Analysis of the role of diffraction in topographic site effects using boundary element techniques

The role played by the diffraction field on the problem of seismic site effects is studied. For that purpose we solve and analyze simple scattering problems under P and SV in-plane wave assumptions, using two well known direct boundary-element-based numerical methods. After establishing the difference between scattered and diffracted motions, and introducing the concept of artificious and physically based incoming fields, we obtain the amplitude of the Fourier spectra for the diffracted part of the response： this is achieved after establishing the connection between the spatial distribution of the transfer function over the studied simple topographies and the diffracted field. From the numerical simulations it is observed that this diffracted part of the response is responsible for the amplification of the surface ground motions due to the geometric effect. Furthermore, it is also found that the diffraction field sets in a fingerprint of the topographic effect in the total ground motions. These conclusions are further supported by observations in the time-domain in terms of snapshots of the propagation patterns over the complete computational model. In this sense the geometric singularities are clearly identified as sources of diffraction and for the considered range of dimensionless frequencies it is evident that larger amplifications are obtained for the geometries containing a larger number of diffraction sources thus resulting in a stronger topographic effect. The need for closed-form solutions of canonical problems to construct a robust analysis method based on the diffraction field is identified.

A novel simple procedure to consider seismic soil structure interaction effects in 2D models

A method is proposed to estimate the seismic soil-structure-interaction （SSI） effects for use in engineering practice. It is applicable to 2D structures subjected to vertically incident shear waves supported by homogenous half-spaces. The method is attractive since it keeps the simplicity of the spectral approach, overcomes some of the difficulties and inaccuracies of existing classical techniques and yet it considers a physically consistent excitation. This level of simplicity is achieved through a response spectra modification factor that can be applied to the free-field 5%-damped response spectra to yield design spectral ordinates that take into account the scattered motions introduced by the interaction effects. The modification factor is representative of the Transfer Function （TF） between the structural relative displacements and the free- field motion, which is described in terms of its maximum amplitude and associated frequency. Expressions to compute the modification factor by practicing engineers are proposed based upon a parametric study using 576 cases representative of actual structures. The method is tested in 10 cases spanning a wide range of common fundamental vibration periods.