Amplification Pattern of Seismic Ground Surface in the Presence of Underground Horseshoe Tunnel Subjected to Incident SH-Wave

Throughout history, earthquake mitigation has always been of vital importance for the humans. Nowadays, by growing technology and computer sciences, several approaches including empirical, analytical and numerical methods are developed and used by researchers to attempt for reducing some possible damages of this phenomenon. Although the responses of analytical methods have high accuracy, various types of arbitrarily shaped topographic features cannot be applied for modeling in reality. It results in the development of numerical methods which have good flexibility. Technically speaking, numerical methods were generally divided into two types, volumetric and boundary methods. Although volumetric methods have advantages such as high accuracy, simple formulation and wide covering range of problems, they have high computations and complex models in the problems with infinite and semi-infinite boundaries. Thus, the field is prepared for the presence of boundary approaches such as Boundary Element Method (BEM). In this method, only the boundaries of the media need to be discretized in order to analyze an elastic continuous media. Considering the automatic satisfaction of the wave’s radiation conditions in the formulation, it is an appropriate method for dynamic analysis.
Two BEM formulations have been proposed to be used in modeling, including full-plane and half-plane. In this paper, the half-plane time-domain BEM was applied to obtain the amplification pattern of the homogeneous ground surface in the presence of unlined horseshoe-shaped tunnels, subjected to propagating obliquely incident out-of-plane SH-waves. In the use of the proposed method, the boundary around the tunnel was only required to be discretized. The Ricker wavelet was assumed as incident wave function. The geometrical properties of the first part from second line of the Karaj metro tunnel were considered as the case study. A sensitivity analysis was carried out on the responses with considering some intended parameters including depth ratio, horizontal location ratio, and angle of incident wave. It should be noted that, to obtain acceptable responses and in order to achieve the dimensionless results, the scale of 50 times was applied in the modeling. The response of the ground surface and the amplification patterns were presented in the time/frequency domains and the synthetic seismograms were obtained.
The results showed that making the meshes to focus only on the tunnel surrounding boundary and leaving the discretized ground surface reduces not only the analysis time, but also the input data and calculations compared to traditional BEM approaches. The verification of the responses versus existing analytical results showed that the used method had great accuracy for modeling underground tunnels. Simple modeling of actual underground structures and obtaining accurate responses through the use of time-domain half-plane BEM were main purposes of this paper. Besides, the presence of metro tunnels was effective on the formation of different seismic patterns of ground surface. The general pattern of responses in the frequency domain showed that, when subjected to vertically propagating incident SH-waves, the isolation effect of the presence of the tunnel was quite pronounced on reducing the ground surface response.