strength assessment of an aged single hull tanker grounded

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Progress in Maritime Engineering and Technology – Guedes Soares & Santos (Eds.)© 2018 Taylor & Francis Group, London, ISBN 978-1-138-58539-3

Strength assessment of an aged single hull tanker grounded in mud and used as port oil storage

N. Vladimir, I. Senjanović & N. AlujevićUniversity of Zagreb, Zagreb, Croatia

S. TomaševićAdriatic Tank Terminals d.o.o., Ploče, Croatia

D.S. ChoPusan National University, Busan, Republic of Korea

ABSTRACT: This paper deals with a practical problem of structural integrity evaluation of a single hull tanker which, after its regular service, was grounded in mud and used as port oil storage. The fore and the aft part of the ship were removed, whereas its middle module was kept to be used as a liquid cargo stor-age and a permanent ballast that ensures the ship continuous contact with the sea bottom. Therefore, the ship can be considered as supported in part by the mud and in the other part by the surrounding water. Although the ship is classed as a stationary object, the reliable strength assessment is still necessary to check its structural integrity in order to avoid potential environmental issues. The analysis was done in two steps. At first, the mathematical model of ship static equilibrium has been formulated, consistently taking into account the supporting mud reaction and buoyancy. Secondly, the developed physically consistent mathematical model is used as a basis for a detailed 3D FEM analysis, where the 3D FEM model is gener-ated based on the available technical documentation and thickness measurements of the whole ship struc-ture, which was performed in order to directly account for the effect of ageing (corrosion). Representative stresses in all structural elements are determined and compared with the permissible ones. Conclusions on ship suitability to serve as port oil storage are drawn.

stationary object with the aim of increasing the port storage capacities. (aft structure from A.P. to FR60 was removed). However, bearing in mind the age of the ship, an extensive structural integrity evaluation was necessary in order to ensure that the risk of the oil loss and the consequent pollu-tion is minimised.

For this purpose, a fully consistent mathemati-cal model is derived, taking into account the fact that the ship is supported by both the mud and the sea water. The ship immersion in the mud is deter-mined by the in-situ water depth readings and the ship dimensions. The developed theoretical model is based on static equilibrium and geometric relations, where the mud mass density is adjusted in order to properly take into account the sea bottom stiffness,

1 INTRODUCTION

Ship hull inspection is a very important task to ensure its structural integrity during the whole life-time. It is well-known that corrosion affects both local and global ship strength so that a number of models have been developed in order to improve structural analysis, inspection and maintenance procedures as for instance (Wirsching et al., 1997; Saad-Eldeen et al., 2014; Ventikos et al., 2017). Moreover, corrosion is one of the time-dependent detrimental phenomena which can lead to cata-strophic failures (Rahbar-Ranji, 2012). On the other hand, grounding of ships is a special problem in maritime sector that has also been extensively considered in the relevant literature (Prestileo et al., 2013; Heinvee and Tabri, 2015).

This paper is devoted to the strength assessment of a grounded aged single-hull oil tanker,

Figure 1, which is being used as port oil stor-age, (Vladimir and Senjanović, 2017a,b). After its regular service, the ship was converted in such a way that its cargo area module can be used as a

Figure 1. Schematic presentation of ship grounded in mud.

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i.e. the bottom reaction force. This is because it was confirmed by observations that the exact ship posi-tion is independent on the loading condition vari-ation. Therefore it must be that the mud reaction continuously changes depending on the cargo filling levels.

A detailed strength assessment is performed by 3D Finite Element Method (FEM), (Senjanović, 2002). As a basis for the calculation, the above mentioned consistent global ship static equilib-rium model is used. Accordingly, besides imposing the ship and cargo weight and surrounding water pressures on the generated 3D FEM structural model, additional bottom pressures are calculated and applied to simulate the effect of the support-ing mud. The analysis was performed by means of general finite element software NASTRAN (MSC, 2005). Two loading conditions, covering the most critical cases are identified and considered in detail. The ageing (corrosion) effect is directly included in the calculation by taking into account the exact plating and stiffener thicknesses. These were obtained through a thickness measurement campaign of the complete ship structure (Vladimir and Senjanović, 2017a,b).

2 MATHEMATICAL MODEL

2.1 Ship static equilibrium

The weight of the grounded ship is equilibrated partly by the water buoyancy and partly by the sea bottom reaction. Hence, the total reaction R = Q-B is known, but its distribution along the ship, which is important for the longitudinal strength analysis, is unknown. To the best of the authors’ knowledge, a directly applicable procedure for determin-ing the distribution of the reaction force has not been previously developed, neither by calculation nor empirically. In the procedure proposed in this paper, it is assumed that the ship hull freely floats in both water and mud. Since the ship does not change her draught at different loading con-ditions, the sea bottom reaction is simulated by buoyancy of a particularly high-density mud. The ship immersed into the water and mud is shown in Figure 2.

