The AASHTO design standard (see reference) was used to estimate the annual probability of collision and the associated return period. The computer program used to perform the computations, along with detailed documentation, are present in our GitHub Repository, with a short summary provided here.
The total Annual Frequency of Collision (AF)total is adapted from the design code (Section 3.14.5) as follows:
The number of components refers to the number of elements of the bridge that are vulnerable to collision. In our current analysis, only certain piers are considered vulnerable to collision with ships depending on their location in the waterway. The number of sizes is described in the next section.
Ship Traffic / Annual Number of Ships
AIS traffic data was collected for six years, from 2018-2023, and divided into six size classes based on their lengths as follows: 150-180 meters, 180-215 meters, 215-250 meters, 250-270 meters, 270-300 meters, and >300 meters. For each of these size classes, Ni is the average number of ships observed in a year (averaged over the six years).
Probability of Vessel Aberrancy
In accordance with Section 3.14.5.2 of the AASHTO design code, we take PA = 0.6 x 10-4, which is the prescribed base aberrancy rate for ships.
Geometric Factor
Section 3.14.5.3 of the AASHTO design code describes how to compute the geometric probability of a ship’s collision with each pier. The pertinent image, taken from the design code, is reproduced on the left.
As indicated in equations 1 & 2, the geometric factor is computed for each pier (index j) for each of the six bridge classes (index i). For each of the six size classes, BM is taken to be the average width of the ships belonging to the chosen size class passing under the bridge. Satellite imagery and design drawings (where available) are used to estimate BP.
The collected AIS ship traffic data is used to find the centerline of vessel training path as the midpoint of all paths taken by ships (of all size classes) under the bridge. The standard deviation of the Normal Distribution is taken to be the nominal length value corresponding to the size class being considered, which is the middle length of each interval, and 300 meters for the largest size class.
Protection Factor
Each pier is provided some protection from collision by dolphins constructed around it. If these dolphins exist, the protection provided is accounted for by the protection factor, computed per Section 3.14.5.5 of the design code for each of the piers and size classes as indicated by equations 1 & 2.
The protection factor for each pier and size class is the sum of the protection provided by each dolphin surrounding a given pier. The surrounding images, taken from the design code, summarize the calculations involved.
