Ship Capsizing Research Articles

Capsize criteria in beam seas: Melnikov analysis vs. safe basin erosion

We study the problem of capsizing of a rolling ship in harmonic and random beam seas, by means of the Melnikov method and safe basin calculations. In the random excitation case, we consider an integro-differential Cummins-type model equation that takes into account the hydrodynamic memory. The non-linear restoring moment is modeled by a high-order polynomial and the Melnikov criteria are evaluated numerically. We also examine a variant of the classical Melnikov method in which the damping terms are incorporated into the unperturbed system and the perturbation takes a modified form. We compare the theoretical predictions with direct (Monte-Carlo) simulations of the safe basins for two existing ships. In the random excitation case, we quantify the erosion by means of a mean integrity index. For weak damping, the classical and modified Melnikov curves coincide and are in good agreement with the onset of the safe basin erosion. As damping increases the Melnikov curves become less and less conservative with respect to the onset of erosion. Finally, the potential of the Melnikov method to provide a ship classification tool is discussed.

ALGORITHM FOR ESTIMATING THE PARAMETRIC ROLL MOTIONS

For a ship, both synchronous and parametric roll motions can be modelled by nonlinear second-order differential equations with the roll angle as dependent variable and the nonlinearities coming from the damping and restoring moments. In the absence of exact solution techniques, approximate solutions for such equations can be obtained, in principle, analytically or numerically. In this paper, we focused on a fast and accurate recursive scheme based on the segmentation of the time domain into a fine grid of intervals of equal lengths. Due to the smallness of each time subinterval, a reset of the terms of the initial nonlinear equation of motion allows replacing it with a linear one in which the constant coefficients represent approximate values of the former variable coefficients in the middle of each subinterval. The linear equation is solved via the Laplace transform and the resulting solution together with its first derivatives is used to generate the iterative algorithm. This technique was applied to the case of two typical roll equations. The first describes the synchronous roll of a vehicle ferry model equipped or not with bilge keels while the second estimates the parametric roll of a container ship model. In both cases, the analyzed recursive algorithm not only generated results in full agreement with those provided by the ode45 solver in Matlab but also lead to a gain in computation time and offered more flexibility in imposing some restrictive conditions associated, for example, with exceeding some oscillation amplitudes or to the ship capsizing. Key words: synchronous and parametric ship rolling, iterative scheme

Stochastic Roll Dynamics of Smooth and Impacting Vessels in Random Waves

Ship instability is frequently associated with extreme roll motion. In this paper smooth and vibro-impact dynamics of vessels rolling under random wave excitations including nonlinearities is investigated. The vessel is represented by a single degree of freedom roll model. The random excitation due to waves and ice is modeled by a sum of random pulses with Poisson arrival rate. Stochastic P-bifurcation analysis is carried out by examining the variation with parameter of the joint probability density functions (jpdf) of the response computed numerically by the solution of the corresponding Fokker–Planck–Kolmogorov (FPK) equation. The finite element (FE), finite difference (FD), path integral (PI) and radial basis neural (RBN) network formulation methods are used in the solution of the FPK equation. The D-bifurcation analysis is analyzed by computing the largest Lyapunov exponent. The mean upcrossing rate is computed using Rice’s formula. The random wave excitation is also modeled as the response of a second order linear filter to white noise and the random response of the ship is investigated by solution of the corresponding FPK equation of the four dimensional Markov system by the FD method. Non-smooth coordinate transformations like the Zhuravlev and Ivanov transformations are used converting the discontinuous systems to equivalent smooth systems in the impact dynamics analysis. The adaptive time stepping method (ATSM) approach is used to accurately locate the discontinuity point and a Brownian tree approach is used to direct the integration along the correct Brownian path. Different models for nonlinear damping and the restoring moment are considered and their effects on ship stochastic response such as chaotic motion, unbounded rotational motion, impact modulation motion and ship capsizing are investigated.

