A linear mathematical model for the seismic inplane behaviour of brick masonry walls part 1: Theoretical considerations

In this study two mathematical models are presented for the linear dynamic behaviour of masonry walls. The study is completed in three stages: experimental observations, selection of a mathematical model and the determination of model parameters through optimization analysis. In the present paper (Part 1) the theoretical analysis used in the development of the mathematical models is presented. Part 2 is devoted to the optimization analysis. Evaluation of the experimental data, which is described in detail in Part 2, indicates that the first two modal frequencies of the wall specimen are close to each other. This may be attributed, on physical grounds, to strong interaction between the brick and mortar phases of the wall. Accordingly, a two-phase mathematical model, namely a mixture model (MM), is chosen to describe the wall behaviour because it can differentiate between the two phases of the wall and take into account the interaction between them. The equations of MM are put into a discrete form to simplify the optimization analysis. As a special case, MM contains a simple one-phase model called the effective modulus model (EMM). The equations of EMM are also established. Finally, the theoretical complex frequency response functions (CFRF) predicted by MM and EMM are obtained. CFRF relates the top acceleration of the wall to its base acceleration and is the response quantity chosen to be matched in the optimization analysis.