This paper investigates the vertical response of end-bearing piles in a homogeneous isotropic linear elastic soil on a rigid bedrock subjected to a vertical harmonic point load at the soil’s surface. A numerical model is used to compute vibration responses. A novel system of dimensionless parameters is established to bring insight into the influence of the relationships between soil and pile properties on the dynamic pile–soil interaction and to allow for general conclusions to be drawn. The results show the conditions under which the relationship between the axial stiffness of the pile and the stiffness of the soil has a significant influence on the end-bearing pile response. Different pile group configurations are considered where the vertical response is found to be bounded by the single pile response, justifying its use as a conservative estimate for the group response. Finally, an expression including only two dimensionless parameters, the pile slenderness ratio and the pile–soil stiffness ratio, is proposed for calculating an estimation of the vertical response of an end-bearing pile from the free field vibrations.

This article investigates the dynamic behaviour of a pedestrian timber truss bridge by in situ testing and numerical modelling. The in situ dynamic tests were performed at three different construction stages: (1) on the finished bridge without the asphalt layer, (2) on the finished bridge with the asphalt layer at warm conditions and (3) same as stage 2 but at cold conditions. The interest of this study is that some modelling details that are usually not considered in the numerical modelling of pedestrian timber bridges are important for this bridge. The stiffness at the connections must be considered in order to obtain accurate numerical results for both lateral and bending modes. The stiffness of the pile foundations has an influence on the first bending mode. In addition, the experimental damping ratio for the first lateral mode is much higher than the values recommended in the design codes.

High-speed railway is expanding drastically in Sweden, necessitating new technology, and improve-ments of existing structures. End-shield bridges are a common and under-tested bridge type inSweden. Their dynamic performance is significantly impacted by their boundary conditions due to thesoil–structure interaction (SSI) and their large masses cantilevering beyond the footings. A specificend-shield bridge was tested under low (5 kN) and high (20kN) amplitude-forced hydraulic excitationfor a wide range of frequencies. Several train passages for typical passenger trains,‘X62’, were meas-ured with the same experimental setup. The results were analysed to isolate the significant modes ofthe system and the natural frequencies. A full 3D numerical model was calibrated and updated inAbaqus, along with a brief sensitivity study to determine the most influential parameters. Finally, theresponse to passing trains and Eurocode design HSLM trains was calculated. The experimental studyshowed that higher loading amplitudes resulted in higher damping and lower natural frequencies. Thenumerical analysis showed that for this bridge type the SSI cannot be neglected and can be success-fully introduced in the model.

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.

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 article investigates the dynamic behaviour of a single span pedestrian timber truss bridge by in situ testing and numerical modelling. The in situ dynamic tests were performed at three different construction stages: (1) on only the truss structure, (2) on the finished bridge without the asphalt layer and (3) on the finished bridge with the asphalt layer. The objective is to better understand how the different parts of the bridge contribute to the overall dynamic properties. The experimental results show that the damping ratios increased significantly for the first lateral mode (from 1.0 to 3.8%) and the first torsional mode (from 1.2 to 3.5%) between stage 2 and stage 3 due to the asphalt layer. The damping ratio is around 1.6% for the first bending mode for the finished bridge. The experimental and numerical results indicate that the stiffness of the asphalt layer is important to consider at stage 3 (10 degrees C) for the first lateral and torsional mode, but not for the first bending mode. Finally, it was concluded that longitudinal springs must be applied at the pot bearings in order to get agreement with the experimental results at all the three stages.

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.

This article studies the dynamic properties of a single span pedestrian timber bridge by in-situ testing and numerical modelling. The in-situ dynamic tests are performed at four different construction stages: (1) on only the timber structure, (2) on the timber structure with the railings, (3) on the timber structure with railings and an asphalt layer during warm conditions and (4) same as stage 3 but during cold conditions. Finite element models for the four construction stages are thereafter implemented and calibrated against the experimental results. The purpose of the study is to better understand how the different parts of the bridge contribute to the overall dynamic properties. The finite element analysis at stage 1 shows that longitudinal springs must be introduced at the supports of the bridge to get accurate results. The experimental results at stage 2 show that the railings contributes to 10% of both the stiffness and mass of the bridge. A shell model of the railings is implemented and calibrated in order to fit with the experimental results. The resonance frequencies decrease with 10–20% at stage 3 compared to stage 2. At stage 3 it is sufficient to introduce the asphalt as an additional mass in the finite element model. For that, a shell layer with surface elements is the best approach. The resonance frequencies increase with 15–30% between warm (stage 3) and cold conditions (stage 4). The stiffness of the asphalt therefore needs to be considered at stage 4. The continuity of the asphalt layer could also increase the overall stiffness of the bridge. The damping ratios increase at all construction stages. They are around 2% at warm conditions and around 2.5% at cold conditions for the finished bridge.