Numerical study on damaged ship rolling and capsizing in irregular beam waves during quasi-steady flooding

To study roll dynamics and capsizing occurrence of damaged ship in irregular beam waves, computational fluid dynamics is used to simulate damaged ship motions at rough sea to high sea states. The velocity-inlet boundary and momentum source are combined for wave generation. A modified formula is adopted to calculate turbulent viscosity to prevent unphysical decay of wave. The lateral drift restrained model is integrated with a combined dynamic mesh strategy to handle the ship's sway, heave and roll motions. Benchmarking study of irregular wave generation and roll response of damaged ship in regular waves is performed. Based on the simulations of motions of intact and damaged ships in irregular waves, the effects of cross flooding and damage orientation on the roll response of ship are discussed. For symmetrical flooding, the roll behaviour of ship is insensitive to the damage orientation. Due to the increase of roll damping, the roll response of damaged ship is smaller than that of intact ship. For asymmetric flooding, the ship is liable to roll toward the damaged side with a large angle. The probability of capsizing of ship caused by waveward damage is high at high sea state.

Extrapolation of ship capsize probability over significant wave height: Foundation on wave groups theory

The paper lays formal foundation for the “extrapolation over significant wave height” technique which has recently been incorporated into the Second Generation Intact Stability Criteria of the International Maritime Organization (IMO) for assessing the dynamic stability of ships in waves. The technique aims at estimating efficiently a ship's tendency to capsize in relatively mild sea conditions through parsimonious simulations of ship motion. To address the rarity of capsizes in such conditions, extrapolation is employed for the probability value obtained from severer sea states differing only in their significant wave heights. In its current version, the approach extrapolates as if capsize was caused solely by exceptionally large wave encounters, thus ignoring phenomena such as resonance or wave grouping. Herein, the concept is revisited from the perspective of the “critical wave groups” method which is demonstrated as a general framework enabling rigorous “extrapolation over significant wave height” formulations. In this setting, two new extrapolation models are developed from basic principles as improvements to the one suggested by the IMO. The first model accounts for the joint effect of wave heights and periods, while the second additionally integrates the temporal dependence between consecutive wave heights into the extrapolation scheme. The accuracy of the theoretical predictions as well as their sensitivity to the amount of available data are evaluated for the case of beam-sea rolling assuming two different spectrum types as possible characterizations of the prevailing wave conditions. Justification about the extrapolation capabilities of the derived models is provided in view of the advances in extreme wave stochastics accommodated by the theory of Quasi-Determinism.

Risk Accident Analysis Due to the Effect of Wrong Loading on Ship Stability

In this study, the effect of laying and shifting load is considered as one of the main factors of ship safety. Ferry Ro-Ro that carry vehicles and passengers were chosen as the object of study with the assumption that the vehicles are not lashed. Safety measurement is carried out through static stability analysis with criteria limits IMO Intact Stability Code 2008 and PM44 2021 and dynamic stability with roll motion limitations due to beam sea to result quantitative risk assessment data. The wave height is taken from the waters of the Bali strait with a Beaufort scale conversion of BF1 to BF6. Because of the vehicle is not lashed, the vehicle is simulated to shift horizontally as far as 10% to stack onto the starboard, while the assumption of passenger movement is vertical and horizontal. The biggest heel angle due to the shifting load is 9 degrees when all loads are stacked on the starboard (G1). Analysis of the calculation of static stability shows that several conditions do not meet the criteria with the greatest Roll Amplitude value of 39.56 deg at BF6 4 m. In dynamic stability conditions through maxsurf motion, the safe wave height for Ferry Ro-Ro operation is up to BF4 1.14 m. The highest risk of ship capsizing occurs when operating on BF5 with wave heights above 2 m.

WEND: An Efficient WSN-Assisted Emergency Navigation Algorithm for Dynamic Hazardous Ship Indoor Environments

