Engineering Analysis with Boundary Elements 105 (2019) 194–206 Contents lists available at ScienceDirect Engineering Analysis with Boundary Elements journal homepage: www.elsevier.com/locate/enganabound A hybrid time-domain half-plane FE/BE approach for SH-wave scattering of alluvial sites A. Nohegoo-Shahvari a , M. Kamalian b,∗ , M. Panji c a Department of Civil Engineering, Arak Branch, Islamic Azad University, Arak, Iran b Geotechnical Engineering Research Center, International Institute of Earthquake Engineering and Seismology (IIEES), No. 26, Arghavan Street, North Dibajee, Farmanieh, Tehran, Iran c Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran a r t i c l e i n f o Keywords: Site effects Half-plane BEM FEM SH waves Wave scattering and diffraction a b s t r a c t In this paper, a hybrid time-domain half-plane finite element-boundary element method (FEM/BEM) is developed to analyze the arbitrarily shaped alluvial sites subjected to propagating vertically incident plane SH-wave. First, the model is decomposed into two parts, a closed alluvial domain and an open valley-shaped feature as the surrounding medium. The former part is modeled by a conventional FE approach and, a recently proposed half- plane BEM is successfully applied to prepare the model of the latter part. After satisfying the continuity conditions at the interface, the coupled equations are solved step-by-step in FE framework to obtain the unknown values. In the use of the method, the interface of the basin needs to be discretized by BE meshes. Finally, the prepared computer algorithm is validated by solving some practical examples. The results show that the models are very simple and, the formulation has the appropriate accuracy. Furthermore, due to the significant reduction of the boundary elements in the half-plane BEM compared to the full plane BEM, the duration of the analysis and error waves in this formulation decreased. Therefore, the proposed hybrid method can be easily used in the nonlinear analysis of site response and the seismic interaction of soil-structure. 1. Introduction Site effects typically lead to considerable damage on buildings close to topographic features after seismic events. For this reason, numerous methods have been introduced for modeling and quantitative definition of these effects. Among these methods, numerical ones, including volu- metric, boundary, and hybrid methods have gained great attention. In volumetric methods, as the first group of numerical methods, the domain of study area is discrete and the governing boundary conditions such as radiation of waves in the infinite are considered by defining ap- proximate energy absorbing boundaries around the target area [1]. The most well-known volumetric methods are FEM, finite difference method (FDM) and spectral finite element method (SFEM). Many studies have been conducted on the seismic response of topographic features using these methods [2–10]. They are powerful tools to perform dynamic anal- ysis on the finite plastic-elastic domains, however, their accuracy is re- duced in the modeling of the infinite and semi-infinite domain and deal with some limitation; therefore, researchers have tried to use a numer- ical method such as BEM. The BEM methods are basically developed for the purpose of analyz- ing the linear elastic domain, they can provide an opportunity for the ∗ Corresponding author. E-mail addresses: a.nohegoo92@iau-arak.ac.ir (A. Nohegoo-Shahvari), Kamalian@iiees.ac.ir (M. Kamalian), m.panji@iauz.ac.ir (M. Panji). user to evaluate the problem using the geometric boundary meshing of the domain. Providing the automatic radiation conditions of waves in an infinite domain is one of the most important advantages of this method. The BEM has been developed in two domains of time and frequency, but the advantages of combining with other numerical methods and analyz- ing various problems involving time dependent geometries and extract- ing real response values are possible only in time domain BEM. Several researchers have tried to improve the formulation of time-domain BEM and provide displacement and traction of the kernel for solving elasto- dynamic problems inside and outside the plane. Nevertheless, due to applying the Heaviside functions in the extraction of the kernel, the re- sults have been reported in different waveforms by a reduction in the accuracy of the traction kernels [11–15]. To deal with this problem, Is- rail and Banerjee [16,17], without considering of Heaviside functions, presented full plane kernels for antiplane elastodynamics as the most accurate and precise results. Later, Kamalian et al. [18] modified the in-plane kernels and implemented them in the time-domain of the BEM algorithm to analyze seismic geotechnical problems [19–21]. Yu et al. [22] and Soares Jr et al. [23] modified the formulation of BEM in time- domain for out-of-plane elastodynamic problems. Sohrabi‐Bidar et al. [24–26] performed a seismic analysis on 3D topographic features by https://doi.org/10.1016/j.enganabound.2019.04.020 Received 21 December 2018; Received in revised form 22 March 2019; Accepted 22 April 2019 0955-7997/© 2019 Elsevier Ltd. All rights reserved.