A Simple Multi-Directional Absorbing Layer Method to Simulate Elastic Wave Propagation in Unbounded Domains

The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or layered solids. Various techniques such as Absorbing Boundary Conditions, infinite elements or Absorbing Boundary Layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this paper, a simple absorbing layer method is proposed: it is based on a Rayleigh/Caughey damping formulation which is often already available in existing Finite Element softwares. The principle of the Caughey Absorbing Layer Method is first presented (including a rheological interpretation). The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types and incidences. A comparison with the PML method is first performed for pure P-waves and the method is shown to be reliable in a more complex 2D case involving various wave types and incidences. It may thus be used for various types of problems involving elastic waves (e.g. machine vibrations, seismic waves, etc)

Modelling strong seismic ground motion: three-dimensional loading path versus wavefield polarization

Seismic waves due to strong earthquakes propagating in surficial soil layers may both reduce soil stiffness and increase the energy dissipation into the soil. To investigate seismic wave amplification in such cases, past studies have been devoted to one-directional shear wave propagation in a soil column (1D-propagation) considering one motion component only (1C-polarization). Three independent purely 1C computations may be performed ('1D-1C' approach) and directly superimposed in the case of weak motions (linear behaviour). This research aims at studying local site effects by considering seismic wave propagation in a 1-D soil profile accounting for the influence of the 3-D loading path and non-linear hysteretic behaviour of the soil. In the proposed '1D-3C' approach, the three components (3C-polarization) of the incident wave are simultaneously propagated into a horizontal multilayered soil. A 3-D non-linear constitutive relation for the soil is implemented in the framework of the Finite Element Method in the time domain. The complex rheology of soils is modelled by mean of a multisurface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan type. The great advantage of this choice is that the only data needed to describe the model is the modulus reduction curve. A parametric study is carried out to characterize the changes in the seismic motion of the surficial layers due to both incident wavefield properties and soil non-linearities. The numerical simulations show a seismic response depending on several parameters such as polarization of seismic waves, material elastic and dynamic properties, as well as on the impedance contrast between layers and frequency content and oscillatory character of the input motion. The 3-D loading path due to the 3C-polarization leads to multi-axial stress interaction that reduces soil strength and increases non-linear effects. The non-linear behaviour of the soil may have beneficial or detrimental effects on the seismic response at the free surface, depending on the energy dissipation rate. Free surface time histories, stress-strain hysteresis loops and in-depth profiles of octahedral stress and strain are estimated for each soil column. The combination of three separate 1D-1C non-linear analyses is compared to the proposed 1D-3C approach, evidencing the influence of the 3C-polarization and the 3-D loading path on strong seismic motions

Seismic response of the geologically complex alluvial valley at the "Europarco Business Park" (Rome - Italy) through instrumental records and numerical modelling

The analysis of the local seismic response in the “Europarco Business Park”, a recently urbanized district of Rome (Italy) developed over the alluvial valley of the “Fosso di Vallerano” stream, is here presented. A high-resolution geological model, reconstructed over 250 borehole log-stratigraphies, shows a complex and heterogeneous setting of both the local Plio- Pleistocene substratum and the Holocene alluvia. The local seismo-stratigraphy is derived by a calibration process performed through 1D numerical modelling, accounting for: i) 55 noise measurements, ii) 10 weak motion records obtained through a temporary velocimetric array during the August 2009 L’Aquila- Gran Sasso seismic sequence and iii) one cross-hole test available from technical report. Based on the reconstructed seismo- stratigraphy, the local seismic bedrock is placed at the top of a gravel layer that is part of the Pleistocene deposits and it does not correspond to the local geological bedrock represented by Plio-Pleistocene marine deposits. 1D amplification functions were derived via numerical modelling along three representative sections that show how in the Fosso di Vallerano area two valleys converge into a single one moving from SE toward NW. The obtained results reveal a main resonance at low frequency (about 0.8 Hz) and several higher resonance modes, related to the local geological setting. Nonlinear effects are also modelled by using strong motion inputs from the official regional dataset and pointed out a general down-shift (up to 0.5 Hz) of the principal modes of resonance as well as an amplitude reduction of the amplification function at frequencies higher than 7 Hz

Strong Ground Motion in the 2011 Tohoku Earthquake: a 1Directional - 3Component Modeling