A reliable and efficient emergency evacuation of a damaged cruise ship is essential for passenger safety. Although many advanced evacuation approaches based on wireless sensor networks (WSNs) are capable of exploring dynamic environmental hazards and provide real-time navigation service, such approaches are mainly used in buildings on land, taking no account of the complex ship structure, deadline for ship survival, and dynamic ship inclination, and therefore may fail to evacuate passengers before ship capsizing. This article proposes WEND, an efficient WSN-assisted emergency navigation algorithm for dynamic hazardous ship indoor environment, which informs each passenger about a hazard-avoid route that minimizes the total dynamic typical delay with error bound guarantee while meeting the deadline for ship capsizing in a real-time manner. To achieve this aim, WEND investigates ship interior layout to construct a 3-D topological model and analyzes the time-history of the roll motion of a damaged passenger ship to evaluate ship survival time and the dynamics of pedestrian movement. Then, an efficient adaptive emergency navigation algorithm building on the ideas of Hassin’s algorithm is presented to provide a hazard-avoid path from each passenger’s current location to boarding stations such that the worst-case delay along this path is no greater than the specified deadline, and the total dynamic typical delay is small. We evaluate our algorithm by conducting extensive simulations. The results demonstrate that WEND improves the navigation success ratio by approximately 30% and 10% compared with the state-of-the-art navigation methods, namely the expected number of oscillations (ENO)-based oscillation-free method (OPEN) and the deadline-aware adaptive emergency navigation strategy (ANT), respectively.

Numerical study of the interaction between the pure loss of stability, surf-riding, and broaching on ship capsizing

Ship capsizing in stern quartering wave is very complicate with a strong correlation to the stability failure modes proposed in second-generation intact stability criteria. It is of great importance to shed some light on this complex phenomenon. In this study, the capsizing behavior of a free-running ONR Tumblehome model in stern quartering seas is investigated by an unsteady Reynolds-averaged Navier–Stokes (URANS) solver coupled with dynamic overset grid approach. Validation study of the URANS solver is performed for the prediction of extreme roll motion of the ship. The comparisons show satisfactory agreement, with an average difference less than 3% between the simulation and experimental results. The correlation between the occurrence of stability failure modes (surf-riding, pure loss of stability, and broaching) and ship capsizing is then assessed under different ship speed and heading angle conditions. It is concluded that the capsizing occurs as the free-running ship sailing with a high speed, which is caused by the interaction between the broaching and severe stability loss. In addition, influenced by the wave-induced moment, both the pure loss of stability and surf-riding modes may cause the broaching, indicating the similar occurring condition and strong relation between these stability failure modes.

Application of SPH method in the study of ship capsizing induced by large-scale rising bubble

In some sea areas, the rising storm of bubbles including the release of large-scale methane gas and eruption of submarine volcanoes will pose a potential threat to the safety of ships. In the former case, a large amount of rising methane gas may generate some large-scale bubbles which may cause sailing ships to capsize. When the size of the bubble is close to the characteristic length of the ship, one single bubble could sink a ship. For the latter, the initial radii of the bubbles formed by the eruption of shallow seafloor volcanoes maybe tens even hundreds of meters, which also largely increases the risk of maritime transportation. In this paper, a 2D smoothed particle hydrodynamics (SPH) model is used to investigate the interaction between a ship and large-scale bubbles. Firstly, the adopted SPH model is validated by comparing with other numerical results. Then, the coupling interaction between a bubble and free-surface is simulated. Finally, under different conditions of different bubble sizes, bubble depths and horizontal distances, interactions between a ship and one or two large-scale rising bubbles are simulated and discussed, aiming to provide a reference for the investigation of ship capsizing caused by large-scale rising bubbles.

Study on extreme roll event with capsizing induced by pure loss of stability for the free-running ONR Tumblehome

International Maritime Organization (IMO) has stated that the direct assessment for the pure loss of stability, one of the typical stability failure modes, is necessary for ship designers and under development currently. In this study, extreme roll motions with large amplitudes, induced by the pure loss of stability, are predicted for a benchmark combatant ONR Tumblehome running in stern quartering waves by the computational fluid dynamics (CFD) simulations. An unsteady Reynolds-averaged Navier–Stokes (RANS) solver coupled with a dynamic overset grid approach is used to predict six degree of freedom (DOF) motions. The discretized propeller model is applied to the free-running model, along with a course keeping controller. Different speed conditions are considered for the ship to investigate the instability zone where the pure loss of stability occurs and the CFD results for the roll amplitude are compared with the experimental data, with an average difference less than 3%. In addition, it is observed that ship capsizing occurs coupled with a rapid increase of yaw angle, which is consistent with the phenomenon in the existed model tests. Overall, it indicates that this viscous simulation model is capable for the prediction of the extreme roll as well as the capsizing.

