Statistics and damage assessment of ship grounding

In this paper, general statistics of ship grounding incidents are considered and the damage extent distributions for Ro–Ro ships are presented from the results of a comprehensive damage data survey conducted using Lloyd's Register's damage database. Theoretical models and semi-empirical formulae based on parametric studies are used to study the damage extents of grounded ships. Two real life grounding accidents are assessed. One is a single hull VLCC grounded onto a single rock and the other is a cargo ship grounded onto multiple rocks. A simulation based on a simple multi-rock scenario has been conducted on a 304-m single hull tanker. Correlation is made between the present calculation method results, statistical results and IMO requirements. The paper concludes with the main findings from the study.     

A simplified method to predict grounding damage of double bottom tankers

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.     

The influence of fluid structure interaction modelling on the dynamic response of ships subject to collision and grounding

Analysis of the dynamic response of ships in accident scenarios requires a realistic idealisation of environmental and operational conditions by multi-physics models. This paper presents a procedure that simulates the influence of strongly coupled FSI effects on the dynamic response of ships involved in typical collision and grounding events. Our method couples an explicit 6-DoF structural dynamic finite element scheme with a hydrodynamic method accounting for (a) 6-DoF potential flow hydrodynamic actions; (b) the influence of evasive ship speed in the way of contact and (c) the effects of hydrodynamic resistance based on a RANS CFD model. Multi-physics simulations for typical accident scenarios involving passenger ships confirm that suitable FSI modelling may be critical for either collision or grounding events primarily because of the influence of hydrodynamic restoring forces.     

Analytical modelling of ship bottom grounding considering combined surge and heave motions

This paper provides a new contribution to the analytical treatment of ship grounding accidents. New formulations are proposed to assess the resisting force of outer/inner bottom plating and transverse floors when the vessel undergoes combined surge and heave motions during the grounding event. Considering shallow and sharp rocks described by parabolic functions, analytical solutions are derived from plastic limit analysis and validated by comparison to non-linear finite element simulations. A failure criterion is also proposed to trigger the rupture of the bottom plating and all the derived closed-form expressions are implemented into an in-house solver. The solver is then coupled to a 6-DOFs external dynamics program, which allows to account for the action of the surrounding water. Resulting tool is first validated on a full scale cruise ship by comparison to finite element results. It appears than although some discrepancies arise, especially in the response of transverse floors after rupture, the bottom damage distribution seems to be well predicted. Finally, the developed tool is used to quickly predict the grounding response of different types of ships and the influence of their mass and hydrodynamic properties on the damage extent is investigated.     

Simplified analytical method for evaluating web girder crushing during ship collision and grounding

The paper presents a simplified analytical method to examine the crushing resistance of web girders subjected to local static or dynamic in-plane loads. A new theoretical model, inspired by existing simplified approaches, is developed to describe the progressive plastic deformation behaviour of web girders. It is of considerable practical importance to estimate the extent of structural deformation within ship web girders during collision and grounding accidents. In this paper, new formulae to evaluate this crushing force are proposed on the basis of a new folding deformation mode. The folding deformation of web girders is divided into two parts, plastic deformation and elastic buckling zones, which are not taken into account for in the existing models. Thus, the proposed formulae can well express the crushing deformation behaviour of the first and subsequent folds. They are validated with experimental results of web girder found in literature and actual numerical simulations performed by the explicit LS-DYNA finite element solver. The elastic buckling zone, which absorbs almost zero energy, is captured and confirmed by the numerical results. In addition, the analytical method derives expressions to estimate the average strain rate of the web girders during the impact process and evaluates the material strain rate sensitivity with the Cowper-Symonds constitutive model. These adopted formulae, validated with an existing drop weight impact test, can well capture the dynamic effect of web girders.     

Glacial ice impacts: Part I: Wave-driven motion and small glacial ice feature impacts

