Nonlinear Dynamic Behavior of Unreinforced Masonry Walls Subjected to Out-of-Plane Loads

An analytical model for the nonlinear dynamic behavior of unreinforced masonry walls subjected to out-of-plane loading is developed. The formulation is based on variational principles, dynamic equilibrium conditions, and the nonlinear constitutive behavior of the materials involved. The model focuses on one-way action through the height of the wall, which is modeled as a structural assembly of masonry units connected by mortar joints. The masonry units and the mortar joints are modeled as first-order shear deformable flexural members with large displacements, moderate rotations, and small strains. The cracking and the nonlinear behavior of the mortar material, the opening and closing of cracks, the rocking phenomenon, and the development of a time-dependent arching force are also considered. A numerical study that examines the capabilities of the proposed model and quantifies some aspects of the dynamic behavior of the masonry wall is presented. It is shown that the dynamic behavior of the wall is a nonperiodic or even chaotic one, which is influenced by the various physically and geometrically nonlinear effects. In particular, the geometrically nonlinear effect of the arching action and the critical influence of the nonlinear-cracking behavior of the mortar or its interfaces on the dynamic behavior of the wall are quantified highlighting the necessity of a nonlinear analysis approach for the assessment of the dynamic response of the wall. A comparison between the theoretical results and experimental results available in the literature reveals the degradation of the natural frequency with the increase of the amplitude of the response and demonstrates the ability of the presented modeling and analysis approaches to quantify the dynamic nonlinear response of the wall