Residual ultimate strength assessment of double hull oil tanker after collision
Joško Parunov
a,⇑, Smiljko Rudan
a, Branka Buzˇancˇic´ Primorac
baUniversity of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Croatia
bUniversity of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Croatia
a r t i c l e i n f o
Article history:
Received 14 February 2017 Revised 6 May 2017 Accepted 4 July 2017
Keywords:
Damaged oil tanker Residual ultimate strength Nonlinear finite element method
a b s t r a c t
The aim of the present study is the assessment of a residual ultimate strength of an Aframax-class double hull oil tanker damaged in collision. A contribution to the research of the problem is given in a systematic investigation of the influence of the rotation of neutral axis (NA), which is performed by imposing appro- priate boundary conditions. Nonlinear finite element method (NFEM), using explicit dynamic integration method implemented in LS-Dyna, is employed. NFEM results are compared with the IACS CSR progressive collapse analysis (PCA) method. Residual strength diagrams are developed for a rapid residual ultimate longitudinal strength assessment in both sagging and hogging and accounting for correction factor because of the rotation of NA. Following this, developed diagrams are compared with previously pub- lished researches. The results of this study may be used by classification societies in a Rules development process, in the risk assessment studies of the maritime transportation and for a quick calculation of the hull girder residual strength of a damaged ship in the situation requiring emergency response action.
Ó2017 Elsevier Ltd. All rights reserved.
1. Introduction
The failure of an oil tanker structure may occur due to unfa- vourable environmental conditions or due to the human errors in ship design or operation of the ship. According to Eliopoulou et al.[1]the 33% among all of the oil tanker accidents are collision accidents. In addition, contact accidents, which are often consid- ered together with collision, represent 11% and 16% of all accidents for large and medium oil tankers respectively. Collisions can have severe consequences, including in some cases the total loss of a ship. After the event of collision, struck ships may capsize rapidly, sink slowly or stay afloat. A holistic approach on the assessment of survivability of a struck ship, combining structural analysis and damage stability analysis followed by risk analysis is presented by Ringsberg[2]. If the ship still stays afloat after collision, hull- girder collapse may occur when the hull’s maximum residual load-carrying capacity (the ultimate hull girder strength, the bend- ing moment capacity) is insufficient to sustain the corresponding hull girder loads applied[3]. The collapse of a hull girder may lead to a massive oil spill which then leads to environmental pollution [4]. Considering such scenario, it is clear why the ultimate hull gir- der capacity, as the most fundamental strength criterion to ensure
the safety of ships, is studied not only for the intact ship but also in the post-collision damaged condition[5]. The Common Structural Rules of the International Association of Classification Societies (IACS CSR), define the mandatory check of ship hull-girder residual ultimate strength for post-collision damage scenarios[6].
Grounding is another type of ship accident that can lead to the post-accidental collapse of the hull girder. New concept for the safety assessment of a ship structure damaged in grounding, which can be applied to other types of accidents including collision, is proposed by Paik et al. [7]. The procedure proposed was based on the damage description using the grounding damage index (GDI) and the calculation of the ultimate strength reduction by the nonlinear design equations depending only on the GDI. The concept is further extended by Kim et al.[8], taking into account the time-dependent corrosion wastage effect.
The ultimate hull-girder bending moment capacity is defined as the maximum bending moment of the hull-girder beyond which the hull will collapse. This moment, generally between the elastic and the fully plastic moment, is the sum of the contribution of lon- gitudinally effective elements, i.e. the first moment of the longitu- dinal stresses in the individual elements around the updated horizontal neutral axes[9]. The ultimate longitudinal strength of ship hulls can be predicted using assumed stress distribution methods, Smith’s progressive collapse analysis (PCA) method, the
http://dx.doi.org/10.1016/j.engstruct.2017.07.008 0141-0296/Ó2017 Elsevier Ltd. All rights reserved.
⇑Corresponding author.
E-mail address:[email protected](J. Parunov).
Contents lists available atScienceDirect
Engineering Structures
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n g s t r u c t
intelligent supersize finite element method (ISFEM) and nonlinear finite element method (NFEM)[10].
Assumed stress distribution method was originally developed by Caldwell[11], which was followed by many researchers includ- ing Paik and Mansour[12], among others. The method is limited to simple structural geometries, and cannot account for a reduced post-collapse strength in compression. The modified Paik- Mansour (P-M) method assumes improved bending stress distribu- tion at the ultimate limit state for the yielded area, i.e. the vertical structure elements close to the tension flange may also have yielded before the hull girder reaches the ultimate limit state [13]. The post-collapse behaviour of a structure is not accounted for by this type of methods, potentially leading to un- conservative ultimate strength predictions. Nevertheless, the method gives ultimate strength predictions comparable to the ones of the other calculation methods for a wide range of hull types.
The progressive collapse analysis (PCA) method, initially pro- posed by Smith, represents nowadays the most frequently used method for the ultimate strength assessment[14]. The crucial part of the Smith’s method is a stress–strain relationship for beam col- umns, of which stiffened panels forming the ship hull are com- posed. Stress–strain relationships most frequently used nowadays are those proposed by IACS CSR[6]. The ultimate bend- ing moment is then calculated by an incrementally iterative procedure.
In recent years, with the advancement of computer technology, many non-linear finite element method programs have been used for the ultimate strength analyses of hull structures, such as ABA- QUS, ANSYS, MARC and ADINA. Although the quasi-static response is commonly of interest in ultimate strength assessment, explicit dynamic solvers, such as LS-Dyna, are now used. The benchmark on a hull girder by Ultimate Strength Committee of ISSC, clearly demonstrates the advantage of the explicit solver calculations [10]. While the implicit static solvers often do not converge up to the final collapse, the explicit dynamic solvers obtain results for all the cases analysed. In those cases where both implicit and expli- cit solvers have given results, it is shown that the results agree well.
