1
Abstract
Chemical tanker traffic constitutes a hazard for the environment; large chemical spills caused by
e.g. ship-tanker collisions can have catastrophic effects in similar manner to oil spills. For this
reason, it is important to have a generalized spill model for chemical tankers so that the spill size
for a given geographical area can be assessed. The spill volume can be used as an indicator of
risk in the given area. Furthermore, such a model can be used to analyze possible effects of
potential risk-mitigating measures such as requiring wider double hulls for chemical tankers. In
this paper a spill model is proposed, which for any given collision scenario can model the
penetration, spill probability and size caused by a ship striking a chemical tanker. This is done
1 Department of Applied Mechanics, Aalto University School of Engineering, Espoo, Finland
2 Department of Marine Technology, Norwegian University of Science and Technology, Trondheim,
Norway
Corresponding author:
Otto-Ville Edvard Sormunen, Department of Applied Mechanics, Aalto University School of Engineering,
Espoo, Finland. Tietotie 1A, FI-02150.
Email: [email protected]
Collision consequence estimation model for chemical tankers
Otto-Ville Edvard Sormunen1, Sören Ehlers
2 and Pentti Kujala
1
The final, definitive version of this paper has been published in Proc IMechE, Part
M: Journal of Engineering for the Maritime Environment, 227 (2) pp. 98 – 106.
by SAGE Publications Ltd, All rights reserved. © Authors.
2
using FEM, MATLAB and statistical metamodels with ship particulars extracted mainly from
AIS-data from the Gulf of Finland.
Keywords
Chemical tankers, ship-ship collisions, FEM, statistical metamodels, chemical spill model
1. Introduction and methodology
Environmental disaster such as the Exxon Valdez grounding and the increasing size of oil
tankers lead to extensive risk-related studies. 1 2 3 4 The Finite Element Method (FEM) is
commonly used to estimate the collision damage for ships, such as chemical and oil tankers. 5 6 7
8 9 However, even though the FEM can produce accurate and detailed results it is also this level
of detail which makes it time consuming and thus not applicable to model thousands of
potential accidents in a larger sea area such as the Gulf of Finland (GoF). Furthermore, in order
to model the expected chemical spill volumes for all chemical tankers in e.g. the GoF, a wide
range of tanker sizes, collision angles and speeds needs to be taken into account. Consequently,
assessments using FE-simulations alone are usually concerned with one or two different tankers
and collision scenarios only. 10 11
More generalized damage assessment models based on accidents statistics are also available
such as the damage rules given in MARPOL Annex I and the HARDER project, which however
do not link the collision variables, such as impact speed with the resulting damage. 12 13
Furthermore, the models are derived for oil tankers, but not for chemical tankers. Thus there is
need for a new, generalized model for chemical tankers that is general enough for all tanker
sizes and able to link the collision variables –such as ship masses, impact speeds, angle and
3
collision location on the struck ship hull with the resulting structural damage. Furthermore, the
model needs to be fast and simple enough for assessing thousands of observations.
Consequently, this paper introduces a new approach comprising a series of characteristic FE-
simulations covering the range of possible collision scenarios, followed by analytical
interpolations to increase the information density for a variety of collision scenarios and a
statistical metamodel to estimate the chemical spill probability and size. The characteristic FE-
simulations are carried out for a series of characteristic chemical tankers of different sizes to
obtain the critical penetration, which causes fracture of the inner hull as a function of the ship
size and collision energy. Furthermore, these results are interpolated using MATLAB to obtain a
simplified collision consequence model for all tanker sizes in question. This results in a
deterministic spill model for each given set of collision variables for the given chemical tanker.
Finally, in order to simplify calculations and to facilitate a sensitivity analysis, a statistical
metamodel is utilized to estimate both the chemical spill probability and the most likely spill
size should a collision occur. As a result, we obtain a fast, relatively easy to use and generalized
chemical spill estimation model, which requires only a small number of reliable FE-based
collision simulations. Thereby this approach is different compared to the existing methods
mentioned above. Namely, it is specific for chemical tankers instead of for oil tankers. Secondly,
the underlying FE-simulations are generalized to cover a wide range of chemical tankers by
interpolating within the FEM-results. Furthermore, the statistical metamodels are applicable for
a wide range of ship sizes, collision speeds, collision angles, etc. This paper is based on work
done by Sormunen 14 in his Master’s thesis. The steps contributing to this new chemical spill
estimation model are summarized in Figure 1.
