Document Type : Article
Authors
1
Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran.
2
Department of Civil Engineering, Islamic Azad University of Zanjan, Zanjan, Iran.
3
Geotechnical Engineering Research Center, International Institute of Earthquake Engineering and Seismology, Tehran, Iran.
10.24200/j30.2024.63886.3294
Abstract
This paper presents a formulation of the attenuated orthotropic time-domain half-space boundary element method for analyzing the orthotropic effect of underground inclusions subjected to transient SH-waves. By changing the spatial variable, the time-domain half-space Green’s functions were obtained in an isotropic-like analytical process by solving the singular form of the scalar wave equation. The stress-free boundary condition at the ground surface is satisfied using wave source image theory. To account for material damping, the Barkan approach is employed to attenuate the half-space by introducing a constant logarithmic reduction into the modified boundary integral equation. The closed-form attenuated orthotropic half-space scalar kernels were obtained in the time-domain for displacement/traction fields by analytical integration of Green’s functions. This method is easily implemented in a time-domain computer code for analyzing seismic homogeneous orthotropic mediums. To model underground inclusions, a sub-structuring approach is introduced to ensure continuity conditions at interfaces based on node position and normal direction. Several practical examples involving SH-waves are solved and compared with existing literature to validate surface response, particularly focusing on isotropic convergence. Favorable agreement is found between responses, confirming the capability of the proposed method for simple modeling of orthotropic subsurface features. Finally, in the form of an advanced numerical study, the surface motions of orthotropic models including an underground inclusion embedded in a linear elastic half-space were successfully obtained under transient SH-wave propagation. Utilizing the time-domain boundary element approach, a simple model was developed only by discretizing the boundaries/interfaces. To illustrate responses in time/frequency-domain, a comprehensive sensitivity analysis is performed considering parameters such as frequency, shape ratio, and isotropy factor, visualized through snapshots, seismograms, and amplification patterns. Results demonstrate that orthotropic anisotropy significantly influences seismic patterns of ground surfaces, highlighting the impact of mentioned parameter variations.
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