Risk assessment of bridge collision – using Monte Carlo Simulation

The E39 road, connecting the Norwegian coastal cities of Kristiansand and Trondheim, includes eight ferry crossings. The Norwegian Public Roads Administration (NPRA) is now investigating how to replace these ferries by fixed crossings. One of the most challenging crossings is the one over Bjørnafjorden south of Bergen – it is 5 km long, and up to 600 metres deep and crosses important shipping lanes. SSPA has been commissioned by the NPRA to conduct ship collision risk analyses and to compare different bridge and tunnel options from a navigational safety point of view.

In order to estimate the probability of different ship-bridge collision scenarios, SSPA has applied a method based on the Monte Carlo technique.

Monte Carlo Simulation 

The Monte Carlo approach is a computational algorithm that relies on repeated random input parameters to a model in order to obtain numerical results; typically compressed time simulations are repeated many times to obtain the distribution of an unknown probabilistic entity.

In this study, a large number of input parameters are randomly generated according to various probability distributions. These parameters represent realistic sets of the operational conditions of the ship traffic.

The ship traffic is simulated by a fleet of vessels, representing the predicted ship traffic in 2035. The outputs are:

  • locations of collision (pattern)
  • collision energy and forces.

This data is used in combination with a prognosis for expected ship traffic frequencies and the probability for various types of failure in order to obtain probabilities for collisions and collision energies exceeding a certain energy level.

The following input parameters have been used and varied in a large number of systematically conducted compressed time simulations:

  • Size and type of ship
  • Ship speed profile
  • Propulsion and rudder systems
  • Metocean data (e.g. wind and current)
  • Bridge configuration
  • Routes for the fleet of representative ships at the bridge crossing and in transit outside the bridge area
  • Probability of the occurrence of technical failures and human errors
  • Probability that failures/ errors are repaired/ corrected in due time to prevent collision.

According to Norwegian design criteria, this type of bridge should be designed to withstand a collision energy that is expected at a return period of 10 000 years. In order to be able to assess an event with this return period, simulations representing failure events and errors expected over a total period of one million years are conducted for each of the addressed bridge and tunnel options. Given the traffic density and probability of technical failures and human errors, it is required to simulate roughly one million vessel transits in the area. 

Each of these simulations is performed using the following sequence:
1. Initiate starting ship position according to routes and traffic distribution in the area. Introduce weather condition based on statistics for the area.
2. At a given time, initiate failure (technical failure or human error) causing the ship to divert from the intended route.
3. If possible due to the type of failure, take evasive actions to avoid grounding or bridge collision.
4. Continue simulation until bridge collision or grounding occurs, or the given repair/ correction time is reached.
5. For each simulation, an extensive set of result variables is stored. In case of bridge collision, these include the location on the bridge element where the collision occurred, maximum collision force, impact energy, etc.)

The simulations generate statistical data on expected collision positions along the bridge and the associated collision energy absorbed by the bridge, as shown in the figures below. The simulations output is also a subject for uncertainty evaluation and sensitivity analysis.

Conclusions and other applications for the methodology

The output from the SSPA analysis provides NPRA with reliable input data on adequate risk-based design loads for ship collision loads for the considered bridge options. The present options comprise a TLP suspension bridge, a floating bridge on pontoons, and a submerged floating tunnel SFT. These will be subjected to comparative analyses. None of the addressed concepts has previously been designed and tested at this scale in terms of length and water
depth – any will become record-breakers.

This Monte Carlo approach has proved powerful and efficient in the simulation of vessel traffic and generating risk figures for complex traffic scenarios and infrastructure constructions. It could also be applied to port and fairway design projects, the optimisation of safe and green shipping routes, the establishment of offshore wind farms, and the near-shore design of sensitive buildings and residential areas, etc.

The combination of SSPA´s well-established simulation models with powerful computational capacity ensures the efficient and reliable analysis of complex scenarios.

Photos and illustrations

The most challenging crossing is the one over Bjørnafjorden south of Bergen, which is 5 km long and up to 600 metres deep. Illustration: NPRA.

Ship tracks from failure simulations for a floating bridge with a centre span width of 400 m and free sailing height of 52 m.

Distribution of expected collision energies along the TLP and the floating bridge for 1 000 000 times, by the year 2035. The blue dots indicate collision with pontoon/ pillar elements and the green dots indicate collision with bridge deck elements. The red line indicates the limit collision energies with a return period of 10 000 years.

Coastal Highway Route E39

Take a look at "Coastal Highway Route E39 animation" (by the Norwegian Public Roads Administration/Statens vegvesen)