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In this paper, a simple numerical model is presented for analyzing trapezoidal alluvial valleys subjected to propagating obliquely incident plane SH-waves. As the literature review shows, the scattering effect of transient SH-waves on the surface of trapezoidal alluvial valleys has not yet been directly analyzed in the time-domain by half-plane BEM. In previous researches, the models were limited to the homogeneous single-material subsurface problems. Although in some researches, the mathematical formulation, numerical implementation, and transient analysis of two-dimensional non-homogeneous solids were presented as well, they were established to obtain the time-domain responses by the inverse Fourier/Laplace-transform from a mechanical problem point of view. Additionally, some researchers were used a full-plane time-domain BEM approach to present the time-domain responses for an alluvial valley. But in this study, based on an advanced half-plane time-domain BEM, the surface responses of a linear elastic trapezoidal alluvial valley are obtained due to propagating obliquely incident anti-plane SH-waves. In the use of half-plane time-domain BEM, the meshes are only concentrated around the interface of the basin. First, the problem is decomposed into two parts including a half-plane valley-shaped feature and closed filled alluvium. Then, the influence coefficients of the matrices are obtained by applying the method to each part. Finally, by satisfying the boundary/continuity conditions on the interfaces, a coupled equation is formed to determine unknown boundary values in each time-step. Then, all ground surface responses are also obtained in a secondary solution as internal points. After implementing the method in a general algorithm previously named DASBEM, several practical examples are analyzed to authenticate the obtained results beside prior published responses by other researchers. The main aims of this study are to present some applicable diagrams for use in engineering/operational projects, present a better view of alluvial valleys’ seismic behavior, and reveal the power of the developed algorithm in the analysis of complicated geotechnical problems. Thus, an advanced numerical study is performed to sensitize the surface motion of trapezoidal alluvial valleys with the variable of shape/impedance ratios as synthetic seismograms and three-dimensional (3D) amplification patterns. In the following, to complete the time-domain results, the transient response of the internal domain of the alluvium as well as the surrounding bedrock is shown by the snapshots’ views. Moreover, the sensitivity analysis is carried out to obtain the seismic amplification pattern of the surface by considering the key parameters including impedance and shape ratios, incident wave angle, and response frequency. Lastly, by collecting the maximum amplification of different scenarios and applying linear fit on the obtained values, the responses are summarized as a series of linear equations and tables. The results showed that the mentioned factors are very effective on the seismic response of the surface. The results of the present study can be used to complete the accuracy of existing codes around the subject of near-filed site effects.

Keywords: Alluvial valley, Half-plane BEM, SH-wave, Trapezoidal valley, Time-domain.

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