Similar methods are recognized in the literature for a calcula- tion of the residual strength of both intact and damaged ship hulls [10]. The approach generally adopted for damaged ship considers that the elements within the damaged area are removed and the ultimate strength is recalculated using the simplified 2D methods.
The results of a benchmark study are reported by Guedes Soares et al.[15]in which the strength of a damaged ship hull was calcu- lated with 3D nonlinear finite elements and was compared with the strength predicted by various codes based on the Smith method showing in general a good correlation.
NFEM is employed in the analysis of the residual strength of damaged lightweight naval vessel[16], bulk carrier and double- hull tanker[17] and ship shaped FPSO[18]. Progressive collapse behaviour of a damaged box girder is studied by Benson et al. using NFEM[19]. Modelling aspects for the NFEM strength capacity com- putations of intact and asymmetrically damaged ship girders are discussed by Koukounas and Samuelides[20]. NFEM analysis of bulk carrier and tanker damaged in collision is described by Zubair [21]in the context of verification of the novel pure incremental collapse method.
One specific problem related to the collision damage is that when the hull cross section is asymmetrically damaged, the neu- tral axis (NA) rotates during progressive collapse and the problem needs to be treated as a biaxial bending problem, even if the load- ing is in the vertical plane only. Recently, a pure incremental method was developed by Fujikubo et al.[22]to derive the biaxial bending moment-curvature relationship taking into account both rotation and translation of the NA in the asymmetrically damaged
hull girders. The method is subsequently utilized by Makouei et al.
[23]to develop several design formulas to predict residual strength of a ship in a damaged condition.
Despite recent research regarding collapse of the asymmetri- cally damaged ship hull, a systematic investigation of the influence of the neutral axis rotation to the progressive collapse is still lack- ing. IACS CSR proposes a calculation of the ultimate longitudinal strength of a damaged section by PCA neglecting the effect of rota- tion of the NA first, and then reducing it by 10% as a consequence of the rotation of the neutral axis[6]. This 10% reduction is not fully justified, since the reduction ratio depends on the location and the extent of the damage in the cross section.
The aim of the present study is to investigate progressive col- lapse behaviour of an Aframax-class double-hull oil tanker dam- aged in collision, with the particular aim to study the influence of the rotation of the NA to the progress of the hull collapse. The progressive collapse analysis is performed by NFEM using explicit dynamic solver LS-Dyna. Analysis is performed separately for the case when outer shell is damaged only and for the case when both outer and inner shells are damaged. That principle is applied for both hogging and sagging loading cases. In each case, damage is assumed to start from the main deck and extends downwards up to 80% of ship depth. The FE model extends over three web frame spacing. Boundary conditions (BC) are specified in a way that the influence of the rotation of the NA can be explicitly studied. Results obtained in the case when BC prevents the rotation of NA are com- pared with IACS CSR PCA. Diagrams are developed for the rapid residual ultimate strength assessment in sagging and hogging and also for the correction factor accounting for the rotation of NA. Design equations are compared with previously published studies and corresponding conclusions are drawn. Finally, some additional aspects that could be subjects of the future researches are emphasized.
2. Finite element model of the intact ship
The ship analysed in the present study is an Aframax-class double-hull oil tanker with the main particulars presented in Table 1. In the longitudinal sense, the cargo tank area is divided into six pairs of oil tanks as well as corresponding pairs of water ballast tanks. Structural design of a tanker is such that the ship is in the full compliance to the latest IACS CSR[6].
The FE model of the intact ship, extending over three web frame spacing is shown inFig. 1. The mesh size of all longitudi- nally effective members is about 100 mm100 mm. Such mesh size is found to be suitable in the convergence study presented by Samuelides et al.[17]. The dynamic explicit solver, similar as in the present study, has been used also for the progressive col- lapse analyses in[17], using ABAQUS software. Five models with different size, i.e. 85 mm, 100 mm, 150 mm, 200 mm and 300 mm, have been used for the convergence investigation. All the values of the FE size were close to the convergence region and therefore the value of 100 mm100 mm was recommended for the FE modelling.
Table 1
Main particulars of Aframax-class double hull tanker.
Dimension Unit (m, dwt)
Length between perp.,LPP 234
Breadth,B 40
Depth,D 21
Draught,T 14
Deadweight, DWT 105,000
The mesh size is gradually increased in transverse structural elements (web frames). All the longitudinals are modelled by shell finite elements, including their flanges. Mesh size 100 mm100 mm enables generating three to four shell elements across the stiffener height, while eight elements between longitu-
dinal stiffeners. Flanges of T-bar stiffeners are modelled by one shell element from each side of stiffener web. Particular attention is given to the shape of finite elements, where in modelling of lon- gitudinally effective members triangular and irregular quadrilat- eral elements are avoided, while rectangular elements are Fig. 1.Finite element model of three web frame spacing in the midship region (finite element mesh, view from the bottom (i), element thickness of the whole model, view from the top (ii), thickness of the typical web frame (iii)).
modelled with the same element width and breadth as much as possible. Finite element model is generated in FEMAP and then exported to LS-Dyna for the analysis.
