A Simplified Elastic Model for Seismic Analysis of Earth-Retaining Structures with Limited Displacements

A simplified elastic model for analyzing static and dynamic interaction between earth-retaining structures and backfill within the range of small displacements is presented. The postulated model covers some of the available models as special cases. The model lends itself readily to the treatment of non-homogeneous backfills with elastic properties varying with depth. Internal (linear) damping in the backfill can be included without impairing the simplicity of the model. Radiation losses due to waves propagating horizontally in fills of semi-infinite extent are inherent to the postulated model. The solutions for some statical and dynamical problems of practical importance show satisfactory agreement with results based on the classical theory of elasticity

Modeling seismic wave propagation and amplification in 1D/2D/3D linear and nonlinear unbounded media

To analyze seismic wave propagation in geological structures, it is possible to consider various numerical approaches: the finite difference method, the spectral element method, the boundary element method, the finite element method, the finite volume method, etc. All these methods have various advantages and drawbacks. The amplification of seismic waves in surface soil layers is mainly due to the velocity contrast between these layers and, possibly, to topographic effects around crests and hills. The influence of the geometry of alluvial basins on the amplification process is also know to be large. Nevertheless, strong heterogeneities and complex geometries are not easy to take into account with all numerical methods. 2D/3D models are needed in many situations and the efficiency/accuracy of the numerical methods in such cases is in question. Furthermore, the radiation conditions at infinity are not easy to handle with finite differences or finite/spectral elements whereas it is explicitely accounted in the Boundary Element Method. Various absorbing layer methods (e.g. F-PML, M-PML) were recently proposed to attenuate the spurious wave reflections especially in some difficult cases such as shallow numerical models or grazing incidences. Finally, strong earthquakes involve nonlinear effects in surficial soil layers. To model strong ground motion, it is thus necessary to consider the nonlinear dynamic behaviour of soils and simultaneously investigate seismic wave propagation in complex 2D/3D geological structures! Recent advances in numerical formulations and constitutive models in such complex situations are presented and discussed in this paper. A crucial issue is the availability of the field/laboratory data to feed and validate such models.Comment: of International Journal Geomechanics (2010) 1-1

Atenuación de ondas elásticas con barreras de pilotes

Se presenta una solución analítica para resolver el problema de aislamiento de cimentaciones, de vibraciones generadas en su cercanía, mediante barreras de pilotes. El sistema de aislamiento está formado por una línea de pilotes elásticos y la exitación está dada por una fuente de ondas cilíndricas SV. El problema se formula bidimensionalmente como uno de difracción múltiple de ondas elásticas, los campos reflejados y refractados por los pilotes se construyen mediante expansiones de funciones de ondas cilíndricas. La solución exacta se obtiene al satisfacer idénticamente las condiciones de continuidad de desplazamientos y esfuerzos en las interfases suelo-pilote, con la ayuda del teorema de adición de Graf. Se presentan algunos resultados numéricos que muestran el comportamiento de barreras de pilotes como sistema de aislamiento, y se define un índice de transmisibilidad para medir su efectividad

2D full-waveform modeling of seismic waves in layered karstic media

We have developed a new propagator-matrix scheme to simulate seismic-wave propagation and scattering in a multilayered medium containing karstic voids. The propagator matrices can be found using the boundary element method. The model can have irregular boundaries, including arbitrary free-surface topography. Any number of karsts can be included in the model, and each karst can be of arbitrary geometric shape. We have used the Burton-Miller formulation to tackle the numerical instability caused by the fictitious resonance due to the finite size of a karstic void. Our method was implemented in the frequency-space domain, so frequency-dependent Q can be readily incorporated. We have validated our calculation by comparing it with the analytical solution for a cylindrical void and to the spectral element method for a more complex model. This new modeling capability is useful in many important applications in seismic inverse theory, such as imaging karsts, caves, sinkholes, and clandestine tunnels

A field expansions method for scattering by periodic multilayered media

The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein described is a boundary perturbation method for the numerical simulation of scattering returns from irregularly shaped periodic layered media. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than finite difference and finite element simulations), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral/element methods. The approach is a generalization to multiple layers of Bruno and Reitich’s “Method of Field Expansions” for dielectric structures with two layers. By simply considering the entire structure simultaneously, rather than solving in individual layers separately, the full field can be recovered in time proportional to the number of interfaces. As with the original field expansions method, this approach is extremely efficient and spectrally accurate

Application of HPM to Solve Unsteady Squeezing Flow of a Second-Grade Fluid between Circular Plates

In this article, Homotopy Perturbation Method (HPM) is used to provide two approximate solutions to the nonlinear differential equation that describes the behaviour for the unsteady squeezing flow of a second grade fluid between circular plates. Comparing results between approximate and numerical solutions shows that our results are capable to provide an accurate solution and are extremely efficient

Accelerated amyloid deposition, neurofibrillary degeneration and neuronal loss in double mutant APP/tau transgenic mice

Even though the idea that amyloid beta peptide accumulation is the primary event in the pathogenesis of Alzheimer's disease has become the leading hypothesis, the causal link between aberrant amyloid precursor protein processing and tau alterations in this type of dementia remains controversial. We further investigated the role of beta-amyloid production/deposition in tau pathology and neuronal cell death in the mouse brain by crossing Tg2576 and VLW lines expressing human mutant amyloid precursor protein and human mutant tau, respectively. The resulting double transgenic mice showed enhanced amyloid deposition accompanied by neurofibrillary degeneration and overt neuronal loss in selectively vulnerable brain limbic areas. These findings challenge the idea that tau pathology in Alzheimer's disease is merely a downstream effect of amyloid production/deposition and suggest that reciprocal interactions between beta-amyloid and tau alterations may take place in vivo

Classical Perturbation Method for the Solution of a Model of Diffusion and Reaction

In this paper, we employ perturbation method (PM) to solve nonlinear problems. As case study PM is employed to obtain approximate solutions for the nonlinear differential equation that models the diffusion and reaction in porous catalysts. We find that the square residual error (S.R.E) of our solutions is in the range and this requires only the third order approximation of PM, which shows the effectiveness of the method