Local wave amplification due to strong seismic motions in surficial multilayered soil is influenced by several parameters such as the wavefield polarization and the dynamic properties and impedance contrast between soil layers. The present research aims at investigating seismic motion amplification in the 2011 Tohoku earthquake through a one-directional three-component (1D-3C) wave propagation model. A 3D nonlinear constitutive relation for dry soils under cyclic loading is implemented in a quadratic line finite element model. The soil rheology is modeled by mean of a multi-surface cyclic plasticity model of the Masing-Prandtl-Ishlinskii-Iwan (MPII) type. Its major advantage is that the rheology is characterized by few commonly measured parameters. Ground motions are computed at the surface of soil profiles in the Tohoku area (Japan) by propagating 3C signals recorded at rock outcrops, during the 2011 Tohoku earthquake. Computed surface ground motions are compared to the Tohoku earthquake records at alluvial sites and the reliability of the 1D-3C model is corroborated. The 1D-3C approach is compared with the combination of three separate one-directional analyses of one motion component propagated independently (1D-1C approach). The 3D loading path due to the 3C-polarization leads to multiaxial stress interaction that reduces soil strength and increases nonlinear effects. Time histories and spectral amplitudes, for the Tohoku earthquake, are numerically reproduced. The 1D-3C approach allows the evaluation of various parameters of the 3C motion and 3D stress and strain evolution all over the soil profile.Comment: Bulletin of the Seismological Society of America 103, 2B (2013) 1394-1410. arXiv admin note: substantial text overlap with arXiv:1308.194

Application of a characteristic periods-based (CPB) approach to estimate earthquake-induced displacements of landslides through dynamic numerical modelling

The interaction between seismic waves and slopes is an important topic to provide reliable scenarios for earthquake-(re)triggered landslides. The physical properties of seismic waves as well as slope topography and geology can significantly modify the local seismic response, influencing landslide triggering. A novel approach is here applied to two case studies in Andalusia (southern Spain) for computing the expected earthquake-induced displacements of existing landslide masses. Towards this aim, dynamic stress–strain numerical modelling was carried out using a selection of seismic signals characterized by different spectral content and energy. In situ geophysical measurements, consisting of noise records and temporary seismometric arrays, were carried out to control the numerical outputs in terms of local seismic response. The results consist of relationships between the characteristic period, Tm, of the seismic signals and the characteristic periods of the landslide masses, related to the thickness (Ts) and length (Tl), respectively. These relationships show that the larger the horizontal dimension (i.e. length of landslide) of a landslide is, the more effective the contribution (to the resulting coseismic displacement) of the long-period seismic waves is, as the maximum displacements are expected for a low Tm at each energy level of the input. On the other hand, when the local seismic response mainly depends on stratigraphy (i.e. landslide thickness), the maximum expected displacements occur close to the resonance period of the landslide, except for high-energy seismic inputs.The authors would like to thank the European Union ERDF for financial support via the “Monitorización sísmica de deslizamientos. Criterios de reactivación y alerta temprana” project of the “Programa Operativo FEDER de Andalucia 2007-2013”

Vibrations induites dans les sols par le trafic ferroviaire : expérimentations, modélisations et isolation.

International audienceRailway traffic induces cyclic and dynamic loadings in the track structure but also in the close environment (Degrande et al. 2006, François et al. 2007, Kausel 2008, Lefeuve-Mesgouez et al 2002, Paolucci et Spinelli 2006). The analysis of such excitations and their effects (e.g. vibrations, waves, etc) is fundamental to estimate their level and mitigate their potential consequences (settlements, nuisances, etc). After a brief summary of the current regulations, in situ experiments show the variability of the parameters characterizing the main phenomena (wave propagation into the soil, induced vibrations, etc). The main dynamic laboratory experiments are then discussed. They allow the estimation of the dynamic features of the materials (e.g. resonant column test), but also a simplified analysis of the main phenomena under controlled conditions (e.g. experiments in a geotechnical pit, centrifuge tests). The vibratory sources and the impedance ratios between the various soil layers (or some inclusions) being known, it is then possible to model some specific or actual configurations through theoretical (transfer functions) or numerical (e.g. finite elements, boundary elements) methods. Parametric studies allow the analysis of the propagation phenomena and the attenuation process in the soil in order to investigate the spatial variations of the vibrations amplitude in such various configurations. Finally, it may be useful to consider mitigation or isolation techniques in order to limit the consequences of the induced vibrations (e.g. vibratory nuisances, radiated noise). Several experimental and numerical results illustrate this key issue.Le trafic ferroviaire induit des sollicitations cycliques et dynamiques dans la structure de la voie mais également dans le sol support et l'environnement (Degrande et al. 2006, François et al. 2007, Kausel 2008, Lefeuve-Mesgouez et al 2002, Paolucci et Spinelli 2006). L'analyse de ces sollicitations et des effets induits (e.g. vibrations, ondes...) est fondamentale pour apprécier leur ampleur et remédier à leurs conséquences éventuelles (tassements, nuisances...). Après un bref rappel de la réglementation, des expérimentations in situ montrent tout d'abord la variabilité des paramètres caractérisant les principaux phénomènes en jeu (propagation d'ondes dans le sol, vibrations induites...). Les principaux essais dynamiques en laboratoire sont ensuite présentés. Ils autorisent la détermination des caractéristiques dynamiques des matériaux (e.g. essais à la colonne résonnante), mais aussi une analyse simplifiée des phénomènes vibratoires en conditions contrôlées (e.g. essais en fosse géotechnique, essais en centrifugeuse). Après avoir caractérisé les sources vibratoires et les contrastes de raideur (ou de vitesse d'ondes) entre les différentes couches de sol (ou diverses inclusions), il est alors possible de modéliser des configurations types ou réalistes à l'aide de méthodes théoriques (fonctions de transfert) ou numériques (e.g. : éléments finis, éléments de frontière). Des études paramétriques permettent d'analyser les phénomènes de propagation et l'amortissement dans le sol afin d'estimer l'évolution spatiale de l'amplitude des vibrations dans ces différentes configurations. In fine, il peut être nécessaire d'envisager, le cas échéant, des techniques de mitigation ou d'isolation afin de limiter les conséquences éventuelles des vibrations induites. Plusieurs résultats expérimentaux et numériques originaux illustreront ce dernier point