Horizontal impact loads and torsional moment induced by partial cargo shifts

Previous studies demonstrate that significant cargo shifts occurred in all cargo holds of vessels in carriage of nickel ores may lead to catastrophic consequences of ship capsizing and sinking. Nevertheless, partial cargo shifts, despite its seldom occurrence in other types of vessels, are not unusual in bulk carriers, specifically for those with nickel ores which tend to liquefy as vessels experience long-time engine vibrations or unfavorable oblique waves. Regrettably, it has not been well described in previous literatures, therefore overlooked by ship operators and naval architects in ship structural design. The instantaneous impact loads to vessel's structures induced by partial cargo shifts, thus, remain unclear. Despite partial cargo shifts being unlikely to lead to life lost or ship capsizing, critical damage to cargo holds, shell plates and precise apparatuses in the wheelhouse can be identified frequently, sometimes even causing ship a hazardous list of 6–15°. Unfortunately, a number of similar accidents occurred in S.E. Asia waters have been found without reporting these accidents to IMO due to various reasons. The instantaneous impact loads, involving the torsional moments and horizontal sectional loads, initially overlooked by plenty of naval architects but subsequently estimated by our research team, are really huge, usually giving rise to a dangerous list of vessels as well as apparent or underlying damage to vessel's configurations. Conventional approaches, such as potential flow theory, volume of fluid method, moving particle semi-implicit method, smoothed particle hydrodynamics, etc., are significantly limited by their unsatisfactory precision in predicting and calculating those extraordinary loads. Here we estimate the torsional moments and horizontal sectional loads in oblique waves at various exciting rolling frequencies using improved Finite Element approach. The final results yielded from the model tests are strikingly in line with that from the numerical approach, manifesting that the modified numerical method behaves in a reasonable manner in tracking and capturing the complicated surface of large viscous fluid.

The Scheme of Re-floating a Grounded Vessel and Risk Analysis Based on M.V. EVER GIVEN

Ship grounding is a major maritime accident, and also the cause of ship capsizing, total loss, serious pollution and etc.. The harm caused by ship grounding is extremely serious, especially for those grounding case in canal or important channels. Some of the grounding cases have brought great impacts to the shipping allover the world. On 23 March 2021, Motor vessel EVER GIVEN, one of the largest container ships in the world with a length of 400 meters, a width of 59 meters, and a gross tonnage of 219,000 tons, ran aground when it was passing through the Suez Canal after its hull went off course, becoming an insurmountable wall across the narrow Suez Canal. The blockage of the Suez Canal, one of the world's most important shipping lanes, has left global supply chains "stuck in their throats" for more 6 days, and has brought huge influence to world shipping. This paper analyzes the concept of confined waters in terms of relative water depth and relative width, the main hazards of large ships navigating in confined waters, such as the impact on the maneuverability and under keel clearance of the vessel, the bank effects and so on. In this paper, we also analyze the main re-floating scheme against the background of the accident of the EVER GIVEN in the confined waters, and provide operational solutions to refloat the grounded vessels to give reference for navigators on board a ship and salvage operators in shipping industry.

Analysis of unsaturated soil columns with application to bulk cargo liquefaction in ships

Over the last 40 years, there have been several ship losses carrying granular mineral ores that are believed to have been caused by the sudden shifting of the cargo as a result of liquefaction. It is known that the initial moisture content during loading is important for cargo types which are considered susceptible to liquefaction. To limit the moisture content, the degree of saturation must be below 80% in compaction tests designed to reproduce the energy associated with loading cargo into a ship’s hold. During transport, ships can experience storms causing cyclic loading which leads to densification of the cargo and increases in the degree of saturation. There can also be transient increases in pore pressure and associated reductions in the cargo material’s resistance, which when the ship heels increase the likelihood of the cargo shifting and in the extreme, the ship capsizing. In this paper, a recently developed fully coupled dynamic finite element analysis and constitutive model for unsaturated soil is used to perform a parametric study to explore the capabilities of the numerical code and the mechanics of the problem. The numerical analyses are shown to be capable of running for up to 2500 cycles and simulating both cyclic loading and simultaneous consolidation and drainage, a computationally very demanding task. Outcomes of the analyses are used to discuss the factors influencing cargo stability and vessel instability.

