A rigid body spring model for the study of rocking motion of masonry walls

Abstract eng:
This paper addresses the numerical modeling of masonry walls as rigid blocks by means of a Rigid Body Spring Model (RBSM). Models based on rigid block assemblies provide a suitable frame work for understanding their dynamic behavior under seismic actions. Therefore, the problem is primarily concerned with Rocking Motion dynamics. In this context, the study of the out-of-plane behavior of unreinforced masonry (URM) walls can be studied as an assemblage of rigid blocks. The pure rocking motion of single rigid bodies can be easily studied with the differential equation of motion which can be solved by numerical integration or by linearization. However, when we deal with sliding and jumping motion of rigid bodies, the mathematical formulation becomes quite complex. In order to overcome this complexity, a Rigid Body Spring Model is proposed for the study of rocking motion of slender rigid bodies, in which the rigid body is considered as a mass element supported by springs and dashpots, in the spirit of deformable contacts between rigid blocks. The RBSM is a semi-discrete model. Therefore, the RBSM can detect separation and sliding of the body. Thus, relative motion between two adjacent elements can occur. However, initial contacts do not change during the analysis and a relative continuity between elements exists, in order to simplify the computational effort. Thus, separation and sliding between the element and its base can occur. Extensive numerical simulations have been carried out. The model here proposed is able to reproduce satisfactorily the rocking, sliding and jumping behavior of the rigid bodies. In the study of top restrained walls the maximum response is a function of the direction of the ground motion. Therefore, the direction of the acceleration should become a new variable in the study of top restrained walls.

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