Ship weight, Q, has to be equilibrated by the water and mud buoyancies, respectively:

Q x g A x xL

m m

L

= ( ) ( )∫ ∫ρ ρw wg A x d d ,00

+ (1)

that gives:

Q gV gVw w m m= +ρ ρ , (2)

where:ρw – water density,ρm – mud density,Vw – volume of ship immersed in water,Vm – volume of ship immersed in mud,Aw – cross-section area immersed in water,Am – cross-section area immersed in mud, andg – gravity constant.

From Eq. (2) one can calculate the mud density necessary to maintain the static equilibrium:

ρ ρm

w w

m

Q gVgV

=− . (3)

Therefore the mud density is determined for each loading condition separately, by assuming that the ship immersion in mud is constant (as confirmed by the in-situ observations).

In case of a unit immersion, Figure 3, additional buoyancy represents the sea bottom (mud) stiff-ness, and yields:

k gBm m= ρ . (4)

where Bm represents the cross-section breadth at the borderline between the mud and water, Figure 2.

Figure 2. Schematic presentation of ship cross-section immersed in water and mud.

Figure 3. Unit immersion of ship in water and mud.

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2.2 Determination of the mud pressure

As mentioned above, the ship is in a static equilib-rium, where the hull and cargo weights are partially equilibrated by the supporting mud pressure. Also, the hull sides are exposed to the hydrostatic pressure of the surrounding water. For the purpose of the anal-ysis, the 3D FEM model weight should be adapted to real ship weight by the material density adjustments. In order to eliminate rigid body motions in the FE model, the ship is supported at three selected nodes for easier modelling. However, it is controlled that reaction forces at these nodes are zero. The bound-ary conditions are shown in Figure 4.

The positions of the supports are shown in Figure 5, where it is indicated that the aft supports are at the cross-sections of the transverse bulkhead at FR91 and longitudinal bulkheads, whereas the fore support is on transverse bulkhead at FR187 in the centreline. The supports are located below very stiff structural elements in order to minimize stress concentrations due to a possibly slightly unbal-anced FE model.

The distribution of the mud reaction along the ship hull is shown in Figure 6. It can be calcu-lated by knowing the total ship and cargo weight, F, and the longitudinal position of the centre of gravity (CG), xCG, which are here taken from the FEM software output file (MSC, 2005). However, based on the static equilibrium of forces shown in Figure 5, the expression for determination of the CG position can be derived:

Fx F aCG∗ = 2 , (5)

where

F F F= +2 1 2. (6)

The distance of CG from aft supports, xCG∗ ,

reads:

x FF

aCG∗ = 2 . (7)

Before calculating mud pressures on the hull, the mud continuous reaction defined by q1 and q2, Figure 6, is expressed via the ship total weight F and the longitudinal position of CG, xCG. Accord-ing to Figure 6, the force and moment equilibrium can be written in the following form:

F q q l q l Fi = +( ) + =∑ 0 12

121 2 1 2 2: , (8)

which gives:

q qll

Fl1 2

2

1 1

1 2+ +

= , (9)

M q q l l

q l l l Fx

i

CG

= +( ) +

+

=

∑ 0 12

12

12

13

1 2 1 1

2 2 1 2

:

,

(10)

q q qll

l ll

FxCG1 2 22

12 1 2

12

2 13

4+ + +

= , (11)

and finally leading to:

q qll

ll l

FxCG1 22

1

2

1 12

1 2 1 13

4+ + +

= . (12)

After substituting (9) into (12), one can write:Figure 4. Boundary conditions of FE model in the supported nodes.

Figure 5. Positions of supports, i.e. reaction forces along the 3D FE model.

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qll

ll

Fl

xlCG

22

1

2

1 1 1

1 23

2 2 1+

= −

. (13)

Based on the above derivation, q2 and q1 can be expressed as:

q

Fl

xl

ll

ll

CG

21 1

2

1

2

1

2 2 1

1 23

=−

+

, (14)

qFl

qll1

12

2

1

2 1= − +

. (15)

For the pressure calculation, the width of the mud waterline, BWLMUD, is relevant, Figure 6. According to Figure 7 one can write:

p qB

p qB

pqBWLMUD WLMUD

pp

p1

12

2= = =, , . (16)

Along a single cargo hold, the mud pressure is assumed to be constant, i.e. a step-like distribution is used for simplicity.