The Stability Analyze of KM. Rejeki Baru Kharisma of Tarakan – Tanjung Selor Route

Ship stability that is not according to the IMO standard will make the ship capsize when operating. The purpose of this research is to determine the cause of the overturn in terms of the stability criteria of the ship. The method used is software of simulation. Stability analysis is carried out with the load case that occurs in the field when an accident occurs and the ideal loadcase according to PM 104 2017 standards about’s the transportation of operation. The results showed is cargo of goods placed on the roof top (loadcase 1) based on the criteria of Intact Stability; area of the stability arm curve at heeling 0° ~ 30° = 0.9417 m.deg, area 0° ~ 40° = 1,0200 m.deg, 30° ~ 40° = 0.0783 m.deg, GZ value at heeling 30° = 0.029 m, angle of occurrence of maximum GZ = 21.8°, and the initial GMt value = 0.135 m, the results stated that all did not meet the Intact Stability code A.749 criteria, while in it was obtained cargo of goods placed in the hull (loadcase 2) based on Intact Stability; area of the stability arm curve at heeling 0° ~ 30° = 4.5338 m.deg, area 0° ~ 40° = 7.1643 m.deg, area 30° ~ 40° = 2.6305 m.deg, GZ value at heeling 30° = 0.265 m, angle of occurrence of maximum GZ = 34.5°, and the initial GMt value = 0.621 m, the results stated that all met the Intact Stability code A.749 criteria

A New Design Criterion to Improve the Intact Stability of Galician Small Fishing Vessels

The first technical factor involved in maritime accidents is related to the lack of intact stability. The current stability criterion, based on fixing a minimum value for each of the different static and dynamic righting arms, is not regarded as satisfactory. Correspondingly, a new criterion based on the transverse metacentric height, dynamic stability up to 70° heel, and critical wave height were considered for fishing vessels less than or equal to 24 m in length. This can be understood as an improvement on the Rahola criterion or an equivalent criterion of dead ship capsize mode, as assumed in the second-generation stability criteria. The proposed criterion, when used in a real case study on the Galician fishing grounds, achieved higher precision. The few vessels that did not comply with the proposed requirement can continue to operate in the area if the Meteorological and Oceanographic Coefficient (CMO) is considered at the time we employ our criteria. As a result, their activity is limited to only a few fishing grounds where adequate weather conditions exist. Finally, the methodology developed can be easily extrapolated to other regions in the world.

A risk model of passenger ship fire safety and its application

A risk model for assessing a passenger ship's fire safety at the design stage is proposed. Current maritime legislation requires, in principle, compliance with prescriptive regulations of fire prevention, protection and extinction. In a forward step, the International Maritime Organization (IMO) permitted acceptance of fire-safety-equivalent designs on the basis of performance-based assessment procedures. However, the inherent randomness of onboard fire events has not yet been systematically accounted. In this respect, procedures currently applied for fire safety evaluation during ship design, lag behind those applied for the avoidance of ship capsize due to watertight compartments’ flooding, where a probabilistic approach has been in place since long ago. The current work is intended to enhance the probabilistic character of performance-based ship fire assessments; and to establish a consistent risk calculation framework which could also serve in the future as the backbone model of a more integrated approach to ship risk calculation. The core of the proposed model is a risk function combining the probability of ignition, the reliability of the installed suppression systems, and the prediction of the loss given a fire's growth. Design details, such as the space layout and the interior design materials, are fully taken into account. The estimation of the loss is realized by high fidelity simulations. The loss appears in the form of a distribution of fatalities. Several practical risk indices are extracted from the risk function, reflecting potential designer preferences. For demonstrating the practicality of the proposed risk model, a part of a cruise ship's fire zone, accommodating public spaces, is considered. The fire safety performance of the design is evaluated by using the extracted risk indices whose consistency in reflecting the safety level are discussed.

