Construction of a mathematical model of the nonlinear, dynamic mechanical properties of unreinforced masonry

Abstract

This presentation reports the results of a study of the construction of a mathematical model for predicting the nonlinear in-plane behavior of clay brick masonry walls when subjected to dynamic excitations. The construction consists of two stages: first the development of the form of the model and then the establishment of the parameter functions appearing in it using experimental data and system identification. In previous work with system identification, it was learned that there are several advantages if the system to be modeled is linear. The optimization is easy and cheap because the iterations minimizing the cost function converge rapidly. Perhaps, even more important is the fact that the transfer function itself is optimized rather than the time response of the model to a particular input, as is the case with nonlinear modeling. Experiments consist of subjecting twin walls of masonry to earthquake excitations on the shaking table at the Earthquake Engineering Research Center (EERC), University of California at Berkeley. The experiments were designed so that the structure was subjected to a series of earthquake inputs of increasing intensity, but so that consecutive intensities differed by a small amount. As a result, the response to an individual excitation, even in the nonlinear material domain (following cracking), is almost linear. It was assumed that the wall would behave isotropically. The subsequent form of the model left two parameter functions to be established, one describes elastic-plastic stresses and depends on strains; the other describes viscous stresses and is a function of strain rates. Experimental data and system identification, using a particular optimization algorithm, showed that both the shear modulus of the masonry and its associated damping factor are bilinear. The experimental time histories of acceleration and displacement were compared with those predicted by the completed model. Even in the highly nonlinear range of material behavior, the two responses were unusually close.