The Equivalent Shear Masonry Model

Abstract

This thesis describes the creation of the Equivalent Shear Masonry Model (ESMM). This is an orthotropic material model for low bond strength masonry that uses a smeared cracking approach. It was developed as an improvement of the Engineering Masonry Model (EMM) and adopts that model’s constitutive relations for the behaviour normal to the bed joints and for the compressive behaviour normal to the head joints. However, the shear failure criterion and the tensile head joint failure options are replaced by a new failure criterion for diagonal staircase cracks that is based on the observation that these cracks often open up horizontally. This failure criterion, the equivalent shear failure criterion, is derived from horizontal force equilibrium and evaluates both the shear stress and the tensile stress normal to the head joints. The combined constitutive relation is based on the Coulomb friction shear behaviour of the bed joints, that consists of linear loading, linear softening and a residual stress plateau. The softening is dictated by both the total shear strain and the total horizontal strain. This thesis first describes the development of this theory and its implementation into a user supplied subroutine for Diana FEA. This code was then verified for a single integration point and compared to the EMM’s Diagonal stair-case cracks option for a selection of load paths, among which combinations of shear and horizontal extension. This verification showed that the ESMM is more stable and provides more probable stress-strain diagrams. Subsequently, the model was validated against a micromodelled masonry unit cell for the same selection of load paths. This validation showed that the ESMM’s stress-strain diagrams are realistic, save some details that could be improved. Finally, the model was validated at a structural level with a macromodelled prediction of shear wall experiments. This validation showed that the ESMM is able to model post-peak behaviour, with both softening and a residual force plateau. The model featured inelastic deformation, hysteresis and even peak force reduction. Compared to the EMM’s Diagonal stair-case cracks option, it had less convergence issues and more realistic crack localisation. Some adjustments to details of the theory and the code are suggested. Also, further validations are required, for more load cases and other applications. Altogether, the Equivalent Shear Masonry Model shows promising characteristics and it is recommended that it is further improved and developed into a convenient, practical material model for low bond strength masonry.