4
Figure 1 Model layout
1.1 FE -simulations
The starting point is a FE-model of a 180 m long, 40 000 DWT chemical tanker with a double
hull width of 2 m, illustrated in Figure 2. The simplified bulb that is used to simulate the bow
section of the striking ship that collides with the chemical tanker side is illustrated in Figure 3.
5
Figure 2 Double-hulled chemical tanker layout used in the FE-simulation15
Figure 3 Rigid bulb used in FE-simulations
6
Figure 4 Main frame section of the chemical tanker, adapted from Sormunen14
For determining the collision consequences, namely the energy versus penetration curve as well
as the critical penetration causing inner shell rupture is assessed as a function of collision
energy, double hull width and striking bulb size. For this end, a discrete number of FE-
simulations are carried out for relative chemical tanker sizes of 50%, 75 %, 100 %, 125 %, 150 %
and 200 % of the reference tanker side structure as shown in Figure 2 and 4. The numerical
model of the tanker presented in Figure 2 is built and geometric scaling of the finite element
model is used to generate vessels of different sizes. Furthermore, the scantlings, see Figure 4, of
the scaled vessels are obtained according to the DNV strength requirements. 16 This compliance
of the scaled main frame sections is acceptable, because the focus of this study lies on the
7
collision resistance of similar side structures found in similar vessels. Therefore, the
modification of the general layout in terms of free heights or superstructure arrangement is
assumed to have a neutral influence on the force-penetration curve of the side structure alone.
Furthermore, the relative size here refers directly to the double hull width, thus a 100 % size
equals a chemical tanker with a 2 m wide double hull, 50 % a 1 m wide etc. Furthermore, for
each different chemical tanker the FE-simulations are carried out using different relative bulb
sizes of 50 %, 100 % and 150 % of the reference bulb size shown in Figure 3. Based on the results
of these different tanker- and bulb sizes, the energy versus penetration curves are interpolated
to obtain the values for all relevant tankers between these sizes in MATLAB, which is described
later on in the paper.
1.2 Quasi-static numerical collision simulation
The solver LS-DYNA version 971 is used for the collision simulation, see Ehlers 8. The
ANSYS parametric design language is used to build the finite element model of the
reference tanker. The three dimensional models are built between two transverse
bulkheads and the translational degrees of freedom are restricted at the plane of the
bulkhead locations. The remaining edges are free. The structure is modelled using four
noded, quadrilateral Belytschko-Lin-Tsay shell elements with 5 integration points
through their thickness. The characteristic element-length in the contact region is 50
mm to account for the non-linear structural deformations, such as buckling and
folding. The element length dependent material relation and failure criterion according
to Ehlers 8 and Ehlers and Varsta 17 is utilized for the simulations; see Figure 5. The
application of this material model including failure enables the collision simulations to
8
be sufficiently accurate, see Ehlers 18. Standard LS-DYNA hourglass control and
automatic single surface contact (friction coefficient of 0.3) is used for the simulations;
see Hallquist19 The collision simulations are displacement-controlled. The rigid bow,
see Figure 3, is moved into the ship side structure at a constant velocity of 10 m/s. This
velocity is reasonably low so as not to cause inertia effects resulting from the ships’
masses, see Konter et al. 20 Furthermore, the rigid indenter results in the maximum
energy absorption of the side structure alone, which is needed for a comparison and
can be considered conservative and thereby suitable for comparative predictions.
a) b)
Figure 5 Strain versus stress relation for mild steel (a) and failure strain versus element
length (b) 8
1.3 FEM results and generalized MATLAB- model
The FE-simulation results obtained with the 100 % bulb are now used to obtain the collision
energy as a function of penetration for different struck chemical tanker double hull widths in
9
Figure 6. The FE –simulations were stopped after the bulb penetrated 3 meters into the struck
ship at a perpendicular angle.
Figure 6 Energy as a function of penetration for different relative double hull widths14
As can be seen in Figure 6, the relationship between energy and penetration is almost linear.
Furthermore, in Figure 7 the FEM- results in terms of energy needed for a 3 meter penetration
is given as a function of the relative double hull width, which also shows a very linear trend. The
latter is shown through a least square fitted line through the FE-based observations marked
with diamond symbols, which has an R2 of 0.997.
