A shear response surface for the characterization of unit-mortar interfaces

Shear behaviour of unit-mortar interfaces is typically characterized through the Mohr-Coulomb failure model and shear stress versus shear strain diagrams. In porous stone masonry types such as tuff masonry, dilatancy plays also a key role and shear strength of unit-mortar interfaces at zero confining normal stress is non-zero due to the slip surface’s roughness. To characterize nonlinear shear behaviour for tuff masonry assemblages, direct shear tests were carried out under different pre-compression levels. This paper summarises the experimental program discussing the main results. Empirical formulas are presented to define shear failure at both peak and residual stress levels. Shear deformation capacity, strength degradation, mode II fracture energy, and dilatancy coefficient were computed. Multiple regression analysis was applied to derive a shear response surface including both stress-strain diagrams and the frictional strength model. Constraints on the continuity of both the shear response surface and its first partial derivatives were imposed to nonlinear regression analysis, in order to represent shear softening behaviour in the inelastic range. The surface was defined in a dimensionless space to be used, in principle, for other stone masonry interfaces. This empirical model allows to simulate the shear behaviour over the whole range of allowable strains, and hence the stress-strain diagram at any confining stress level. The experimental results and the proposed empirical models could be employed in both micro-modelling numerical strategies and simplified nonlinear analysis methods based on the macro-element idealisation of masonry walls with openings.