Probabilistic Models and Fragility Estimates for Unreinforced Masonry Walls Subject to In-Plane Horizontal Forces

Unreinforced masonry (URM) buildings make up a significant portion of the built environment, with hollow clay being the predominant choice for the units. The capacity of URM buildings is a function of the capacity of its walls, both to vertical and horizontal forces. However, URM is particularly vulnerable to the effect of horizontal forces due to the low tensile strength of the mortar that holds the units together. URM walls are subject to significant in-plane horizontal forces during seismic events, so that a proper quantification of the capacity of URM walls to this type of forces is required. The models in design codes are often conservative and do not capture the uncertainties required for estimating the failure probability of URM walls. This paper develops probabilistic capacity models for URM walls with hollow clay units subject to horizontal in-plane forces. The models are developed considering diagonal cracking, flexural/rocking, and sliding failure as possible failure modes. The models are constructed starting from existing physics-based models that attempt to capture the underlying physics, and then developing correction terms that improve the accuracy of the models and remove the inherent bias. Unknown parameters for the proposed models are calibrated using a Bayesian updating approach. The proposed models are probabilistic and capture the relevant uncertainties. The proposed models are used to assess fragility functions of example URM walls subject to horizontal in-plane forces. The comparison of the fragility functions shows the effect of selected variables.