2.1. Boundary conditions - intact ship models
Boundary conditions are defined in a way that all the nodes of the fore and aft cross sections are coupled to define a rigid body at each section. Translation and rotation of the nodes of the fore and aft sections were controlled by the control points, one on each rigid body, that were situated in the centre of gravity of the corre- sponding intact section. A rotation of the control points in vertical plane was applied, imposing gradually in that way a curvature of the model and the associated bending moment is the reaction moment that is developed to the control points to achieve the applied curvature. No other constraints on displacements or rota- tions of control points except forced rotation in vertical plane are used in the progressive collapse analysis of the intact ship. The same boundary conditions were used by Samuelides et al. [17]
using dynamic explicit solver implemented in ABAQUS. Other com- binations of boundary conditions that may be used in progressive collapse analysis are reviewed and compared by Koukounas and Samuelides[20].
The fore and aft section boundary conditions were set as shown inFig. 2.
2.2. Computational aspects
When an explicit dynamic NFEM analysis is performed a stabil- ity of the calculation and reliability of the results must be ensured.
Several aspects of the computation were considered to ensure that.
The overall time step increment is automatically determined by LS-Dyna in each step of the analysis and it is a function of the material density and the characteristic finite element length. Stable time step of 1.58104s was determined automatically by the algorithm implemented in LS-Dyna explicit solver. Depending on the finite element type, the algorithm considers the size of the ele- ment and the speed of sound in the material and then determines the time step so that change of any physical value cannot exceed the wave propagation velocity.
The rotation of both control point nodes was gradually applied from 0 to ± 9104radians in 10 s (sign depends on cross section side and either hogging or sagging situation). Only minor dynamic effects were noticed at the start of each simulation but were quickly damped out, without any artificial damping imposed.
Standard Belytschko-Tsay shell element formulation was used to define shell elements resulting in robust calculations that lasted in average 4 h on Xeon E5-2680 (processors) based IBM Flex Sys- tem x240 server with 24 cores, using 4 cores for each individual calculation. A single precision LS-Dyna solver R7.1.1 was used for the calculation.
2.3. Results of the collapse analysis of the intact ship
In addition to the NFEM, the ultimate longitudinal strength assessment is also performed using PCA method according to IACS CSR, as implemented in BV software Mars [24]. Geometry of the midship section and plate thickness is presented in Fig. 3, while longitudinal stiffener scantlings are presented inTable 2.
The comparison of the ultimate strength values calculated by two methods is presented in Table 3, while the comparison of the moment-curvature diagrams is presented inFig. 4.
Expectedly, ultimate strength obtained by NFEM is higher, when compared with IACS CSR PCA, since initial imperfections and residual stresses were not included in the former method, while implicitly considered in the latter. Discrepancy between NFEM and IACS CSR PCA is larger in sagging than in hogging, as the failure in hogging is initiated by the yielding of the main deck and consequently the influence of initial imperfections and resid- ual stresses is lower compared with the sagging failure mode.
Namely, the main consequence of the initial imperfections and residual stresses is a decrease of the elasto-plastic buckling capac- ity of plates and stiffened panels, which is particularly important for the sagging failure mode.
Von Mises stress distribution on a deformed model at the col- lapse (actual curvature corresponding to the ultimate bending moment) is presented inFig. 5. Only a central part of the model, between the web frames, is shown. It appears form Fig. 5 that the ultimate failure in sagging is caused by the elasto-plastic buck- ling of stiffened panels, before the yielding of the ship bottom occurred. On the contrary, collapse in hogging occurs when panels of the ship bottom buckle, although a large part of the main deck structure already was subjected to the significant material yielding.
3. Finite element model of a damaged ship
Collision damage is assumed to start from the main deck down- wards. Although conservative, such assumption is often employed in the residual strength assessment, e.g. Hussein and Guedes
Fig. 2.Boundary conditions at fore and aft section of the three-bay finite element model.
Soares[25]. Two types of damages were considered: damage of the outer shell only and a damage of the both outer and inner shell.
Damage of the outer shell only includes damage of the main deck and longitudinal stringers up to the inner shell.
Considering the FE model, damage is modelled in a way that damaged elements are deleted from the model in the middle bay between the two web frames. Damaged FE models with both outer and inner shell damage, with extent of 40% of ships depth, are shown inFig. 6, together with the IACS CSR PCA models. In IACS CSR PCA models, it is assumed that damaged elements are com- pletely removed from the section. This so-called ‘damaged element removal method’ has been used in several related studies, e.g.
Youssef et al.[26], and is used herein as well.
3.1. Boundary conditions - damaged ship models
Two sets of boundary conditions were defined. First set of boundary conditions is identical to the one defined in the intact FE analysis. This means that all the nodes of the fore and the aft cross sections are coupled to define a rigid body at each section (Fig. 2). The control point has been selected in the centre of gravity Fig. 3.Midship section (geometry of the midship section (i), plate thickness and stiffener numbers (ii)).
Table 2
Scantlings of longitudinal stiffeners of the midship section shown inFig. 3.