0
10
20
30
40
50
60
70
80
0 1 2 3 4
Ene
rgy
[MJ]
Penetration [m]
125 %
100 %
75 %
50%
FEM 100 %
10
Figure 7 Energy needed for a 3 m penetration as a function of relative double hull width14
Furthermore, the results of the FE-simulations with all the different bulb sizes and double hull
sizes are presented in Table 1. Therein, the energy needed to penetrate 3 meters perpendicularly
into the side of the struck ship as a function of the struck ship double hull width and the relative
bulb size compared to Figure 2 and Figure 3 is presented.
y = 82,457x - 31,7 R² = 0,9966
0
20
40
60
80
100
120
140
0% 50% 100% 150% 200% 250%
MJ
Relative double hull width
MJ needed for 3 mpenetration
Linear (MJ needed for3 m penetration)
11
Table 1 Energy required for 3 m penetration in MJ as a function of double hull width and
bulb size
50 % 75 % 100 % 125 % Relative struck ship size
Relative bulb size Bulb factor 1 1.5 2 2.5 Double hull width [m]
50 % 0.8 10.4 21.6 38.4 57.6
100 % 1 13 27 48 72
150 % 1.2 15.6 32.4 57.6 86.4
Consequently, it can be seen in Table 1 that the bulb size directly affects the energy needed for
penetrating 3 meters into the side structure of a tanker. Based on these FEM-results, the general
penetration model is then constructed in MATLAB as a series of m-files in a following manner:
The required energies are interpolated linearly according to the striking ship length to obtain
the bulb factor , which is then directly multiplied with collision energy in Equation 2.
{
(1)
where
is the length of the striking ship in m.
12
Furthermore, to obtain the perpendicular displacement in meters as a function of double hull
width, collision energy and striking ship bulb size, a linear interpolation is carried out in
MATLAB according to the following equation:
(
)
( ) (2)
where
WDH is the double hull width of the struck tanker in meters, FB is the bulb factor and the
perpendicular collision energy in mega joules, calculated in this paper according to Zhang’s
collision energy model. 21
For avoiding negative energy values it is assumed that WDH has a minimum value of 1 when
calculating . Furthermore, because of the limitations of the FE- simulations, only the
perpendicular displacement is calculated accurately and consequently the total penetration
length is conservatively calculated using basic trigonometry
( )
(3)
After calculating the displacement it is compared to the double hull width in order to determine
whether the inner hull is breached and a spill occurs. The double hull thickness is taken from
IMO MARPOL Annex I oil tanker regulations. 13
13
{
(4)
with an absolute minimum width of 0.76 m and a maximum required width of 2 m.
Furthermore, based on the observations from the FE- simulations it is possible that with a large
bulb the perpendicular penetration depth can exceed the double hull width and still not cause
any rupture in the inner hull by creating a dent-formed deformation. The opposite is also true:
Smaller bulbs are more prone to pierce the inner hull by pushing material located between the
two hulls into it. Thus small bulbs can cause a leak with a penetration depth that is actually less
than WDH. Due to this, for the purposes of determining if the inner hull is breached or not, WDH
temporarily becomes
{
(
)
(5)
If the displacement exceeds the double hull width, the location of the bulb at the end of the
collision is overlaid with a generalized chemical tanker layout in MATLAB to check which (if
any) cargo tanks are breached. Based on tanker specifics obtained from 13 chemical tankers, the
following generalizations are made for a virtual chemical tanker model regardless of the size of
the chemical tanker: 22 23 24
- Tankers have 20 tanks in 2 rows.
- All 20 tanks are of equal size.
- Total tank size in m3 is 1.11 DWT, all tankers are assumed to be 98 % laden when struck.
14
- Tanks are located between 20 % of tanker length from aft to 10 % of tanker length from
forward.
In Figure 8 an example of the general chemical tanker layout is given for a 120 m long chemical
tanker. Therein, the boxes mark the chemical cargo tanks, with the aft to the left in the figure
and the bow to the right with a 100 % size bulb shown penetrating two chemical cargo tanks.
Figure 8 Virtual 120 m long example tanker layout as seen from above generated in
MATLAB with penetrating bulb shown
1.4 Collision variables from traffic simulation
The striking and struck ship particulars are taken from output of Goerlandt and Kujala’s 25
discrete fast-time GoF traffic simulation based on 2007 AIS-data done for all ship types.The
chemical tanker cases were filtered out by Sormunen 14 by comparing oil- and chemical tanker
deadweight statistics, yielding a total of 5976 potential chemical tanker cases. In addition to the
variables presented in Equations 1-5, the following variables are used in the analysis:
LA, LB: length of striking (A) and struck (B) ship in m
MA, MB: mass of striking and struck ship in tonnes
0 20 40 60 80 100 120
0
5
10
15
20
15
VA,VB: velocity of striking and struck ship
β: absolute value of collision angle in ˚, where 0˚ equals a perpendicular collision and 90˚ a
head-on or overtaking collision.
xL: relative impact location on struck ship hull [0;1], where 0 is aft and 1 is forward.
