Simplified analytical models for partially grouted reinforced masonry shear walls

Abstract

Partially grouted (PG) masonry shear walls have commonly been used for construction in seismic regions. However, predicting their behaviour is quite complicated due to the non-uniformity presented by the materials’ variety. In this paper, an extensive analytical study was carried out to establish simplified backbone models referred here as “analytical models” as a first attempt in the literature to simulate PG masonry walls’ behaviour. A nonlinear finite element model was developed and validated against several experimental specimens from the literature. The numerical model was then utilized to compensate for the lack of experimental data by generating a comprehensive matrix of 196 numerical models covering a wide range of design and detailing parameters. These parameters include the aspect ratio, the spacing between vertical and horizontal grouted cells, the axial load, the ratio of vertical and horizontal reinforcement, and the compressive strength of grouted and ungrouted masonry units. Subsequently, three penta-linear load–displacement backbone models were proposed using linear regression analysis. Five secant stiffness expressions, namely: cracking, yielding, ultimate, 20% strength reduction, and 40% strength reduction, were derived to define the backbone curve of each wall category. Consequently, the proposed analytical models were examined against samples from the numerical matrix and the experimental specimens, which were not considered in the calibration of the analytical models. The results showed that the proposed analytical models provide good predictions of the response of PG masonry walls. Finally, the stiffness reduction factor provided by CSA S304-14 for masonry, α, was updated by developing three new coefficients for the PG walls’ categories based on regression analyses between the numerical stiffnesses at yielding and their corresponding values calculated using α.