Stiff. No. Stiff. position Bar type Dimension
1–22 Bottom shell T 420.011.0/
120.022.0
23, 25–28 Side shell T 340.011.0/
120.020.0
24 Side shell T 340.011.0/
140.020.0
29–37 Side shell T 300.011.0/
120.020.0
38–40 Side shell T 280.011.0/
100.015.0
41–45 Side shell/main deck B 280.012.0
46–58 Main deck T 360.012.0/
140.022.0
59–67 Main deck T 360.014.0/
140.022.0
1–19 Inner bottom T 400.011.0/
120.022.0
20–21 Hopper T 380.011.0/
120.020.0
22–23 Hopper T 350.011.0/
120.020.0
24–28 Inner side T 300.011.0/
120.020.0
29–34 Inner side T 280.011.0/
120.015.0
35–37 Inner side T 280.011.0/
100.012.0
38, 40 Inner side B 260.012.0
39 Inner side A 650.014.0/135.0x15.0
1–3 Central bottom girder B 220.011.5
4–7 Long. bulkhead T 350.011.0/
150.015.0
8–12 Long. bulkhead T 320.011.0/
120.015.0
13–18 Long. bulkhead T 280.011.0/
120.012.0
19–20 Long. bulkhead B 260.011.0
21, 23–24 Long. bulkhead B 260.012.0
22 Long. bulkhead A 650.014.0/150.017
1–8, 11, 13 DB&DH long. girders F 150.012.0 9, 11, 13 Long. bulk. insp. stringer F 150.012.0 10, 12, 14 Long. bulk. insp. stringer F 150.017.0
Table 3
Comparison of ultimate bending moments by three methods (MNm).
NFEM PCA
Sagging 10467 9607
Hogging 11604 11556
-15 000 -10 000 -5 000 0 5 000 10 000 15 000
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
curvature 1/km
M (MNm)
NFEM IACS CSR PCA hog
sag
Fig. 4.Moment – curvature diagrams for intact section.
of a related intact section. The rotation around transversal axis (y- axis) is then applied to each control point, imposing gradually a curvature of the model, while the associated bending moment is determined as the reaction moment that is developed to the con- trol points to achieve the applied curvature. Except the rotation around transversal axis of the control points, there are no other constraints of any kind within the first set of boundary conditions.
The second set of boundary conditions is the same as the first one, except that the rotation around vertical axis (z-axis) is pre- vented as well. By applying such boundary condition, a rotation of the neutral axis is actually prevented. Therefore the influence of the rotation of neutral axis may be systematically studied by comparing solutions with two different sets of boundary conditions.
Boundary conditions are presented in Table 4, in which, the constrained degrees of freedom and the degrees of freedom where the rotations are applied, are indicated.
3.2. Results of the collapse analysis of a damaged ship
Moment-curvature diagrams in the case of damage of the outer and inner shell with extents 20%, 40% and 60% of ship depth are shown inFig. 7. Diagrams include two sets of NFEM results – one for the case of free NA rotation and one for the case the rotation of the NA is prevented as well as results according to IACS CSR PCA method. It may be seen that the ultimate strength is always lower when free rotation of NA is allowed. Also, ultimate strength
obtained by IACS CSR PCA is consistently slightly lower compared with the NFEM results with fixed rotation because of the degrading effect of initial deformations, as already discussed for the intact structure.
Ultimate strength for damage cases when the inner hull is not damaged is almost the same with and without NA rotation. For the model with both inner and outer hull damage, differences in results are obvious and are increasing with the increase of the damage amount.
Von Mises stress distribution on the deformed model (middle bay) for the 40% damage case, is presented inFigs. 8 and 9 for the damage of the outer shell only and for the damage of both inner and outer shell, respectively. In these cases NA rotation is allowed.
It may be concluded, upon the examination of the results pre- sented inFigs. 8 and 9that hull-girder collapse occurs when critical stiffened panel of the main deck or the ship bottom buckles. Such buckling of the stiffened panels is in this particular case a combina- tion of the buckling of the plates between the stiffeners, and stiff- ener tripping failure. In general, however, depending on the geometrical configuration and imposed loading other types of stiff- ener collapse, as beam-column type buckling or local buckling of stiffener web may also occur. It may also be observed in Figs. 8 and 9that the failure in sagging occurs before a tensioned hull gir- der flange (in double bottom) yields. In hogging, however, signifi- cant yielding of the main deck, which acts as a tensioned hull girder flange, occurs before the complete hull girder collapse.
i)
ii)
Fig. 5.Von Mises stress distribution at collapse of the middle part of the intact model (sagging – view from below (i), hogging – view from above (ii)).
4. Residual strength index of damaged Aframax-class double hull oil tanker
A residual strength index (RSI) is defined as the ratio of the ulti- mate longitudinal strength in damaged versus intact condition:
RSI¼Mud
Mu0; ð1Þ
whereMudis the ultimate vertical bending moment capacity of a damaged ship andMu0 is the ultimate vertical bending moment capacity of an intact ship.
RSI versus damage height diagrams are developed as a tool for quick estimation of the residual strength after a collision accident, on the basis of the calculations of the damaged ship collapse, as described in previous section. For each of the damage types (only outer shell damage or both outer and inner shell damage) ultimate strength analysis is performed for the following damage heights (hdamage) relative to the ship depth (D): 5% and from 10% to 80%
with step of 10%. All calculations were performed for two sets of boundary conditions (free and fixed rotation of the NA) as well as by CSR PCA using program Mars.
Diagrams for outer shell damage are presented in Fig. 10, for sagging and hogging loading cases.
i)
ii)
iii)
iv)
Fig. 6.Ship models for damage height equal to 40% of the ship depth: finite element model of outer shell damage (i), IACS CSR PCA model of outer shell damage (ii), finite element model of both inner and outer shell damage (iii), IACS CSR PCA model of both inner and outer shell damage (iv).
It may be seen fromFig. 10that the residual bending moment is always higher than 90% of the ultimate bending moment of the intact ship. Influence of the rotation of the neutral axis is relatively low: the residual strength obtained by model with fixed NA rota- tion is less than 5% larger than the residual strength obtained by free rotation of the NA. Results obtained by CSR PCA are always between the two sets of NFEM results. Therefore CSR PCA is consid- ered as reliable method for the residual strength assessment of a double hull tanker with outer shell damage only, despite the fact that it does not allow the rotation of the NA.
