The effective width is a relevant parameter for the design of bridge overhang slabs under concentrated loads. Experimental tests have been used to assess expressions for its calculation. However, the load capacity increases with the width until a transition area is reached. Test specimens may have lacked enough width to reach full shear capacity, affecting thus the evaluation of the results. On the other hand, within the transition area, a threshold value has been hypothesized to match the effective width. This paper aims to provide recommendations for minimal widths that guarantee the full capacity of overhang slabs and to assess the calculation of the effective width by means of the threshold value and other formulations. The effect of the edge beam is also considered. A campaign of validated non-linear FE-simulations based on experiments on range of width-span ratios was performed. The results suggest using a width-span ratio of at least 4.0 for slabs without an edge beam and 5.3 for slabs with an edge beam for the experimental practice. The efficiency of the formulation for the effective widths is diffuse and the use of threshold value leads to unsafe predictions. Instead, linear-elastic FE-analyses are recommended for the design practice.

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.

The dimensioning of overhang slabs in bridge decks is usually based on simplified, thus conservative methods. The resulting over-dimensioned overhang bridge slabs can also affect the design of the girders. In this paper, an optimization procedure for the design of this structural element is presented. The aim is to minimize investment cost and global warming potential in the material production stage simultaneously while fulfilling all safety requirements. The design variables used in this study are the thicknesses of the overhang slab and the height of the edge beam. However, a complete detailed design of reinforcement is performed as well. Both a single-objective and a multi-objective formulation of the nonlinear problem are presented and handled with two well-known optimization algorithms: pattern search and genetic algorithm. The procedure is applied to a case study, which is a bridge in Sweden designed in 2013. One single solution minimizing both objective functions is found and leads to savings in investment cost and CO2-equivalent emissions of 4.2% and 9.3%, respectively. The optimization procedure is then applied to slab free lengths between 1 and 3 m. The outcome is a graph showing the optimal slab thicknesses for each slab length to be used by designers in the early design stage.

This paper investigates the influence of an unsaturated layer in a soft soil on the dynamic response of piles subjected to an incident wave field caused by a vertical surface load. The free field response is compared to the response of single floating and end-bearing piles, and different configurations of square end-bearing pile groups. Simulations are made using a finite element model with perfectly matched layers where the incident wave field is computed from a separate source model employing a subdomain formulation. The presence of the unsaturated layer results in a resonance phenomenon in the top layer, amplifying critically refracted waves as they reach the surface. The associated response is shown to be significantly lower for concrete piles subjected to the same incident loading and practically independent of the pile end condition, in contrast to the response associated with the incident surface waves. For small end-bearing pile groups, the response caused by surface waves are further reduced while the response due to layer resonance show no further reduction. As a consequence, the frequency content associated with the layer resonance might constitute the dominating part of the vertical velocity response for end-bearing pile groups.

This paper presents novel measurement data on the dynamic soil-structure interaction of an end-bearing pile foundation. The purpose is to assess the ability to predict the foundation impedances based on the small-strain properties of the soil obtained from site investigations. Measurements were performed in two stages of construction, allowing to assess interaction between the piles through the soil. First, single pile impedances and interaction factors between the piles were experimentally obtained for the four piles when they were free to move at the surface. Second, the impedances of the square pile group were measured after casting a concrete pile cap. The piles were additionally instrumented with accelerometers at depth along the centerline of each pile, allowing to illustrate the global behaviour of the piles within the soil. Numerical predictions based solely on information of the small-strain soil properties obtained from extensive site investigations are compared to the experimental results. The impedances of the individual piles are overestimated compared to the measurements, while the interaction factors show a better agreement. The pile group impedances are better captured than the individual ones, using the same soil model. The pile-soil-pile interaction is clearly manifested in the experimental results by pronounced peaks in the pile group vertical impedance, validating results from previous numerical studies.

The objective of this article is to study the dynamic behaviour of a timber pedestrian bridge by performing in-situ tests 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. The study included numerical calculations with a 2D finite element model. Two modal parameter extraction methods were implemented during the post-processing. The modes of vibration were analysed with the modal assurance criterion (MAC) to ensure their validity. The results show that the presence of the railings during stage 2 increases the resonance frequencies with 0-2 % compared to stage 1, despite an approximately 5 % increase of the total mass of the bridge. The vertical resonance frequencies decreased 12-22 % when the asphalt was installed at stage 3 compared to stage 2, due to an approximately 70 % increase of the total mass and the asphalt’s low stiffness due to a high temperature. The resonance frequencies increased 14-27 % during cold conditions at stage 4 compared to stage 3. This was mainly due to an increased stiffness of the asphalt layer due to a low temperature. Adding railings therefore resulted in a higher overall stiffness of the bridge, whereas asphalt essentially only added mass to the bridge at warm conditions but increased the stiffness at cold compared to warm conditions. The damping ratios increased for each construction stage and were approximately 2-3 % for the finished bridge. The two modal parameter extraction methods produced similar results which ensures that reliable results are obtained. The auto-MAC indicated well-separated modes and the cross-MAC ensured comparison of the same modes. The finite element model showed that some stiffness was lacking for the first bending mode. This stiffness could be due to shear deformation of the plastic pads at the bridge supports.

Precast hollow-core concrete (HC) slabs are widely used in construction, especially in Nordic countries. The combination of prestressing and low self-weight due to the voids makes it possible to build long-span floors. However, this also makes the floors more sensitive to vibrations from human activities. In this paper, experimental and finite element (FE) analyses of a test HC slab and four in-situ experiments performed in three buildings are presented. For each case, the dynamic assessment is performed using two design guides: SCI P354 (2009) and the Concrete Center (2006). These analyses show that the proposed FE models give accurate results compared to experimental findings and that the Concrete Center design guide gives lower predictions than the SCI P354 guide. In addition, several recommendations can be derived from these studies for the dynamic assessment of HC floors in the design process. The most important is that for some structures, the accelerations calculated using the design guides are significantly higher with an FE model including the considered floor and the surrounding walls than with an FE model including also the lower and higher floors.

Environmental vibrations induced by human activities such as traffic, construction or industrial manufacturing can cause disturbance among residents or to vibration sensitive equipment in buildings. In Sweden, geological formations of soft clay overlying a stiff bedrock are soil conditions prone to ground vibrations that are encountered both in urban areas and along parts of the national railway network. This paper presents an extensive investigation of the small-strain soil properties for the prediction of environmental ground vibrations in a shallow clay where the bedrock is situated at 7.5 m depth. The small-strain properties are estimated using available empirical correlations, bender elements, seismic cone penetration tests, seismic refraction and inversion of surface wave dispersion and attenuation curves. The results are synthesised into a dynamic layered soil model which is validated by measurements at the soil's surface at source-receiver distances up to 90 m in the frequency range 1-80 Hz. Analyses of uncertainties in the estimated values of wave speeds and material damping are performed by model investigations, indicating that surface wave tests overestimate the damping compared to bender element tests. The properties of the topmost unsaturated part of the soil is found to have a significant influence on the response at large distances, caused by critically refracted P-waves resonating in the top layer.

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.