Efficiency of Higher Order Finite Elements for the Analysis of Seismic Wave Propagation

The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one must consider a specific problem known as the numerical dispersion of waves. Numerical dispersion may increase the numerical error during the propagation process as the wave velocity (phase and group) depends on the features of the numerical model. In this paper, the numerical modelling of wave propagation by the finite element method is thus analyzed and dis-cussed for linear constitutive laws. Numerical dispersion is analyzed herein through 1D computations investigating the accuracy of higher order 15-node finite elements towards numerical dispersion. Concerning the numerical analy-sis of wave attenuation, a rheological interpretation of the classical Rayleigh assumption has for instance been previously proposed in this journal

Numerical analysis of seismic wave amplification in Nice (France) and comparisons with experiments

The analysis of site effects is very important since the amplification of seismic motion in some specific areas can be very strong. In this paper, the site considered is located in the centre of Nice on the French Riviera. Site effects are investigated considering a numerical approach (Boundary Element Method) and are compared to experimental results (weak motion and microtremors). The investigation of seismic site effects through numerical approaches is interesting because it shows the dependency of the amplification level on such parameters as wave velocity in surface soil layers, velocity contrast with deep layers, seismic wave type, incidence and damping. In this specific area of Nice, a one-dimensional (1D) analytical analysis of amplification does not give a satisfactory estimation of the maximum reached levels. A boundary element model is then proposed considering different wave types (SH, P, SV) as the seismic loading. The alluvial basin is successively assumed as an isotropic linear elastic medium and an isotropic linear viscoelastic solid (standard solid). The thickness of the surface layer, its mechanical properties, its general shape as well as the seismic wave type involved have a great influence on the maximum amplification and the frequency for which it occurs. For real earthquakes, the numerical results are in very good agreement with experimental measurements for each motion component. Two-dimensional basin effects are found to be very strong and are well reproduced numerically

Biot-JKD model: simulation of 1D transient poroelastic waves with fractional derivatives

A time-domain numerical modeling of Biot poroelastic waves is presented. The viscous dissipation occurring in the pores is described using the dynamic permeability model developed by Johnson-Koplik-Dashen (JKD). Some of the coefficients in the Biot-JKD model are proportional to the square root of the frequency: in the time-domain, these coefficients introduce order 1/2 shifted fractional derivatives involving a convolution product. Based on a diffusive representation, the convolution kernel is replaced by a finite number of memory variables that satisfy local-in-time ordinary differential equations. Thanks to the dispersion relation, the coefficients in the diffusive representation are obtained by performing an optimization procedure in the frequency range of interest. A splitting strategy is then applied numerically: the propagative part of Biot-JKD equations is discretized using a fourth-order ADER scheme on a Cartesian grid, whereas the diffusive part is solved exactly. Comparisons with analytical solutions show the efficiency and the accuracy of this approach.Comment: arXiv admin note: substantial text overlap with arXiv:1210.036

Numerical modeling of 1-D transient poroelastic waves in the low-frequency range

Propagation of transient mechanical waves in porous media is numerically investigated in 1D. The framework is the linear Biot's model with frequency-independant coefficients. The coexistence of a propagating fast wave and a diffusive slow wave makes numerical modeling tricky. A method combining three numerical tools is proposed: a fourth-order ADER scheme with time-splitting to deal with the time-marching, a space-time mesh refinement to account for the small-scale evolution of the slow wave, and an interface method to enforce the jump conditions at interfaces. Comparisons with analytical solutions confirm the validity of this approach.Comment: submitted to the Journal of Computational and Applied Mathematics (2008

Time domain numerical modeling of wave propagation in 2D heterogeneous porous media

This paper deals with the numerical modeling of wave propagation in porous media described by Biot's theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which is valid in the low-frequency range. The coexistence of propagating fast compressional wave and shear wave, and of a diffusive slow compressional wave, makes numerical modeling tricky. To avoid restrictions on the time step, the Biot's system is splitted into two parts: the propagative part is discretized by a fourth-order ADER scheme, while the diffusive part is solved analytically. Near the material interfaces, a space-time mesh refinement is implemented to capture the small spatial scales related to the slow compressional wave. The jump conditions along the interfaces are discretized by an immersed interface method. Numerical experiments and comparisons with exact solutions confirm the accuracy of the numerical modeling. The efficiency of the approach is illustrated by simulations of multiple scattering.Comment: Journal of Computational Physics (March 2011

Application of the multi-level time-harmonic fast multipole BEM to 3-D visco-elastodynamics

