A simplified method to predict grounding damage of double bottom tankers

•Formulas are derived to calculate the size of damage opening in tanker groundings.•The simplified formulas are derived based on a set of numerical simulations.•The grounding resistance is expressed via average contact pressure and contact area.•The damage opening widths are given for two ranges of relative rock sizes.•Critical relative penetration depth for inner hull failure as a function of the ratio of the rock size and the ship breadth.

This paper presents a set of analytical expressions for the calculation of damage opening sizes in tanker groundings. The simplified formulas were given for the grounding force, longitudinal structural damage and the opening width in the inner and outer plating of a tanker's double bottom. The simplified formulas derived are based on a set of numerical simulations conducted with tankers of different dimensions- 120, 190 and 260 m in length. The simulations were performed for five penetration depths and for several rock/ground topologies.The formula for the horizontal grounding force was derived provided the grounding force is proportional to the contact area and the contact pressure. By use of regression analysis it was shown that the contact pressure for any combination of ship and rock size can be expressed with a single normalized polynomial. The actual contact pressure was found by scaling the normalized pressure with the structural resistance coefficient. Given the formulation for the normalized contact pressure, the actual contact force for a ship can be found as a product of average contact pressure and the contact area.The longitudinal length of the damage was evaluated based on the average contact force and the kinetic energy of the ship. The damage opening widths in the outer and inner bottom of the ship were derived separately for two ranges of relative rock sizes as they have strong influence on the deformation mode. The damage widths were given as a function of rock size, penetration depth and double bottom height. To improve the prediction of the onset of the inner bottom failure, a critical relative penetration depth as a function of the ratio of the rock size and the ship breadth was established.Comparison to the numerical simulations showed that the derived simplified approach describes the horizontal grounding force and the damage length well for the penetration depths above 0.5 m. For the range of specified relative rock sizes, the damage width in the inner and outer bottom deviates from numerical simulations approximately up to 25%, which was considered sufficient for the analyses where rapid damage assessment is needed. Comparison was also made to real accidental damage data and to the results of several simplified formulas.