Seismic motion in urban sites consisting of blocks in welded contact with a soft layer overlying a hard half space: II. large and infinite number of identical equispaced blocks - Archive ouverte HAL Access content directly
Journal Articles Geophysical Journal International Year : 2008

## Seismic motion in urban sites consisting of blocks in welded contact with a soft layer overlying a hard half space: II. large and infinite number of identical equispaced blocks

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Armand Wirgin
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Jean-Philippe Groby

#### Abstract

We address the problem of the response to a seismic wave of an urban site consisting of a large and infinite number ($N_{b}$) of identical, equispaced blocks overlying a soft layer underlain by a hard substratum. The results of the theoretical analysis, appealing to a space-frequency mode-matching (MM) technique, are compared to those obtained by a space-time finite element (FE) method. The two methods are shown to give rise to much the same prediction of seismic response for $N_{b}=10$. The MM technique is also applied to the case $N_{b}=\infty$, notably to reveal the structure and natural frequencies of the vibration modes of the urban site. The mechanism of the interaction between blocks and the ground, as well as that of the collective effects of the blocks, are studied. It is shown that the presence of a large number of blocks modifies the seismic disturbance in a manner which evokes, and may partially account for, what was observed during many earthquakes in Mexico City. Disturbances at a much smaller level, induced by a small number of blocks are studied in the companion paper.

### Dates and versions

hal-00110570 , version 1 (30-10-2006)

### Identifiers

• HAL Id : hal-00110570 , version 1
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### Cite

Armand Wirgin, Jean-Philippe Groby. Seismic motion in urban sites consisting of blocks in welded contact with a soft layer overlying a hard half space: II. large and infinite number of identical equispaced blocks. Geophysical Journal International, 2008, 172, pp.725-758. ⟨hal-00110570⟩

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