Diagrams for inner and outer shell damages for sagging and hogging are presented inFig. 11.
Considerable influence of the NA rotation is obvious when both outer and inner shells are damaged. Thus, for the damage height of 0.6 D, which is the ‘‘design‘‘ damage height according to IACS CSR, RSI in sagging is decreased from 87% to 76% as a consequence of the NA rotation. A decrease in hogging is also large but it is less impor- tant for design, as the sagging is critical load case for damaged double-hull oil tanker.
One may notice fairly close agreement between the residual strength RSI calculated by NFEM with fixed NA rotation and the one calculated by IACS CSR PCA. The residual strength calculated by NFEM is slightly higher than IACS CSR PCA, probably as a conse- quence of the stiffening effect of the undamaged structure aft and forward of the damaged part, since in IACS CSR PCA damaged ele- ments are completely removed from calculations.
Diagrams for the residual strength may be presented in the form of the 3rd order polynomials:
RSI¼a3
hdamage
D
3
þa2
hdamage
D
2
þa1
hdamage
D
þa0 ð2Þ Coefficientsa0–a3for sagging and hogging and for two differ- ent damage cases (only outer shell damaged and both outer and inner shell damaged) are specified inTable 5. In all cases, coeffi- cient of determination (R2), between the fitted curves and the cal- culated results, was higher than 0.995 indicating that the polynomial approximation is reliable. The coefficient of determina- tion is standard statistical measure of how well observed outcomes are replicated by the model, i.e. by the polynomial approximation.
The coefficient of determination ranges from 0 to 1, where 1 indi- cates perfect prediction when all predicted values are equal to observed while large differences between predicted and observed values would result in low coefficient of determination. Following formula for coefficient of determinationR2is employed:
R2¼1SSres
SStot ð3Þ
whereSStotis the total sum of square deviations of observed values with respect to the mean of observations, whileSSresis the sum of squares of residuals.
Very often RSI diagrams are provided without considering the influence of the rotation of the neutral axis, e.g. Andric´ et al.[28].
The reason for that is that there is still no method, approved and accepted by all IACS members, which would include this effect.
Pure incremental method developed by Fujikubo et al. [22] is promising, but still not in use by the classification societies. There- fore, it is reasonable to assume that ship structural designer in practice would employ IACS CSR PCA method and then modify results due to the rotation of the NA. Since the correction in sag- ging is of practical importance, when both outer and inner shells are damaged, only that case is considered herein. Diagram of cor- rection factor (CNA) is presented inFig. 12as a function of the dam- age height.
Fig. 12presents RSI diagram obtained by IACS CSR PCA method calculation, without the effect of the rotation of NA, then RSI dia- gram obtained by NFEM, which includes effect of NA rotation, and finally diagram of correction factor (CNA) necessary to multiply residual strength calculated by IACS CSR PCA method to obtain NFEM results. Diagram of correction factors may be expressed as the linear function of the non-dimensional damage height as:
CNA¼10:1732 hdamage
D
ð4Þ Coefficient of determination R2 of this linear approximation, which is based on a least square method, reads more than 0.96 and it is therefore a reliable estimate. For,hdamage/D= 0.6, which is a damage requirement according to IACS CSR, correction factor reads 0.9. Coincidently, that correction is actually the same as CNAproposed in IACS CSR[6].
5. Discussion
Several authors proposed diagrams for rapid RSI assessment of a double hull oil tanker. Basically, diagrams may be distinguished by the assumed transverse damage penetration: some authors assumed that only the outer shell is damaged, while others assumed that both the inner and the outer shells are damaged.
These two assumptions are discussed separately, as they result in large differences in the residual strength estimation.
5.1. Comparison of the RSI diagrams for the outer shell only damaged Formulae for the prediction of the RSI in sagging and hogging, without a need to perform detailed step-by-step calculations, are Table 4
Boundary condition cases - the red colour means constrained degree of freedom. The symbol * means that rotation is applied to the d.o.f. (T: translation, R: rotation, Longitudinal axis: x, Transverse horizontal and vertical axes: y and z respectively).
presented by Wang et al.[27]. The assumption that only the outer shell is damaged in collision was used, while equations are valid up tohdamage/D= 0.4. Following expressions for the RSI are proposed for a double hull oil tanker of comparable size as the one studied herein:
For sagging:
RSI¼10:177 hdamage
D
þ0:140 hdamage
D
2
þ0:038 hdamage
D
3
ð5Þ
For hogging:
RSI¼10:138 hdamage
D
þ0:235 hdamage
D
2
0:126 hdamage
D
3
ð6Þ Hussein and Guedes Soares [25] proposed following linear expression for RSI in both hogging and sagging for the case of the outer shell damage:
RSI¼0:980:084 hdamage
D
ð7Þ
i)
-15 000 -10 000 -5 000 0 5 000 10 000 15 000
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
curvature 1/km
M (MNm)
NFEM IACS CSR PCA NFEM - rot fix hog
sag
ii)
-15 000 -10 000 -5 000 0 5 000 10 000 15 000
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
curvature 1/km
M (MNm)
NFEM IACS CSR PCA NFEM - rot fix hog
sag
iii)
-15 000 -10 000 -5 000 0 5 000 10 000 15 000
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
curvature 1/km
M (MNm)
NFEM IACS CSR PCA NFEM - rot fix hog
sag
iv)
-15 000 -10 000 -5 000 0 5 000 10 000 15 000
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
curvature 1/km
M (MNm)
NFEM IACS CSR PCA NFEM - rot fix hog
sag
v)
-15 000 -10 000 -5 000 0 5 000 10 000 15 000
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
curvature 1/km
M (MNm)
NFEM IACS CSR PCA NFEM - rot fix hog
sag
vi)
-15 000-10 000 -5 000 0 5 000 10 000 15 000
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60
curvature 1/km
M (MNm)
NFEM IACS CSR PCA NFEM - rot fix hog
sag
Fig. 7.Moment – curvature diagrams for damaged sections (20% outer shell damage (i), 20% inner and outer shell damage (ii), 40% outer shell damage (iii), 40% inner and outer shell damage (iv), 60% outer shell damage (v), 60% inner and outer shell damage (vi)).
