Dynamic Modeling of a Bridge Subjected to Seismic Waves

Abstract

I denne kandidatopgave undersøges udbredelsen af seismiske bølger op gennem et givet antal jordlag og videre igennem en brokonstruktion med en total længde på 2 km. Det er kun horisontale forskydningsbølger der undersøges, da horisontale accelerationer er mest kritisk for de fleste konstruktioner i forhold til vertikale accelerationer. For seismisk design har lokale dæmpnings- og isærforstærknings effekter stor betydning mht. udbredelsen af seismiske bølger. Bølgeudbredelsen gennem bløde jordlag er modeleret ved brug af en endimensional dynamisk lineær viskoelastisk semi-analytisk Domain Transformation Method (DTM) model, samt ved brug af en dynamisk viskoelastisk endimensional Finite Element Method (FEM) model. Resultaterne for de to modeller er sammenlignet for at evaluere modellerne, og de stemmer godt overens. Modellerne er løst i frekvensdomænet for at gøre det muligt at anvende hysteretisk dæmpning, som er anset for at være en udmærket dæmpningsmodel for jord. En delvis lineær model er introduceret i FEM modellen for at tage hensyn til reduktion af tangentforskydningsmodulet samt forøgelse af dæmpningsfaktoren ved stigende forskydningstøjninger. Jordskælvsdata fra jordskælvet i Aqaba 1995 er anvendt. Responsen fra de anvendte jordlag er bestemt og derefter brugt som input til de bropiller, som står på de bløde jordlag. Der sker betydelig forstærkning, når jordskælvet udbredes op gennem de bløde jordlag. Bølgeudbredelsen for broen er bestemt ved anvendelse af en tredimensional dynamisk viskoelatisk FEM model. Både tryk, vridnings samt forskydningsbølger kan modelleres med modellen. Et lille parameterstudie er udført, hvor den horisontale retning for de seismiske bølger varieres. En anden parameter som varieres er den tilsyneladende hastighed som de seismiske bølger udbreder sig med gennem klippen under de bløde jordlag. Variation af denne parameter medfører en forsinkelse af signalet fra bropille til bropille. Resultatet af parameter studiet viser, at en udbredelses retning langs med broen er mest kritisk. Nogle af bropillerne er placeret i vand, hvorfor hydrodynamisk masse er anvendt i modellen.

In this thesis the propagation of seismic waves through a number of soft soil layers and up into a bridge with a total span of 2 km is investigated. Only horizontal shear waves (SH-waves) are modeled, as most buildings are often most vulnerable to excitations in the horizontal direction. In seismic design the local site effects of soft layers is often of big significance, as the amplification of seismic waves when they propagate through soft soil layers is often quite significant. The wave propagation through the soft soil layers are modeled using both a dynamic linear viscoelastic semi-analytic Domain Transformation Method (DTM) and a dynamic linear viscoelastic Finite Element Method (FEM) model. The models are compared in order to validate the results, and the results fit quite nicely. The models are solved in the frequency domain in order to use hysteretic damping, which is recognized as a good damping model for soils. A partly linear model is introduced in the FEM soil model in order to take into account decrease of the small strain shear modulus and increase of the damping ratio as the shear strain amplitude increases. Strong motion data for the 1995 Aqaba Earthquake, which had a moment magnitude of 7.3, is used. The soil response is determined and used as an input to the bridge model. It is found that the soft soil layers amplifies the seismic waves with several magnitudes. The wave propagation through the bridge is modeled using a dynamic linear viscoelastic three dimensional FEM beam model. Both compressional, torsional and shear wave propagation through the bridge can be modeled. The angle at which the the SH-waves hits the bridge can also be varied, which is used in a small parameter study. Another parameter, which is investigated is the delay at which the seismic waves hits the different columns. The results of the parameter study show that the critical direction of the earthquake is parallel to the bridge due to the fact that high normal stresses and thus compressional waves occur in the bridge deck. The bridge is located in water and hydrodynamic mass is therefore applied in the bridge model. Soil structure interaction is also taken into account by using a lumped parameter model to model the rotational as well as the torsional stiffness of the foundations which are located on the soft soils. For the columns founded directly on bedrock, however, the rotational and torsional stiffness is assumed infinitely stiff.

A master thesis from Aalborg University

Dynamic Modeling of a Bridge Subjected to Seismic Waves

[Dynamisk modelering af en bro udsat for seismiske bølger]