A Simple Mathematical Model for Extreme Flood Actions on Superstructures of Coastal Bridges

Abstract

Coastal bridges may be strongly affected by extreme flood actions (mainly tsunamis), which may be caused by earthquakes, volcanic eruptions, and other underwater explosions (including detonations, landslides, glaciers calvings, meteorite impacts, and other disturbances) above or below water. A simple mathematical model for analysis, processing, and easy yet effective mathematical manipulation is proposed and studied with the aid of simple principles of hydraulics, for investigating the aforementioned effects, in order to avoid rigorous analyses using ocean and coastal engineering. The main idea is based on the investigation of a water vein squirted from a height with a constant horizontal initial velocity, and the analysis of the critical wave in water veins. The results obtained, including the dynamics of deck superstructures and safety issues, reveal the critical situation for avoiding the devastating phenomena of rocking, overturning, and shifting in exemplary small and large coastal bridges. It is found that larger (longer) bridges exhibit acceptable deformations, contrary to smaller ones, while the overturning phenomenon seems to be the most critical one for both types of bridges.