Various software packages are available to conduct one-dimensional (1D) and twodimensional (2D) site response analyses (SRAs). In this article, a finite element program is tested with the purpose of assessing the importance of several aspects on the obtained results and verifying the software. Abaqus (Dassault Systèmes) is compared with the 1D SRA software STRATA (Kottke & Rathje, 2008) for simple 1D models to understand the influence of the boundary conditions; as being a 1D SRA program, STRATA does not require vertical boundary conditions. For Abaqus the subroutine by Nielsen (2006Nielsen ( , 2014 is used to implement free-field boundary conditions.In addition, we test the influence of mesh dimension and Rayleigh damping as well as the importance of buffer-zone width. 2D SRAs with Abaqus and FLAC3D (Itasca Consulting Group, 2012), which is commonly used for geotechnical analyses, are compared as part of the assessment. Similar results are obtained from the two programs but Abaqus is preferred as it is more efficient for linear elastic analyses than FLAC3D, which, on the contrary, performs well for soil presenting strongly non-linear behaviour and effective stress. We demonstrate that reliable results can be achieved, not only for simple uniform sites but also for complex sites with multiple layers and dipping stratigraphy. KeywordsOne-dimensional, two-dimensional, site response analysis, free-field boundary conditions, damping 1.IntroductionAn important part of geotechnical earthquake engineering is the study of the response of the ground under earthquake excitation by means of site response analysis (SRA). Based on the characteristics of the problem studied, several approaches can be used: from one-dimensional (1D) to threedimensional (3D) analyses and from linear-elastic to fully non-linear soil behaviour. 1D linearelastic SRA is often a good starting point for all such studies, even though it is unrealistic in many cases (e.g. when the site is subject to high-amplitude shaking, for which a non-linear analysis would provide more accurate results, and in the case of sedimentary valleys and basins, where 3D effects are pronounced). A complete SRA should include a consideration of the 3D geometry and nonlinear soil behaviour and the consideration of effective stress, which is important, for example, for the study of soil liquefaction. The seismic waves, under these conditions, can generate an increase in the pore water pressure producing a reduction of stiffness and strength of the soil. However, it is not common to perform such analyses, because the more complex a model is, the more input parameters are needed, which means that a full characterization of the site must be available to the engineer. In addition, 3D and non-linear analyses require long computational times, sophisticated software and much experience in conducting the analyses and in interpreting the results.In this work, we test several approaches, but we will limit ourselves to 1D and 2D SRA and to linear-elastic behaviour with viscous damping. A ...

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.