3 SHIP DATA, DESCRIPTION OF FEM MODEL AND CALCULATION SETUP

3.1 Ship data

The considered single hull oil tanker was built in 1956, with the following main particulars:

Length between perpendiculars: LPP = 149.07 mBreadth: B = 25.72 mDepth to main deck: H = 14.1 m

The tank layout is shown in Figure 8. The cen-tral cargo tanks 4C-9C are intended to be used as oil storages. The side tanks 1 L, 1D, 4 L and 4D are aimed to be empty, whereas tanks 2 L, 2D, 3 L, 3D, 5 L, 5D, 6 L and 6D contain permanent ballast (sea water, 95% of tank capacity), that together with the ballast in the fore peak (20% of FP capac-ity) and the lightship mass, ensure a permanent contact between the ship structure and the bottom. This tank filling strategy is summarized in Table 1 together with the tank capacities.

An extensive thickness measurement campaign has been performed in order to accurately take into account the corrosion effect, i.e. to reliably simulate a realistic ship condition. It should be mentioned that condition based maintenance is regularly carried out in this case, meaning that if excessive

Figure 6. Longitudinal distribution of mud reaction.

Figure 7. Longitudinal mud pressure distribution.

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corrosion or pitting is noticed, Figure 9, the struc-ture is locally remedied, Figure 10.

As claimed by the ship-owner, ship was made of steel, and for the needs of the calculation the val-ues of Young’s modulus, material density and Pois-son’s ratio are set at 2.1 × 1011 N/m2, 7850 kg/m3 and 0.3, respectively.

3.2 FEM model

A fine mesh 3D FEM model of the tanker is generated in order to calculate local stresses. The

axonometric view on the FEM model (stretch-ing from FR60 (in this case AP, x = 0 m) to FR219 (x = 124.179 m)) is shown in Figure 11. In Figure 12 the model is shown without deck plating and beam elements in order to ensure better vis-ibility of the internal structure.

Before going into details on the calculation setup, a more detailed overview of the FEM model is provided. In Figure 13 a typical cargo tank struc-ture together with the side (ballast) tank structure is presented in an axonometric view.

Besides ordinary frames, the analysed ship struc-ture is characterized by both semi-web frames, Figure 14, and web frames, Figure 15.

In total, the FE model used for the analysis has 30762 nodes and consists of 64733 elements, whereas 34434 are the plate elements and 30299 are the beam elements. The mesh density in the longitudinal direction equals to the ordinary frame spacing (781 mm). The only exception is the fore part of tanks 1 L/1D where the mesh density is two times coarser. The mesh density in the transverse direction is equal to the spacing of the longitudinal stiffeners.

In Figure 16 a view of a side tank without the side shell is given, so that the internal tank framing can be seen. Also, one can see the vertical stiffeners of the transverse bulkhead.

The complete FEM model was updated with thickness measurement data, as for instance shown in case of a typical transverse bulkhead,

Figure 17, and a typical cargo and side tank structure, Figure 18.

3.3 Calculation setup

Two representative load cases are defined next, i.e. LC1 and LC2. Load case LC1 is characterized by full cargo tanks 4C, 6C and 8C, Figure 19, whereas in load case LC2 cargo tanks 5C and 8C are empty, and the other cargo tanks are full, Figure 20.

Figure 8. Ship general arrangement with tank disposition.

Table 1. Containment of ship tanks and tank capacities.

Tank designation Filling Capacity, m3

1C None N/A 2C None N/A 3C Pump room N/A 4C Oil 3000 5C Oil 3000 6C Oil 3000 7C Oil 3000 8C Oil 3000 9C Oil 300010C None N/A1 L/D None N/A2 L/D Ballast (95%) 15003 L/D Ballast (95%) 7504 L/D None N/A5 L/D Ballast (95%) 15006 L/D Ballast (95%) 703

Figure 9. Corroded tank bottom plating.

Figure 10. Remedied tank bottom plating.

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For both of the above defined load cases, the total weight and the centre of gravity are deter-mined, and the mud pressure for each tank is calculated.

Figure 11. 3D FEM model used in the structural analysis.

Figure 12. 3D FEM model used in structural analysis without deck plating and without beam elements.

Figure 13. Typical cargo and side (ballast) tank structure.

Figure 14. Typical view on semi-web frame.

Figure 15. Typical view on web frame.

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Figure 16. Side tank internal structure and stiffeners of longitudinal and transverse bulkhead.

Figure 17. Plate thicknesses of transverse bulkhead at FR139 [mm].

Figure 19. Schematic representation of LC1.

Figure 18. Plate thicknesses in Tank 5C and corre-sponding side tanks [mm].