RSI diagrams in sagging and hogging are compared inFig. 13.
Diagrams obtained in the present study are conservative for both cases, sagging and hogging although, in general, analysis by Hussein and Guedes Soares[25]and present analysis provide sim- ilar results. Results presented by Wang et al.[27]are unconserva- tive that may be the consequence of a different description of the damage. In the present analysis, all elements between the side shell and the inner hull are removed from calculation. In[27], only side shell and side longitudinals are assumed to be damaged, while the longitudinal stringers are intact.
5.2. Comparison of the RSI diagrams with the assumed both inner and outer shell damaged
Andric´ et al.[28]proposed following 2nd order polynomials for the residual ultimate strength in sagging and hogging respectively, for the case when both the inner and outer shell of an doubler hull oil tanker are breached:
RSI¼0:99270:5802 hdamage
D
þ0:4516 hdamage
D
2
ð8Þ
RSI¼0:99480:3494 hdamage
D
þ0:2544 hdamage
D
2
ð9Þ
Additionally, in the IACS CSR background document[29], fol- lowing linear Eqs.(10) and (11)are proposed for sagging and hog- ging case respectively, for an FPSO with both inner and outer hull damaged:
RSI¼10:4 hdamage
D
ð10Þ
RSI¼10:267 hdamage
D
ð11Þ Comparison of the corresponding diagrams is presented in Fig. 14.
Results by IACS CSR background document[29] are obtained based on NFEM analysis, considering the effect of the NA rotation.
Consequently, as it may be seen inFig. 14, the results from[29]
agree, in general, quite well with the results obtained in the pre- sent study. However, linear trend assumed in[29]is over simpli- fied. Results presented by Andric´ et al. in [28]overestimate the actual residual ultimate strength. That is expected, as in[28]rota- tion of NA is not considered.
5.3. Comparison of correction factors
Correction factors by Eq.(4)may be compared with the ones obtained by approximate expression derived in Fujikubo et al.[22]:
i)
ii)
Fig. 8.Von Mises stress distribution at collapse of the middle part of the model with 40% outer shell damage and with free NA rotation (sagging – view from below (i), hogging – view from above (ii)).
i)
ii)
Fig. 9.Von Mises stress distribution at collapse of the middle part of the model with 40% inner and outer shell damage and with free NA rotation (sagging – view from below (i), hogging – view from above (ii)).
Fig. 10.RSI versus damage height diagrams for outer shell damage in sagging (i) and hogging (ii).
Fig. 11.RSI versus damage height diagrams for inner and outer shell damage in sagging (i) and hogging (ii).
MuV MuVjCASE2
¼CNA¼ IHHIVVI2HV ðyCyGÞIHVþ ðzCzGÞIHH
ðzCzGÞ
IVV ð12Þ
where:
y,z- transverse horizontal and vertical axis, respectively yC,zC–location of the critical member on the ship main deck yG,zG–centroid coordinates of the damaged cross section
IVV–axial moment of inertia (vertical) of the damaged cross section relatingyaxis
IHH–axial moment of inertia (horizontal) of the damaged cross section relatingzaxis
IHV–centrifugal moment of inertia of the damaged cross section relatingyandzaxes
MuV– residual vertical hull girder strength in sagging including effect of rotation of NA
MuVjCASE2– residual vertical hull girder strength in sagging with- out rotation of NA.
The coordinatesycandzcof the two points, namely ‘‘L1” and
‘‘L2”, are suggested by Fujikubo et al.[22] as the coordinates of the potentially critical member location on the ship main deck.
First option is point ‘‘L1”, located on the main deck at centreline and the second option is point ‘‘L2”, located on the main deck at the distance B/4 from the damaged side shell. Both locations are considered and compared with the present results. Comparison of the correction factorsCNAis presented inFig. 15.
It may be seen from Fig. 15 that much better agreement is obtained if the point ‘‘L2” is selected in Eq.(12), compared with the point ‘‘L1”. The choice of ‘‘L1” would lead to the overestimation ofCNA, i.e. the underestimation of the effect of the rotation of NA.
Table 5
Coefficients of RSI versus damage height diagrams represented as 3rd order polynomials.
a0 a1 a2 a3
Outer shell damage only Sag 1 0.3123 0.2118 0.0256
Hog 1 0.2117 0.1043 0.0399
Outer and inner shell damage Sag 1 0.7779 0.7916 0.2581
Hog 1 0.4226 0.1663 0.079
0.80 0.85 0.90 0.95 1.00
0.70 0.75 0.80 0.85 0.90 0.95 1.00
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
CNA
RSI
hdamage/D IACS CSR PCA
NFEM CNA
Fig. 12.Diagram of correction factors (CNA) for inner and outer shell damage in sagging.
