Geert Lombaert

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.

The experimental validation of a numerical model for the prediction of the vibrations in the free field produced by road traffic

The objective of the present paper is the experimental validation of a numerical model for the prediction of traffic-induced vibrations. The vibrations in the free field, generated by the passage of a vehicle on an uneven road, are predicted in two stages. First, the equations of motion of the vehicle are solved to determine the dynamic axle loads. Next, these axle loads are applied to the road and the free field vibrations are computed. An elaborate measurement campaign has been set up to validate this model. The response of a Volvo FL6 truck and the response in the free field have been measured simultaneously during the passage of the truck over an artificial road unevenness. The parameters related to the vehicle, the road and the soil have been determined experimentally. A comparison of the predicted and the measured response demonstrates the predictive qualities of the numerical model. Furthermore, the results provide a clear insight in the influence of the vehicle speed on the vehicles and the free field response.

Finite-Element Model Updating for Assessment of Progressive Damage in a 3-Story Infilled RC Frame

AbstractThis paper presents a study on the identification of progressive damage, using an equivalent linear finite-element model updating strategy, in a masonry infilled RC frame that was tested on a shake table. A two-thirds-scale, 3-story, 2-bay, infilled RC frame was tested on the UCSD–NEES shake table to investigate the seismic performance of this type of construction. The shake table tests induced damage in the structure progressively through scaled historical earthquake records of increasing intensity. Between the earthquake tests and at various levels of damage, low-amplitude white-noise base excitations were applied to the infilled RC frame. In this study, the effective modal parameters of the damaged structure have been identified from the white-noise test data with the assumption that it responded in a quasi-linear manner. Modal identification has been performed using a deterministic-stochastic subspace identification method based on the measured input–output data. A sensitivity-based finite-ele...

An efficient formulation of Krylov’s prediction model for train induced vibrations based on the dynamic reciprocity theorem

In Krylovs analytical prediction model, the free field vibration response during the passage of a train is written as the superposition of the effect of all sleeper forces, using Lambs approximate solution for the Greens function of a halfspace. When this formulation is extended with the Greens functions of a layered soil, considerable computational effort is required if these Greens functions are needed in a wide range of source-receiver distances and frequencies. It is demonstrated in this paper how the free field response can alternatively be computed, using the dynamic reciprocity theorem, applied to moving loads. The formulation is based on the response of the soil due to the moving load distribution for a single axle load. The equations are written in the wave-number-frequency domain, accounting for the invariance of the geometry in the direction of the track. The approach allows for a very efficient calculation of the free field vibration response, distinguishing the quasistatic contribution from the effect of the sleeper passage frequency and its higher harmonics. The methodology is validated by means of in situ vibration measurements during the passage of a Thalys high-speed train on the track between Brussels and Paris. It is shown that the model has good predictive capabilities in the near field at low and high frequencies, but underestimates the response in the midfrequency band.

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.

Uncertainty Quantification in the Assessment of Progressive Damage in a 7-Story Full-Scale Building Slice

AbstractIn this paper, Bayesian linear finite-element (FE) model updating is applied for uncertainty quantification (UQ) in the vibration-based damage assessment of a 7-story RC building slice. This structure was built and tested at full scale on the University of California at San Diego-Network for Earthquake Engineering Simulation shake table: progressive damage was induced by subjecting it to a set of historical earthquake ground motion records of increasing intensity. At each damage stage, modal characteristics, such as natural frequencies and mode shapes, were identified through low-amplitude vibration testing; these data are used in the Bayesian FE model updating scheme. To analyze the results of the Bayesian scheme and gain insight into the information contained in the data, a comprehensive uncertainty and resolution analysis is proposed and applied to the 7-story building test case. The Bayesian UQ approach and subsequent resolution analysis are shown to be effective in assessing uncertainty in FE...