Figure 20. Schematic representation of LC2.

It has been found that the variation of sea level due to tide and ebb has no significant influence the results. Therefore the average value of sea level (water depth) is assumed. Also, some local dete-riorations (like pitting) are not considered in this calculation. After imposing the mud pressures on the bottom, the above-mentioned reactions in the three supporting nodes are checked. Each load case is characterised by the same filling of ballast tanks, i.e. only the filling of the cargo tanks is variable.

4 RESULTS

The static analysis is performed by NASTRAN software (MSC, 2005) and von Mises stresses are obtained for LC1 and LC2 in all elements of the structural model. They are compared with the maximum allowable stress which reads 230 N/mm2 (CRS, 2016). It is found that the calculated stresses are below the allowable stresses for both load cases within the complete FE model. Next, an overview of the results is given where stress distributions are shown for characteristic structural members within the cargo area. The maximum calculated stresses are tabulated in Tables 2 and 3.

Von Mises stress levels in the complete ship structure for LC1 and LC2 are illustrated in Figures 21 and 22, respectively. Stress units in all figures below are N/m2.

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Table 2. Von Mises stresses in representative structural elements for LC1.

Name TankPosition along the ship

Maximum von Mises stress (N/mm2)

Transverse bulkhead 10C FR60 65.2Transverse bulkhead 9C, 10C FR75 35.6Transverse bulkhead 8C, 9C FR91 190.7Transverse bulkhead 7C, 8C FR107 196.7Transverse bulkhead 6C, 7C FR123 189.9Transverse bulkhead 5C, 6C FR139 208.3Transverse bulkhead 4C, 5C FR155 200.1Transverse bulkhead 3C, 4C FR171 206.3Bottom plating 10C FR60-FR75 123.9Bottom plating 9C FR75-FR91 41.1Bottom plating 8C FR91-FR107 36.2Bottom plating 7C FR107-FR123 52.9Bottom plating 6C FR123-FR139 41.0Bottom plating 5C FR139-FR155 64.1Bottom plating 4C FR155-FR171 45.5Bottom plating 3C FR171-FR187 53.8Tank internal structure

(central bottom girder, deck girder, bulkhead central web, web frames, floor plates)

10C FR60-FR75 97.5 (floor plate at FR67)

Tank internal structure (central bottom girder, deck girder, bulkhead central web, web frames, floor plates)

9C FR75-FR91 158.2 (connection of bulkhead web and bulkhead at FR91)












3C FR171-FR187 152.4 (connection of bulkhead web and central bottom girder at FR174)

Longitudinal bulkhead, port side 10C FR60-FR75 42.0Longitudinal bulkhead, port side 9C FR75-FR91 82.1Longitudinal bulkhead, port side 8C FR91-FR107 61.2Longitudinal bulkhead, port side 7C FR107-FR123 65.4Longitudinal bulkhead, port side 6C FR123-FR139 53.7Longitudinal bulkhead, port side 5C FR139-FR155 66.2Longitudinal bulkhead, port side 4C FR155-FR171 52.6Longitudinal bulkhead, port side 3C FR171-FR187 77.0

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Table 3. Von Mises stresses in representative structural elements for LC2.

Name TankPosition along the ship

Maximum von Mises stress (N/mm2)

Transverse bulkhead 10C FR60 82.4Transverse bulkhead 9C, 10C FR75 189.0Transverse bulkhead 8C, 9C FR91 208.9Transverse bulkhead 7C, 8C FR107 174.9Transverse bulkhead 6C, 7C FR123 49.0Transverse bulkhead 5C, 6C FR139 208.0Transverse bulkhead 4C, 5C FR155 199.9Transverse bulkhead 3C, 4C FR171 202.6Bottom plating 10C FR60-FR75 184.8Bottom plating 9C FR75-FR91 38.0Bottom plating 8C FR91-FR107 57.4Bottom plating 7C FR107-FR123 50.1Bottom plating 6C FR123-FR139 59.3Bottom plating 5C FR139-FR155 76.3Bottom plating 4C FR155-FR171 57.9Bottom plating 3C FR171-FR187 62.0Tank internal structure (central

bottom girder, deck girder, bulkhead central web, web frames, floor plates)

10C FR60-FR75 138.4 (bulkhead web at FR72)














3C FR171-FR187 171.7 (connection of bulkhead web and central bottom girder at FR174)

Longitudinal bulkhead, port side 10C FR60-FR75 64.4Longitudinal bulkhead, port side 9C FR75-FR91 59.4Longitudinal bulkhead, port side 8C FR91-FR107 82.2Longitudinal bulkhead, port side 7C FR107-FR123 67.8Longitudinal bulkhead, port side 6C FR123-FR139 64.8Longitudinal bulkhead, port side 5C FR139-FR155 78.7Longitudinal bulkhead, port side 4C FR155-FR171 59.8Longitudinal bulkhead, port side 3C FR171-FR187 83.6

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Figure 21. Von Mises stresses in plate elements of ship hull, LC1.

