This paper deals with the evaluation of seismic site effects due to the local topographical and geotechnical characteristics. The amplification of surface motions is calculated by a numerical method combining finite elements in the near field and boundary elements in the far field (FEM/BEM). The numerical technique is improved by time truncation. In the first part of this article, the accuracy and the relevance of this optimized method are presented. Moreover, parametric studies are done on slopes, ridges and canyons to characterize topographical site effects. The second part deals with sedimentary valleys. The complexity of the combination of geometrical and sedimentary effects is underlined. Extensive parametrical studies are done to discriminate the topographical and geotechnical effects on seismic ground movement amplifications in two-dimensional irregular configurations. Characteristic coefficients are defined to predict the amplifications of horizontal displacements. The accuracy of this quantitative evaluation technique is tested and discussed.
It has often been reported, after destructive earthquakes in mountain areas, that buildings located at the top of cliffs or hills suffer much more intensive damage than those located at the base. For example, the 1968 Tokachi-Oki earthquake in Japan produced considerable damage to buildings close to the edge of a cliff, contrary to buildings located relatively far from the edge. The 1995 Kozani earthquake in Greece brought the evidence of serious damage for villages built on hills. Particularly, high accelerations were recorded at the crest of the Pacoima Dam (around 1.25 g) during the 1971 San Fernando earthquake in California [1]. Experimental studies dealing with topographical effects are also reported in [2] and [3]. A state of the art is also done in [4] and [5].
A considerable amount of theoretical work has been reported in the literature of geotechnics and seismology, in order to model, quantify and predict the effects of the basin topography. As the subject is complex, analytical solutions can only be derived for a very limited number of simple configurations. The exact solutions found by Sanchez-Sesma for triangular wedges are exposed in [6] and [7]. Analytical solutions for semi-circular and semi-elliptical canyons are presented in [8] and [9].
In order to model site effects in more realistic circumstances (for P-SV waves and for an arbitrary shape of topographical feature), numerical methods have to be used. The finite difference method [10], [11] and [12], the finite element method (FEM) [13] and [14], the discrete wavenumber method [15] and [16], and the boundary element method (BEM) [5], [17], [18], [19], [20], [21], [22] and [23] are the most frequently used. Domain-based methods such as the FEM represent excellent tools in analyzing heterogeneity and non-linearity in the soil. However, the size of the problem can easily exceed computing capacities and time because of the difficulty of modelling wave propagation in unbounded domains. In recent years, the BEMs, based on the discretization of integral equations, have gained importance in the resolution of wave propagation problems. These techniques can avoid the introduction of fictitious boundaries and reduce the dimensionality of the problem. In order to benefit from the advantages of both domain- and boundary-based methods, the BEM was coupled with the FEM [24] and the finite difference method [25]. Extension of BEM to unsaturated porous media has been achieved recently in [26] and [27].
In this paper, the two-dimensional wave scattering due to the presence of topographical irregularities is studied with the aid of a hybrid numerical technique, combining finite elements in the near field and boundary elements in the far field. The program used is HYBRID, developed by Gatmiri and his coworkers [24], [28], [29] and [30]. The integration process is approximated in the domain by time truncation [31]. Hence, calculations are performed faster, with a good accuracy compared with traditional boundary integration methods. Several types of topography (slope, canyon or ridge) are considered. The role of some key parameters, such as exciting frequency, depth and shape of the relief, are described and discussed.
Site effects have been studied by means of HYBRID, a hybrid numerical program combining finite elements in the near field and boundary elements in the far field. Integrals in the domain are approximated by time truncation. Precision is controlled by two parameters: a number of time steps give the backtracking limit, and a tolerance coefficient cuts the calculation when the terms become negligible. This numerical technique is fast and accurate. Moreover, artificial waves generated at the truncation points of the model vanish easier if the optimized method is used.
Several parametric studies based on this fast hybrid numerical technique have been used to find out the main characteristics of topographical site effects. In absence of sediment, ground motion is generally amplified at the crest of ridges, at the upper corner of slopes and at the edges of canyons. It is systematically attenuated at the base of these relieves. At a distance depending on the exciting frequency and on the dimensions of the topography, the response of the site approaches that of the half-space. Steep slopes and rectangular shapes make topographical effects more critical. At high exciting frequencies, topographical effects are complex and ground movement amplifications get higher.
The amplification phenomena caused by the presence of a one-dimensional sedimentary layer is well-known. The analysis of the geotechnical contribution to site effects is more complex in two-dimensional configurations. The superposition of the influences of geometry and stratigraphy makes it difficult to identify the more prominent parameters. In the second part of this paper, parametric studies using the same numerical technique are done in order to discriminate site effects due topographical irregularities and site effects due to alluvial filling. A predictive calculation process is also defined in order to evaluate the amplification of surface horizontal displacements in sedimentary valleys.
