Earthquake induced ground strains in the presence of strong lateral soil heterogeneities

Transient ground strains are recognized to govern the response of buried elongated structures, such as pipelines and tunnels, under seismic wave propagation. Since a direct measure of ground strains is not generally available, simplified formulas relating peak ground strain to peak ground velocity, and based on 1D wave propagation theory in homogeneous media, are typically used for seismic design. Although they are adopted by most of the available technical guidelines, the use of these formulas may be questionable in complex realistic situations as either in the presence of strong lateral discontinuities, or in the epicentral area of large earthquakes, or in sites where relevant site amplification effects and spatial incoherency of ground motion are expected. To provide a contribution to overcome the previous limitations, a simplified formula relating peak ground longitudinal strain to peak ground velocity is proposed in this paper, as a function of the geometrical and dynamic parameters which have the major influence on strain evaluation. The formula has been obtained under small-strain assumptions, so that it can reasonably be applied under linear or moderately non-linear soil behaviour. The adequacy of this formula in the most common case of vertically propagating S-waves has been checked against 2D numerical solutions by Spectral Elements (SE) for representative geological cross-sections in Parkway Valley (New Zealand) and in the cities of Catania (Italy) and Thessaloniki (Greece). The shear strain and the longitudinal strain variability with depth is also investigated, through some qualitative examples and comparisons with analytical formulas.