Fig. 13.Comparison of RSI versus damage height diagrams when only the outer shell is damaged for sagging (i) and hogging (ii).
Fig. 14.Comparison of graphs for residual strength prediction when both inner and outer shells are damaged for sagging (i) and hogging (ii).
6. Conclusion
The aim of the present study is to investigate the progressive collapse of an Aframax-class double-hull oil tanker damaged in col- lision with the particular aim to study the influence of the rotation of the NA. The progressive collapse analysis is performed by NFEM using explicit dynamic solver LS-Dyna, for the two cases: the dam- age of the outer shell only and the damage of both the outer and the inner shell. In both cases, damage is assumed to start from the main deck and to have a shape of the rectangular box. RSI ver- sus damage height diagrams are developed in sagging and hogging, as well as the diagram for the correction factor accounting for the rotation of NA. In addition, diagrams are compared with the previ- ously published studies.
From the results obtained, the following conclusions can be drawn:
1. Explicit dynamic NFEM solver provides stable and consistent solution in all cases.
2. Influence of the neutral axis rotation on the ultimate longitudi- nal strength is relatively low for cases when only the outer shell is damaged. However, when both the outer and inner shells are damaged, the vertical bending moment capacity in both sagging and hogging is significantly reduced because of the NA rotation effect.
3. For damage height equal to 60% of the ship depth, which is in IACS CSR [6] prescribed as the ‘‘design” damage height, the same correction factor, required to take into account the NA rotation effect, is obtained by NFEM and specified in the IACS CSR, i.e. 10% reduction of the residual longitudinal strength cal- culated with fixed NA rotation.
4. RSI as a function of the damage height can be adequately described by 3rd order polynomial for sagging and hogging cases. Correction factors due to the NA rotation may be approx- imated by the linear function of the damage height. Comparison with other published RSI diagrams shows important differences in some cases.
5. Correction factor for NA rotation in sagging proposed by Fujikubo et al.[22] is in good agreement with NFEM results, providing that it is calculated at the critical location on the main deck at the distance B/4 from the damaged side shell. If critical location is assumed to be on the main deck at the centre line, correction due to NA rotation is largely underestimated.
Results of the present study may be used by classification societies in rule development, in the risk assessment studies of the maritime transportation and for a rapid calculation of the hull girder residual strength of a damaged ship in emergency rescue.
7. Future research needs
In the current shipbuilding industry, most calculations used to achieve the safety criteria are defined by dealing with the worst possible scenario. Thus, the ship classification rules[6,30]define the post-collision impact damage scenarios by assuming damage in the shape of a ‘‘rectangular box‘‘, starting from the main deck.
Such approach, adopted also in the present study may be criticized for two reasons.
Firstly, assumption that a damage shape has a form of a ‘‘box‘‘ is not justified as the shape of the damage induced in the struck ship is generally more complex. Integrated analysis of the collision sim- ulation and hull-girder PCA using NFEM is presented by Notaro et al.[18], while NFEM collision simulation with realistic damage shapes, combined with the intelligent supersize finite element method (ISFEM) is described by Youssef et al.[26]. Considering such realistic collision damage scenarios, Youssef et al.[32]related RSI to the collision damage index (CDI), defined as the reduction ratio of the vertical hull girder moment of inertia of intact and damaged ships.
Secondly, the nature of ship collision impact damage is unclear and involves a variety of influencing parameters, such as collision location along the stricken ship, speed of striking ship and collision angle, that are naturally probabilistic and thus a probabilistic approach is necessary. Such approach is proposed by Faisal et al.
[31]where a relevant set of ship collision scenarios are defined by dealing with the influencing parameters of a ship’s post- collision impact damage as random variables. As per the simula- tion results associated with the RSI, the probability density func- tion of RSI is developed in[31].
The applicability of the results for other types of double hull oil tankers may also be commented. RSI diagrams for double-hull tan- kers of different sizes are calculated by Andric´ et al.[28], showing very close agreement between RSI for Aframax, Suezmax and VLCC tankers. Based on that, provisionally may be stated that present results have wide applicability for double-hull tankers of different classes, although this needs further validation.
It should be emphasised that, regardless of the neutral axis rota- tion, the ultimate hull girder strength should be evaluated with respect to the axis parallel to the water surface. If the ship position is inclined due to water ingress or oil outflow, then the ultimate hull girder strength should be evaluated with respect to the inclined axis that is parallel to the water surface. Further research is therefore required for progressive collapse analysis of inclined ship.
Acknowledgement
The work has been fully supported by the Croatian Science Foundation within the project 8658.
References
[1] Eliopoulou E, Diamantis P, Papanikolaou A. Casualties of medium size tankers.
In: 3rd Int. Symposium on Ship Operations, Management and Economics”, Athens, The Greek Section of the SNAME; 2010.
[2]Ringsberg JW. Characteristics of material, ship side structure response and ship survivability in ship collisions. Ships Offshore Struct 2010;5(1):51–66.
[3] Jia H, Moan T. Reliability analysis of oil tankers with collision damage. In: 27th International Conference on Offshore Mechanics and Arctic Engineering, Estoril, Portugal, 2008. Paper number; 57102.
[4]Kim YS, Youssef SAM, Ince ST, Kim SJ, Seo JK, Kim BJ, et al. Environmental consequences associated with collisions involving double hull oil tankers.
Ships Offshore Struct 2015;10(5):479–87.
[5]Paik JK, Thayamballi AK, Yang SH. Residual strength assessment of ships after collision and grounding. Marine Technol 1998;35(1):38–54.
