Refined model for calculating the dynamic amplification factor for road bridges
Abstract: The objective of the thesis is to simulate and evaluate vehicle-bridge interaction (VBI) due to road surface irregularities and soil-structure interaction (SSI) with different vehicle models and suspension properties. Parameter studies will be carried out for integral and slab bridges. The aim is to compare the results with the current formula for the dynamic amplification factor (DAF) according to Trafikverket (TDOK 2013:0267) and provide appropriate recommendations. The difference between two suspension types, i.e. air and leaf suspension, will be evaluated as well. Suggestions of measures taken for platoons if they prove to be a problem concerning resonance in bridges will also be presented. The aim is also to evaluate the influence of SSI and other parameters that affect the DAF. A toolbox in MATLAB that solves the VBI has been verified and used. The vehicles are modeled as mass-spring-damper systems moving across the bridge. The two subsystems, i.e. bridge and vehicle, are coupled using the contact forces and displacements. The coupled equations are solved with the finite element method (FEM) and the time-varying dynamic response is solved with the Newmark-beta integration scheme. Road surface irregularities are generated using Power Spectral Density (PSD) functions according to ISO-8608. Vehicle properties are taken from previous studies for both air and leaf suspension. Bridge properties are retrieved from constructional drawings from ELU Konsult and damping according to SS-EN 1991-2. Soil properties are gathered from previous studies and a simplified soil model is used. Information of traffic composition and flow rate is gathered from weigh-in-motion (WIM) measurements of Swedish bridges. Traffic is simulated using statistical assumptions from previous studies. Information of distances between trucks in a platoon is gathered from the results of different European projects. The results from the parameter studies shows that the DAF exceeds the Swedish norm for both single and multiple truck events. The main factor to the exceeding is coincidental frequencies, i.e. when the eigenfrequencies of the vehicles coincide with the bridge's fundamental frequency. An example of a refined model of the DAF based on bridge fundamental frequency is therefore presented, which also includes the speed limit of the bridge. It is shown that heavier vehicles provides a lower DAF compared to lighter vehicles. Air suspension is also shown to give a lower response than leaf suspension when the lowest vehicle modes (suspension modes) are close to the bridge's fundamental frequency. When the bridge fundamental frequency exceed the highest vehicle modes the response is similar for the two suspension types. Platoons are shown to induce resonance which is largest for the slab bridges due to their larger mass and lack of rotational stiffness at the boundaries compared to the integral bridges. Having random distances between vehicles as a safety measure is therefore recommended. SSI provides an amplified response for the VBI and it is shown that the response is attenuated with increasing stiffness and damping on the soil.
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