Engineering Analysis with Boundary Elements 84 (2017) 220–230 Contents lists available at ScienceDirect Engineering Analysis with Boundary Elements journal homepage: www.elsevier.com/locate/enganabound Transient SH-wave scattering by the lined tunnels embedded in an elastic half-plane Mehdi Panji ∗ , Bahman Ansari Department of Civil Engineering, Zanjan Branch , Islamic Azad University, Zanjan, Iran a r t i c l e i n f o Keywords: Half-plane BEM Time-domain Single/twin lined tunnels SH-wave Seismic analysis Surface response a b s t r a c t A direct half-plane time-domain boundary element method (BEM) was developed and successfully applied to analyze the transient response of ground surface in the presence of arbitrarily shaped lined tunnels, embedded in a linear elastic half-space, subjected to propagating obliquely incident plane SH-waves. To prepare the model, only the interface and inner boundary of the lining need to be discretized. The problem was decomposed into a pitted half-plane and a closed ring-shaped domain, corresponding to the substructure procedure. After computing the matrices and satisfying the compatibility as well as boundary conditions, the coupled equations were solved to obtain the boundary values. To validate the responses, a practical example was analyzed and compared with those of the published works. The results showed that the model was very simple and the accuracy was favorable. Advanced numerical results were also illustrated for single/twin circular lined tunnels as synthetic seismograms and three-dimensional frequency-domain responses. The method used in this paper is recommended to obtain the transient response of underground structures in combination with other numerical methods. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction According to the extensive development of urban texture and the vi- tal necessity of lifelines, infrastructure and underground openings have found an important role in human societies. A full understanding of the behaviors of underground tunnels including tunnels for transporta- tion, water, and facilities, can assist in presenting an optimum layout. The importance of this issue has increased because of the complex per- formance of the tunnels against seismic loads. The seismic analysis of underground tunnels has been used by the researchers for almost half a century. A complete review up to 1981 can be found in Ariman and Muleski [1] about the methods employed for analyzing the ground with underground tunnels. Apart from experimental and field approaches, solution methods can be divided into three categories: analytical, semi- analytical, and numerical [2]. To analyze the ground response in the presence of unlined and lined tunnel cases, analytical and semi-analytical methods were developed as well. Lee [3], Datta and Shah [4], Lee et al. [5], Tsuar and Chang [6], and Gao et al. [7] investigated the unlined tunnels subjected to seismic waves by analytical approaches. The seismic analysis of a single-phase medium including a lined tunnel was presented in the analytical studies of Lee and Trifunac [8], Balendra et al. [9], Smerzini et al. [10], Zhang et al. [11], Li et al. [12], Min and Bing-Yu [13], Liu et al. [14], Xu et al. [15], and Yi et al. [16]. In the use of analytical procedures, the problem ∗ Corresponding author. E-mail addresses: m.panji@iauz.ac.ir (M. Panji), bahman.ans@chmail.com (B. Ansari). of lined tunnel embedded in a multi-phase medium was explored by Shi et al. [17], Hasheminejad and Kazemirad [18], and Jiang et al. [19]. In this regard, some studies can be found in the literature on modeling the embedded lined tunnels with the help of semi-analytical approaches which include Datta et al. [20], Wong et al. [21], Chin et al. [22], Moore and Guan [23], Manoogian [24], Davis et al. [25], Yeh et al. [26], Liao et al. [27], and Liu et al. [28] in a single-phase medium, and Zhou et al. [29] in a multi-phase medium. According to what is observed in the nature, although the responses of analytical or semi-analytical methods have a high accuracy, various types of arbitrarily shaped topographic features cannot be applied for modeling in reality. It results in the development of numerical methods with a good flexibility. Generally, these methods can be divided into two types of volumetric and boundary methods. Despite the develop- ment of volumetric methods such as finite element method (FEM) or fi- nite difference method (FDM) and their simple formulations, the whole body including the inside and boundaries must be discretized in order to model unlined/lined underground tunnels and topographies (e.g. Be- sharat et al. [30]; Esmaeili et al. [31]; Faccioli et al. [32]; Gelagoti et al. [33]; Huang et al. [34]; Narayan et al. [35]; Rabeti and Baziar [36]; Yiouta-Mitra et al. [37]). As a result, special attention has been paid to the boundary element method (BEM) among the various existing nu- merical methods in the recent three decades. Full reviews of BEM and its application can be respectively found in Beskos [38] and Stamos and Beskos [39] for underground structures. http://dx.doi.org/10.1016/j.enganabound.2017.09.002 Received 18 March 2017; Received in revised form 4 September 2017; Accepted 5 September 2017 0955-7997/© 2017 Elsevier Ltd. All rights reserved.