Glacial ice features in the northern and central Barents Sea may threaten ships and offshore structures. Particularly, small glacial ice features, which are difficult to detect and manage by concurrent technologies, are of concern. Additionally, small glacial ice features are more susceptible to wave-driven oscillatory motions, which increases their pre-impact kinetic energy and may damage ships and offshore structures. This paper is part of three related papers. An initial paper (Monteban et al., 2020) studied glacial ice features’ drift, size distribution and encounter frequencies with an offshore structure in the Barents Sea. The following two papers (Paper I and Paper II) further performed glacial ice impact studies, including impact motion analysis (Paper I) and structural damage assessment (Paper II). This paper (Paper I) studies the wave-driven motion of small glacial ice features and their subsequent impact with a given offshore structure. The aim here is to develop a numerical model that is capable of efficiently calculating the relative motion between the ice feature and structure and to sample a sufficient amount of impact events from which statistical information can be obtained. The statistical information entails the distributions of the impact location and associated impact velocities. Given the distributions of the impact velocities at different locations, we can quantify the kinetic energy for related impact scenarios for a further structural damage assessment in Paper II (Yu et al., 2020).In Paper I, a numerical model that separately calculates the wave-driven oscillatory motion and the mean drift motion of small glacial ice features is proposed, implemented and validated. Practical and fit-for-purpose hydrodynamic simplifications are made to simulate and sample sufficient impact events. The numerical model has been favourably validated against existing numerical results and experimental data. A case study is presented where a 10 m wide glacial ice feature is drifting under the influence of surface waves towards an offshore structure. The case study shows that if an impact happens, the overall impact location and impact velocity can be best fitted by the Normal and Weibull distributions, respectively. Additionally, the impact velocity increases with impact height. Moreover, the impact velocity increases and the impact range is more dispersed in a higher sea state. It is also important to notice that the approaches and methods proposed in this paper adhere to and reflect the general requirements stated in ISO19906 (2019) and NORSOK N-003 (2017) for estimating the design kinetic energy for glacial ice impacts.     

Analysis of ship–ship collision damage accounting for bow and side deformation interaction

This paper presents a procedure to analyse ship collisions using a simplified analytical method by taking into account the interaction between the deformation on the striking and the struck ships. Numerical simulations using the finite element software LS-DYNA are conducted to produce virtual experimental data for several ship collision scenarios. The numerical results are used to validate the method. The contributions to the total resistance from all structural components of the collided ships are analysed in the numerical simulation and the simplified method. Three types of collisions were identified based on the relative resistance of one ship to the other. They are denoted Collision Types 1 and 2, in which a relatively rigid ship collides with a deformable ship, and Collision Type 3, in which two deformable ships are involved. For Collision Types 1 and 2, estimates of the energy absorbed by the damaged ships differ by less than 8% compared to the numerical results. For Collision Type 3, the results differ by approximately 13%. The simplified method is applicable for right angle ship collision scenario, and it can be used as an alternative tool because it quickly generates acceptable results.     

Onboard monitoring of fatigue damage rates in the hull girder

Most new advanced ships have extensive data collection systems to be used for continuous monitoring of engine and hull performance, for voyage performance evaluation etc. Such systems could be expanded to include also procedures for stress monitoring and for decision support, where the most critical wave-induced ship extreme responses and fatigue damage accumulation can be estimated for hypothetical changes in ship course and speed in the automatically estimated wave environment.The aim of this paper is to outline a calculation procedure for fatigue damage rate prediction in hull girders taking into account whipping stresses. It is conceptually shown how such a method, which integrates onboard estimation of sea states, can be used to deduce decision support with respect to the accumulated fatigue damage in the hull girder.The paper firstly presents a set of measured full-scale wave-induced stress ranges in a container ship, where the associated fatigue damage rates calculated from a combination of the rain-flow counting method and the Palmgren-Miner damage rule are compared with damage predictions obtained from a computationally much faster frequency fatigue analysis using a spectral method. This analysis verifies the applied multi-modal spectral analysis procedure for fatigue estimation for cases where hull girder flexibility plays a role.To obtain an automated prediction method for the fatigue damage rates it is in the second part of the paper shown how a combination of the full-scale onboard acceleration and stress measurements can be used to calculate sea state parameters. These calculated environmental data are verified by a comparison to hindcast data.In the third part of the paper the full-scale fatigue stress ranges are compared to results from an analytical design oriented calculation procedure for flexible ship hulls in short-term estimated sea states.Altogether, it is conceptually shown that by a combination of the onboard estimated sea state parameters with the described analytical fatigue damage prediction procedure a method can be established for real-time onboard decision support which includes estimates of fatigue damage rates.     

Updated vertical extent of collision damage

The probabilistic distribution of the vertical extent of collision damage is an important and somewhat controversial component of the proposed IMO harmonized damage stability regulations for cargo and passenger ships. The only pre-existing vertical distribution, currently used in the international cargo ship regulations, was based on a very simplified presumption of bow heights. This paper investigates the development of this damage extent distribution based on three independent methodologies; actual casualty measurements, world fleet bow height statistics, and collision simulation modeling. The results from the three methods are compared, and a proposed distribution for the new harmonized regulations is presented.     

