Amplification Pattern of Gaussian-Shaped Orthotropic Valley

Authors

1 Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran

2 Geotechnical Engineering Research Center, International Institute of Earthquake Engineering and Seismology, Tehran, Iran

10.22034/ceej.2024.59064.2296

Abstract

Studies indicate that the behavior of various materials, such as soils and rocks forming topographic features like valleys, which are plentiful on the Earth's surface, is influenced by anisotropy. In earlier research, isotropic cases were predominantly examined due to their simplicity in modeling and analysis. Although these studies provided valuable insights into the seismic behavior of valleys at the time, their findings notably diverge from the actual behavior observed in nature. These solutions are typically classified into analytical and numerical methods. Numerical approaches offer greater flexibility, facilitating the modeling and analysis of complex problems, divided into volumetric (FEM & FDM) and boundary methods (BEM). The utilization of BEM provides advantages such as reducing one dimension in models, satisfying wave radiation conditions at infinity. Compared to domain approaches, employing BEM results in mesh concentration exclusively around the desired topographic boundary, automatic fulfillment of wave radiation conditions at far boundaries, reduced input data volume, substantial reductions in random-access memory, storage space, and analysis time. Significantly, the method offers extremely high accuracy in results due to the significant contribution of analytical processes in problem-solving. In this area, the studies of Panji et al. (2020), Panji & Mojtabazadeh (2018, 2020 & 2021), and Mojtabazadeh et al. (2020 & 2022b) demonstrate the seismic behavior of various topographic features using a straightforward process in half-space time-domain BEM. Notable researchers in the development of anisotropic BEM include Dravinski (2003), Daros (2013), and Chiang (2018). Additionally, Wang et al. (1996), Zhang (2002), Wunsche et al. (2009), Furukawa et al. (2014), and Parvanova et al. (2016) illustrated wave propagation in anisotropic mediums. Furthermore, Zheng & Dravinski (1998 & 2000) and Dineva et al. (2014) investigated the scattering of seismic waves in an orthotropic half-space. Recently, Mojtabazadeh et al. (2024) were able to analyze the seismic responses of heterogeneous orthotropic hill-shaped topographies by a time-domain boundary element method (TD-BEM) based on half-space Green’s functions. The historical review of anisotropic studies not only underscores a notable gap in the comprehensive exploration of orthotropic topographic features but also draws attention to a similar gap in the investigation of hollow valleys. Therefore, this paper presents the seismic response of an orthotropic Gaussian-shaped valley subjected to incident SH-waves. The time-domain orthotropic half-space boundary element method, previously proposed by the authors for analyzing the aforementioned problem, is employed. Material damping is indirectly applied using logarithmic functions in the formulation. Additionally, the results are validated through a convergence approach for a circular valley, assuming certain key model parameters such as isotropy factor, valley aspect ratio, and frequency content. The obtained responses are primarily presented as two/three-dimensional graphs in both the time and frequency domains.

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Journal of Civil and Environmental Engineering
Volume 54, Issue 117 - Serial Number 117
Winter 2025
March 2025
Pages 1-16

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