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: otto.sormunen@aalto.fi

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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