Ground-borne vibration from roads or railways is a growing concern in the planning of new buildings in urban environments. Vibration assessment is often based on initial measurements of the free field vibrations to estimate building vibrations by either empirical or numerical procedures. Dynamic interaction between the soil and the foundation has an important influence on the transmitted vibrations, especially for embedded foundations, and should therefore be properly accounted for. This paper presents the results from a series of full-scale field experiments that were performed to characterise the vibration response of an end-bearing pile group foundation in soft clay subjected to a dynamic load applied at the ground surface. Controlled dynamic excitation is applied vertically at the ground surface from 10 and 20 m horizontal distance using an electrodynamic inertial shaker. Accelerations are measured at different construction stages: prior to construction, after driving of the piles and after completion of the pile cap. Predictions from a numerical model and from a hybrid method utilising measurement data acquired in an earlier construction stage are both validated with the data from the field tests. The results indicate that the relationship between the amplitudes of the vertical foundation and free field responses are insensitive to source–receiver distance. It is also found that pile–soil–pile interaction has an important influence on the vertical response of the piles.

In this paper, the performance of a single-span railway bridge with integrated retaining walls during high-speed train passage is investigated by considering different uncertainties originating from modeling assumptions and measurement processes. For this purpose, a single-span railway bridge is equipped with numerous accelerometers and is excited using a hydraulic actuator across different frequency ranges. A comprehensive 3D model of the bridge and the surrounding soils is created in Abaqus. Different sets of material properties for concrete and soil components are derived by converging the frequencies and damping ratios of the first three structural modes, using both the Error-Domain Model Falsification (EDMF) and Residual Minimization (RM) methods. These material properties are subsequently utilized in high-speed train passage analysis, and the results are compared.

The influence of pile–soil–pile interaction on the vertical response of end-bearing pile groups when subjected to an incident wave field generated from a vertical load at the soil's surface is investigated. A numerical model which allows for considering or disregarding the influence of pile–soil–pile interaction is adopted. Vertical end-bearing pile groups with different pile axial stiffness and pile-to-pile spacing are considered. This study shows that in contrast to floating piles in homogeneous soil, the interaction effects caused by wave scattering between the piles are important for end-bearing piles. These may either reduce or amplify the group response, depending on the wavelength in the soil, the spacing between the piles, the pile slenderness and the pile–soil stiffness ratio. The interaction between the piles which are aligned in the direction transverse to the propagation direction of the incident wave field is found to amplify the group response at certain frequencies. Reducing the pile spacing in this direction is found to influence the vertical vibration response of end-bearing pile group foundations considerably by shifting the amplification effects due to pile–soil–pile interaction to higher frequencies.

This paper presents an efficient 2D beam model of a continuous single-trackconcrete slab bridge considering the effect of surrounding soil conditions at the location ofthe retaining walls. A 3D model is used to investigate the backfill soil’s added flexibility fordifferent soil properties. It is shown that for the first bending mode, the additional dynamicstiffness of the backfill soil can be modeled using equivalent vertical and rotational springs.Various experimental tests have been performed on the studied railway bridge, including forcedvibration tests and train passage loadings. Good agreement is found between the 2D model andthe experimental data. It is shown that removing the soil causes both a shift in the structure’snatural frequencies (and their corresponding resonant speed) and a substantial increase inacceleration amplitude. This may give the impression that the bridge is not suitable for highspeedtrain passage. It is also shown that the bridge’s response to train passage is mainlygoverned by the first bending mode.

In this study, the influence of Soil-Structure Interaction (SSI) on the dynamic behavior of a three-span concrete slab railway bridge with integrated retaining walls is investigated. The bridge is subjected to controlled excitations using a hydraulic actuator with different frequencies and load amplitudes. A 3D model of the railway bridge-soil system is implemented and calibrated using the experimental frequency response functions at each sensor location. A soil-free model is also created to compare with the calibrated model. It is observed that the dynamic behavior of the railway bridge is substantially altered by the presence of the surrounding soils, and neglecting SSI can lead to underestimation and inaccurate results. Additionally, the calibrated model is used for further train-passage analyses. For the studied bridge, neglecting SSI increases the maximum acceleration response of the bridge during high-speed train passages from 5.5 m/s2 up to 14.5 m/s2. It is also shown that the response of the bridge during train passage is predominantly influenced by its first bending mode, with higher modes inducing no discernible effect. Finally, parametric studies are performed in order to study the uncertainties related to the soil properties.

