“Unexpected” failure patterns and dynamic collective behaviour of an assembly of buildings subjected to horizontal impact

Abstract Based on a fully-coupled rigorous mathematical approach, we analyse the anti-plane collective behaviour of a group of identical buildings that stand at regular spatial intervals on a linear elastic half-space and are subjected to dynamic horizontal impact load. Each building in this “town” is assumed to consist of an elastic spring that connects a concentrated mass at the top and the rigid foundation at the bottom. We show that, due to the multiple interactions between the buildings through (the waves in) the ground, the eigenfrequencies of the structural group (town) become lower than the resonant frequency of a single building. This shift of eigenfrequencies may be called the “town (or city) effect,” and may give rise to “unexpected” dynamic structural failure patterns at lower frequencies. We summarise some quantitative information about this town effect and suggest its significance by investigating the actual structural failure patterns found on the occasions of the 1976 Friuli, Italy, and 2007 Noto Peninsula, Japan, earthquakes. The elastodynamic collective failure analysis here is different from the conventional ones in engineering seismology where each individual structure is handled separately. The frequency shifts and “unexpected” structural behaviour may be recognised if the mechanical movement of the structural group is analysed jointly. The town effect may be induced by dynamic structural impact in general (e.g., blasting, aircraft impact), and therefore, the simple analytical model handled here may contain the essential features that will be of crucial importance in evaluating more general dynamic performance and safety of structural groups in urban environments.