of Fiber Reinforced Cementitious Matrix (FRCM) systems externally applied to curved masonry pillars. One of the main features of the approach consists of considering the strengthening system composed by three separated components: external mortar layer, central fiber net and internal mortar layer. These components, assumed subjected to a longitudinal state of stress, interact one each other through tangential stresses developing at the level of zero-thickness interfaces. Regarding the latter, a tri-linear shear stress-slip relationship is assumed to account for a first elastic phase, a second phase exhibiting linear softening and a third phase with a possible non-null residual strength. Since in case of curved substrates, by equilibrium, normal stresses at the interfaces between fiber and matrix arise, which modify the peak tangential resistance and the ductility, a classic Mohr-Coulomb criterion is introduced in the approach. Additionally, the central fiber net progressively transfers along the bond length the force applied at its loaded end by means of an elastic interface interposed between the internal mortar layer and the substrate, the latter assumed rigid and infinitely resistant. The longitudinal equilibrium equations written for the two mortar layers, suitably re-arranged considering the constitutive behavior of the layers, allow to deduce a field problem governed by six first order differential equations into six unknowns. The non-linearity is tackled by means of a recursive elastic numerical algorithm where the elastic modulus of the damaged materials is progressively dropped down, subdividing the bonded length into small portions where the material properties are assumed constant. For each element the solution of the field problem is known in closed form and the only variables to determine are the integration constants coming from the solution of the differential equation system. After a standard assemblage, all constants are derived imposing the boundary conditions at the extremes of the elements, which depend on the state of cracking of the matrix layer. The validation of the proposed approach is carried out with reference to recent experimental tests carried out by the Authors. The obtained results show the reliability of the approach to account for the influence of the curvature of the substrate on the debonding process of FRCM systems.