The Earthquake Engineering Online Archive

A mathematical model of masonry for predicting its linear seismic response characteristics

Mengi, Yalçin; McNiven, Hugh D.

UCB/EERC-79/04, Earthquake Engineering Research Center, University of California, Berkeley, 1979-02, 115 pages (515/M39/1979)

This report represents work that is part of a study of the seismic behavior of masonry. The major part of the work is experimental, but this part is devoted to developing a mathematical model for masonry which could be used to derive the elastic stress field in a wall or pier subjected to seismic loads. Because masonry is made of two materials, and because its geometry is so complicated, it is necessary in studying stress fields that could arise to replace the composite material by a homogeneous one. The model material must display the same constitutive characteristics as the prototype and must have the same wave dispersive properties. It is the mathematical model of such a homogeneous material that is developed in this report. The development is made in three steps. In the first, a general theory is constructed for two-phase materials. The second step is to adapt the general theory to a particular geometry. In the third phase, the model is appraised by comparing the responses predicted by the model for a transient input with those observed experimentally. Experimental data permit comparisons of the behavior of dilatational waves travelling both parallel and perpendicular to the layers in plates and semi-infinite bodies. Where possible, comparison is also made with responses predicted by the exact theory. Responses in the model are found using the method of characteristics. Comparison, which is exhibited in a number of figures, shows that the responses predicted by the theory are quite accurate. The accuracy is not restricted to early arrival times but extends to behavior far behind the head of the pulse.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-79-04.pdf (6 MB)