Seismic Wave Amplification in 3D Alluvial Basins: 3D/1D Amplification Ratios from Fast Multipole BEM Simulations

📝 Abstract

In this work, we study seismic wave amplification in alluvial basins having 3D standard geometries through the Fast Multipole Boundary Element Method in the frequency domain. We investigate how much 3D amplification differs from the 1D (horizontal layering) case. Considering incident fields of plane harmonic waves, we examine the relationships between the amplification level and the most relevant physical parameters of the problem (impedance contrast, 3D aspect ratio, vertical and oblique incidence of plane waves). The FMBEM results show that the most important parameters for wave amplification are the impedance contrast and the so-called equivalent shape ratio. Using these two parameters, we derive simple rules to compute the fundamental frequency for various 3D basin shapes and the corresponding 3D/1D amplification factor for 5% damping. Effects on amplification due to 3D basin asymmetry are also studied and incorporated in the derived rules.

💡 Analysis

In this work, we study seismic wave amplification in alluvial basins having 3D standard geometries through the Fast Multipole Boundary Element Method in the frequency domain. We investigate how much 3D amplification differs from the 1D (horizontal layering) case. Considering incident fields of plane harmonic waves, we examine the relationships between the amplification level and the most relevant physical parameters of the problem (impedance contrast, 3D aspect ratio, vertical and oblique incidence of plane waves). The FMBEM results show that the most important parameters for wave amplification are the impedance contrast and the so-called equivalent shape ratio. Using these two parameters, we derive simple rules to compute the fundamental frequency for various 3D basin shapes and the corresponding 3D/1D amplification factor for 5% damping. Effects on amplification due to 3D basin asymmetry are also studied and incorporated in the derived rules.

📄 Content

Bulletin of the Seismological Society of America June 2016

1

TITLE: Seismic Wave Amplification in 3D Alluvial Basins: 3D/1D Amplification Ratios from Fast Multipole BEM Simulations

AUTHORS’ NAMES: Kristel C. Meza-Fajardo(1)(*), Jean-François Semblat(2), Stéphanie Chaillat(3) and Luca Lenti(4)

CORRESPONDING AUTHOR: Kristel C. Meza-Fajardo Department of Civil Engineering, Universidad Nacional Autónoma de Honduras Tegucigalpa, Honduras E-mail: kristelmeza@unah.edu.hn (*) Formerly at IFSTTAR, Départ. GERS, 20 Boulevard Newton, Champs sur Marne, France.

ABSTRACT In this work, we study seismic wave amplification in alluvial basins having 3D standard geometries through the Fast Multipole Boundary Element Method in the frequency domain. We investigate how much 3D amplification differs from the 1D (horizontal layering) case. Considering incident fields of plane harmonic waves, we examine the relationships between the amplification level and the most relevant physical parameters of the problem (impedance contrast, 3D aspect ratio, vertical and oblique incidence of plane waves). The FMBEM results show that the most important parameters for wave amplification are the impedance contrast and the so-called equivalent shape ratio. Using these two parameters, we derive simple rules to compute the fundamental frequency for various 3D basin shapes and the corresponding 3D/1D amplification factor for 5% damping. Effects on amplification due to 3D basin asymmetry are also studied and incorporated in the derived rules.

Bulletin of the Seismological Society of America June 2016

2

INTRODUCTION The amplification of seismic waves in alluvial deposits is strongly influenced by the geometry and mechanical properties of the surficial layers. The estimation of this amplification in codes is mainly performed through simplified 1D approaches. However the amplification process can significantly differ between the 1D (horizontal layering) and the 2D/3D cases because of focusing effects and waves generated at basin edges, (e.g., Paolucci 1999). Some analytical and numerical results have been already derived by various authors for the response of basins with simple geometries to incident seismic waves. Bard and Bouchon (1985) studied rectangular and sine-shaped soft layers embedded in a rigid half space considering incident plane SH-waves. The propagation of plane vertical SH-waves in 2D cylindrical basins was analyzed by Semblat et al. (2010) and Bonnet (1999) using the Boundary Element Method in the frequency domain. Rodriguez-Zuñiga et al. (2005) studied the case of a 3D cylindrical basin having a rectangular vertical cross-section and found a large difference between the 2D and 3D response at the center of the basin. Papageorgiou and Pei (1998) considered incident body and Rayleigh waves in 3D cylindrical basins with semicircular cross-section. In the works of Bard and Bouchon (1985) and Jiang and Kuribayashi (1988), it was reported that the fundamental frequencies of the basins only depend on the aspect ratio and the 1D fundamental frequency at the center of the valley. The 3D wave diffraction by a semi-spherical canyon has been also studied (Lee 1978; Kim and Papageorgiou 1993; Yokoi 2003; Liao et al. 2004; Chaillat et al. 2008) and 3D wave amplification due to surface heterogeneities has also been quantified (Sánchez-Sesma and Luzón, 1995; Komatitsch and Vilottte 1998; Drawinski 2003; Moczo et al. 2002; Chaillat et al. 2009). Smerzini et al. (2011) made comparisons of 3D, 2D and 1D amplification using the Spectral Element Method with a 3D model of the Gubbio plain in Italy. Olsen et al. (2000) found differences among 3D/2.5D/1D amplification and duration with a 3D finite difference model of the Upper Borrego Valley, California. The 2D amplification features may be interpreted through 2D/1D amplification factors with respect to the case of a horizontal layer (Chavez-Garcia and Faccioli 2000, Gélis et al. 2008; Makra et al. 2005; Semblat et al. 2010). The estimation of 3D/1D amplification factors in different 3D configurations is the main goal of this paper. The 3D amplification of seismic waves is modeled through the Fast Multipole Method (FMM). This formulation of the Boundary Element Method (BEM) allows the acceleration of iterative solvers for the global linear system of equations. The application of the Fast Multipole Boundary Element Method (FMBEM) is beneficial in problems of elastic wave propagation involving strong velocity gradients or 3D unbounded domains since large BEM meshes are required (Makra et al. 2005; Chaillat et al. 2008; Chaillat et al. 2009; Delépine & Semblat 2012). Extension of the FMBEM to propagation in weakly dissipative viscoelastic media was carried out by Grasso et al. (2012). In this work, we apply the formulation of the FMBEM for viscoelastic media to study wave amplification phenomena in 3D basins with canonical geometrie

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