Influence of Soil Nonlinearities on Dynamic Soil-Structure Interaction

For moderate or strong seismic events, the maximum strains can easily reach the elastic limit of the soil behavior. Considering soilstructure interaction, the nonlinear effects may change the soil stiffness at the base of the structure and the energy dissipation into the soil. To take into account the nonlinearity of the soil in the dynamic soil-structure interaction (DSSI), a 3D constitutive model, proposed by Iwan, is used to investigate DSSI in the framework of the Finite Element Method. The model accounts for the nonlinear hysteretic behavior of soils and only needs the shear modulus degradation curve to characterize the soil behavior. This feature is very important since complex constitutive models generally involve numerous mechanical parameters difficult to characterize experimentally. A parametric study is carried out for different types of structures to characterize nonlinear effects in the time domain. Through these numerical simulations, the nonlinear behavior of the soil is shown to have beneficial or detrimental effects on the dynamic response of the structure depending on the way the interaction process is modified: change in the amplitude and frequency content of the waves propagated into the soil, fundamental frequency of the response of the soil-structure system and energy dissipation

Unconventional pseudostatic stability analysis of the Diezma landslide (Granada, Spain) based on a high-resolution engineering-geological model

A novel unconventional pseudostatic analysis is proposed here to infer on the sensitivity of a landslide to earthquakes characterized by different physical properties. Several sine waves with different amplitudes, frequencies and phases were applied to the landslide mass assuming limit equilibrium conditions. The unconventional approach was used for the Diezma landslide case study. The landslide is located 25 km from the city of Granada (Spain). Although the slope had repeatedly suffered small-scale stability problems since the construction of the A-92 highway, a larger failure occurred on 18 March 2001 and damaged the highway between kilometers 272.6 and 272.8. The landslide had an estimated volume of 1.2 Mm3 and involved a disordered deposit of silt and clay with heterometric blocks within the Numidoide Formation, which outcrops along the contact between the Maláguide and Dorsal domains of the Betic Cordillera mountain range. Despite the 18 million Euros spent since 1999 on geotechnical investigations and stabilization solutions, the numerous reactivations that occurred through 2010 and 2013 demonstrate the persistent activity of the landslide. The geometry of the large slope failure corresponding to the first activation of the Diezma landslide was used to back-analyze the stability of the slope based on a high-resolution engineering-geological model. The model was developed from the analysis of numerous borehole logs as well as from geophysical investigations consisting of seismic noise measurements. The results demonstrate that the safety factor (SF) of the Diezma landslide varies significantly for frequencies less than 1 Hz; moreover, unstable conditions are reached at frequency values between 0.5 and 1 Hz for water pressure distributions corresponding to Bishop factors (ru) between 0 and 0.36. To estimate the co-seismic displacements, the geometrical and mechanical properties of the landslide mass were used to derive its characteristic periods for thickness (Ts) and length (Tl), which were compared with the characteristic period of the earthquake (Tm). The results indicate that the maximum expected co-seismic displacements are up to 2 m for an earthquake with a Tm value close to 1 s and an Arias Intensity on the order of 1 m/s