Variable xL is randomly generated from a uniform distribution as specified in the HARDER-
project damage rules. 12 As a result, the most important collision variables are illustrated in
Figure 9.
Figure 9 Histograms of most important collision variables
0 10 20 300
500
1000
1500
Speed at moment of collision [kn]
Striking ship
0 20 40 60 800
500
1000
Collision angle [o]
0 50 100 1500
1000
2000
3000
Mass of striking ship [kt]
0 20 40 60 800
500
1000
1500
DWT of chemical tankers [kt]
16
For calculating the perpendicular collision energy Eξ, the model presented by Zhang was used,
illustrated in Figure 10. 7.7 % of the cases the collision energy exceeded 200 MJ.
Figure 10 Histogram of the perpendicular collision energy using Zhang’s energy model.
2. Penetration depths, lengths and spill volumes
Following the above mentioned procedure using MATLAB based on a generalization of the
FEM- results presented in Equations 1-5, the following results are obtained for perpendicular
penetration depth, total penetration length and spill volume, see Figure 11. The range for the
simulated chemical spills is 120 -28 338 m3 with a median of 2105 m3. The simulated non-
dimensional penetration depth was less than 0.05 in 35.72 % of the cases but supposedly
exceeded the ship width in 10.6 % of cases, which, however, are not shown in Figure 11.
Furthermore, in 51 % of the cases the perpendicular penetration was no more than 3 m. The
0 20 40 60 80 100 120 140 160 180 2000
200
400
600
800
1000
1200
1400
1600
1800
2000
E [MJ]
17
non-dimensional penetration length was less than 1 % in 28.9 % of the cases and over 0.5 in 1.2
%.
Figure 11 MATLAB collision damage model results
3. Spill metamodeling and sensitivity analysis
In order to facilitate sensitivity analysis and to make the spill model more accessible for others,
a statistical metamodel is presented here which uses the output from the MATLAB- based
simulation model for estimating the probability of chemical spill in any given collision situation
and the spill size in a case of a given collision situation.
0 5000 100000
100
200
300
400
500
Chemical spill volume [m3]
Observ
ations
0 0.5 10
500
1000
1500
2000
Non-dimensional penetration depth
0 0.1 0.2 0.3 0.40
1000
2000
Non-dimensional penetration length
Observ
ations
18
3.1. Probability of chemical spill in any given collision
situation
For estimating the spill probability using a given set of collision variables, logistics regression is
used with calculations done with the IBM SPSS Statistics 20 software package. The independent
variables were selected based on their statistical significance and explanatory power. For
determining whether the impact happened where the cargo tanks are located along the hull on
the tanker or not, an additional variable δ was added, which has the value 1 if 0.2 ≤ xL ≤ 0.9, 0
otherwise.
Table 2 Results of logistic regression
Independent variable x b
Standard
error Sig. eb
Lstriking (LA) 0.013 0.001 0 1.013
Vstriking (VA) 0.357 0.014 0 1.429
Double hull width (WDH) -2.310 0.137 0 0.099
Collision in tank compartment (δ) 6.277 0.211 0 531.9
Collision angle |0;90| (β) -0.082 0.003 0 0.922
Constant (x0) -3.980 0.323 0 0.019
As can be seen in the Sig. column, all the independent variables are statistically significant on a
0.05 significance level as the p-values are ~0.
19
The probability of spill is
( | )
, (6)
where
The sensitivity of the variables is as follows: if δ increases from 0 to 1, the probability of spill is
531 times higher as if the collision would happen outside the tank compartment (all other things
being equal). Adding one meter to the double hull width decreases the spill probability by a
multiplier of 0.099 whereas for each knot increase in striking ship speed the spill probability
becomes 1.429 times higher etc. Using 80 % of the observations to train the model, the correct
classification percentage into spill / no spill is 89.9 %, ( | ) being the cut-off point.
The 20 % of the observations that were not included in training the model are used to validate
model performance, resulting in a correct classification rate of 87.4 %.
3.2. Spill size in case of collision
For estimating the most likely spill size in case of collision, the number of breached tanks is
estimated so that the spill volume can be calculated based on the DWT of the tanker as
(7)
where = 20.