Engineering Analysis with Boundary elements (accepted, to appear)International audienceThis article extends previous work by the authors on the single- and multi-domain time-harmonic elastodynamic multi-level fast multipole BEM formulations to the case of weakly dissipative viscoelastic media. The underlying boundary integral equation and fast multipole formulations are formally identical to that of elastodynamics, except that the wavenumbers are complex-valued due to attenuation. Attention is focused on evaluating the multipole decomposition of the viscoelastodynamic fundamental solution. A damping-dependent modification of the selection rule for the multipole truncation parameter, required by the presence of complex wavenumbers, is proposed. It is empirically adjusted so as to maintain a constant accuracy over the damping range of interest in the approximation of the fundamental solution, and validated on numerical tests focusing on the evaluation of the latter. The proposed modification is then assessed on 3D single-region and multi-region visco-elastodynamic examples for which exact solutions are known. Finally, the multi-region formulation is applied to the problem of a wave propagating in a semi-infinite medium with a lossy semi-spherical inclusion (seismic wave in alluvial basin). These examples involve problem sizes of up to about $3\,10^{5}$ boundary unknowns

Permeability-porosity relationships in seafloor vent deposits : dependence on pore evolution processes

Author Posting. © American Geophysical Union, 2007. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 112 (2007): B05208, doi:10.1029/2006JB004716.Systematic laboratory measurements of permeability and porosity were conducted on three large vent structures from the Mothra Hydrothermal vent field on the Endeavor segment of the Juan de Fuca Ridge. Geometric means of permeability values obtained from a probe permeameter are 5.9 × 10−15 m2 for Phang, a tall sulfide-dominated spire that was not actively venting when sampled; 1.4 × 10−14 m2 for Roane, a lower-temperature spire with dense macrofaunal communities growing on its sides that was venting diffuse fluid of <300°C; and 1.6 × 10−14 m2 for Finn, an active black smoker with a well-defined inner conduit that was venting 302°C fluids prior to recovery. Twenty-three cylindrical cores were then taken from these vent structures. Permeability and porosity of the drill cores were determined on the basis of Darcy's law and Boyle's law, respectively. Permeability values range from ∼10−15 to 10−13 m2 for core samples from Phang, from ∼10−15 to 10−12 m2 for cores from Roane, and from ∼10−15 to 3 × 10−13 m2 for cores from Finn, in good agreement with the probe permeability measurements. Permeability and porosity relationships are best described by two different power law relationships with exponents of ∼9 (group I) and ∼3 (group II). Microstructural analyses reveal that the difference in the two permeability-porosity relationships reflects different mineral precipitation processes as pore space evolves within different parts of the vent structures, either with angular sulfide grains depositing as aggregates that block fluid paths very efficiently (group I), or by late stage amorphous silica that coats existing grains and reduces fluid paths more gradually (group II). The results suggest that quantification of permeability and porosity relationships leads to a better understanding of pore evolution processes. Correctly identifying permeability and porosity relationships is an important first step toward accurately estimating fluid distribution, flow rate, and environmental conditions within seafloor vent deposits, which has important consequences for chimney growth and biological communities that reside within and on vent structures.Support from the National Science Foundation under grants NSF OCE-9986456 (W.Z. and M.K.T.) and NSF OCE-0327488 (P.R.C.) is gratefully acknowledged. We also thank the WHOI summer student fellowship for providing support to H.G

A finite element model for the thermo-elastic analysis of functionally graded porous nanobeams

In this study, for the first time, a nonlocal finite element model is proposed to analyse thermo-elastic behaviour of imperfect functionally graded porous nanobeams (P-FG) on the basis of nonlocal elasticity theory and employing a double-parameter elastic foundation. Temperature-dependent material properties are considered for the P-FG nanobeam, which are assumed to change continuously through the thickness based on the power-law form. The size effects are incorporated in the framework of the nonlocal elasticity theory of Eringen. The equations of motion are achieved based on first-order shear deformation beam theory through Hamilton's principle. Based on the obtained numerical results, it is observed that the proposed beam element can provide accurate buckling and frequency results for the P-FG nanobeams as compared with some benchmark results in the literature. The detailed variational and finite element procedure are presented and numerical examinations are performed. A parametric study is performed to investigate the influence of several parameters such as porosity volume fraction, porosity distribution, thermal loading, material graduation, nonlocal parameter, slenderness ratio and elastic foundation stiffness on the critical buckling temperature and the nondimensional fundamental frequencies of the P-FG nanobeams. Based on the results of this study, a porous FG nanobeam has a higher thermal buckling resistance and natural frequency compared to a perfect FG nanobeam. Also, uniform distributions of porosity result in greater critical buckling temperatures and vibration frequencies, in comparison with functional distributions of porosities