The direct boundary element method: 2D site effects assessment on laterally varying layered media (methodology)

Abstract

The Direct Boundary Element Method (DBEM) is presented to solve the elastodynamic field equations in 2D, and a complete comprehensive implementation is given. The DBEM is a useful approach to obtain reliable numerical estimates of site effects on seismic ground motion due to irregular geological configurations, both of layering and topography.The method is based on the discretization of the classical Somigliana's elastodynamic representation equation which stems from the reciprocity theorem. This equation is given in terms of the Green's function which is the full-space harmonic steady-state fundamental solution. The formulation permits the treatment of viscoelastic media, therefore site models with intrinsic attenuation can be examined. By means of this approach, the calculation of 2D scattering of seismic waves, due to the incidence of P and SV waves on irregular topographical profiles is performed. Sites such as, canyons, mountains and valleys in irregular multilayered media are computed to test the technique. The obtained transfer functions show excellent agreement with already published results.

The use of direct boundary element method for gaining insight into complex seismic site response

“…[25][26][27][28][29][30][31][32]). The main goal of this paragraph is to give an overview of the adaptation of the DBEM to the computation of the local site response in laterally varying stratified media, presented in [7,18].…”

“…Once the boundary dD is discretized into N constant elements-in [7,18] this approach has been validated for site effects assessment, expression (1) yields the following system of equations:…”

“…The DBEM has been applied and validated for the computation of seismic response at 2D site models [7,18], which represent irregular stratified media. The established problem is as follows: given a model of the site, see Fig.…”

“…Refs. [1][2][3][4][5][6][7] are just examples of the vast bibliography devoted to the understanding of seismic site effects. Seismic codes are echoing the importance of site effects by approaching a more detailed quantification of soil effects [8].…”

“…A way of shedding light on the understanding of the site-response phenomena consists in developing high-performance numerical methods for simulations on complex sites. This issue is addressed, in this work, by the application of the Direct Boundary Element Method (DBEM) formulation, presented in [7,18], to a realistic site such as the Volvi Sedimentary Basin (Greece). It is a test-site where the geometry, dynamic properties and stratigraphy are well known.…”