Transient Response of the Surface by Twin Underground Inclusions Subjected to SH-Waves

In recent decades, the recognition of seismic ground motions and damage investigations in the presence of subsurface heterogeneities including cavities and inclusions during an earthquake have been considered among the seismologists. This issue is more significant for subsurface inclusions because they can change the initial nature of incidence waves and amplification/de-amplification on different zones of the surface. Therefore, evaluating various effective factors including geometry and type of features, site conditions, type of incident waves and paths of wave motion requires appropriate methods for their analysis and detailed understanding. Using these approaches allows modeling the problems of wave scattering and predicting the real seismic responses. Technically, researchers have proposed various approaches for seismic analysis. These methods can be divided into analytical, semi-analytical, experimental, and numerical ones. Despite the high accuracy of analytical methods, their lack of flexibility in the modeling of complex features has forced the researchers to use alternative approaches such as numerical methods. In recent years, increasing the power of computers has helped to solve complex engineering problems using numerical methods. In the use of numerical methods, one can never claim that the obtained results are completely exact; rather, the main purpose is to move toward accurate responses as close as possible. The numerical methods are divided into two general categories known as the domain and boundary methods. The common domain methods include the finite element method (FEM) and finite difference method (FDM). Moreover, the boundary methods are separated into two categories including full-plane and half-plane, in which each part is developed in the transformed and time domains as well. In the use of boundary element methods (BEM), one dimension of the model is reduced and the radiation conditions of waves at infinity are satisfied. The advantages of the BEM compared to the domain approaches are include the concentration of meshes only around the boundary of desired features, the satisfaction of wave radiation conditions in far boundaries, low volume of input data and memory seizure, a significant reduction in analysis time and high accuracy of the results.In this study, step-by-step transient analysis of arbitrarily shaped twin elliptical inclusions are presented subjected to propagating obliquely incident plane SH-waves using the direct half-plane time-domain BEM approach. Based on the sub-structuring process, the model of twin subsurface inclusions was decomposed into a dual pitted half-plane and twin closed filled solids. By determining all the related matrices and applying the continuity conditions of the displacements and tractions at the interfaces, the coupled matrix was achieved to obtain all unknown boundary values. After developing the method to analyze the problem of twin inclusions, it was implemented in the general algorithm previously called DASBEM and its validity was evaluated by some practical examples. The key parameters of the shape ratio of inclusions and incident wave’s angle were considered to sensitize the response behavior. In order to complete the numerical results, some synthetic seismograms and 3D (three-dimensional) blanket amplification patterns were presented to illustrate the time and frequency-domain responses in the presence of twin inclusions. The results clearly demonstrate the significant role of the elliptical twin inclusions on the seismic response of surface and show that the maximum scattering and amplification are achieved in minimum shape ratio for vertical incident waves. It should be noted that the main objectives of the present study are presenting the ability of the proposed method in preparing simple twin inclusions models, transient analysis of complex engineering problems, obtaining high accuracy results, and illustrating a better view of subsurface irregularities interactions in the field of geotechnical earthquake engineering.