A Methodology to Account for Crushing Effects During Out-of-Plane Collapse of Masonry

Out-of-plane collapse of walls is perhaps one of the most common modes of failure of masonry structures during earthquakes. Depending on the restraint conditions, walls can fail by developing a hinge along their height, thereby resulting in the formation of a two-block out-of-plane collapse mechanism. Equations of motion derived for this mechanism thus far have modelled the cracked wall as a single-degree-of-freedom (SDOF) system made up of two rigid bodies. However, most of these formulations assume that the interfaces between the blocks themselves, as well as between the blocks and the supports, are rigid. Alternatively, equations of motion have also been derived for two-block systems with flexible interfaces, which model the system as having four degrees of freedom, which is considerably more complicated than the SDOF model. Neither of these formulations account for the finite compressive strength of the interfaces, upon the exceedance of which crushing occurs, thus further reducing the dynamic resistance of the structure. This paper presents the derivation of an equation of motion for a cracked wall section taking into account the presence of flexible interfaces as well as crushing effects. Using as a case-study a typical multi-story spanning masonry wall, the importance of considering crushing during out-of-plane collapse is then quantified for a range of interface properties and loading conditions.