Figure 22. Von Mises stresses in plate elements of ship hull, LC2.

Besides the von Mises stresses in the trans-verse bulkheads, Figure 23, shear stresses are also checked, Figure 24.

Typical von Mises stress distribution in a cargo tank area is shown in Figure 25.

In Figure 26 the stress distribution in the typical ballast tank structure is presented, while

Figure 27 shows characteristic structural elements with the highest stress levels for LC2 (transverse bulkhead at FR91).

The results in Tables 2 and 3 clearly indicate that the maximum stresses are obtained in the transverse bulkheads of central tanks, and their maximum levels are obtained if two consecutive

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Figure 24. Shear stresses in transverse bulkhead at FR139, LC1.

Figure 25. Von Mises stresses in tank 6C, LC1.

Figure 26. Von Mises stresses in stringers and internal walls of tank 3 L, LC1.

Figure 27. Tanks 8C and 9C with transverse bulkheads at FR75 and FR91, one-half of the model, LC2.

Figure 23. Von Mises stresses in transverse bulkhead at FR139, LC1.

tanks have significantly different filling ratios (i.e. full and empty tanks are altering). Therefore, the stresses can be minimized if similar filling level in adjacent tanks is kept.

5 CONCLUDING REMARKS

The strength assessment of a single hull tanker, converted to port oil storage and grounded in mud, has been carried out by 3D FEM. A 3D finite ele-ment model of the ship structure is generated. A special mathematical model for loading of the ship grounded in the mud has been developed in

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order to take into account the external loading by both the mud and the surrounding water. In such a model the total loading of the FEM ship structure consists of 1) ship weight, 2) liquid cargo pressure, 3) surrounding water pressure on ship sides and 4) mud buoyancy. The mud buoyancy is imposed as a hydrostatic pressure on the ship bottom. Von Mises stresses and shear stresses are taken as the representative ones for the evaluation of structural integrity.

Locations with the highest stress levels are iden-tified for selected load cases. Despite the selection of the most severe loading conditions, represented by different combinations of successive empty and full cargo tanks, the calculated stresses are below permissible values for all structural members. Maximum stress levels are regularly obtained in transverse bulkheads of central tanks. Therefore, if the cargo amount in the adjacent tanks is simi-lar, stresses in bulkheads between them will be minimized.

Moreover, the obtained results show that the ship in its current static equilibrium position can be exploited with arbitrary combinations of cargo tank fillings. However, due to safety reasons and bearing in mind the age of the ship, the structural elements should be continuously surveyed.

ACKNOWLEDGEMENTS

The investigation presented in this paper is funded by the Adriatic Tank Terminals d.o.o. and the European Union’s Horizon 2020 research and innovation programme under the Marie Sklo-dowska-Curie grant agreement no. 657539 STAR-MAS. Publication of this paper is also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) through GCRC-SOP (No. 2011-0030013), and within the project Green Modular Passenger

Vessel for Mediterranean (GRiMM), funded by the Croatian Science Foundation (Project No. 2017-05-UIP-1253).

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Heinvee, M., Tabri, K. 2015. A simplified method to predict grounding damage of double bottom tankers. Marine Structures, 43:22–43.

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Prestileo, A., Rizzuto, E., Teixeira, A.P., Guedes Soares, C. 2013. Bottom damage scenarios for the hull girder structural assessment. Marine Structures, 33:33–55.

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Saad-Eldeen, S., Garbatov, Y., Guedes Soares, C. 2014. Strength assessment of a severely corroded box girder subjected to bending moment. Journal of Construc-tional Steel Research, 92:90–102.

Senjanović, I. 2002. Finite element method in analysis of ship structures, University of Zagreb, Zagreb. (text-book, in Croatian).

Ventikos, N., Sotiralis, P., Drakakis, M. 2018. A dynamic model for the hull inspection of ships: The analysis and results. Ocean Engineering, Volume 151, Pages 355–365.

Vladimir, N., Senjanović, I. 2017a. Evaluation of struc-tural integrity of a ship hull used as port oil storage, Part I: 1D FEM analysis, University of Zagreb, Fac-ulty of Mechanical Engineering and Naval Architec-ture, (internal report).

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strength assessment of an aged single hull tanker grounded

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