Development of discrete element method for nonlinear analysis of unreinforced masonry members

One of the oldest and most durable building materials used for a large number of ancient structures by mankind is the masonry material. Few maintenance costs of masonry building, as well as its proper resistance to fire, have caused to be the boost building materials nowadays. Two major modeling approaches for simulating the behavior of masonry members are micro-modeling (heterogeneous model) and macro-modeling (homogeneous model). In the micro-modeling approach, the failure mechanisms and cracking pattern are precisely determined; but because of the required specifications and details, it is considered as a sophisticated modeling approach. In this study, the main purpose is to develop micro-modeling approach based on a discrete element method (i.e. rigid block and spring method) for simulating in-plane behavior of unreinforced brick masonry buildings. For modeling each brick masonry wall in this paper, the masonry unit is defined which is consisted of just one rigid block in the transverse direction and four blocks in the horizontal direction with two different types of springs. This unit represents, in fact, two bricks and connecting mortar in real condition. According to the assumption of the rigid block and spring method, the properties of the normal and shear springs are considered independently. In this situation, it is not practically possible to accurately estimate the behavior of masonry member. In order to model cracking in brick, the two-way crack hypothesis and for subsequent behavior in each masonry unit, the idea of fixed smeared crack approach is implemented in this research. The properties of the normal and shear springs, simulating behavior of the mortar and the brick-mortar interaction, are determined separately by estimating the cracking opening and shear displacement in the crack surface. The Mohr-Coulomb criterion is used to evaluate the behavior of mortar-brick interface. The computational algorithm and developed FORTRAN code are described and validated. Comparison of analytical and experimental results showed that the developed program by introducing the smeared crack approach and the assumed behavioral models of the masonry material is capable of accurately evaluating the nonlinear behavior of masonry structures, along with different failure mechanisms and cracking patterns.