Ground-Borne Vibration due to Railway Traffic: A Review of Excitation Mechanisms, Prediction Methods and Mitigation Measures

The aim of this paper is to provide a comprehensive overview of the state of the art on railway-induced ground vibration. The governing physical mechanisms, prediction methods, and mitigation measures of ground-borne vibration are discussed, with focus on low frequency feelable vibration and the case of railway traffic at grade. In order to clarify the importance of quasi-static and dynamic excitation, the basic problems of a moving load with constant magnitude and harmonic magnitude are discussed first. Dynamic excitation due to wheel and track unevenness and parametric excitation is shown to be the dominant source of environmental vibration in most cases. Next, an overview of prediction methods for ground-borne vibration is given. The advantages and limitations of numerical methods, based on physical or mechanical models, and empirical models, derived from measured data, are discussed. Finally, the mitigation of railway-induced ground vibration is considered, where the focus goes to mitigation measures at source (wheel and rail unevenness, rolling stock, track) and measures on the transmission path (trenches and barriers, wave impeding blocks, subgrade stiffening, and heavy masses next to the track). In conclusion, a number of open points requiring further research is given.

Identification and Modelling of Vertical Human-Structure Interaction

Slender footbridges are often highly susceptible to human-induced vibrations, due to their low stiffness, damping and modal mass. Predicting the dynamic response of these civil engineering structures under crowd-induced loading has therefore become an important aspect of the structural design. The excitation of groups of pedestrians and crowds is generally modelled using moving loads but also the changes in dynamic characteristics due to human-structure interaction are found to significantly affect the footbridge response. The present contribution investigates the influence of the presence of the pedestrians onto the dynamic characteristics of the occupied structure by means of an extensive experimental study on a footbridge in laboratory conditions. The analysis shows that the natural frequencies slightly reduce due to the additional mass but more significant is the observed increase in structural damping. Similar observations are made on a in situ footbridge. This interaction is simulated using a coupled human-structure model in which the human occupants are represented by simple biomechanical models.

Random Vibration Analysis of Dynamic Vehicle-Bridge Interaction Due to Road Unevenness

Vehicle-bridge interaction has been studied for a long time to investigate the structural behavior of bridges and vehicle ride comfort. An original frequency domain method is presented where the vehicle-bridge interaction problem is solved in a frame of reference that moves with the vehicle. The Fourier transform of the interaction force is computed directly from the vehicle compliance and bridge compliance, without requiring any iterations. The method is particularly useful when a closed-form solution of the bridge compliance is available, as in the case of a simply supported Euler-Bernoulli beam model for the bridge. The solution is, therefore, well-suited for parametric studies on the bridge and vehicle response characteristics and offers a reference for more detailed models of the bridge and thevehicle or more complicated bridge configurations (e.g., continuous beam on multiple supports). The frequency domain approach also leads to enhanced physical understanding, because it shows how the interaction force decomposes into a term resulting from the dynamic response of the bridge to the constant moving load component and a term because of road surface unevenness. An efficient solution procedure based on random vibration analysis is presented, which allows for the computing of the statistical characteristics of the bridge and vehicle response from the power spectral density function of the unevenness. The procedure is validated by means of Monte Carlo simulation results for the case where the passage of a heavy vehicle on a highway bridge is considered. DOI: 10.1061/(ASCE)EM.1943-7889.0000386.

Numerical and Experimental Evaluation of the Dynamic Performance of a Footbridge with Tuned Mass Dampers

AbstractThis article presents an evaluation of the dynamic behavior of a slender steel footbridge before and after the installation of two tuned mass dampers (TMDs). The results of the experimental study show that the damping devices lead to an increase of the effective damping ratio of the critical mode. Additional tests involving the structural vibrations induced by a limited number of persons revealed that the TMD units are effective in reducing the structural response. However, the obtained reduction highly depends on the type of human excitation. To verify the response of the footbridge for large groups and crowds, a comprehensive numerical analysis is performed. The results are compared to the response predicted by the procedures of the Setra and HiVoSS design guides. For the bridge without TMD units, a significantly higher structural response is predicted by the design guides; the bridge has a short span and is lightly damped, so the steady-state resonant conditions assumed in the design guides are...