Understanding ship-grounding events

The paper presents a simple procedure to estimate the damage to a ship bottom and the associated seabed topology that results from a dynamic grounding event. The seabed is modeled as a rigid body and parameterized by a quadratic surface, i.e., a paraboloid, which can in principle model a wide range of seabed topologies. A nonlinear finite element program (LS-DYNA) is used to simulate the contact force versus the lateral penetration, from which the horizontal force component of powered grounding is estimated. The simplified procedure for analyzing dynamic and static grounding events is outlined. Simulations are performed for different ship speeds and for different initial levels of obstruction over the keel. It is shown that a static approach may replace the dynamic grounding simulation, thereby considerably reducing the computational work. The static approach allows for the quick estimation of the energy absorption during powered grounding, which is imperative for decision making during critical situations. The ultimate goal of the study is to provide a near real-time prediction of the risk of rupture of the cargo tanks and hull girder failure. Moreover, the residual strength of damaged ships is an important issue that is related to operations involved in the salvage of wrecked vessels, such as re-floatation and towing.     

Bottom damage scenarios for the hull girder structural assessment

This article covers the reliability assessment of the hull girder of a crude oil tanker, referring to a scenario in which the ship is exposed to sea loads after a damage to the bottom of the hull has occurred. A number of possible flooding configurations are examined, each one caused by a group of damage cases, characterized by different location and extent. Static loads, wave loads and residual structural resistance are determined for each damage case, with the objective of obtaining a prediction for the probability of the hull girder's failure. The various damage cases are compared to each other and unconditioned to derive the probability of failure extended to the ship's life due to a generic bottom damage.A probabilistic Bayesian Network model has been created to deal with these variables and with the dependency relationships existing between them. The results provided by the model are analyzed with the aim of identifying the parameters most influencing the problem. The work is intended to contribute to the development of a more rational treatment of accidental conditions in design structural requirements for ships.     

Motion sickness onboard ships: subjective vertical theory and its application to full-scale trials

This article presents a new approach for the prediction of motion sickness on ships, with a focus on high-speed craft. The methodology presented is based on a variant of the sensory conflict hypothesis and the human vestibular system. The proposed model was developed using control theory and is capable of taking account of all six degrees of freedom vessel motion for the prediction of motion sickness. Furthermore, full-scale trials were carried out onboard three different high-speed craft to measure the ship motions and consequently to analyse their effects on passengers in terms of motion sickness. Through the accumulated results, the developed model was validated and was compared with existing methods/criteria for the prediction of the incidence of motion sickness.     

Plate tearing and bottom damage in ship grounding

A theoretical method for plate tearing by a rigid wedge is developed in this paper. The studied model is an idealization of ship-grounding and collision damage. The analysis model postulates that the plate curls up into two curved surfaces behind the wedge tip and that the plate material ahead of the wedge is tensioned and ruptured due to the direct pushing. Based on a parametric study, a semi-empirical formula is proposed for determining grounding force in the event of a ship running onto rocks in a high-energy grounding. The bottom strengths of single hull structures and double hull structures in ship-grounding incidents are compared. Finally, simple formulae for determining damage resistance and the extent of damage in ship grounding, expressed in terms of the ship principal particulars, are developed.     

Rapid prediction of structural responses of double-bottom structures in shoal grounding scenario

This study presents a simplified analytical model for predicting the structural responses of double-bottom ships in a shoal grounding scenario. This solution is based on a series of analytical models developed from elastic-plastic mechanism theories for different structural components, including bottom girders, floors, bottom plating, and attached stiffeners. We verify this simplified analytical model by numerical simulation, and establish finite element models for a typical tanker hold and a rigid indenter representing seabed obstacles. Employing the LS-DYNA finite element solver, we conduct numerical simulations for shoal-grounding cases with a wide range of slope angles and indentation depths. In comparison with numerical simulations, we verify the proposed simplified analytical model with respect to the total energy dissipation and the horizontal grounding resistance. We also investigate the interaction effect of deformation patterns between bottom structure components. Our results show that the total energy dissipation and resistances predicted by the analytical model agree well with those from numerical simulations.     

