Numerical Simulation of Hydrodynamic Forces on Bridge Decks

Abstract

Highway bridges along the coast and small river bridges in mountainous regions can be submerged during storm surges or strong rainfall events, respectively. Loss of serviceability during these conditions can dramatically hamper the evacuation plan and the capacity for emergency transportation, thus it is essential to ensure the stability of bridges in extreme hydrological events. Correct estimates of the hydrodynamic forces on a bridge allows bridge designers to evaluate the robustness of the bridge in a more sophisticated approach rather than relying on a constant force magnitude obtained from a small range of physical tests. 
This study presents numerical simulations performed to quantify the hydrodynamic forces on a bridge deck with a rectangular cross section. The results of the numerical model are validated against the results of physical experiments. More than 700 simulations were performed to thoroughly investigate the effect of certain parameters on the flow field and forces on the deck. The parameters considered include: the water level, the Froude number, the blockage ratio, the proximity of the deck to the channel floor, the inclination of the deck, and the aspect ratio of the deck.
 The lift force is found to be downward unless the deck is significantly submerged i.e., inundation ratio (h*) is greater than 3.5, and the upstream velocity is relatively small, Frd<0.6. For h*<3.5 the development of flow patterns on the upper side of the deck is constrained by the presence of the free surface which causes an asymmetric pressure distribution in the vertical direction and ultimately results in a downward force. Increase in flow velocity results in a higher downward force and hence increase the bridge stability (provided that the submergence of the bridge is not too high, h*<4). When considering the trend of changes in lift and drag forces simultaneously, it can be said that the combination of small velocities and inundation ratios higher than 2 results in the most critical situation for the vertical stability of the bridge deck.
 An increase in the blockage ratio results in an increase in the drag coefficient. On the other hand, a decrease in the blockage ratio shifts the drag coefficient towards the value of 1.56, which corresponds to the drag coefficient of a rectangular cylinder in an unbounded flow. Considering the common flow conditions of practical interest for bridge designers, the upper boundary of the drag coefficient for the box deck was found to be 2.8. Incipient failure analysis is performed to establish a hydrodynamic situation that can cause the failure of the deck. Regardless of the proximity ratio and the Froude number, the bridge deck collapsed when the inundation ratio was higher than 1.3. This indicates that the deck is more susceptible to high water levels than to flood velocity or to the distance to the channel floor. Moreover, no bridge failure occurred for inundation ratios lower than 1.3, indicating that the deck must be deeply submerged to fail. By extracting the starting point of failure for a wide range of inundation ratios, proximity ratios, and Froude numbers, contour lines of the threshold of failure are drawn. These contour lines representing the starting point of failure provide the basis for more accurate estimates of the failure of the bridge due to flood loadings and can be considered to be included in the bridge design codes and guidelines. In fact, this proposed method is more reliable than the traditional method which assumes a constant value for drag and lift. The traditional methods are still present in some guidelines such as the AASHTO Load and Resistance Factor Design (LRFD) Bridge Design Specifications.
 Attaching wing-shaped structures on the sides of the deck was proposed as a countermeasure to avoid failure of the bridge decks. Although the projected area of the deck perpendicular to the direction of flow was kept constant, it was expected that CD, CL, and CM would change; since they are dependent on the geometry of the deck, and the flow pattern is altered significantly due to the presence of wings. Results of several simulations for six different shape of wings under different inundation ratio and Froude number indicated that a rational shape of the wings can significantly alter the flow pattern around the deck and postpone occurrence of failure during conditions of really high water levels (h*>2.5) and high flood velocity (Fr>0.65). The proposed countermeasure can be considered as a robust solution for the wide range of probable floods, because of the fact that firstly, occurrence of this extreme hydrological situation is rare, and secondly, the stability of the deck in that situation might not be the first priority, especially compared with the risk of flooding a large part of the upstream land.