A stochastic numerical approach on the diagonal shear behavior of brick masonry wallettes fabricated with traditional lime-sand mortar

The mechanical properties of masonry materials have an inherent variability which may be attributed to the type of material (brick and mortar) and workmanship. Therefore, using a stochastic approach to investigate the behavior of Un-Reinforced Masonry (URM) structures provides a more realistic insight about their behavior. In this paper, the diagonal shear behavior of square wallettes constructed with traditional lime-sand mortar and clay bricks is evaluated through a Stochastic Finite Element Analysis (SFEA) combined with Monte Carlo Simulation (MCS). For this purpose, two important mechanical properties of the masonry, including the compressive strength of the masonry prism and the brick-mortar bond strength are considered as the stochastic input variables. To find the appropriate probabilistic distributions for these parameters, extensive material tests (masonry compression test and brick-mortar shear bond cohesion test) were conducted. Furthermore, diagonal shear tests were carried out on masonry wallettes made with the same materials and workmanship. In order to conduct the stochastic analysis, a Finite Element (FE) model based on a simplified micro-modeling approach was developed in software ABAQUS and validated with the results of the diagonal shear tests. Then, the key response parameters of the masonry wallettes including shear stress-drift curve, maximum shear strength, drift capacity, and the failure mechanism, determined through SFEA, are presented. The results demonstrate that the Normal distribution is the best fitted probability of distribution model for the two stochastic input parameters. Also, for two response parameters including drift capacity and maximum shear strength, the best fitted probability distributions are Weibull and Gamma distributions, respectively. Subsequently, according to the acceptance criteria related to the lateral drifts of URM walls corresponding to the collapse performance level provided in the design codes, the probability that the drift capacity of the wallettes exceeds the allowable drift corresponding to collapse performance level is calculated and discussed.