On damaged ship motion and capsizing in beam waves due to sudden water ingress using the RANS method

Computational fluid dynamics was used to solve the problem of damaged ship behaviour in waves when sudden water ingress occurs. The computational model was based on the Reynolds-averaged Navier-Stokes equations combined with the volume-of-fluid free-surface capturing scheme. Both the sliding interface and dynamic layering techniques were adopted to handle the mesh update in the numerical simulation. To validate its performance, this method was first applied to three test cases, including wave generation, roll decay of a damaged frigate DTMB-5415 in calm water and frigate motion in regular beam waves. The numerical results agree with the theoretical and experimental results. Then, the cases of sudden water flooding of the frigate in beam waves were studied. Discussions were focused on the effect of the damage occurrence timing, compartment arrangement and wave height on the flooding process and ship motion. The mechanism of a damaged ship capsizing in waves was partly explained.

Geometry of escape and transition dynamics in the presence of dissipative and gyroscopic forces in two degree of freedom systems

Escape from a potential well can occur in different physical systems, such as capsize of ships, resonance transitions in celestial mechanics, and dynamic snap-through of arches and shells, as well as molecular reconfigurations in chemical reactions. The criteria and routes of escape in one-degree of freedom systems have been well studied theoretically with reasonable agreement with experiment. The trajectory can only transit from the hilltop of the one-dimensional potential energy surface. The situation becomes more complicated when the system has higher degrees of freedom since the system state has multiple routes to escape through an equilibrium of saddle-type, specifically, an index-1 saddle. This paper summarizes the geometry of escape across a saddle in some widely known physical systems with two degrees of freedom and establishes the criteria of escape providing both a methodology and results under the conceptual framework known as tube dynamics. These problems are classified into two categories based on whether the saddle projection and focus projection in the symplectic eigenspace are coupled or uncoupled when damping and/or gyroscopic effects are considered. For simplicity, only the linearized system around the saddle points is analyzed, but the results generalize to the nonlinear system. We define a transition region, Th, as the region of initial conditions of a given initial energy h which transit from one side of a saddle to the other. We find that in conservative systems, the boundary of the transition region, ∂Th, is a cylinder, while in dissipative systems, ∂Th is an ellipsoid.

Evaluation of the critical wave groups method in calculating the probability of ship capsize in beam seas

The paper proposes certain improvements in the setup of the “critical wave groups” method which has been introduced in the past for calculating the probability of extreme roll responses. Moreover, a precise mathematical formulation of the “critical wave groups” concept is presented and the selection of key parameters for its computational setting is discussed. The most significant development concerns the hitherto assumption of zero initial conditions of the vessel at the instant of a wave group encounter, which is now removed through probabilistic treatment of ship's initial state. The improved method is evaluated for its potential to produce accurate estimates in the various regions of roll response distribution including the tail, where the efficiency of direct Monte Carlo simulations is very low. In the range of intermediate responses, it is demonstrated that the method becomes more effective when employing the expected wave sequences given a sea state, instead of regular waveforms, for determining “critical” (for ship stability) wave episodes. Lastly, two alternative implementations of the “critical wave groups” concept are assessed; one empirical, where the distributions of main parameters, such as the wave period and height, are deduced from simulations of the wave field; and one where they are calculated directly from the spectrum.

Validation of a combined dynamic mesh strategy for the simulation of body's large amplitude motion in wave

The computational fluid dynamics (CFD) method based on solving the Reynolds-averaged Navier-Stokes equations was used to simulate the flow field of the body-wave interaction. A dynamic mesh strategy, which combines the sliding interface technique and the dynamic layering technique, was adopted to handle the mesh update due to the body motion in the simulation. This mesh strategy was capable of treating the arbitrary translational and rotational motions of the body. To validate its performance, the mesh strategy was implemented with the CFD solver ANSYS-Fluent and was applied to solve the 2-D problem of a freely floating box-shaped structure subjected to the focused wave. The present numerical results were compared with the published experimental data and numerical results. For the case of wave generation, the present dynamic mesh strategy incurred 4% loss in accuracy and 6% loss in efficiency compared to the static mesh strategy. For the case of body-wave interaction, the accuracies of the present dynamic mesh strategy and the dynamic overset mesh technique were at the same level. In addition, an application of the present dynamic mesh strategy to the 3-D simulation of a damaged ship capsizing in regular beam wave was demonstrated.