Explicit approach for the in-plane cyclic behaviors of unreinforced masonry structures using finite particle method

Masonry structures, especially historical ones, are vulnerable to earthquakes. Their structural performance subjected to cyclic loadings such as earthquakes should be fully understood before retrofitting. This study proposes an explicit approach for analysis of the in-plane cyclic behavior of masonry structures, combining the finite particle method and an elaborated mesoscale model. The proposed approach is intrinsically dynamic, and it can deal with both quasi-static and dynamic problems in the same framework. Specifically, kinetic damping and static convergence criteria are incorporated to accelerate quasi-static analysis. In the modeling, the rigid element is proposed for bricks based on rigid-body motion assumption. The zero-thickness interface element for mortar joints is derived, and the plastic behaviors in the tension regime, shear regime, and composite regime are developed. Specifically, the strength softening, residual plastic displacement, and stiffness degradation during cyclic loadings are fully considered. A single-story masonry wall subjected to quasi-static loads is analyzed, and the crack lines and horizontal force - rotation curve agree well with those in the experiment. The behavior of a two-story masonry wall subjected to seismic loads is then investigated, and the crack pattern and the first-order frequencies before and after cracking agree well with those in the shaking table test. The results indicate a decrease of the natural frequencies as well as story stiffnesses due to fracture in the mortar joints.