双层底船搁浅场景下结构响应的快速预报（英文）

This study presents a simplified analytical model for predicting the structural responses of double-bottom ships in a shoal grounding scenario. This solution is based on a series of analytical models developed from elastic-plastic mechanism theories for different structural components, including bottom girders, floors, bottom plating, and attached stiffeners. We verify this simplified analytical model by numerical simulation, and establish finite element models for a typical tanker hold and a rigid indenter representing seabed obstacles. Employing the LS-DYNA finite element solver, we conduct numerical simulations for shoal-grounding cases with a wide range of slope angles and indentation depths. In comparison with numerical simulations, we verify the proposed simplified analytical model with respect to the total energy dissipation and the horizontal grounding resistance. We also investigate the interaction effect of deformation patterns between bottom structure components. Our results show that the total energy dissipation and resistances predicted by the analytical model agree well with those from numerical simulations.     

Experimental and analytical investigations on the response of stiffened plates subjected to lateral collisions

Rational structural design of ships or offshore platforms against collisions requires prediction of the extent of damage to stiffened plates generated by lateral impact. In predicting the extent of collision damage, most researchers employ numerical analysis methods using commercial software packages. Like other structural problems, any nonlinear dynamic analysis methods should be substantiated with relevant test data prior to being employed for design. Unfortunately, full-scale collision tests on marine structures are very rare. Still, results from collision tests on marine structural elements can help to substantiate theoretical methods for collision analyses. Lateral collision test data for unstiffened plates are available, but it is difficult to find results from tests on stiffened plates in the open literature. In this paper, the results of lateral collision tests on 33 stiffened plates are reported. A simplified analytical method is developed for the prediction of the extent of damage to stiffened plates due to lateral collisions and this method is substantiated with the test results. Also proposed is a simple criterion with which the occurrence of crack damage can be judged.     

高能搁浅下双层底结构的损伤特性研究

船舶搁浅事故会引起船体破损、环境污染和人员伤亡等严重后果.研究船舶搁浅,不仅有利于海上生命安全、防止海洋污染,还可为船体结构的抗冲击设计及规范航运繁忙区域中船舶的航速、操作规程提供一定的依据.本文用数值仿真法研究了船舶高能搁浅中的内部力学问题,分析了典型双层底结构的损伤变形、受力和能量耗散等结果,提出了一种新式的抗搁浅YF双层底结构,并与原结构进行了比较.研究表明,损伤变形集中于结构与礁石相接触的区域,高能搁浅内部力学问题的研究可以主要考虑局部的船体结构;肋板的存在显著增加了船底结构的抗搁浅能力;高能搁浅过程中,由于垂直方向的接触力,礁石对双层底的垂向贯入量会略有减小;当纵桁远离搁浅区域时,它的吸能能力无法发挥,抗搁浅作用很弱;YF双层底结构比原结构具有更大的吸能能力和抗搁浅力.     

受损船体极限强度分析与可靠性评估

对预报船舶极限强度的解析公式作局部改进，使其更有效地用于评估或预报现代船舶剩余极限强度。将该方法同MVFOSM相结合，对一艘油船进行了完整船体（新建／老龄）与受损结构（搁浅／碰撞）极限总纵强度分析和可靠性评估及预报；某些结论可作为深入研究剩余强度理论或指导实船结构设计的参考。     

Verification of a simplified analytical method for predictions of ship groundings over large contact surfaces by numerical simulations

In this paper, a verification is presented of a simplified analytical method for the predictions from numerical simulations of structural performance during ship groundings over seabed obstacles with large contact surfaces and trapezoidal cross-section. This simplified analytical method was developed by Lin Hong and Jørgen Amdahl and calculates grounding characteristics, such as resistance and distortion energy, for double-bottomed ships in shoal grounding accidents. Two finite-element models are presented. One was built for a hold, and the other was built for a hold and a ship hull girder and also considers sectional properties, ship mass, added mass and the hydrodynamic restoring force. The verification was completed by comparing horizontal and vertical resistances and the distortion energy between seven numerical-simulation cases and a set of corresponding cases computed by a simplified analytical method. The results show that the resistances obtained by the simplified analytical method are close to the mean values of the resistance curves obtained by numerical simulations. The comparisons prove that the energy dissipation-prediction capability of the simplified analytical method is valuable. Thus, the simplified analytical method is feasible for assessing ship groundings over seabed obstacles with large contact surfaces and trapezoidal cross-section. Furthermore, studies of the influence of ship motion during groundings ascertained that ship motion affects structural performance characteristics. Resistances are lessened at the end of the grounding due to the reduction of indentations caused by heave and pitch motions of the ship hull girder. Finally, a new method for predicting the structural performance of the time-consuming complete-ship model by applying a combination of normal numerical simulations and ship-motion calculations is proposed and proven.