[6] IACS. Common Structural rules for Bulk Carriers and Oil Tankers” (IACS CSR).
International Association of Classification Societies; 2014.
[7]Paik JK, Kim DH, Park DH, Kim MS. A new method for assessing the safety of ships damaged by grounding. Trans Roy Inst Naval Arch 2012;154(A1):1–20.
Fig. 15.Comparison of the graphs of correction factorsCNAfor the rotation of NA in sagging load case, when both inner and outer shells are damaged.
[8]Kim DK, Kim BJ, Seo JK, Kim HB, Zhang XM, Paik JK. Time-dependent residual ultimate longitudinal strength-grounding damage index (R-D) diagram. Ocean Eng 2014;76:163–71.
[9]Hughes OF, Paik JKE. Ship structural analysis and design. New Jersey: SNAME;
2010.
[10] Yoshikawa T et al. ‘‘Ultimate strength”, Committee III.1, Proceedings of the 19th International ship and offshore structures congress (ISSC 2015), 7–10 September 2015, Cascais, Portugal.
[11]Caldwell J. Ultimate longitudinal strength. Trans Roy Inst Naval Arch 1965;107:411–30.
[12]Paik JK, Mansour AE. A simple formulation for predicting the ultimate strength of ships. J Mar Sci Technol 1995;1(1):52–62.
[13]Paik JK, Kim DK, Park DH, Kim HB, Mansour AE, Caldwell JB. Modified Paik- Mansour formula for ultimate strength calculation of ship hulls. Ships Offshore Struct 2013;8(3–4):245–60.
[14] Smith C. Influence of local compressive collapse on ultimate longitudinal strength of a ship’s hull. In: Proceedings of the International Symposium PRADS. Tokyo (Japan): The Society of Naval Architects of Japan; 1977.
[15]Guedes Soares C, Luís RM, Nikolov PI, Modiga M, Quesnel T, Dowes J, et al.
Benchmark study on the use of simplified structural codes to predict the ultimate strength of a damaged ship hull. Int Shipbuild Prog 2008;55(1–
2):87–107.
[16] Downes J, Ham WL, Dow RS. assessment of the residual strength of a lightweight naval vessel. In: Proceedings of the PRADS2013, pp. 1189–1196, 20–25 October 2013, CECO, Changwon City, Korea.
[17] Samuelides MS, Koukounas D, Pollalis C. Residual strength of Damaged Ship’s Hull, Proceedings of the PRADS2013, 20–25 October, 2013, CECO, Changwon City, Korea, pp. 1003–1010.
[18] Notaro G, Østvold TK, Steen E, Oma N. Collision damages and residual hull girder strength of a ship shaped FPSO. In: Proceedings of the PRADS2013, 20–
25 October, 2013, CECO, Changwon City, Korea, pp. 1011–1019.
[19]Benson S, Anuar Abu Bakar A, DOW RS. A comparison of computational methods to predict the progressive collapse behaviour of a damaged box girder. Eng Struct 2013;48:266–80.
[20] Koukounas D, Samuelides M.S. Modeling aspects of strength capacity of intact and damaged ship girders. In: Guedes Soares, Romanoff, editor. Analysis and Design of Marine Structures. London: Taylor & Francis Group; 2013, pp. 157–
65, ISBN 978-1-138-00045-2.
[21]Zubair MA. Residual hull girder strength of asymmetrically damaged ships Doctoral Dissertation. Graduate School of Engineering, Osaka University; 2013.
[22]Fujikubo M, Zubair MA, Takemura K, Iijima K, Oka S. Residual hull girder strength of asymmetrically damaged ships. J Jpn Soc Naval Arch Ocean Eng 2012;16:131–40.
[23] Makouei SH, Teixeira AP, Guedes Soares C. A study on the progressive collapse behavior of a damaged hull girder. In: Guedes Soares C, Santos TA, editors.
Maritime Technology and Engineering. London, UK: Taylor & Francis Group;
2015, p. 405–16.
[24] MARS, User’s manual. Bureau Veritas, Paris, 2013.
[25]Hussein AW, Guedes Soares C. Reliability and residual strength of double hull tankers designed according to the new IACS common structural rules. Ocean Eng 2009;36:1446–59.
[26]Youssef SA, Faisal M, Seo JK, Kim BJ, Ha YC, Kim DK, et al. Assessing the risk of ship hull collapse due to collision. Ships Offshore Struct 2016;11(4):335–50.
[27]Wang G, Chen Y, Zhang H, Peng H. Longitudinal strength of ships with accidental damages. Mar Struct 2002;15:119–38.
[28]Andric´ J, Kitarovic´ S, Piric´ K. Residual hull girder ultimate strength of a double hull oil tankers. Brodogradnja 2015;66(3).
[29] IACS. Common Structural Rules for Bulk Carriers and Oil Tankers. International Association of Classification Societies, TB report no. Pt 1 – Residual strength, Ch 5, Sec 3; 2014.
[30] AMERICAN BUREAU OF SHIPPING. Guide for assessing hull girder residual strength. Houston (TX): American Bureau of Shipping; 1995.
[31]Faisal M, Noh SH, Kawsar RU, Youssef SAM, Seo YK, Ha YC, et al. Rapid hull collapse strength calculations of double hull oil tankers after collisions. Ships Offshore Struct 2017;12(5):624–39.
[32] Youssef SAM, Noh SH, Paik JK. A new method for assessing the safety of ships damaged by collisions. Ships Offshore Struct 2017.http://dx.doi.org/10.1080/
17445303.2017.1285679.
