Seismic motion in urban sites consisting of blocks in welded contact with a soft layer overlying a hard half-space

We address the problem of the response to a seismic wave of an urban site consisting of N-b blocks overlying a soft layer underlain by a hard substratum. The results of a theoretical analysis, appealing to a space-frequency mode-matching (MM) technique, are compared to those obtained by a space-time finite-element (FE) technique. The two methods are shown to give rise to the same prediction of the seismic response for N-b= 1, 2 and 40 blocks. The mechanism of the interaction between blocks and the ground, as well as that of the mutual interaction between blocks, are studied. It is shown, in the first part of this paper, that the presence of a small number of blocks modifies the seismic disturbance in a manner which evokes qualitatively, but not quantitatively, what was observed during the 1985 Michoacan earthquake in Mexico City. Anomalous earthquake response at a much greater level, in terms of duration, peak and cumulative amplitude of motion, is shown, by a theoretical and numerical analysis in the second part of this paper, to be induced by the presence of a large (>= 10) number of identical equi-spaced blocks that are present in certain districts of many cities.