Probabilistic analysis of unreinforced brick masonry walls subjected to horizontal bending

Abstract

Unreinforced masonry walls subjected to out-of-plane horizontal bending can fail by two alternate modes: stepped failure along the brick-mortar bond, or line failure cutting directly through the bricks. Because of random variations in material properties throughout a panel and the tendency for failure to occur across the weaker elements, vertical cracks will generally exhibit a combination of the two modes. This paper develops a pair of analytical methodologies that treat this phenomenon using a stochastic approach. The first part deals with calculating the ultimate moment capacity by allowing for the weakening effect associated with the mixed (stepped and line) mode of failure. This effect is quantified in terms of strength-reduction factors for mean and characteristic (0.05 quantile) values of strength, which may be applied toward generic ultimate strength design. The second part deals with estimating the relative probability of each failure mode and the probability distribution for the relative proportions of each failure mode along a crack. This is of particular relevance to seismic performance because the two failure modes lead to significantly different postcracking behavior.