An accessible approach for the site response analysis of quasi-horizontal layered deposits

This study focusses on site response analysis for sites that are neither strictly one-dimensional (with flat parallel soil layers) nor clearly two-dimensional (steep valleys, canyons and basins). Both these types of geometries are well studied in the literature. There is a lack of studies, however, for all those geometries that are in between these two worlds, such as sites with gently dipping layers. Theoretically, such sites should be studied with a two-dimensional dynamic approach because of the formation of surface waves due to the non-horizontal layering. In certain situations, however, the one-dimensional dynamic assumption leads to minor errors and it may save a lot of effort in terms of defining a two-dimensional model, computing the response and interpreting the results. As a result of these practical advantages, an accessible approach is presented here to determine when one-dimensional analysis can be used for geometries consisting of quasi-horizontal layers. The methodology is based on the construction of a chart, delimiting the applicability of the one-dimensional approach, using simple but valid variables, such as the slope of the critical subsurface interface and the impedance contrast at this interface. Indeed, we propose our guidance on the limits of the one-dimensional analysis in the form of this power law separating the one-dimensional and two-dimensional dynamic regimes: I _z = 6.95 γ ^−0.69 , where I _z is the impedance contrast and γ is the angle in degrees of the sloping critical subsurface interface. Site response analysis for geometries with values of I _z below this critical value can be computed using a standard one-dimensional approach without large error whereas geometries with values of I _z above this threshold require two-dimensional calculations.