Didier Clouteau

Numerical modelling of free field traffic-induced vibrations

This paper deals with the numerical modelling of free field traffic-induced vibrations during the passage of a vehicle on an uneven road. The road unevenness subjects the vehicle to vertical oscillations that cause dynamic axle loads. The latter are calculated from the vehicle transfer functions and the frequency content of the road profile as experienced by the vehicle axles. A transfer function between the source and the receiver that accounts for the dynamic interaction between the road and the soil is used to calculate the free field response. Its calculation is based on a dynamic substructure method, using a boundary element method for the soil and an analytical beam model for the road. The methodology is validated with analytical results and is finally illustrated by a numerical example where the free field vibrations during the passage of a vehicle on a traffic plateau are considered.

Numerical Modelling of Traffic Induced Vibrations

A solution procedure is presented to compute free field vibrations induced by train or road traffic, the excitation being either deterministic or stochastic. The full interaction between the vehicle, the track or road and the soil is accounted for, using a substructure approach that takes advantage of the fact that the properties of the track or road and the soil do not change along the longitudinal direction. A time-frequency approach is proposed to characterize the free field radiated in the soil. The examples show the importance of guided waves along the track for understanding the dynamic behavior of the track or the road.

Modeling of random anisotropic elastic media and impact on wave propagation

The class of stochastic non-gaussian positive-definite fields with minimal parameterization proposed by Soize (Soize, 2006) to model the elasticity tensor field of a random anisotropic material shows an anisotropy index which grows with the fluctuation level. This property is in contradiction with experimental results in geophysics where the anisotropy index remains limited whatever the fluctuation level. Hence, the main purpose of this paper is to generalize the Soize’s model in order to account independently for the anisotropy index and the fluctuation level. It is then shown that this new model leads to major differences in the wave propagation regimes.

Equivalent-Linear Dynamic Impedance Functions of Surface Foundations

AbstractAn approximate linearization method using the familiar concept of G-γ and D-γ curves is presented for determining the dynamic impedance (stiffness and damping) coefficients of rigid surface footings accounting for nonlinear soil behavior. The method is based on subdivision of the soil mass under the footing into a number of horizontal layers of different shear modulus and damping ratio, compatible with the level of strain imposed by an earthquake motion or a dynamic load. In this way, the original homogeneous or inhomogeneous soil profile is replaced by a layered profile with strain-compatible properties within each layer, which do not vary in the horizontal sense. The system is solved in the frequency domain by a rigorous boundary-element formulation accounting for the radiation condition at infinity. For a given set of applied loads, characteristic strains are determined in each soil layer and the analysis is repeated in an iterative manner until convergence in material properties is achieved. B...

Stochastic Simulations in Dynamic Soil-Structure Interaction

This paper deals with several numerical techniques that account for random excitations and random material parameters occurring in earthquake engineering. It focuses in sequence on the influence on the structural response of the variability of the incident field using filtering theory, on the soil variability by coupling Stochastic Finite Elements, integral operators and Monte-Carlo simulation, and finally on the influence on the site response of a random building distribution using periodic simulations. In each case, practical examples are given to help illustrate the numerical techniques and to underline the importance of randomness in earthquake engineering problems.

Elastodynamic wave scattering by finite-sized resonant scatterers at the surface of a horizontally layered halfspace

The present paper deals with the multiple scattering by randomly distributed elastodynamic systems at the surface of a horizontally layered elastic halfspace due to an incident plane wave. Instead of solving this problem for a particular configuration of the system, multiple scattering theory is used to compute the ensemble response statistics. The Dyson equation is used to calculate the mean field, while the nonstationary second order statistics are obtained by means of the Bethe-Salpeter equation. This allows for the determination of the mean square response of the system in the time and frequency domains. This model is used to study multiple scattering between buildings under seismic excitation. The influence of multiple scattering on the seismic site response is verified. Furthermore, the influence of the footprint and the damping of the buildings are investigated. The results are compared to results of a coupled finite element/boundary element solution for a group of buildings.

Probabilistic nonparametric model of impedance matrices: Application to the seismic design of a structure

Economic and legal pressures on the structural engineers force them to consider uncertainty in the domains interacting, through boundary impedances, with their design structure. A probabilistic model of this impedance is constructed around a mean hidden state variables model using a nonparametric method. This mean model is constructed using only deterministic tools. The methodology is applied to the design of a gas tank on a layered soil.

A coupled periodic FE-BE model for ground-borne vibrations from underground railways

An efficient and modular numerical prediction model is presented to predict vibrations in the free field due to metro trains in the tunnel. The three-dimensional dynamic tunnel-soil interaction problem is solved with a subdomain formulation, using a finite element formulation for the tunnel and a boundary element method for the soil. The periodicity of the tunnel and the soil in the longitudinal direction is exploited using the Floquet transform, limiting the discretization effort to a single bounded reference cell. The Craig-Bampton substructuring technique is used to efficiently incorporate a track in the tunnel. The track-tunnel-soil interaction problem is solved in the frequency-wavenumber domain and the wave field radiated into the soil is computed.

Parametric and nonparametric models of the impedance matrix of a random medium

Two approaches are presented for the modeling of the impedance matrix of a random medium: one parametric and the other nonparametric. The former allows to take into account the data uncertainties while introducing a model error, that yields, in some cases, very high levels. The latter is based on a much simpler, deterministic, model, for which both data uncertainties and model errors are accounted for. When the model error is negligible, the parametric approach can be used for the identification of the parameters of the nonparametric model of the impedance matrix.

A time-reversal process for beam trusses subjected to impulse loads

Spatial structures are often subjected to impulse loads which give rise to high-frequency (HF) waves. The objectives of the research outlined in this paper are twofold: (i) develop a reliable direct model of the transient dynamic response of built-up structures subjected to such impulse loads and (ii) use this model in a time-reversal inverse process in order to possibly detect the location of the shocks. The present study is more particularly focused on beam assemblies, as typically encountered in aerospace applications. At first, a transport model describing the evolution of the HF vibrational energy density in a three-dimensional beam truss is outlined, with an emphasis on the consideration of the reflection/transmission phenomena at the beam junctions. The latter contribute to spread HF waves within the entire structure, yielding a diffuse (noisy) vibrational energy field amenable to be efficiently time-reversed for the purpose of locating the source which has generated it. The time-reversal process itself is presented in a subsequent part. Its originality lies in the consideration of quadratic observables (energy densities) as the processed data. The approach is illustrated by a numerical simulation performed on a three-dimensional beam truss.