In this paper, the dynamic behavior of four railway bridges with integrated retaining walls, considering the effect of soil-structure interaction (SSI), is investigated both numerically and experimentally. Among these bridges, two are single-span, and the remaining two are three-span. Each bridge is equipped with numerous accelerometers and is excited by a hydraulic actuator across various frequencies. Full 3D solid Finite Element (FE) models incorporating the railway bridges and surrounding soils are developed and calibrated using the Frequency Response Functions (FRFs) from each accelerometer. Furthermore, simplified 3D solid and 2D beam models are created for each railway bridge, incorporating springs and dashpots to account for the effect of surrounding soils. The values for these springs and dashpots are obtained from simple equations, except for the impact of the backfill soil in the simplified 2D beam models, which are derived from the impedance functions of the soil medium. The performance of these simplified models is then compared to the calibrated 3D models in terms of modal properties of the first bending mode and the maximum acceleration response during highspeed train passages. The results indicate that the simplified models closely align with the calibrated models in terms of modal properties and high-speed train passage response and can be used as simple and efficient alternatives for practical usage in bridge design.

Structural damping is an important characteristic in railway bridges, which affects the performance of the structure, especially for bridges with train speeds higher than 200 km/h. The accurate evaluation of damping must be performed properly to correctly assess the structural performance of the bridge under dynamic loading conditions. The present article introduces an alternative methodology that contributes to the assessment of damping coefficients with application to railway bridges. The methodology is based in the Prony method with an energy-sorting technique for the identification of dominant frequencies of a free vibration signal of a passing train. The numerical validation of the method is based on a sensitivity analysis of the free vibration periods of signals through the evaluation of influence lines of displacement and numerically simulated receptance tests, and in the estimation of the damping coefficient from the free vibration period obtained in a train-bridge interaction dynamic analysis with a known imposed value. Finally, and in the scope of the In2Track2 and In2Track3 projects, the experimental assessment of damping coefficients using this methodology was carried out, considering four filler-beam bridges from the Portuguese Railway Network. The ambient vibration tests allowed the evaluation of the main frequencies and damping in these bridges, and the dynamic tests under railway traffic allowed the definition of the dynamic response of these bridges and subsequent application of the Prony method for two types of trains. The results of this work allow a new update of the database for damping coefficients of filler-beam railway bridges, contributing to future revisions of EN1991-2.

In this paper, a closed-form approximate formula for estimating the maximum resonant response of beam bridges on viscoelastic supports (VS) under moving loads is proposed. The methodology is based on the discrete approximation of the fundamental vertical mode of a non-proportionally damped Bernoulli-Euler beam, which allows the derivation of closed-form expressions for the fundamental modal characteristics and maximum amplitude of free vibration at the mid-span of VS beams. Finally, an approximate formula to estimate maximum resonant acceleration of VS beams under passage of articulated trains has been proposed. Verification studies prove that the approximate closed-form formula estimates the resonant peaks with good accuracy and is a useful tool for preliminary assessment of railway beam bridges considering the effect of soil-structure interaction at resonance. In combination with the use of full train signatures through the Residual Influence Line (LIR) method, the proposed solution yields good results also in the lower range of speeds, where resonant sub-harmonics are more intensely reduced by damping.

This paper presents an efficient approach for the modal analysis of coupled soil-structure systems, for which the dynamic response is strongly influenced by the embedment in the soil. The methodology is based on a finite element-perfectly matched layer model that allows for the derivation of frequency-independent system matrices and the computation of the modal properties of the coupled system. This is achieved by solving a nonlinear eigenproblem using a Compact Rational Krylov (CoRK) eigensolver. A procedure is developed to sort the computed eigenpairs, filter out the spurious modes of the system which are related to the near-field and truncated far-field soil subdomains and select the physical structural modes of system. The proposed method can be used in the dynamic assessment and structural identification of strongly coupled soil-structure systems such as fully or partially buried structures and allows for the interpretation of experimentally identified modal properties of these systems, especially in the presence of highly damped or closely spaced coupled modes. The applicability and the scalability of the proposed approach for 2D and 3D problems is demonstrated in two case studies.

In this work, the effect of the surrounding soil condition on the fundamental modal characteristics and dynamic response of railway bridges with integral abutments is studied. Due to the computational cost of the full FE models and the lack of reliable simplified models, the effect of the soil-structure interaction is usually neglected in the vibration analysis of the high-speed railway bridges. In the present study, an efficient simplified numerical model is employed to evaluate the modal characteristics of the railway bridge-soil systems. After verifying the accuracy of the simplified numerical model against rigorous models, the effect of the span length and abutment/soil stiffness on the dynamic response of the studied bridges is investigated through a comprehensive parametric study. Several case studies which covers different span lengths and abutment conditions are chosen. It is shown that the SSI has substantial effect on the dynamic response of the short and stiff bridges while its effect decreases as the ratio between the deck stiffness and the abutment/soil stiffness decreases. The results may lead to review the recommended modal damping ratios for this type of bridges in the code provisions and design manuals.