Due to the apparently random nature of the dependency between number of tanks breached and
the collision input variables, an ordinal logistic regression model was found to only somehow
20
adequately model . In ordinal logistic regression, the event of interest is observing
a particular score or less for
( ) ( ) (8)
with being the threshold value for each j.26 The quantity to the left of the equal sign is called a
logit or the log of the odds that an event occurs. In this case the values are j = 0, 1, 2, …, or 9
breached tanks, 9 being the maximum observed in the simulation. The probability that
is calculated as follows:
( )
( )
( )
…
( ) ( ) ( ) (9)
The category with the highest probability is chosen as the model prediction for the value of
The SPPS Statistics analysis results are presented in Table 3.
21
Table 3 Ordinal logistic regression results from SPSS Statistics 20
Parameter estimates Estimate Std. Error Sig.
95% Confidence Interval
Lower
Bound
Upper
Bound
Threshold
[N_tanks_breached = 0] 3.957 0.232 0 3.503 4.411
[N_tanks_breached = 1] 5.150 0.238 0 4.685 5.616
[N_tanks_breached = 2] 6.938 0.249 0 6.450 7.427
[N_tanks_breached = 3] 7.67 0.254 0 7.175 8.172
[N_tanks_breached = 4] 9.306 0.270 0 8.777 9.836
[N_tanks_breached = 5] 10.704 0.293 0 10.129 11.279
[N_tanks_breached = 6] 11.929 0.332 0 11.279 12.580
[N_tanks_breached = 7] 12.968 0.397 0 12.191 13.745
[N_tanks_breached = 8] 15.072 0.777 0 13.549 16.595
Location
Lstriking (LA) 0.017 0.001 0 0.016 0.019
Vstriking (VA) 0.298 0.008 0 0.282 0.315
Double hull width (WDH) -2.619 0.096 0 -2.808 -2.431
Collision in tank
compartment (δ) 5.390 0.151 0 5.094 5.686
Collision angle |0;90| (β) -0.056 0.002 0 -0.059 -0.052
The first nine rows of the Estimate column are the thresholds or :s. All of the independent
variables are statistically significant on a 0.05 significance level as all the values in the Sig.
column are < 0.05.
22
The ordinal logistic regression based meta-model is thus ( ) (
).
Using this model, was correctly classified in 64.8 % of all cases in the training data
as well as the validation data set. The number of tanks breached was off no more than +/1 from
the results obtained with the MATLAB-based in 82.6 % of the cases using the training data as
well as the validation data set.
4. Discussion and conclusions
This paper contributes to filling the a gap in chemical tanker collision consequence analysis by
presenting a spill model that can be applied for estimating chemical spills caused when another
ship strikes a chemical tanker. Furthermore, simpler but faster and more accessible calculation
tools in form of two meta-models are presented as well for breach probability and spill size
estimation using logistic regression. This model can be used for estimating the volume of
chemical spills for a larger geographical area over a longer time period as well as showing what
effects the changing e.g. the double hull width will have on the overall spill volume and spill
probability. Thus it can be used of e.g. in IMO’s Formal Safety Assessment’s risk evaluation or
similar analytical frameworks that aim at increasing maritime safety. The model presented here
is very general but is so at the expense of accuracy due to the simplifications done in the
modeling process: Besides the simplifications made in the virtual MATLAB- tanker layout, the
FEM- calculations are quasi- static and assume e.g. that the penetration happens in a straight
line into the side structure of the struck ship. The displacement as a function of energy is
assumed to be linear even when exceeding the 3 meter limit in the FE-simulations and the
calculations are done using a rigid bulb. Striking locations close to the bow or rear of the struck
ship (xL ≤ 0.1 or xL ≥ 0.9) are assumed not to cause spills, thus especially influencing e.g. the
23
logistic regression results with regards to δ. No sinking or potential fires caused by a collision
are modeled at this stage. Furthermore, the struck tanker structure is linearly scaled for the
different FEM-simulations; this e.g. the scantlings do not fully correspond. When it comes to
spill estimation, the tankers are assumed to sail fully laden and that the full content of each
breached tank is spilled to sea. However, the effect of liquids in the cargo tanks is not taken into
account in the FE- simulations. A more in-depth analysis of the model quality including a more
detailed epistemological uncertainty analysis and result validation is proposed as future
research along with refining the model by building a model that does not need to make
simplifications mentioned above.
Acknowledgements
The paper was done as a part of the TEKES and EU- funded CHEMBALTIC- project in co-
operation with Merikotka, NesteOil, Vopak, Port of HaminaKotka, TraFi, Finnish Port
Association and Finnish Ship-owners Association. Furthermore, authors would like to thank
Floris Goerlandt, Jakub Montewka anonymous reviewers for valuable feedback.
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